Chapter 3 — When Is Understanding Achieved, and by Whom?

Knowledge, Explanation, and Opaque Artificial Inquiry

1. Knowledge and understanding as achievements that research may seek

The working characterization orients research toward epistemic achievement, which this book examines principally through knowledge and understanding (Chapter 1, Section 1). Chapter 2 took up knowledge. This chapter takes up understanding: what would count as understanding, how it relates to knowledge, who can have it, and what follows for artificial research when the achievement sought is understanding, when knowledge is reached without it, or, on some accounts, when understanding is reached without new knowledge. It treats the two as achievements that research may seek separately or together, and asks how they differ and when they come apart.

The preceding chapter ended with a deliberately strong boundary case, which this chapter calls the strong predictive case, in which the two may come apart. An artificial system identifies a previously unknown regularity. Independent evidence supports the claim within a specified domain. The relevant community can use the result, track its uncertainty, and revise its reliance if the evidence changes. Yet no human member of the community can explain why the regularity holds, and the system supplies no usable representation of the dependence responsible for it.

The case raises questions that cannot be answered by repeating that the result is accurate. Accuracy does not by itself establish knowledge, but suppose that the further conditions of an account adopted in the preceding chapter have been met. Has understanding then been realized anywhere: in the system, whose states may or may not amount to understanding (Section 6), in some human, or in the community? If the attempt sought understanding of why the regularity holds, has it reached its target, although knowledge that the regularity holds has been obtained? Does knowledge of this kind require understanding, so that the two cannot come apart here? And has the community made progress if it can predict more while understanding no more? Whether the activity is research for the community does not turn on these answers, since research is characterized by the attempt rather than by its success (Chapter 1, Section 3).

These are not different formulations of one question. They concern different objects of evaluation (compare the evaluations distinguished in Chapter 2, Section 8.1):

1. whether an activity is research for S in the sense of the working characterization;
2. whether an output has attained the status of knowledge, who, if anyone, knows it, and whether it has entered the epistemic situation of the society S for which it is sought (Chapter 1, Section 2; Chapter 2, Section 6);
3. whether some subject, human, artificial, or collective, understands, and whether that understanding has entered, or become available to, S (Section 6);
4. whether the wider program has made progress;
5. whether the continuing research system (an artificial system alone, or the people, institutions, and artificial components that carry inquiry on over time) preserves the capacities required for criticism, transfer (carrying a result over to other conditions or problems), diagnosis, and correction; and
6. whether the result is important or valuable relative to relevant purposes and affected parties.

A failed investigation can be research without producing the achievement it sought. A community may know that a regularity holds without understanding why. A model that misrepresents some features of its target may nevertheless improve understanding. A locally warranted result may enter a research ecology that is becoming more homogeneous and less capable of detecting its own errors. These judgments interact, but none substitutes for the others.

These distinctions specify the work left by the general orientation toward epistemic achievement. If understanding differs from knowledge, which is sought is part of specifying the target; if some knowledge requires understanding, that constrains the proposed separation. Under the working characterization, neither research as such nor any single research act is required to bring about an epistemic achievement, knowledge or understanding (Chapter 1, Section 3). Where an attempt's purpose is understanding, however, obtaining knowledge does not by itself show that the attempt has reached its target. Sections 4 and 7 examine these alternatives, and Section 9 asks what they require of artificial research.

The chapter proceeds as follows. Section 2 separates prediction from explanation. Section 3 sets out what the main accounts count as understanding, and Section 4 applies them to the strong predictive case to ask whether knowledge and understanding come apart there. Section 5 asks whether the system's opacity undermines the warrant for that result or rules out understanding, by locating what is opaque, in what role, to whom, and at what stakes. Section 6 asks who understands: the system, those who use it, or a collective. Section 7 asks what understanding is valued for and what it may enable over time, and Section 8 why a local achievement does not settle the capacities of continuing inquiry. Section 9 asks what accounts of understanding require of artificial research, showing how the answer changes with the achievement claimed, its bearer, and its use, and closing by returning to the chapter's question.

2. Prediction and explanation are related but non-identical achievements

A simple route into the problem is to distinguish the questions that an inquiry can answer. A prediction identifies what will occur, what value to expect, or which outcome belongs to a case. It need not concern the future: retrodiction, classification, and prediction of an unobserved property can have the same functional form. An explanation addresses why a phenomenon occurs or how it depends on mechanisms, causes, constraints, unifying patterns, reasons, or other relations judged explanatorily relevant.

Success at one does not logically guarantee success at the other. A model can predict a target while exploiting a stable proxy and reveal nothing about the dependence investigators want to understand. An explanatory model can identify a mechanism while producing poor point estimates because initial conditions are unknown. A highly idealized representation can make a pattern intelligible while sacrificing predictive precision. Prediction and explanation are therefore not two names for a single scalar measure of scientific success.

Nor are they opposing kinds of artifact. An explanation can generate new predictions. Predictive failure can discriminate among explanations. Rich counterfactual performance, answering correctly a wide range of questions about what would happen if conditions were different, can provide evidence that a model captures relevant dependencies. In some domains, the same model contributes to both. The stable claim is only that answering a predictive question does not, by that fact alone, answer an explanatory one.

Positions on how the two achievements are related diverge further than this. De Regt, whose account of understanding is examined in Section 3.1, argues that prediction without understanding is not merely insufficient for science but impossible in practice: on de Regt's account, successful prediction from a theory requires that the theory be intelligible to those who use it, and the ability to recognize the theory's qualitative consequences in turn shows that it is (de Regt 2017, 91–92, 107). The understanding this requires is understanding of the theory, which de Regt calls its intelligibility and which, as illustrated with cases from behaviorist psychology and quantum physics, is needed for applying the theory to concrete phenomena. On this account it is distinct from scientific understanding of the phenomena, which also requires an explanation (Section 3.1). In a later co-authored chapter, Florian Boge and de Regt describe deep neural networks as data-driven rather than theory-driven and write that, at first sight, such networks may excel in predictive power while providing little understanding, because they lack intelligible theories (Boge and de Regt 2025, 419–420). Their chapter does not address de Regt's earlier claim that prediction without understanding is impossible in practice. The two need not conflict, since that claim concerns successful prediction from a theory, and the networks are described as lacking an intelligible theory. Potochnik argues that the aims of science are in tension: tools suited to one aim are poorly suited to others, a consequence, on this view, of the complexity of phenomena and the limits of human cognition and action. Robustness analysis across climate models with competing assumptions, for example, is used to generate predictions, although none of the models is expected to represent the causal influences on climate accurately or to explain climate change; Potochnik concludes that successful prediction should not be expected to facilitate explanation, nor the reverse (Potochnik 2015, 16–21). On this account the aims are valued for furthering human comprehension and control of a complex world, and their pursuit is relative to human limitations (19–20). Potochnik does not discuss artificial inquirers; applied to research done by one, the complexity of phenomena remains, while which limitations the tension answers to depends on whose comprehension the research is to further, the system's own or that of a human S.

For deep neural networks, machine-learning models in which many intermediate layers of interconnected units map inputs to outputs, Claus Beisbart asks under what conditions scientists who obtain a prediction from a trained network thereby understand why what it predicts is the case, which Beisbart calls explanatory understanding. The conditions are stated broadly, in parallel with the traditional analysis of knowledge as justified true belief, so that several accounts of explanation can fill them in. On this account, the scientists must have an explanation, that is, an argument that meets some further condition, such as containing a law, citing causes or a mechanism, or unifying, and that contains no irrelevant information; the explanation must be correct; and the scientists must accept it, be justified in accepting it, and be able to draw inferences with it (Beisbart 2025, 5–8). These conditions are applied to what Beisbart calls the simple setting, in which scientists know how to train the network and interpret its inputs and outputs but need not know what it does with the data (8). Beisbart's central argument concerns the first condition. The network's computation can be reconstructed as an argument that runs from its input, together with the assumption that the input–output function it realizes holds of the target system, to its output. Unless more is known about the network, however, nothing shows that this argument draws on a law, specifies causes or a mechanism, or unifies, whereas a computer simulation that takes the Navier–Stokes equations of fluid motion as premises is known to contain laws of nature (10–11). Scientists therefore cannot tell whether the network contains an explanation (13). The other conditions, on this argument, fail with this one. A track record of successful predictions can justify accepting that the network's input–output function is correct, but scientists cannot justifiably accept an explanation they do not know, and they cannot use an explanation they cannot state to draw the inferences that understanding requires (14, 16). Beisbart concludes that, in this setting, a scientist typically does not understand why the predicted outcome holds (24).

Beisbart's argument bears closely on the strong predictive case without establishing it. It shows how justified reliance on a predictor can coexist with the absence of explanatory understanding, and which conditions fail when it does. Beisbart's question, however, concerns a single predicted event or state rather than a regularity, the conclusion is that such understanding is typically absent rather than impossible, and the argument treats the network as a tool used by humans, leaving aside whether the network itself understands (4, 9, 18). Section 4 returns to the routes by which, on Beisbart's account, networks can still contribute to understanding. The more general distinction between prediction and explanation is left to the theories of explanation and understanding examined below.

That answering a predictive question does not by itself answer an explanatory one is a question-relative point rather than a universal ranking. If an inquiry asks which compound will bind to a target, a domain-bounded predictive answer may satisfy the question even when the mechanism remains unknown. If it asks why the compound binds, the same output is incomplete. If it asks for a proof, an interpretation, a construction, or an intervention, predictive accuracy can be useful without being the requested achievement. The working characterization of research is broad enough to include these inquiries precisely because it does not identify research with prediction.

Prediction itself also comprises several distinct claims. Evidence that one output is correct is not automatically evidence that a rule is reliable in a reference class. Reliability in one distribution does not establish transfer under shift. Observational prediction does not by itself establish the result of an intervention. A model–target correlation does not establish that the model represents an explanatory dependence. Reliability can also change between development, deployment, and later sociotechnical adaptation (Grote, Genin, and Sullivan 2024).

Woodward's account of causal explanation traces the gaps between reliability and transfer and between observational prediction and intervention to what different uses of a relationship require. Woodward argues that one variable can make another more predictable even though interventions on the first would not change the second (Woodward 2014, §7), and, writing with Kenneth Kendler, that how far a predictive relationship continues to predict well in other populations or circumstances is a question that can be asked even of relationships that are not causal (Woodward and Kendler 2023, 14). On Woodward's account, two representations can agree about the correlations so far observed and still disagree about what would happen under an intervention, so learning through passive observation that two variables are correlated does not by itself tell an agent whether changing one would change the other; where the correlation comes from a common cause, an intervention on one of the variables breaks the causal connection that produced it, and the correlation no longer holds (Woodward 2023, §5).

Otsuka gives the gap between observational prediction and intervention a statistical form. On Otsuka's account, inferential statistics presumes that the population behind the data, described by a probability model, stays the same across observed and unobserved cases, whereas an intervention changes the structure of the population itself; handling causal effects therefore requires further ontological assumptions. In the approach of structural causal models, the causal structure that generates the population cannot be determined from probability distributions alone, and assumptions such as the Markov condition and faithfulness (the assumption that every independence in the data comes from the causal structure rather than from accidental cancellation) are posited as bridges between causal structure and probability distributions, through which the results of interventions are evaluated and causal structure is inferred from statistical data (Otsuka 2018, 188–189).

The strong predictive case of Section 1 can therefore be assessed only once it specifies what is known, and the distinctions drawn above separate the possibilities. The community might know that a regularity holds within conditions C, know that a predictor has error rate e in reference class R, or know that an intervention yields an outcome under a controlled protocol. It does not acquire an unexplained universal law merely because one benchmark is accurate. Specifying which proposition is known and over what range, together with naming which object and kind of understanding is claimed or absent (Section 4), is required before the relation between knowledge and understanding can be tested at all, since how much understanding is missing depends on what is known.

3. What would count as understanding?

Understanding is not a theory-neutral success label. The current philosophical literature disputes its objects, the psychological relation that understanding requires a subject to bear to those objects, and the normative relation that makes apparent understanding successful (Grimm 2021). Only once these three dimensions are explicit can a claim that a system understands something, or an aim of bringing understanding about, be stated precisely enough to be evaluated or built toward.

The object may be a proposition, an explanation, a phenomenon, a subject matter, a dependence structure, a model, a practice, or another perspective. The relevant psychological relation may involve belief, acceptance, representation, coherent organization, inferential ability, manipulation, practical skill, or perspective-taking. The normative relation may require truth, empirical adequacy, appropriate grounding in reasons or evidence, non-accidentality, explanatory correctness, or something weaker than the justification required for knowledge.

A further dispute cuts across these dimensions: whether understanding is a species of knowledge. Grimm, Khalifa, and Greco treat the normative profile of understanding as essentially that of knowledge, whereas Kvanvig, Pritchard, Hills, and Dellsén argue that understanding tolerates kinds of luck or defeat that knowledge does not. Pritchard's case shows what kind of luck is at issue. Someone asks a genuine firefighter what caused the fire at their house and is correctly told that it was faulty wiring; but nearby are people dressed as firefighters, and had the person asked one of them, they would easily have got a false answer. On Pritchard's account, the person lacks knowledge, since they could easily have been wrong, but understands why the house burned down, since luck that lies only in the surroundings is compatible with understanding, provided that the person grasps how faulty wiring could cause the fire (compare Section 7.1). If the person had asked one of the impostors and the answer had happened to be right, they would have neither knowledge nor understanding. Dellsén argues similarly about defeat: if an engine actually works as someone was taught, misleading evidence that the teacher was unreliable does not take away their understanding of how the engine works (Grimm 2021, §2.3; Pritchard 2008, §§9–10). On the first view, an attempt directed at understanding is directed at knowledge of explanations or dependencies, not only at knowledge that something is the case, so that who bears that knowledge and whether it has entered S's epistemic situation are the questions Chapter 2 asked of knowledge (Chapter 2, Sections 6–7). On the second, understanding can be present where knowledge is absent, and absent where knowledge is present, so that whether it has been realized, in whom, and whether it has entered S's epistemic situation need accounts of their own (Section 6).

This map already prevents several shortcuts. Producing an explanation-shaped sentence does not show that anyone understands it. Acting successfully does not by itself identify the object that is understood. A false model is not automatically useless, but neither does usefulness alone establish understanding. The same artificial behavior can count as strong evidence under one account and weak evidence under another. In what follows, this book groups the accounts into families by the dimension each emphasizes; the families are not mutually exclusive, since several accounts combine dimensions.

Mathematical practice gives a compact illustration. Two proofs can establish the same theorem while differing in explanatory depth, the dependencies they expose, the strategies they transmit, and the new problems they make tractable. Rav, whose account Chapter 1, Section 4 introduced, holds that the path a proof charts between concepts not only serves to convince but establishes interconnections that illuminate mathematical ideas, and Thurston emphasizes the growth of concepts and ways of thinking (Rav 1989, 67, 73 n. 30; Thurston 1994). Knowing that the theorem is true can be held fixed while the candidate achievement of explanation or understanding varies. For example, a collectively written paper that gave a new proof of the density Hales–Jewett theorem, first proved in 1991 by ergodic methods, gave two reasons for doing so: its elementary argument yields explicit bounds that the earlier proofs could not give even in principle, and it gives what the authors called arguably the simplest known proof of Szemerédi's theorem. The authors also wrote that they did not fully understand why their argument generalized so readily beyond its first case (Polymath 2012, 3–4). With the theorem held fixed, what the new proof added included propositions not known before, namely the bounds, and a simpler route to Szemerédi's theorem; what its authors said they lacked was a full understanding of why the argument generalized so readily. On Rav's account, the new proof itself would contribute more than the propositions it added, since the path a proof charts between concepts does more than convince of its theorem: it establishes interconnections that illuminate mathematical ideas (Rav 1989, 73 n. 30). Neither the contrast between proofs nor the collectively written paper decides which theory of understanding is correct; both show why the achievement needs to be assessed separately from knowledge that the theorem is true, whether it is then counted as further knowledge, of an explanation or of dependencies, or as understanding distinct from knowledge.

3.1 Explanatory accounts

On explanatory accounts, understanding a phenomenon requires grasping an appropriate explanation of it. Strevens states the strong thesis that there is no scientific understanding without explanation (Strevens 2013). Khalifa defends a deliberately reductive version: understanding why something is the case is, at its best, scientific knowledge of an explanation of it, and lesser understanding approximates such knowledge (Khalifa 2022, 1–5; see Grimm 2021, §4.1). De Regt's contextual theory concerns the understanding of why a phenomenon occurs that a scientific explanation of it provides. Its criterion counts a phenomenon as scientifically understood in this sense if and only if there is an explanation of it that is based on a theory intelligible to the scientists who use it and that conforms to the values of empirical adequacy and internal consistency. The theory is contextual because, on de Regt's account, intelligibility is not an intrinsic property of a theory but a value that scientists attribute to the qualities of a theory that facilitate its use, so that whether a theory is intelligible depends on contextual factors such as their skills and background knowledge (Boge and de Regt 2025, 417, following de Regt 2017, 40). One sufficient test of intelligibility that de Regt proposes is whether those scientists can recognize qualitatively characteristic consequences of the theory without performing exact calculations (de Regt 2019, 336 and n. 11). This account is therefore also ability-based. Strevens, by contrast, treats the ability to construct an explanation as strong evidence of understanding why rather than a condition of it (Strevens 2013).

These accounts make the verdict on an unexplained opaque prediction relatively clear. It may support predictive knowledge, but it does not thereby produce scientific understanding of the phenomenon. On these accounts, explanation-shaped output is also insufficient: what they require is an explanation that is appropriately correct, supported, and available in a form that realizes the relation the account requires.

Explanatory accounts also differ over which relation makes an explanation a source of understanding. De Regt and Dennis Dieks examine unificationism, on which science advances understanding by showing how many phenomena can be derived from few patterns or assumptions, as one of the main conceptions of explanatory understanding (de Regt and Dieks 2005, §3.2). Schurz and Lambert give this idea an explicitly relative form. In Gijsbers's summary of their account, understanding is relative to the cognitive corpus of an epistemic subject, whether an individual or a community: an answer to the question why P can contribute understanding of P to the corpus only if it shows how P fits into the corpus, by connecting P with other elements of it, and only if the corpus, as changed by the answer, is more unified than before (Gijsbers 2011, 17). Gijsbers, who has no quarrel with their account as a theory of unification, argues that as a theory of explanation it makes unification neither sufficient nor necessary: an accidental generalization, such as that all members of a club are bald, increases unification once it has enough instances and would then count as explaining them, while legitimate explanations can rest on premises no less in need of explanation than what they explain, even when those premises disunify the corpus (Gijsbers 2007, 22–30). Drawing on historical variation in scientists' standards of intelligibility, de Regt and Dieks conclude that unification is an effective tool for achieving understanding but one among several, rather than its universal standard (de Regt and Dieks 2005, §3.2). Applied to artificial research, the relative form makes explicit two questions that such research raises sharply: relative to whose corpus, an artificial system's, a research team's, or a scientific community's, an answer is supposed to yield understanding; and whether a given artificial system has a corpus in their sense at all, that is, a set of sentences it believes and a set of arguments, deductive, inductive, or probabilistic, that it has mastered (Gijsbers 2011, 17), a question that an account framed in terms of corpora leaves open. Section 6 returns to the bearer of understanding.

3.2 Objectual and dependency accounts

Not every theory makes possession of an explanation necessary. Dellsén's dependency-modeling account says, roughly, that a subject understands a phenomenon by grasping a sufficiently accurate and comprehensive model of its place in a network of dependence relations (Dellsén 2020). Accuracy here concerns whether the model misrepresents those relations, and comprehensiveness whether it represents them, including what the phenomenon does not depend on; Section 7.3 returns to both. This is an account of objectual understanding, understanding of a phenomenon or subject matter as a whole, designed to reach beyond knowing an explanation of one target. Explanatory accounts also address objectual understanding; the dispute is whether it can outrun explanation. Dellsén has also defended the more radical claim that understanding need not require justification or belief in the manner knowledge commonly does, while still requiring a grasp of approximate truth (Dellsén 2017). Earlier, in examples that Strevens and Dellsén discuss, Lipton argued that even understanding why can be gained without an explanation. As Strevens, who rejects the conclusion, reports the argument, understanding can on Lipton's account come by grasping facts that are not explanatory. After working with a physical model such as an orrery, for example, one may understand why the planets sometimes appear to move backward and yet be unable to say what one has learned. Since on Lipton's account what cannot be made explicit cannot be an explanation, the understanding in such a case does not pass through an explanation. And Galileo's thought experiment, which shows by reductio that bodies must fall with the same acceleration whatever their mass, lets one understand, on Lipton's account, why this is so without grasping the scientific explanation of it (Strevens 2013). Explanatory theorists reply that such cases involve grasping part of an explanation, perhaps tacitly, while Dellsén accepts some of them only as objectual understanding (Strevens 2013; Dellsén 2020). De Regt, whose criterion in Section 3.1 concerns the understanding that explanations produce, notes the disagreement over whether understanding why can be had without explanation and sets it aside, while holding that understanding why is a cognitive achievement in its own right, not reducible to explanation (de Regt 2020, 924). Gijsbers, whose criticism of unification as a theory of explanation was noted in Section 3.1, has argued that successful classification yields a kind of understanding of its own. On Gijsbers's account, a purely classificatory biology that selected the anatomical features supporting reliable inductions would let investigators predict properties of newly discovered species and see how organisms hang together through relations of similarity, while explaining nothing; this understanding differs from the understanding that explanations give through relations of determination, and the account locates the achievement not in the inductions themselves but in the hard-won selection of the features that support them (Gijsbers 2011, 178–181). If this view is adopted, the strong predictive case of Section 4 turns on a further question: whether the features on which a validated predictor's classifications rest are available to be grasped.

Under such views, absence of a conventional why-explanation does not settle the case. A machine-generated representation might support understanding if it makes an accurate and sufficiently comprehensive model of the relevant dependence relations available to be grasped. By the same token, a large collection of correct point predictions need not constitute objectual understanding if it supplies no integrated representation of how the phenomena depend on one another. A distinction of Greco's, as Grimm reports it, makes the role of such a representation more precise. The object of understanding is the thing understood; a vehicle of understanding is a representation through which one understands it, as a good map of a city is typically a vehicle for grasping how its streets and landmarks are laid out. A representation can itself become an object of understanding (Grimm 2021, §2.1). An account, too, can be the object: someone can know their way around astrology, on Elgin's example, although astrology affords no understanding of the cosmos (Elgin 2007, 4–5). Carried over to machine-generated models, the distinction allows such a model to stand in either relation. Used as a vehicle, it may support understanding of the dependence relations it represents; taken as the object, it may itself be understood without that understanding extending to the phenomenon. Evidence that investigators understand an artificial system's representation is therefore not by itself evidence that they understand the phenomenon through it.

3.3 Ability and intelligibility accounts

Ability-based accounts locate the grasp that understanding requires in what a subject can do, and they cut across the distinction drawn above. Hills characterizes the abilities that understanding why p involves, where q is why p, as cognitive control (Grimm 2021, §2.2). As Emma Gordon reports Hills's account in the Internet Encyclopedia of Philosophy, these abilities let one treat q as the reason why p rather than merely believe that it is: abilities to follow another person's explanation of why p, to explain p in one's own words, to draw the conclusion that p from the information that q, and to give q as the right explanation when given p, together with the last two abilities for relevantly similar cases (Gordon n.d., §3c). Hills's account is ability-based but still requires an explanation. Wilkenfeld's representation-manipulability account instead concerns understanding an object and does not require one: a subject understands an object when it has a representation of the object that it could modify to support effective inferences about it or manipulations of it (Wilkenfeld 2013, 1, 8–9). De Regt's intelligibility condition, described above, is also ability-based (see the overview in Grimm 2021, §2.2). Such accounts suggest tests of what a subject can do: draw consequences, answer what-if questions, explain relevantly similar cases, or modify a representation to support new inferences. These ideas are attractive for evaluating artificial systems because they suggest observable tests rather than an appeal to an inaccessible feeling of grasp.

They also introduce a construct-validity problem. The accounts themselves do not count shortcuts as understanding; Wilkenfeld's, for example, excludes lucky performance and the mere application of a memorized algorithm (Wilkenfeld 2013, 8–9). The difficulty is that a benchmark may not discriminate such shortcuts from the required abilities. A system may answer a benchmark through memorization, retrieval, contamination, hidden tools, or a second opaque procedure. Correct performance on selected counterfactuals may show a useful capacity without showing that the system possesses an integrated understanding of the subject matter. Performance on such tests is therefore evidence about the abilities that a specified account takes to constitute or indicate understanding; if it is to separate those abilities from shortcuts, it needs to be gathered across adversarially chosen variations. Such a battery of tests is not a theory-neutral checklist that defines understanding by stipulation.

3.4 Factivity, idealization, and epistemically useful distortion

Knowledge that p, in the strict propositional use on which the preceding chapter centered its analysis, is factive. Whether understanding is factive in the same way is disputed. Elgin argues, as Grimm and de Regt summarize her view, that understanding is not factive: models, idealizations, and thought experiments that are known not to be true can be felicitous falsehoods, which advance understanding by exemplifying features of their targets, that is, by highlighting those features while downplaying others. Elgin grants that understanding still in some way answers to the facts (Grimm 2021, §4.2; de Regt 2018). Potochnik suggests that pervasive idealization calls into question the idea that science aims at truth, and that its epistemic aim is understanding, which is one of several aims of science (Potochnik 2015, 1, 4, 16). De Regt likewise argues that achieving understanding often requires giving up representational accuracy, and that idealizations and other inaccurate representations are often used as tools for enhancing scientific understanding (de Regt 2020, 932). Rejecting factivity need not mean rejecting every correctness condition, and accounts that keep one differ over what it covers. On Potochnik's account, understanding still answers to the world: it requires that each posit in a representation be epistemically acceptable, its divergence from the truth insignificant given its role in the representation and the purpose of the research, and that the causal pattern grasped be one the phenomenon actually embodies (Potochnik 2020, 6–8). Strevens counts an idealizing explanation as correct when its explanatory content, roughly its claims about what does and does not make a difference, is true (Strevens 2013), whereas Potochnik allows idealizations to stand in even for factors that make a significant difference when those factors are not the focus of the research (Potochnik 2015, 10–12).

A related issue concerns what model evaluation can establish. Oreskes, Shrader-Frechette, and Belitz argue, specifically for numerical models of open natural systems, that verification or validation cannot amount to a conclusive demonstration of truth: empirical agreement supplies partial confirmation, and different models can remain compatible with the available observations (Oreskes, Shrader-Frechette, and Belitz 1994). Parker's adequacy-for-purpose account offers a different evaluative target. A model is assessed relative to a target, user, methodology, circumstances, and purpose, rather than only by its overall representational accuracy (Parker 2020, 458, 464–465). These positions are not one consensus theory, and the first is not a claim about every formal or scientific model. Together they show why the model was validated does not by itself say whether it is adequate for prediction, explanation, intervention, teaching, or another use.

The dispute matters for distinguishing the conditions of knowledge and understanding. A literally false model cannot itself supply knowledge of the false proposition. It may still reorganize a domain, reveal a dependence, support an ability, or increase understanding. Some of its contribution may be reconstructed through true propositions about what the model represents or enables. Kelp's knowledge-based account of understanding offers such a reconstruction for idealized models: one can know what a theory containing the ideal gas law says, that actual gases approximate ideal gases in various respects and to various degrees, and where the idealization's limitations lie, and on Kelp's account this knowledge is part of one's understanding of the physics of gases (Kelp 2017, 18). Whether such a reconstruction exhausts the achievement is disputed. Potochnik also gives truth a place, holding that an idealized representation can be true of the causal pattern it depicts while false of the phenomena that embody it, but maintains that understanding consists in grasping such a pattern, which does not require belief, and is therefore distinct from knowledge (Potochnik 2020, 6–7, 14–16; Potochnik 2015, 7–8). On accounts that count such contributions as understanding, understanding is therefore not simply a more verbose form of propositional knowledge.

For artificial research, the immediate implication is not that utility takes the place of truth. On the accounts above, an idealized model contributes to understanding only relative to what it idealizes and for which purpose. An artificial system working with models may therefore need to retain what each representation idealizes, which target and purpose it bears on, which inferences it supports, and where rival models remain compatible with the evidence, for those who assess and use its results as much as for any understanding credited to the system itself. Weisberg's account of a model's construal gives these items a structure. A construal assigns parts of a model to parts of its target and says which parts are to be ignored, fixes the intended scope, and sets two kinds of fidelity criteria: dynamical criteria, how close the model's output must be to the phenomenon, and representational criteria, whether the model makes the right predictions for the right reasons (Weisberg 2007b, 14–17). On Weisberg's account the construal depends on the intentions of the model user, so for an artificial modeler, whose intentions fix it is a further question (Chapter 8, Section 2.2).

The need to keep such items is not peculiar to artificial systems. Cleland, for example, reads the Miller–Urey experiments, which were presented as a test of the hypothesis that life on Earth originated in a primordial soup, as a test of whether some basic building blocks of life, amino acids, can be produced by electrical discharges in a particular gas mixture, and holds that the logical relation between the hypothesis actually tested and the hypothesis about the origin of life winds through numerous highly speculative assumptions, from conditions on the early Earth to biochemical possibilities (Cleland 2002, 484). Likewise, a more detailed or predictively accurate model need not be better for every explanatory or intervention purpose, and a useful idealization does not become a literally true description merely because it performs well. Elgin argues, for example, that the ideal gas law remains justified alongside the virial equation, which can be made arbitrarily precise, because what is wanted of a model is a representation that affords understanding of the phenomena rather than one that replicates them, and different models of one target exemplify different features (Elgin 2022, 18–20).

Weisberg's classification of idealization bears on what changes when the modeler is a machine, because it distinguishes kinds of idealization by their justification. Galilean idealization introduces distortion to make a theory computationally tractable; since its justification is pragmatic and tied to tractability, advances in computational power and mathematical technique should, on Weisberg's account, lead the idealizer to de-idealize. Minimalist idealization keeps only the causal factors that make a difference to the phenomenon; its justification lies in explanation and, on this view, should not be expected to abate with the progress of science. Multiple-models idealization builds related but incompatible models without expecting a single best one; where desiderata such as generality, accuracy, precision, and simplicity trade off, Weisberg takes its justification to be permanent, since such tradeoffs are consequences of logic and mathematics (Weisberg 2007a, §I). Matthewson and Weisberg argue that some of these tradeoffs arise from logic and representation alone and will not dissipate with scientific progress (Matthewson and Weisberg 2009). Weisberg also takes all three kinds to be compatible with a realist view of science, so the classification does not side with Elgin's denial of factivity (Weisberg 2007a, §IV). Carried over to a system with far more computational capacity than its human counterparts, the classification implies that only idealizations justified by tractability give that system a reason to de-idealize. Levins, whom Weisberg quotes, traced the multiplicity of models partly to a mind that can cope with only a few variables at a time, a premise about human cognition; the tradeoffs that arise from logic and representation alone do not rest on that premise, so the reasons for keeping several models of one target that rest on them survive the change of modeler. These positions do not fix a single design, but a research system could therefore preserve families of purpose-relative representations rather than force every inquiry into a single increasingly literal world model.

These families of accounts expose different possible targets and different burdens of evidence. Each changes what an artificial researcher would have to represent, do, communicate, or make available to another subject.

4. Knowledge without explanatory understanding

Section 3 set out, account by account, what would count as understanding. This section applies those accounts to the strong predictive case and asks whether knowledge and explanatory understanding come apart there, whether that holds whichever account is chosen, and, where they do, what follows for the target of the attempt and for progress.

Return to the strong predictive case. The new regularity is true. The claim is restricted to an explicit domain. Independent measurement routes and groups support it. The predictor's error characteristics are known, dependencies among the checks are recorded, and defeaters would lead the community to revise its reliance. No human member of the community grasps an adequate explanation of the target regularity, even tacitly, or can give one; whether the system itself understands it is left open (Section 6).

The accounts of understanding examined in Section 3, together with the preceding chapter, support a conditional but substantive point:

Knowledge that a regularity holds and explanatory understanding of why it holds are conceptually separable. Under several important accounts of knowledge, the former can be realized in the strong predictive case and, on suitable accounts of possession, enter the community's epistemic situation, while, on accounts requiring an explanation for understanding why, the latter is realized in none of its human members. Whether this particular result is knowledge, and whether it has entered that situation, remains relative to which of the conditions compared in the preceding chapter are adopted.

The distinction between knowing that and understanding why does not by itself settle whether understanding why is absent in the stipulated case. Explanatory accounts, ability accounts of understanding why such as Hills's, and reductive accounts that treat understanding why as knowledge of an explanation all distinguish knowing that a regularity holds from understanding why it holds. Dellsén, who allows objectual understanding without explanation, holds that understanding why cannot come apart from explanation (Strevens 2013; Dellsén 2020; Grimm 2021, §4.1). The accounts differ over whether some understanding of the phenomenon can remain when no explanation is available: dependency accounts such as Dellsén's and Wilkenfeld's representation-manipulability account (Sections 3.2 and 3.3) allow objectual understanding without one, and Lipton argued for understanding why without one, so that on Lipton's account the stipulation that no human member grasps or can give an explanation does not by itself settle that none of them understands why the regularity holds.

The separation has also been defended, and its consequences resisted, in discussions of automated science. Humphreys, considering the worry that easing humans away from the centre of science could cost understanding of the world, holds that, under an expansive conception of knowledge, we ought to allow scientific knowledge "beyond the current understanding of humans." The cases cited are effective prediction and manipulation without understanding of the mechanisms involved, as with aspirin, cholera, and many types of cancer, and quantum mechanics, predictively successful for decades without a satisfactory explanation of measurement. Humphreys keeps a further worry, that errors go undetected when humans do not understand the science, on both of the views of science's aim, that it aims chiefly at knowledge and understanding of the world and that it aims chiefly at prediction and manipulation, since automated methods can fail suddenly when the conditions for their stability are not met (Humphreys 2020, 14–15). Boon, in the same volume, ties scientific knowledge to its use. On Boon's account, data-models that are opaque and sit inaccessibly in the machine, so that humans cannot obtain them and use them in self-chosen epistemic tasks, are not scientific knowledge as traditional scientific practice produces it, which consists of scientists' conceptions represented as public and transferable epistemic tools; the account leaves open whether machine learning could in principle meet the pragmatic criteria that make knowledge manageable for humans (Boon 2020, 14–15, 16–17 n. 11). Boon's criterion does not deny the displayed claim: in the strong predictive case the validated regularity is stated and used by the community, and what the criterion denies the status of scientific knowledge is the opaque model inside the predictor. Boon states the criterion for human practice; applied to an artificial S, which is not discussed there, it would ask whether a model can serve as an epistemic tool for that society's members.

Beisbart's argument about deep neural networks (Section 2) applies the separation to one kind of predictor; it does not show that every prediction lacks understanding. On Beisbart's account, scientists can be justified by a network's track record in accepting that it maps inputs to outputs correctly while lacking explanatory understanding of what it predicts (Beisbart 2025, 14, 18). The argument also bears on the question on which the accounts above divide. A scientist who has learned, for example by running the network many times, to anticipate how its output changes with its input can draw some of the inferences that understanding requires. Beisbart counts this as some degree of objectual understanding of the predicted phenomenon, but not as explanatory understanding, because those inferences do not rest on an explanation the scientist has (16–17). The option of letting the scientist draw the inferences by running the network itself is also considered and set aside: what would then understand, strictly, is the coupled system of the human and the computer, a different subject from the unaided human whose understanding is in question (17–18; Section 6 takes up who understands). The argument does not, however, rule out that networks contribute to explanatory understanding. If scientists know that a network is sensitive to explanatorily relevant features, for instance through methods from explainable AI that detect which variables affect its output, and if they justifiably accept the explanation it contains and can work with it, they can understand why the predicted outcome holds (15, 18). Outside the simple setting, running a network on many varied inputs can identify explanatorily relevant factors, such as a partial cause, and Beisbart counts this as one sense in which networks enhance understanding; it requires, however, prior knowledge of the explanation and falls far short of a full explanation (21–23). The argument further leaves open that success across an extremely broad range of cases could give reason to think that a network tracks laws or causes, while holding that present-day networks, whose range of application is typically small, give no such reason (15–16). Beisbart concludes that how far networks can be brought to provide understanding depends on what humans do with them (25). Measured against these routes, the strong predictive case excludes by stipulation the route through knowing what the network is sensitive to, since no human can explain the regularity and the system supplies no usable representation of the dependence responsible for it. The route through repeated runs remains open, as a source of explanatorily relevant factors short of an explanation.

Chirimuuta argues, for one area of neuroscience, that the shortfall in understanding can outlast improvements in method. In two cases, decoders of motor-cortex activity and models of visual neurons, Chirimuuta's paper traces a shift from simple, largely linear models, which were intelligible but predicted poorly outside simple laboratory conditions, to artificial neural networks that predict far better but do not let their builders anticipate qualitatively how the model will respond. It finds in the earlier models four sources of intelligibility that the networks lack: visualisability as a circuit diagram, articulated theoretical assumptions about the neural code, linearity, and functional transparency, that is, explicit knowledge of the function the trained model computes. Because the networks' accuracy comes from approximating a complex nonlinear function, the argument goes, even an ideally reverse-engineered network, its input–output function written down, would remain less intelligible than its hand-coded predecessors, so that the trade-off between prediction and understanding would persist; Chirimuuta expects it beyond the two cases wherever targets involve complex nonlinear dependencies and predictions are needed outside controlled conditions. On this account such networks can supply some kinds of explanation, but "they tell you what is to be expected, but not why" (Chirimuuta 2021, 15–23). Where Beisbart makes the networks' contribution to understanding depend on what humans do with them, Chirimuuta's argument gives a reason to think that, for targets of this kind, the networks would remain less intelligible than simpler rivals however far such methods go, because the limit comes from the complexity that makes them accurate. Since the paper calls intelligibility "a human-relative virtue of models" (26), the trade-off expected to persist can be read as one between prediction and intelligibility to humans. Chirimuuta does not discuss artificial understanders; applied to one, the complexity that makes a network accurate remains, but whether it limits that understander's grasp depends on what is intelligible to it, the question of who understands that Section 6 takes up.

De Regt's account, as the following shows, sits less easily with the strong predictive case. On de Regt's view, successful prediction from a theory requires that the theory be intelligible to those who use it (Section 2); if the predictor were a theory in this sense, its users would have to find it intelligible, so the case could not lack understanding altogether, although understanding why the regularity holds would on this account still require an explanation based on that theory. For data-driven networks of the kind Boge and de Regt describe, which may predict well while providing little understanding, the separation applies as stated.

The claim that knowledge can be realized in the strong predictive case does not depend on treating accuracy as knowledge. The case stipulates the further evidence, reliability, basing, anti-luck, or social conditions demanded by the relevant account. Internalism does not automatically defeat it: a community can have accessible reasons for believing that the regularity holds without possessing an explanation of why it holds. Reliabilism can license the case through an appropriately established truth-conducive route. A competence or modal account will ask whether success manifests ability and could too easily have failed. A social account will ask who possesses the attitude and how assessment, uptake, and correction are organized.

The separation also permits more than one kind of understanding. Investigators may understand why the evidence warrants reliance on the predictor while not understanding why the target regularity obtains. They may understand the predictor's operating limits without understanding its internal computation. They may acquire a thin dependency representation that some accounts call partial understanding. Knowledge without understanding is therefore informative only when it names the object and kind of understanding that is absent. Several kinds of understanding can be present or absent within a single achievement. After the central theorem of the Liquid Tensor Experiment (Chapter 1, Section 3) had been formally verified, for example, Peter Scholze wrote that the formalization had shown what actually makes the proof work. Scholze also wrote that, whereas verifying a proof usually involves trying small variations of the argument to see whether they break, the formalization had yielded reassurance that the proof's route succeeds but still no sense of the terrain around it (Scholze 2021). In this case, understanding of why the route works was gained, while a sense of how variations of the route would fare was not.

The strong predictive case, the principal case of this chapter, concerns knowledge that a regularity holds without explanatory understanding of why it holds. The separation is not peculiar to artificial predictors. For example, Morris Tanenbaum, recalling in a 2004 interview his early work on silicon transistors at Bell Laboratories, said that he had had to use annealing techniques to obtain transistors from crystals whose conductivity type changed when they were heated and quenched, and that only afterwards did a colleague show that the impurity responsible was oxygen; of a related regularity noticed in growing the crystals, that the effect was much weaker when the melt was not stirred, he said, "We didn't know why" (Tanenbaum 2004, 42–43).

That knowledge can be attained without explanatory understanding does not make understanding subordinate to knowledge: where understanding is the target, attaining knowledge that the regularity holds does not reach it. Accounts of progress draw a related contrast with Bird's epistemic account, on which progress consists in the accumulation of knowledge (Chapter 2, Section 8.3). Dellsén's noetic account argues that scientific progress is better understood as increased understanding than as accumulated knowledge, and its grounds lie in cases where the two diverge. On the one hand, Einstein's 1905 explanation of Brownian motion counts, on Dellsén's account, as progress; yet, on the same account, Einstein then knew neither the kinetic theory of molecules nor the phenomenon it explained, since neither was justified well enough for him to know it, so no knowledge was added. On the other hand, knowledge of random experimental results, of merely apparent correlations such as that between the number of storks and the number of births, or of observational records too meager to support any explanation or prediction can, on this account, accumulate without bringing any progress (Dellsén 2016, §§3–4; Dellsén 2021). Potochnik likewise motivates understanding as an epistemic aim of science while emphasizing the plurality of scientific aims (Potochnik 2015). De Regt places understanding at the center of successful science without reducing it to predictive success (de Regt 2020, 932).

The reasons de Regt and Dieks give for this view apply directly to the strong predictive case. They rest on contrasting a successful scientific theory with a hypothetical oracle whose pronouncements always prove true: the oracle would secure empirical adequacy, but would not count as a great scientific success, because there would be no understanding of how its perfect predictions were brought about (de Regt and Dieks 2005, §2). De Regt and Dieks likewise hold that meteorologists who did nothing but compute correct forecasts by solving the governing equations numerically would fail to understand the weather (de Regt and Dieks 2005, §4.1). On de Regt's criterion, a validated predictor that supplies no explanation based on an intelligible theory would leave the regularity without the scientific understanding that criterion characterizes, whatever its status as knowledge.

Dellsén's understanding is objectual rather than narrowly explanatory. In the restated account, increased understanding is a more accurate or comprehensive model of dependence relations, which grounds prediction and manipulation as well as explanation, and progress lies in publicly available information that enables relevant members of society to increase their understanding (Dellsén 2021). On this reading, whether the strong predictive case counts as noetic progress turns on whether the validated regularity improves such a model, not simply on whether an explanation is available. Dellsén's earlier formulation was more direct about prediction. There, grasping how to predict some aspect of a target correctly across a variety of circumstances counted as partial understanding even without an explanation: someone who can predict changes in the weather from a range of barometer readings, for example, partially understands the weather, although a single correct prediction, or the memorized steps of one, would not suffice (Dellsén 2016, §2). On that formulation, predictive grasp without explanation can itself be partial understanding. Such grasp falls outside de Regt's criterion, which requires an explanation based on an intelligible theory (de Regt 2019, 334), although, as Section 3.2 noted, de Regt sets aside whether understanding why can be had without explanation. In the restated account, prediction figures instead among the benefits that understanding brings (Dellsén 2021, 11256). Truthlikeness and problem-solving accounts, introduced in Chapter 2, make the verdict turn less directly on understanding.

Woodward's interventionist account, introduced in Section 2, yields a further verdict. On this account, an explanation answers what-if-things-had-been-different questions: it tells how the explanandum would have been different under changes in the factors it cites, using a generalization that continues to hold under at least some interventions on them (Ross and Woodward 2023, §3). Candidates that answer no such questions do not explain at all; above that threshold, explanations differ in depth according to how much information relevant to answering such questions they provide (Ross and Woodward 2023, §4). So understood, Woodward's account leaves the strong predictive case without explanation unless the validated predictor also supports correct answers about what would happen under interventions. A predictor that supports such answers explains to that extent, provided the information is accessible to those who use it, a condition to which Section 6 returns.

The positions surveyed need not deny that the community knows the regularity. They can deny that knowledge is the achievement sought, or all of it, or that its increase is the progress that matters. The working characterization, which leaves open whether knowledge or understanding is sought, allows this difference but does not resolve it: reorganizing a domain through idealization, explanation, or objectual grasp still requires an account of success. Nor does a local increment in either knowledge or understanding alone settle how a wider program has progressed.

The strong predictive case can therefore support different judgments. On accounts separating knowledge of a regularity from understanding why it holds, an activity can reach its knowledge target while an inquiry directed toward understanding remains unfinished. De Regt's requirement that a theory be intelligible to its users qualifies the predictive case differently (Section 2): where the predictor is a theory in that sense, its successful use presupposes, on de Regt's account, that its users understand the theory, though not that they understand why the regularity holds. Accounts that make understanding central to science or its progress, such as those of Potochnik, Elgin, and Dellsén (Section 7.1), add priority claims that the working characterization neither establishes nor excludes. The characterization itself requires no individual research operation, and no research activity as such, to bring about any achievement, knowledge or understanding (Chapter 1, Section 3). Whether understanding is needed for success depends on what the attempt is directed at, and the direction of an organized attempt, its eventual success, and the contribution of a particular operation are distinct.

This distinction of scale is important. A research program can aim at understanding even when one constituent experiment produces only a measurement. A field can progress through an explanatory synthesis assembled from results none of which is explanatory alone. Conversely, a project can produce many true local claims without advancing the understanding its participants sought. A theory of the aims or progress of science cannot be converted without argument into a membership condition for each activity called research.

On some accounts, the separation also runs in the other direction. Dellsén holds that understanding need not require justification or belief in the manner knowledge commonly does (Section 3.2). Elgin holds that felicitous falsehoods advance understanding, and Potochnik that understanding consists in grasping a causal pattern, which does not require belief and is therefore distinct from knowledge (Section 3.4); in a case Dellsén offers, a physicist who, from methodological reservations, does not believe string theory but accepts it and uses it to explain understands, on Dellsén's account, what the theory describes (Section 6). On such accounts, an attempt directed at understanding can bring about understanding new to S, for example through an idealized model or an accepted but unbelieved theory, without thereby bringing about new knowledge, and an evaluation that counts only knowledge or validated results would not register that success. Khalifa analyzes ideal understanding why as scientific knowledge of an explanation, and Kelp analyzes maximal understanding as maximally comprehensive and well-connected knowledge (Sections 3.1 and 7.1). These analyses alone do not establish that an increase in understanding must add knowledge. Kelp's account makes this explicit in one direction. In his litmus-paper case, an agent who knows every member of the full account of an event from separate sources, while the basing relations among those beliefs do not reflect the explanatory and support relations the agent knows to hold, has little understanding of the event; Kelp notes that it is not clear that adding further knowledge would remedy this, and on his account the degree of understanding rises as the knowledge becomes well connected (Kelp 2015, 16–18). On this account, then, understanding can deepen without new facts being known. Applying this to understanding new to S presupposes that such a reconnection takes place within S's epistemic situation. Kelp's account also lets understanding coexist with beliefs that fall short of knowledge, because what carries the understanding is the knowledge around them. Against Kvanvig's case of a historian whose true beliefs about the Comanche are Gettiered, Kelp's first reply is that those beliefs may well be knowledge; but he adds that on his account understanding can be attributed even if many of the inquirer's beliefs are Gettiered, since the knowledge that remains, of what the relevant theory says and that it is highly plausible, can be enough for the standard a context sets (Kelp 2017, 16–17). The same holds for understanding why. In Pritchard's case of a man who is told why his house burned down by the one real firefighter among several impostors, Kelp's first response is to deny that the man lacks knowledge, but he also offers an account on which, if that intuition is granted, the man understands why without knowing why, because he knows enough to give an explanation that is well-founded, that is, ultimately grounded in a source that does know (Kelp 2014, 11, 13–15). In both cases what carries the understanding, on Kelp's account, is the knowledge the inquirer does have.

5. Opacity has an address

The system in the strong predictive case supplies no usable representation of the dependence it tracks; it is opaque. Two objections then suggest themselves: that its opacity undermines the warrant for the knowledge that Section 4 allowed, and that it settles that nobody understands the regularity. If the first held, the case would lose the knowledge it was built on in order to isolate the absence of understanding. This section takes up both. Sections 5.1 to 5.3 ask where the opacity lies and what it bears on for warranted reliance, and Section 5.4 asks whether understanding can be supplied through a reconstruction or a further model while the computation remains opaque. Who understands is taken up in Section 6, once opacity has been indexed to a subject.

Calling a system a black box does not yet draw the distinctions needed to evaluate an artificial result. Opacity is informative only when it is indexed to what is opaque, the role the opaque element performs, the subject to whom it is opaque, and the stakes of depending on it. Writing about computer simulation and computational science, Humphreys indexes epistemic opacity to a subject and a time, in a definition that Winsberg and Alvarado quote in their encyclopedia entry on computer simulations in science: a process is epistemically opaque relative to a cognitive agent at a time just in case the agent does not then know all of the epistemically relevant elements of the process. Humphreys calls a process essentially epistemically opaque to an agent when it is impossible, given the agent's nature, for the agent to know all of those elements (Winsberg and Alvarado 2026, §2.5). Because essential opacity is relative to the agent's nature, a process essentially opaque to human agents need not be so to an artificial one, so which subject opacity is indexed to matters wherever artificial agents take part in assessing or using a result (Section 5.2). Durán and Formanek, whose account Section 5.3 discusses, take their notion of essential opacity from this definition.

Humphreys argues that the speed and complexity of simulations put their computational details beyond human inspection (Humphreys 2009a, §3.1). Durán quotes Humphreys's earlier argument that even a computationally irreducible process would become inspectable if slowed until a human could examine each step. On that argument, the practical need for computational speed is the root of opacity in this area; because humans cannot circumvent that constraint, transparency has to be given up as a requirement for computational science (Durán 2025b, §1). The argument separates what a change of subject could and could not alter. Humphreys does not discuss artificial inspectors, but applied to one that could follow each step at the speed required, the account implies that the steps would not be beyond its inspection, while irreducibility, the absence of a shortcut to the outcome, would remain. Inspecting the steps would not by itself establish that the inspector understands the process as a whole.

Later accounts differ over how much opacity a more capable agent could remove. Alvarado, in a preprint, argues that some opacity in computational methods does not respond to any change in the agent. On this account, opacity is agent-neutral when it arises from a feature that all epistemic agents share, such as being finite, a limit of the kind that Cherniak assigned to any finite agent (Chapter 5, Section 6.5); Alvarado's example, an estimate taken from Symons and Horner, is that checking every path through a program of realistic size would take several times the age of the universe, so that the opacity remains even for agents with millions of years to spare. Alvarado calls opacity agent-independent when it arises from features of the process itself that do not respond to agential resources, with examples including stochastic and vastly overdetermined processes, rounding errors bundled across the components of coupled simulations, and the weights of a deep network, set by automated training from partly random initial values (Alvarado 2021, 10–15). Boge and Grünke, also in a preprint, argue instead that because simulations and machine-learning methods are algorithmically transparent, an idealized agent such as a Laplacean demon could step through them, so that the opacity of the computation, essential opacity included, is contingent on the epistemic conditions of actual agents. What they suspect may be fundamental is what they call model-opacity: there seems to be no algorithm leading from what a trained network does to a model of the physical mechanisms behind its outputs, a difficulty they take to be closely related to the problem of unconceived alternatives (Boge and Grünke 2019, 11–14, 26–27, 30). They consider only human agents, but applied to an inquirer more capable than humans, their account implies that it might remove the opacity of the route by which a result was computed while still facing opacity about the target, the matter of the third adequacy question that Section 5.3 poses, whether an account adequately represents the phenomenon that inquiry seeks to explain; on Alvarado's account, some opacity of the route itself would remain for any finite inquirer.

Section 5.1 takes up the role of the opaque element, separating the generation of a candidate from the warrant for accepting it; Section 5.2 maps the other dimensions together; Section 5.3 asks whether transparency is necessary or sufficient for warranted reliance; and Section 5.4 shows that a later reconstruction need not be mere rationalization, an after-the-fact excuse.

5.1 Candidate generation and final warrant

Among the roles an opaque element can perform, generating a candidate answer can be separated from supplying the warrant for accepting it. On the distinction between the contexts of discovery and justification that Reichenbach introduced (Chapter 5, Section 4.1), and on Duede's application of it to deep learning below, a limited permission for opacity in generation follows:

The route that generates a candidate answer need not be the route that warrants accepting it.

A conjecture can arise from analogy, aesthetic judgment, accidental observation, a dream, random search, or an opaque model. On these accounts its origin need not supply its warrant. Duede argues directly that deep-learning opacity can be compatible with scientific discovery when a model operates in the context of discovery and the result is justified through distinct means (Duede 2023). A requirement of public rational reconstruction for every generative move would apply to ordinary human discovery as much as to machine discovery. Other accounts narrow the permission. On reliabilist accounts (Chapter 2, Section 4.1), and on the virtue-epistemological reading discussed in Section 5.3, the reliability or credited competence of the source can itself supply warrant; on those accounts, how a candidate was generated can be part of what warrants it, and assessing the generator becomes part of assessing the result.

Duede and Davey develop a sharper mathematical case. An opaque system may produce a formally represented proof too large for humans to survey, while a transparent proof checker verifies the stored derivation. On their account, the checker can support a priori mathematical knowledge even though humans cannot grasp the generative process or inspect the proof step by step (Duede and Davey 2025). The result is deliberately domain-specific. It depends on a formal proof object and a checker whose mathematical role is transparent; it does not show that an empirical claim can be warranted merely by placing another opaque model after the first. It nevertheless makes the logical separation vivid: opacity in candidate generation need not be opacity in the route that warrants the conclusion. The Liquid Tensor Experiment (Chapter 1, Section 3) shows, for example, where the human share of such a route can lie. Scholze found the formal definitions and theorem statements surprisingly readable but could not read the proofs at all, and the formalizers added formally proved results about the objects involved, such as that Lean's real numbers form the unique complete ordered field, as evidence that the checked statement concerned the intended objects (Scholze 2021; Buzzard 2022). What the checker left to human judgment was whether the checked statement was the intended theorem, not whether each step of the derivation was valid.

Pelc, arguing against the formalist view that the formal derivations underlying proofs contribute to confidence in theorems, took a more skeptical view than Duede and Davey of what formal checking contributes to the reliability of mathematics. Pelc argued that derivations would add confidence if reasonably short ones could be carried out, that this is not known to be possible for deep theorems in the present state of knowledge, so that no link between proofs and derivations can at present add confidence, and that confidence in theorems is instead built through a social process, in which a result becomes more worthy of belief as its proof is re-verified and used by others (Pelc 2014, 5–7, 25–26, 29). Pelc also quotes two objections of Rav's: proofs are held together by arguments based on the meanings of their terms, which formal calculi cannot capture, and transcribing an informal proof as a derivation calls on a logician's know-how, a transcription that cannot itself be checked mechanically, so that a positive verdict from a proof checker may reassure one only that the formalization and the checking were carried out correctly (Pelc 2014, 6–7). Pelc rejects part of the second objection: a positive verdict, were one available, would on his view raise confidence not in the informal proof but in the theorem itself, and his own objection is rather that for many theorems no such verdict can be had, since no sufficiently short derivation is available (Pelc 2014, 6–8). In the Liquid Tensor Experiment, a formal derivation was carried out, but the judgment whether the checked statement expressed the intended theorem remained with the human participants. Applied to this case, the transcription objection quoted by Pelc concerns the relation between the formal statement and its intended meaning. Neither observation settles Pelc's thesis that confidence in theorems comes from a social process.

Ochigame, writing about automated mathematics from the history and sociology of proof, treats the standard of proof itself as something that mathematicians have revised. Borrowing Hacking's contrast between a Cartesian ideal of proof, on which one understands a proof and can get it in one's mind all at once, and a Leibnizian ideal, on which every step can be checked mechanically, Ochigame traces practical standards derived from both. Of these, the standard that computer-encoded proofs have advanced is that every step can be checked by a program and derived from its axiomatic foundations, and that "one understands or trusts the encoding of the proven statement." Ochigame argues that such proofs therefore still demand social consensus that a piece of code corresponds to the claimed statement, and so do not eliminate social institutions of adjudication, which are needed still more for judging the importance and value of results. Mathematicians now face, on this account, two decisions: whether computer-encoded proofs should become required, and whether completely inscrutable, deeply automated proofs, which one would accept by trusting the programs that constructed and checked them, should be accepted; Ochigame declines to defend a position on either (Ochigame 2024, §§2–4). On Ochigame's account, the judgment that the Liquid Tensor Experiment left to its human participants belongs to a standard of proof that the community could still revise, and the second decision asks whether S would accept a result that no member understands even in outline.

The permission to separate generation from warrant does not make generation epistemically irrelevant. The route can reveal data leakage, prior exposure, selection effects, undisclosed human filtering, duplicated work, or evaluator dependence. Nor can an allegedly independent check merely reproduce the generator's training data, measurement errors, or background assumptions. The distinction is between epistemic roles, not necessarily a rigid temporal sequence and not a guarantee that the roles are causally independent.

5.2 A multidimensional map of opacity

Generation and warrant are too coarse to classify all relevant opacity. Creel distinguishes functional, structural, and run transparency in complex computational systems: roughly, knowledge of the algorithm a program instantiates, of how the code realizes that algorithm, and of a particular run on particular hardware and input data. Creel argues that the three are dissociable, so that a system can be transparent in one of these ways without being transparent in the others (Creel 2020, §§3a–3d). The analysis concerns only opacity that remains for skilled and knowledgeable creators and users of such systems, and sets aside opacity produced by concealment or by a user's lack of the relevant expertise (Creel 2020, §3).

Sullivan locates a different source of difficulty, outside the model, and argues that what primarily limits the understanding an opaque model can provide is not its complexity or the opacity of its implementation but what Sullivan calls link uncertainty: a lack of scientific and empirical evidence supporting the link that connects the model to its target phenomenon. The reason is comparative. Three deep-learning models with the same degree of opacity, one predicting many diseases from medical records, one classifying melanoma from images of moles, and one classifying sexual orientation from facial images, differ in the understanding they yield, and on Sullivan's analysis the difference follows how well evidence from outside each model connects it to its target. Extensive dermatological knowledge supports that connection in the melanoma case, whereas in the facial-image case existing evidence points the other way and the model tracks cultural cues such as grooming. The claim is qualified: it holds so long as a model is not opaque at the highest level, where only its inputs and outputs are known, and Sullivan argues that deep neural networks are not, because their general architecture and the modelling process that produces them are known (Sullivan 2022b, §§3.2, 4.3, 5.2–5.3, 6).

In a paper that builds on this account, Sullivan brings inductive risk to bear on both the link and the model's interior. Inductive risk is the risk of error that remains when a hypothesis is accepted or rejected, or a model is used, on evidence that cannot make it certain; on the argument from inductive risk, how much support is enough depends on how bad the possible errors would be, including their non-epistemic consequences, that is, consequences for matters other than truth, such as harm to people (Chapter 11, Section 4). On Sullivan's account, accepting that a model can explain a phenomenon involves such a judgment, because one must accept both that its data are adequate and that the counterfactual dependencies it captures, what would differ in the target if a feature were different, hold of the target. Where wrongly accepting them would be harmful, more evidence is required; for the facial-image classifier the paper cites the scientific controversy over such dependencies, the use of phrenology and physiognomy to justify racism, sexism, and eugenics, and the discrimination that gay people face (Sullivan 2022a, 1067–1070). Two consequences follow on this account. Externally, the greater the inductive risk, the stronger the independent evidence needed to reduce link uncertainty, for example further empirical research beyond the model or, when the target is a statistical correlation, robustness checks across several models. Internally, a model learned from data does not contain its dependencies in explicit form, so they have to be extracted after training, for example with saliency maps, which highlight the parts of an image that contribute most to a classification; the greater the inductive risk, the higher the standard for verifying that what is extracted is faithful to how the model works rather than an artifact. Sullivan has in mind mainly what Creel calls functional transparency, while allowing that the stakes may also demand structural or run transparency. The paper further argues that these demands rise with the stakes even when the researchers' question and target are held fixed, and restricts the claim to explanation and understanding rather than the use of a model in practice (Sullivan 2022a, 1070–1074). On Sullivan's account, the present limits of interpretability methods therefore need not prevent understanding of low-stakes phenomena, but can prevent it where a model bears on matters with serious social consequences (Sullivan 2022a, 1072–1073). Beisbart distinguishes the obstacle to explanatory understanding from both notions. On this account, a highly opaque computer simulation is often still known to contain the relevant explanatory laws, so epistemic opacity in Humphreys's sense is not the obstacle; and strong evidence that a network tracks correlations in its target makes link uncertainty low without helping with explanation, although whether an explanation the network contains is the actual one may, Beisbart allows, count as part of link uncertainty. What is lacking, the argument continues, are informative descriptions of what the network does in terms of variables or processes of the target system (Beisbart 2025, 24).

The following diagnostic grid is put together here from Creel's and Sullivan's distinctions, extended to cover also the forms of opacity Creel sets aside. The target link listed under Object and the costs of error under Stakes come from Sullivan's two analyses; distribution shift, also listed under Stakes, is carried over from Section 2, and reversibility, novelty, and time horizon are not among the considerations Sullivan discusses. The Subject coordinate has a precedent in Zednik's adaptation of Humphreys's definition to machine learning. On Zednik's account opacity is relative to an agent; the stakeholders in a machine-learning system differ in role, among them operators, executors, decision subjects, data subjects, creators, and examiners; and which elements of a system are epistemically relevant, the elements an agent can cite to explain its behavior, differs with the agent and its role (Zednik 2021, §§2.2, 3.1–3.2). Zednik does not consider artificial stakeholders, but applied to the value another AI, the account implies that a subject fixes not only to whom a system is opaque but also which of its elements count as relevant.

Each row names one coordinate and the question that fixes it, and a case of opacity is located by answering all four questions together. The items named in each question are common examples of the values a coordinate can take; other objects, roles, subjects, and stakes can be added.

Table 3.1. Coordinates for locating opacity in research systems

Coordinate	Question
Object	Is the generator, code, data, learned relation, evidence, target link, or institution opaque?
Role	Does it perform search, measurement, prediction, warrant, explanation, decision, or correction?
Subject	Is it opaque to the developer, operator, scientist, reviewer, affected public, another AI, or the collective?
Stakes	What are the costs of error, reversibility, novelty, distribution shift, and time horizon?

The grid is not a list of four required modules. It prevents opacity in one place from being treated as opacity everywhere. A model may be computationally opaque to a domain scientist while its domain-bounded reliability is publicly testable. A transparent algorithm may rely on an opaque dataset or an invalid measurement model. A human-readable rationale may conceal an untraceable evidential route. A distributed collaboration may be locally opaque to every participant while maintaining reliable collective checks.

5.3 Is transparency necessary or sufficient?

The accounts compared in this section differ over where the reasons for reliance lie: in a reliable process or a credited model, which on the analysis of this section can both be shown by a system's record; in how a system was built and what grounds it; or in access to how a system operates. On some accounts, internal transparency is not universally necessary for warranted reliance. Durán and Formanek develop a computational-reliabilist account on which researchers can be justified in believing the results of essentially opaque simulations when the simulation is a reliable process. They name four sources of that reliability: verification and validation, robustness analysis, a history of (un)successful implementations of theories, models, and building techniques, and expert knowledge, which they regard as a rather weak source when taken alone (Durán and Formanek 2018, §§3.1, 4). In its 2018 formulation, their account is not purely externalist. At a second step it requires that these sources be shown reliable in turn, so that a researcher who takes a verification procedure to be reliable must give reasons for doing so (Durán and Formanek 2018, §3.2). It is a substantive position, not a theory-neutral solution. It still raises questions about how the reliable process, which it identifies with the simulation, is to be typed (Chapter 2, Section 4.2), where the chain of showing the reliability of a source of reliability by a further source ends (Chapter 11, Section 5.2), and whether the environment in which reliability was established remains stable. Durán later presents computational reliabilism as an externalist epistemology of algorithms in the sense that justification rests on reliability indicators external to the algorithm rather than on showing its internal workings, and Durán states it for a human agent who believes an algorithm's output (Durán 2025a, §2); externalism in this sense concerns the algorithm, not whether the one who believes must have reasons.

Grote, Genin, and Sullivan press the last of these questions for machine learning. On their reading, the account's safeguards concerning a history of implementations and the trust of relevant experts presuppose that a model is embedded in an epistemically well-ordered environment, whereas machine-learning models implemented in domains such as criminal justice, clinical medicine, or science can disrupt the epistemic norms of those domains. These difficulties, they argue, raise the possibility that the account presupposes what it is meant to provide (Grote, Genin, and Sullivan 2024, 6).

Otsuka offers a different diagnosis for deep-learning models. On Otsuka's account, conventional statistical methods give explicit criteria for, and a theoretical understanding of, how far a hypothesis is warranted by the evidence, whereas deep learning has no principled evaluative methods on a par with them. Justification is instead empirical, established on benchmarks case by case, and so reliability comes to be attached to individual, named models. Otsuka suggests that this model- or agent-based justification aligns closely with virtue epistemology, which grounds justification in an agent's epistemic capabilities, or virtues, and that the AI research community appears to justify a model's performance on the basis of its epistemic virtues as measured by its benchmark scores; Otsuka then asks what such virtues are and how one could tell whether machines possess them, if they do at all (Otsuka 2026, "Understanding the Machine Virtues"). Although they address different systems, Durán and Formanek's account and Otsuka's locate the reliability that grounds reliance differently: in a simulation process whose reliability rests on the four sources named above, or in an individual model credited with an ability.

Otsuka also distinguishes two approaches to justifying the judgments of such models, corresponding to Sosa's distinction between animal knowledge, which animals and humans obtain through the proper functioning of their belief-forming processes, and reflective knowledge, which involves a higher-order awareness of the reliability of those processes. One approach asks whether a model has animal knowledge, much as a physiological investigation can show how a frog's perceptual mechanisms let it catch flies reliably: research on model architectures and training, including mechanistic interpretability, seeks the mechanistic structures that underlie a model's inductive performance. The other asks whether the model has reflective knowledge, and attends to the internal reasons on which it bases its conclusions. Reflective knowledge, Otsuka notes following Sosa, assesses the conditions under which first-order animal knowledge functions properly, which in machine learning are matters of robustness and of extrapolation beyond the training domain, and Otsuka counts research on explainable AI among the lines of work directed at the reflective knowledge of deep-learning models (Otsuka 2026, "Understanding the Machine Virtues"). On these two questions Otsuka's earlier treatment goes further, holding that it would be hard to deny that deep-learning models already have some form of animal knowledge, whereas it is not evident whether they have or will acquire reflective knowledge (Otsuka 2023, 136–139). Section 5.4 returns to Otsuka's argument that there may be no uniquely correct interpretation of such a model's internal representations.

In the preprint version of a paper on AI as an epistemic technology, Alvarado argues that trusting AI in the appropriate way requires access to how it operates. On this account, AI is an epistemic technology, relied on as a source of knowledge; the only trust appropriate to such a technology is epistemic trust, which must rest on epistemic reasons; and assessing those reasons requires access to the epistemically relevant elements of how the technology operates, so that explainability plays a crucial role. A hammer may be accepted without knowing how it works, Alvarado argues, but without such access it will be increasingly difficult to justify epistemic trust in an epistemic technology, justifying the acceptance of an opaque one may prove significantly harder, and appeals to prudential considerations will not suffice; if AI is essentially opaque, the argument concludes, we cannot trust it (Alvarado 2023, §3). Alvarado cites Durán and Formanek for the requirement that such technologies be assessed by sound epistemic means, but where they take sources such as verification, validation, and a history of implementations to ground reliance on opaque simulations, Alvarado takes an understanding of how the system operates, and so explainability, to be needed. The two positions can be read as differing over whether the reasons that justify relying on or trusting a system must concern how a system operates or may concern its record. Because essential opacity is relative to the agent's nature, the verdict of an account that places the reasons in access can also change with the relier: an artificial member of S able to follow a computation that is essentially opaque to human members might have the access such an account requires, although on Alvarado's account of agent-neutral opacity some of the route stays opaque to any finite relier (Section 5).

An older position places the reasons for reliance entirely in the record. Reichenbach considered a clairvoyant who could name the limiting frequency of a series at an early stage of it. On Reichenbach's account nothing about how the clairvoyant works need be known: the forecasts are compared with later observations, and if they are borne out, induction itself recommends preferring them to direct inductive estimates, whereas clairvoyance cannot be admitted without such a check (Reichenbach 1938, 353–354, 358–359, 363–364). Placed within the division just described, Reichenbach's view sits on the record side, and it makes the check itself an induction over the series of the source's past forecasts, which raises again the question of Chapter 2, Section 4.2 of how that series is to be typed.

Humphreys, who gave up transparency as a requirement for computational science (Section 5), placed the reasons for relying on an opaque simulation partly in how it was built. In earlier articles, he makes construction part of a model's justification and connects construction assumptions with prior justification (Humphreys 1995, abstract; Humphreys 2002, abstract). Barandiaran quotes Humphreys's account of how virtues such as stability under perturbations of boundary conditions, scale invariance, and agreement with available analytic solutions can be achieved through trial and error that treats the connection between a computational model and its solutions as opaque (Barandiaran 2008, 53). Irvine quotes his further point that theory may justify a parametric family, with empirical data specifying its details (Irvine 2016, manuscript 17). Humphreys also argues that knowledge of the physical and computational processes producing data can support the detection and correction of artifacts; a record of successful uses need not include objects sufficiently like future ones to reveal their artifacts (Humphreys n.d., §4). Construction grounds thus differ from a history of implementations, one of Durán and Formanek's sources, without excluding support from such a history. Humphreys wrote about models that humans construct; applied to a model that an artificial system builds or selects, the account implies that members of S can draw on the reason from construction only if the grounds of the construction are recorded and can be assessed by them.

Symons and Alvarado, also writing about simulation, deny that, in science, pragmatic reasons alone ground warranted trust. As Winsberg and Alvarado report the argument, part of the task of an epistemology of computer simulation is, on Symons and Alvarado's account, to explain the difference between the position of scientists who use epistemically opaque simulations and the relation of oracle believers to their oracles; pragmatic and epistemic considerations coexist, and it is epistemic reasons that ultimately explain and ground the pragmatic ones; a simulation, on the same account, must have warrants of its own rather than inherit them from the methods used to build it (Winsberg and Alvarado 2026, §2.3). Construction contributing to justification on Humphreys's account does not settle Symons and Alvarado's question of what warrants the particular implemented simulation. A different construction-sensitive position is Winsberg's: as Winsberg and Alvarado report it, techniques used to build simulations acquire credentials through an extended history of use (Winsberg and Alvarado 2026, §2.1.1). On that view, construction and accumulated experience work together; the warrant is neither a record alone nor a survey of each computational step.

For deep-learning models, two later accounts argue that the grounds on which such reliance draws are not available in the same way. Duede, who does not deny that scientists can be justified in relying on such models, argues that the justification reduces neither to that for instruments nor to that for experts. On this account, a model's record on test data is not enough, since many equally well-performing models can behave very differently once deployed and real-world data are often fat-tailed; the model is not a physically mediated instrument, since no causal process connecting it to the world mediates its outputs; unlike a simulation, whose procedure rests on well-established principles of numerical analysis, it does not, on the present state of interpretability research, reveal which principles its learned procedure operationalizes, which is what justifying a theoretically mediated instrument would require; and even granting that it has reasons for its outputs, those reasons are not open to evaluation by others as an expert's are (Duede 2022, §§2–4). Interpretability methods that study the models themselves with the methods of observation and experiment are, Duede concludes, a new category of reliability (§5). Alvarado argues that among the elements of a system relevant to relying on it, those concerning error cannot be left out: what reliance requires is neither a survey of how the system works nor a failure rate alone but knowledge of the nature and sources of its errors. In deep networks, on this account, such errors are often untraceable, since the same result can be reached along many paths, natural inputs can cause errors as adversarial examples do, errors are distributed across many weights, and erroneous outputs are delivered with the same confidence as correct ones (Alvarado 2025, §§3.2–3.3). On Duede's account, then, the grounds for treating a simulation as a theoretically mediated instrument are not available for deep-learning models in the same form. Alvarado's requirement of knowledge of the nature and sources of errors bears on the diagnostic role of production knowledge in Humphreys's artifact discussion; on Alvarado's account, such models often withhold that knowledge. Rathkopf, writing about generative models and holding that they produce such errors whatever their architecture, replies that Alvarado's dilemma assumes that the model is the unit at which reliability must be assessed. In Rathkopf's cases, AlphaFold 3 and the ensemble weather forecaster SEEDS, outputs are ranked, filtered, annotated with confidence scores, or embedded in ensembles by procedures built from independent knowledge of the target system, so that a workflow can be reliable without its errors being traced to their source; such workflows, Rathkopf adds, can be built only where sufficiently mature knowledge of the target is already in place (Rathkopf 2026, 13–15, 17–18, 20–21). The reply moves what is required from knowledge of the model's failures to knowledge of the target, and so leaves reliance unsecured where research for S has not yet produced that knowledge.

Whichever view is taken of whether access to how a system operates is necessary, internal transparency is not sufficient. An execution trace can faithfully show how an output was computed without showing that the data measure the target, that the inference is warranted, or that the model explains the phenomenon. A feature attribution can reveal sensitivity inside a classifier while failing to establish a causal or stable relation in the world. Woodward notes that in some derivations the "manipulation" is mathematical or conceptual rather than possibly physical: one constructs a model in which, for example, the dimensionality of a system is different and calculates the consequences, which shows what difference the dimensionality makes without describing a physical transformation of the system (Woodward 2018b, §3). A model's input can likewise be varied without anything in the world being changed. Doing so shows what the model would output; it shows what an intervention on the target would do only if the relation the model encodes is invariant under that intervention. A fluent chain of reasoning can be legible and false.

This book distinguishes at least three adequacy questions:

1. Does an account faithfully describe the process that produced the output?
2. Does it adequately articulate why the available grounds support accepting the claim?
3. Does it adequately represent the phenomenon or dependence the inquiry seeks to explain?

A full process trace can satisfy the first while being scientifically unilluminating. An evidential argument can satisfy the second without answering why the target regularity holds. A simplified explanatory model can contribute to the third while deliberately failing to reproduce the discovering system's computation. The artifacts may support one another, but no one automatically substitutes for the others.

5.4 Later reconstruction is not automatically rationalization

Post-hoc explanations are often what is offered for a black box, and, like black box (Section 5), the term post-hoc explanation can name two different things. Both are accounts produced after a result. One is a persuasive story produced after the result and unconstrained by the process, evidence, or target. It can sound intelligible without explaining anything. The other is a legitimate reconstruction: an elegant proof found after an ugly search, a simple theory developed after a complex prediction, or an idealized model that isolates the relation relevant to a why-question. A reconstruction, in the sense meant here, restates the result, or how it can be reached or why it holds, in a more surveyable form than the route by which it was actually obtained.

Fleisher argues that an idealized account of a black box can contribute to understanding without being a literal replay of its algorithm. Fleisher's case is post-hoc explainable AI (XAI): after a classifier has been used, and without altering it, a second and simpler model is built to explain why the classifier made a particular decision. LIME, the main example, fits a linear model to the classifier's outputs on slightly altered copies of the input to be explained. Critics object that such explanations are mere rationalizations, because they compute a different function from the classifier and do not always reproduce its outputs. Fleisher replies that the same holds of idealized scientific models, and that such models are widely held to provide genuine understanding. The ideal gas law, for example, represents gas molecules as not interacting (compare Section 3.4). The understanding at issue is explanatory understanding: understanding why the system made a decision. Following Potochnik, Fleisher takes it to consist in grasping information about the causal patterns relevant to that decision, that is, accepting the information and being able to use and manipulate it. The understanding in view is that of the system's developers, of those who deploy it, and of those affected by its decisions (Fleisher 2022, 535–536, 540, 542–544, 547–550). Fleisher does not thereby license arbitrary surrogates, but takes three features from the literature on idealization as particularly helpful for thinking about XAI. On Fleisher's account, they are signs that a misrepresentation is an idealization rather than a mere distortion. The misrepresentation makes the model simple enough to be intelligible; it flags features that make no difference to the outcome; and it focuses attention on the causal patterns that matter to those who need the explanation. These signs count together with the usual marks of a successful model, such as empirical adequacy and predictive power. Fleisher also requires a high degree of agreement with the original model's outputs near the input explained, holds that explanation models are to be judged by the same standards as scientific models, and grants that many current uses may fall short of them, since different XAI methods often disagree (Fleisher 2022, 541, 551–556). Generalizing these conditions from explanation models to reconstructions in general, one can take a reconstruction to be legitimate to the extent that it is constrained by the target it claims to represent, the purpose it serves, and relevant requirements of fidelity, empirical adequacy, or relation preservation. Read against the adequacy questions of Section 5.3, Fleisher's explanation models take the classifier itself as their target. They therefore bear on the question of how the output was produced, while answering it in idealized rather than literal form. The models discussed next are instead kept alongside a computation to represent the phenomenon.

De Regt and Dieks describe practices in which scientists keep an intelligible model alongside a computation that, on their own account, does not supply understanding. In quantum chromodynamics, reliable tests are possible only by numerical lattice techniques that work as a black box and do not by themselves give insight, whereas the MIT bag model, although its predictions agree only modestly with data, provides understanding, de Regt and Dieks argue, because the visualizable model allows qualitative predictions about hadron structure without lattice calculations. In meteorology, reasoning with potential vorticity supplies a qualitative picture alongside numerical forecasting (de Regt and Dieks 2005, §§4.1–4.2). Such models are not accounts of what the computation does; they are kept alongside it to represent the phenomenon. The cases therefore bear not on the first adequacy question of Section 5.3, how faithfully an account renders the process that produced the output, but on the third, whether it adequately represents the phenomenon the inquiry seeks to explain. The lattice case also bears on the claim reported in Section 2, that successful prediction from a theory requires that the theory be intelligible to those who use it, although de Regt and Dieks do not relate the two in this discussion. If that requirement concerns the users' grasp of the theory, which models such as the bag model help to supply, rather than each procedure through which a prediction is obtained, the two are consistent.

Hartmann, whose case study of hadron models discusses the bag model, gives a different reason for retaining it. On Hartmann's account, physicists entertain the MIT bag model despite its modest empirical adequacy not only because it is easy to apply and extend but because the story that goes with it is a good one: a narrative that cannot be deduced from quantum chromodynamics but is plausible given it, and that argues why the feature the model isolates is relevant and why the others are insignificant. Hartmann treats a model as an interpreted formalism together with such a story. A story must not contradict the theory, a criterion that Hartmann calls necessary; the non-formal criteria, which the same study calls much weaker, include that it be plausible and that it help in understanding the physical mechanisms; and Hartmann grants that how a model and its story provide understanding is very difficult to explicate (Hartmann 1999, 10–11, 17). In another hadron model examined in the same study, a story was used to argue away the model's lack of confinement, and one consequence of that story, that higher-lying hadrons should be more sensitive to the shape of the effective potential, was confirmed in numerical studies (Hartmann 1999, 16). Brought to the third adequacy question, Hartmann's cases suggest that the story of a model kept alongside a computation bears on it only as far as what the story sets aside as insignificant has itself been checked.

A further line of argument questions whether a model's internal reasoning has a uniquely correct rendering at all. Otsuka compares the evaluation of a deep-learning model's internal representations with Quine's radical translation, the situation of translating a wholly unknown language from its speakers' behavior alone, in which, Quine argued, mutually incompatible translations can fit all the evidence equally well (Otsuka 2021, 11–12; Otsuka 2026, "Can We Understand What Machines Think?"). What a model labels "cat" may be the animal we mean by that concept, or, as a study Otsuka cites suggests, merely a combination of properties and backgrounds typical of cats, and Otsuka argues that which of these is correct may not be uniquely settled, and that there may be no single correct answer at all. Nevertheless, on this account, the search for explanations of such models cannot simply be dismissed, because what a model takes to exist matters to its social application: unless people know to some extent what kinds of things the recognition model used in automated driving takes to exist, they will not be willing to entrust their lives to it (Otsuka 2021, 12). On that view, a requirement of fidelity to a model's reasoning, once that reasoning is rendered in human concepts, may have no unique fact to be faithful to, even where the computation itself can be traced exactly. Chapter 8, Section 3.1 contrasts this Quinean worry, on which there may be several equally good renderings, with Kuhn's, on which a statement may have no adequate rendering at all.

Either way, the question that matters here is not when an account was produced. It is which object it claims to explain and what makes the account adequate to that object.

For artificial research, the cases of this subsection bear on more than how outputs are assessed. A legitimate reconstruction can itself be an achievement that research brings about. An elegant proof found after a search, a simpler theory developed after a complex prediction, or an intelligible model kept alongside a computation moves from a result that is warranted but not understood toward understanding. In the strong predictive case, an attempt directed at understanding why the regularity holds could pursue it in this way, whether the reconstruction is produced by the system, by its users, or by both together. What makes such a reconstruction count is what the constraints above require: that it answer to the target it claims to represent and to the purpose it serves, and, as Hartmann's cases suggest, that what it sets aside as insignificant has itself been checked. If Otsuka's comparison with radical translation holds, a further consequence follows for the route such an attempt takes. A rendering of a deep-learning model's internal reasoning in human concepts may have no unique fact to be faithful to, whereas a model of the phenomenon answers to the third adequacy question, which concerns the target rather than the computation; where understanding of the phenomenon is sought, that route does not wait on settling the first adequacy question, whether an account faithfully describes the process that produced the output. In whom understanding brought about in this way is realized, whether in the system, in members of S, or in both, is the question of Section 6. Where S is human, the reconstruction has to be usable by its human members; where the recipients are artificial systems that can operate on the model's representations, a rendering into human concepts may not be needed at all (compare Chapter 8, Section 3.4).

The two objections with which this section began fare differently. Whether opacity undermines the warrant for the knowledge that Section 4 allowed depends on the account of warranted reliance (Section 5.3): it can on accounts that require access to how a system operates, such as Alvarado's, and need not on those that place the reasons in a system's record or in how it was built, although each of these leaves questions of its own. That opacity settles that nobody understands the regularity does not follow, since understanding can be sought through a reconstruction or a model kept alongside the computation, as described above.

The distinctions also bear on how such work is recorded. An artificial research system whose outputs are to be assessed on each of the three adequacy questions of Section 5.3 would need to keep process provenance, evidential support, target-level explanation, and pedagogical presentation as distinguishable artifacts, even when a human interface combines them; Section 9 relates each to the function it serves. Calling all four reasoning invites an articulate narrative to stand in for both warrant and understanding.

6. Who understands?

Where humans conduct research, those who produce a result are usually also among those who understand it, so the bearer of understanding seldom needs to be named separately. Where an artificial system produces a result, it need not be what understands it, and the bearer becomes a question of its own. A claim that research has brought about understanding can accordingly be at least three distinct claims:

1. an AI helps another agent or a community, human or artificial, understand;
2. the AI itself understands;
3. a human–AI collective or artificial community understands.

Each of these concerns who understands. Whether understanding realized in any of them has entered S's epistemic situation is a further question (Chapter 1, Section 2), taken up below.

The first does not require the second. A telescope can disclose a phenomenon without seeing it, and a search procedure can enable a proof without understanding the theorem. Krenn and colleagues draw the same separation for AI in science. The roles they distinguish through which AI can support scientific understanding, among them revealing patterns and serving as a source of inspiration, fall under the first claim; AI as an agent of understanding, which they raise as a further and stronger possibility, would fall under the second (Krenn et al. 2022). Their framework does not establish that present systems are agents of understanding in this sense.

Their earlier study of Theseus, a computer program for designing quantum-optics experiments, supplies a concrete case of the first claim. The study reports that the program's graph-based representation and automated search yielded solutions to open problems in quantum optics from which the investigators extracted new concepts (Krenn et al. 2021). The authors describe the system as contributing to conceptual understanding. What the case directly shows is that an artificial procedure and an interpretable representation can mediate human understanding.

The second claim, that the AI itself understands, takes up most of this section. What follows first sets out what different accounts would test; positions that address directly whether machines can understand come next, from de Regt, alone and with coauthors, to Wilkenfeld; and the section then asks whether understanding requires belief. How the claim is assessed depends on the selected theory. An explanatory account may ask whether the system represents and appropriately grasps an explanation. An ability account of understanding why, such as Hills's, may test whether the system can follow an explanation, give one, and draw conclusions and give explanations in similar cases; a representation-manipulability account may test whether it can modify a representation to support counterfactual reasoning, intervention, transfer, and error diagnosis. A dependency account may ask whether a coherent dependence model is integrated into the system's inference and action. These tests are informative only if they go beyond fluent report generation. On accounts that also tie understanding to a felt sense of grasp, such as Potochnik's (below), these tests leave a further question open; on accounts that require only a functional or representational relation, the artificial realization could differ from the human one while satisfying it.

One position bears directly on the second claim. De Regt holds that the skills needed to construct and evaluate scientific explanations involve tacit knowledge of how to apply rules in the appropriate circumstances. Following Collins, de Regt classifies this as collective tacit knowledge, which on this account can be acquired only by taking part in a social practice and cannot be made explicit in a scientific description that could be used to build a machine mimicking human behavior (de Regt 2017, 27–30). De Regt likewise reports, following Kaiser, that some physicists learned from published sources alone how to calculate with Feynman diagrams but did not learn to use them on completely new problems (de Regt 2017, 252–253). The argument is directed against capturing such skills in explicit rules or descriptions. It leaves open whether a system that acquires its dispositions through training, rather than from an explicit description, could come to take part in the relevant practices. Because the argument concerns what joining a practice requires, it also does not address whether a practice among artificial agents could itself be a social practice in which such collective tacit knowledge is held. The Feynman-diagram case, as de Regt reports it, suggests only that published texts transmitted part of what practitioners could do.

Later work co-authored by de Regt reads de Regt's own account in two ways. The chapter with Boge cited in Section 2 presents the contextual theory as applying specifically to human scientific understanding: it was developed by analyzing how human scientists achieve understanding, and intelligibility, its central notion, is relative to scientists with particular skills in particular historical, disciplinary, and social contexts (Boge and de Regt 2025, 418). The authors then consider whether a deep neural network could come to understand in this sense. At first sight it could not: on the contextual theory, understanding comes from explanations based on intelligible theories, whereas a network's predictions are not based on scientific theories and it supplies no intelligible models of the phenomena (Boge and de Regt 2025, 419). The notion of theory involved is not demanding, however. De Regt takes a theory, following Giere, to be a collection of principles whose building blocks are concepts. If a network's abstraction of features from data is regarded as acquiring concepts, a network could build theories from concepts of its own. The difficulty is that these concepts can differ wildly from human ones. Even if a network acquired understanding through theories based on its own concepts, that understanding might then not be accessible to humans, since human scientists cannot use concepts they cannot grasp to construct explanations themselves (Boge and de Regt 2025, 420, 429). The authors call the result a divide between human and artificial scientific understanding, an obstacle to progress in scientific understanding as a whole, and look for a way across it in proposals for testing whether, and measuring how far, an AI can transfer its understanding to human experts (Boge and de Regt 2025, 427–428). In the terms of Chapter 1, Section 2, theirs is a case in which understanding might be realized in an artificial system without entering the epistemic situation of a human S. Chapter 1, Section 6 read Ted Chiang's story as a thought experiment of a similar shape, in which results realized in bearers outside a human S are recorded in a form that no member can yet follow, and on two of the three readings given there a decipherment can be new to S although its result is not new to those who hold it. On those readings, bridging the divide that Boge and de Regt describe could itself be an achievement new to a human S.

The other reading treats the account as applicable to humans and machines alike. Barman, Caron, Claassen, and de Regt take scientific understanding to be an ability, assessed through what an agent can do rather than through its internal mechanisms or a feeling of understanding, and they argue that understanding could be realized through mechanisms different from human ones. Starting from de Regt's criterion, they shift its focus from the phenomenon to the agent and make it a matter of degree: an agent understands a phenomenon to the extent that it has a sufficiently complete representation of it, can generate internally consistent and empirically adequate explanations of it, and can draw a broad range of correct counterfactual inferences about it, abilities they propose to test with what-, why-, and what-if questions (Barman et al. 2024, 2–6). A preprint by Merijn Moody and de Regt adopts the contextual theory's test of intelligibility, recognizing a theory's qualitatively characteristic consequences without exact calculation, as a functional definition of scientific understanding. The objections they mean to avoid are modelled on John Searle's Chinese room argument. A person who knows no Chinese follows a book of instructions for manipulating Chinese symbols and passes back answers that, from outside, look like those of a Chinese speaker, yet the person understands none of it; Searle concludes that running a program, however appropriate its outputs, does not by itself produce understanding (Cole 2024, §§1, 3). Moody and de Regt's definition identifies understanding with an ability and asks for nothing beyond it, so on their account it sidesteps such objections by construction. On indirect evidence that language models answer a wide range of out-of-distribution scientific questions accurately, they credit current models with a non-trivial but brittle degree of such understanding, while noting that extensive evaluation has yet to be carried out (Moody and de Regt 2026, 9, 23).

Accounts of what has been called pragmatic understanding, understanding how to do something with a system rather than why something is so, divide on the same point. Lenhard, as reported by Westerblad and Stuart, takes pragmatic understanding to consist in abilities to predict and control phenomena; in Lenhard's case from nanoscience, simulations stand in for theory, and design rules let scientists build artifacts and control phenomena whose dynamics are not theoretically understood (Westerblad 2026, 13; Stuart 2025, 4). On such an ability view, Stuart notes, AI systems could have understanding (12). Stuart rejects the view, holding instead that an agent has pragmatic understanding of a system if and only if it has the skills to manipulate the system or its parts robustly and successfully to achieve its goals and is responsible, in the sense of being praiseworthy, for having gained those skills; skills, unlike mere abilities, are task-specific, learned, and deployed under some cognitive control (6–8). For this reason Stuart doubts that the benchmark of Barman and colleagues, which measures what an agent can do, captures what understanding requires (12–13). The article concludes that current and near-future AI systems lack pragmatic understanding, on a premise that it says it does not argue but takes from what it calls the majority view in the philosophy of AI, that such systems cannot bear responsibility; and since explanatory and objectual understanding often require skills such as conceptual mastery, it concludes that in many scientific cases the systems lack these too (13–14). Stuart nonetheless credits pragmatic understanding to a laboratory in which some members have the relevant skills and are responsible for them, with AlphaFold among its instruments, and sketches, without adopting, ways in which the responsibility condition might be dropped or met by artificial systems (14 n. 7, 16). On this account, then, whether A understands in this sense turns not on any battery of tests but on whether A is a praiseworthy agent with respect to the skill, the fourth of the senses of credit that Chapter 7, Section 3.3 keeps apart from true output, reliable process, and success attributable to competence. Westerblad, replying to Humphreys, holds that an instrument becomes functionally intelligible to scientists through an inquiry procedure, a publicly available way of using it to reach an aim, and that new instruments extend such procedures by being calibrated against those already accepted, so that, on this account, the means by which science extends human abilities do not move beyond human limitations (Westerblad 2026, 15–20). The agents who check, verify, and compare are, in this discussion, human scientists, and Westerblad notes that the conclusion bears on the view that science is no longer done by or for people, although the paper does not argue the point explicitly (20). Applied to an artificial A that calibrated new procedures against accepted ones, Westerblad's account would make whether the extension remains within the grasp of a human S turn on whether the procedures are available to its members, not on who carried out the calibration.

Wilkenfeld presents artificial intelligence as perhaps the field best placed to use the representation-manipulability account, introduced in Section 3.3. On that account a subject understands an object when it has a representation of the object that it could itself modify in small ways to produce a new representation supporting effective inferences about the object or manipulations of it. Wilkenfeld's examples include noticing that one has learned a rule of logic wrongly and correcting it, and adapting a proof one understands to a slightly different system; a proof one has only memorized cannot be adapted in this way (Wilkenfeld 2013, 9–10). Two features of the account bear on artificial understanders. First, it asks little of what a representation is: only that it be a computational structure with content that can be transformed. Wilkenfeld states this as a claim about human minds, consistent with classical computationalism, a language of thought, and some non-eliminative interpretations of neural networks, that is, interpretations on which the states of a neural network carry content (Wilkenfeld 2013, 8–9). The account therefore does not exclude a system as an understander because its representations are not symbolic. Second, the contextual standards that decide which manipulations count as understanding belong to the characterization made by whoever attributes understanding; the understander need not represent them, and need only be able to modify its representations and make the inferences (Wilkenfeld 2013, 19). If the understander in question is an artificial system, whether S is human or artificial, what the account leaves to be asked is whether the system has states that represent the object, and whether the system itself, rather than someone who edits its internal states from outside, can modify them in this way. Wilkenfeld does not take up this question. The reason given for turning to artificial intelligence is that building a computer that behaves like a human cognizer requires being clear about what human cognizers do when they understand (Wilkenfeld 2013, 18–19).

A related question is whether there can be artificial understanding without artificial belief. Dellsén's claim, noted in Section 3.2, that understanding need not require justification or belief in the way knowledge does, bears on it, but how it bears depends on what is meant by belief. In Dellsén's central case, a physicist in a world where string theory is true has methodological reservations about the theory and does not believe it, yet accepts it and uses it to explain; Dellsén argues that the physicist understands what the theory describes (Dellsén 2017, 2, 13–15). The contrast on which the case relies is one that Dellsén takes from L. J. Cohen: to believe that p is to be disposed to feel that p is true, whereas to accept that p is to adopt a policy of treating p as given (Dellsén 2017, 13–14). Belief in this sense is narrower than the belief discussed in Chapter 2, Section 2.1. On the functional and dispositional accounts described there, stable integration of p with inference, prediction, action, and revision is stronger evidence of belief than its storage or utterance, so conduct that Cohen classifies as acceptance can itself count as evidence of belief in that broader sense. Elgin, who draws heavily on Cohen's distinction, reads it as an explication of the commonsense notion of belief, which has two components: feeling, or being disposed to feel, that p is so, a largely involuntary component for which Cohen reserves the term "belief", and acceptance (Elgin 2025, 35–36).

Potochnik also separates acceptance from belief. Using a definition on which to accept something is to presuppose it for specific reasons, Potochnik holds that contributors to understanding, including idealizations, are to be epistemically accepted, that is, presupposed for epistemic reasons, but need not be believed; idealizations are not believed or asserted but assumed contrary to fact (Potochnik 2015, 8, 13, 16–17). Potochnik's account does not, however, free understanding from psychological conditions. On this account, understanding is a cognitive state as well as an epistemic achievement (Potochnik 2015, 5). As Raja and Sanches de Oliveira report Potochnik's account, understanding requires both successfully grasping a causal pattern and feeling that one has grasped it (Raja and Sanches de Oliveira 2024, §§3.1–3.2, 10–13). Van der Merwe also reports her formulation that genuine understanding arises from information of the right kind to induce that feeling (van der Merwe 2023, 330).

These views agree that understanding can go with acceptance rather than belief, but they define acceptance differently, and so they leave different things to be asked when the understander in question is an artificial system, whether S is human or artificial. On Dellsén's use of Cohen's distinction, understanding requires acceptance together with a mastery of the subject matter that enables correct explanation, whereas knowledge, on this view, still requires belief: the physicist in the string-theory case understands without knowing (Dellsén 2017, 14, 17–18). If belief is a disposition to feel that p is true, a system to which feeling cannot be attributed may still accept, and understanding would then lie closer to it than knowledge does. What remains to be asked is whether using p as a premise in explaining amounts to adopting a policy, which Dellsén describes as something one decides to do. Elgin defines acceptance as being willing and able to use p in inference and action when one's ends are cognitive, counts rules, standards, and methods among what can be accepted, and holds that, unlike belief in Cohen's sense, which is largely involuntary, acceptance is voluntary; belief in that sense, on her account, is spectatorial, whereas acceptance is agential (Elgin 2025, 11, 35–36). On Elgin's account the question for an artificial system moves from feeling to whether it has cognitive ends and accepts in this voluntary sense. On Potochnik's account as reported above, setting belief aside does not make the artificial case easier, since the felt sense of understanding is still required (Raja and Sanches de Oliveira 2024, §3.1, 11); Potochnik also takes what promotes understanding to depend on features of human cognition (Potochnik 2015, 11, 15–16). How much any of this matters depends, finally, on the account of belief adopted, the question raised in Chapter 2, Section 2.1. On a narrow account such as Cohen's, acceptance can be realized without belief. On the functional and dispositional accounts discussed there, acceptance put to work in explanation, as in Dellsén's case, may itself count as evidence of belief, so that understanding without belief offers an artificial system no separate route. What remains clearly distinct from belief on those accounts is a posit known to be false and presupposed only within one research purpose, which need not show the stable integration with inference, action, and revision that they treat as stronger evidence of belief.

The third claim, that a human–AI collective or an artificial community understands, requires an account of how the group's understanding relates to what its members, human or artificial, understand (compare the accounts of group knowledge in Chapter 2, Section 6). Distributed task success alone does not show that the group understands. Different agents can jointly produce a correct answer while no component and no organized whole can represent the relation that explains it, use it beyond the task, or respond to challenges. On accounts that attribute understanding to a group as an organized whole, a collective-understanding claim needs to identify how partial representations, abilities, communication, and correction compose into the attributed achievement; on accounts that ground it in members' understanding, the claim turns on what those members understand.

The three claims all concern who understands. The rest of this section turns to the question set aside at its start, whether understanding realized in some bearer has entered S's epistemic situation, beginning with a distinction between an individual's understanding and understanding credited to science. Boge, Schuster, and Stoll distinguish scientists' understanding, which an individual scientist has by grasping an explanation of a phenomenon, entertaining a coherent body of information accounting for it, or grasping a model of its dependencies, and which may be tacit or inarticulable, from scientific understanding, which on their account obtains only when there is a scientific explanation of the phenomenon communicable to a sufficiently broad scientific audience. That audience may be a small group of experts, and the explanation need not yet have been communicated (Boge, Schuster, and Stoll 2026, 2, 5–7). In one of their cases, Feynman understood why Feynman diagrams worked before Dyson's proofs gave an explanation that other physicists could follow (Boge, Schuster, and Stoll 2026, 9–10). The authors stress that the difference is not that one kind is explanatory and the other objectual: while individual scientists may come to understand on the basis of an explanation, science as a whole, on their account, comes to understand by means of one. They add that a scientist's understanding may be a very important epistemic achievement but is not yet scientific understanding (Boge, Schuster, and Stoll 2026, 4, 6). Their distinction can be read as concerning what is counted as the achievement rather than how understanding is realized in individuals and in communities. It is a distinction between what is credited to an individual and what is credited to science. In that respect it corresponds, on the side of understanding, to two distinctions drawn in Chapter 1, Sections 2 and 6, and taken up for knowledge in Chapter 2, Sections 2.1 and 6. One is between the actor conducting the research and the society relative to which an achievement is new and for which it is sought; the other, where success is assessed, is between an achievement realized in some bearer and one that has entered that society's epistemic situation. In each pair the two can coincide, but neither determines the other. The parallel is partial. On their account, the achievement credited to science requires only that a communicable explanation exist, not that members of the community have taken it up. What is credited to science thus corresponds to the achievement's being available to the society rather than to its members' holding it, a difference that Chapter 2, Section 7 discusses for knowledge as that between being in a position to know and knowing. The parallel is partial in a second respect as well: the individual in their cases both produces the result and understands it, whereas the distinctions of Chapter 1 allow the actor who produces a result and the bearer who understands it to differ. The proposal takes one side of a disputed question, whether scientific understanding requires explanation, and is not the settled meaning of scientific understanding.

The questions that the distinction separates remain open. One position can allow a researcher to understand tacitly before articulation; explanatory accounts can accept this too, since grasping an explanation need not include the ability to state it (Strevens 2013). Grimm, defending a dependency account, argues that articulacy is not necessary for understanding, citing evidence that young children and some animals grasp causal dependencies they cannot articulate (Grimm 2017). Another position can reserve scientific understanding for representations that support communication and criticism. Boge, Schuster, and Stoll hold both, reserving scientific understanding for communicable explanations: they read Elgin's account as concerned with scientists' understanding and de Regt's as concerned with scientific understanding, and take the two to be complementary rather than rival (Boge, Schuster, and Stoll 2026, 3, 14). An account that extended Bird's group-functional account of knowledge (Chapter 2, Section 6) to understanding would attribute understanding to an organized system even when no individual possesses the whole. These positions make different demands on an artificial researcher, according to where they locate understanding. If understanding can lie in a researcher's own tacit grasp, as the first position allows, an artificial researcher that is itself to understand must grasp the dependencies or the explanation, though it need not be able to state them. If scientific understanding requires a communicable explanation, as on Boge, Schuster, and Stoll's account, the researcher must yield an explanation communicable to the relevant audience, which has to be human-facing when that audience is human. If understanding can be attributed to an organized system, as on an extension of Bird's account, what is required is that the researcher's contribution be integrated into a collective epistemic capacity that the organization realizes as a whole.

As the second of these demands shows, who bears understanding and for whom it is sought are different matters. The bearer of understanding and the society for which that understanding is sought are analytically distinguishable, the first being whoever understands and the second one of the two parties to a research claim (Chapter 1, Section 2). Whether understanding realized in some bearer has entered that society's epistemic situation is a further question, the counterpart for understanding of the third judgment distinguished there, and the positions above answer it differently. On accounts that ground a group's understanding in its members', it has entered when relevant members, human or artificial, understand; on an extension of Bird's account such as the one just described, when the society's organization realizes it as a whole. Boge, Schuster, and Stoll's scientific understanding requires only that a communicable explanation exist, and Dellsén's restated noetic account locates progress in public information that enables relevant members of society to understand (Dellsén 2021). Both concern what is available to the society rather than what its members hold, so whether such availability already amounts to entry, or leaves the society only in a position to understand, is the counterpart of the dispute between Bird and Lackey over knowledge (Chapter 2, Section 7).

Applied to artificial systems, these distinctions separate at least the following possibilities. An artificial system might enable human understanding without itself understanding. It might supply humans with warranted knowledge while neither humans nor the machine possess explanatory understanding. Under a sufficiently non-anthropocentric account, it might instead organize dependencies in a form that supports its own inference, intervention, and error correction while remaining unintelligible to humans. Such an organization might serve only the system's own inference, or it might be communicable to other artificial members of S without being communicable to humans. A human–AI organization might also realize an integrated capacity not possessed by any one member.

The evidence reviewed in this chapter does not establish, as a description of existing systems, the possibility that an artificial system organizes dependencies in a form that supports its own inference while remaining unintelligible to humans. Even so, the possibility exposes an important choice of target. Intelligibility to the relevant audience can be necessary when the intended achievement is understanding that is to enter S's epistemic situation, such as public scientific understanding, without being built into every possible account of artificial understanding; it needs to be human-facing only when that audience includes humans. Conversely, evidence that a representation is useful inside an artificial system does not establish that it is understandable, warranted, or valuable for S. As research by artificial systems spreads, knowledge and understanding may therefore advance along different trajectories for different epistemic societies. This is more than an interface problem: it concerns whose epistemic capacities an artificial research system extends. The divergence need not run only between societies. Venkatesh, writing about pure mathematics, holds that concepts achieve an economy of thought fitted to human limits of memory and time, and that machines compete with concepts for that function. Venkatesh then suggests that mechanical reasoning may transform mathematical language and concepts so thoroughly that present and near-future mathematicians might struggle to understand one another, and takes earlier rewritings of mathematics to show that such unintelligibility is a real possibility (Venkatesh 2025, 94–99). On this account the divergence could arise within a human S, between its members at different times, through machine participation in their research. Since Venkatesh holds, with Davis and Hersh, that communicability is "part of its very definition," such a rewriting would on that view change not only how mathematics is done but what it is (84, 112).

The possibility that an artificial system organizes dependencies while remaining unintelligible to humans contains two claims: that an artificial organization of dependencies captures causal relationships, a claim about the world, and that it explains them or affords understanding of them, a claim about bearers and users. Woodward's account of causal explanation separates the two. On this account, causal relationships are features of the world, and Woodward's characterization of an intervention makes no reference to human agency: a process with the right causal characteristics qualifies, including a natural process in a world without people (Woodward 2023, §8). On this account, then, an artificial organization of dependencies could capture causal relationships while remaining unintelligible to humans. Explanation, by contrast, is an activity that Woodward attributes to humans and conceivably some other animals, as Bassi reports (Bassi 2013, 123–124). Woodward also requires that the information giving an explanation its import be epistemically accessible to those who use it (Woodward 2000, 248 n. 11). Woodward's account does not settle whether artificial systems can be among those users. Whether such an organization would also explain depends, on this account, on whom the explanation is for and on whether those users, human or artificial, have access to the relevant information.

Potochnik's account of explanation makes the audience part of what explains. On this account explanations must generate understanding in those who seek them, and which of the many dependence relations responsible for a phenomenon explains it depends on what that audience seeks to understand (Potochnik 2016, 9–13, 17). Potochnik develops the account for human science, holding that explanations must be comprehensible to humans and tying the contribution of broad patterns to features of human understanding (Potochnik 2016, 17–18; Potochnik 2015, 11, 25). Among the features of an audience that, on this account, shape what counts as explanatory, Potochnik lists its epistemic circumstances and interests and, for humans in general, cognitive features (Potochnik 2016, 4–5, 17). Extended to artificial organizations of dependencies, the account would make the question whether such an organization explains anything, and to whom, partly a question about the cognitive needs of its audience, human or artificial, and it gives no reason to assume that what explains for one audience would explain for the other.

In sum, the three claims call for different evidence: what a system enables others to understand, what the system itself can do with its representations under a selected account, and how a group's partial representations and abilities compose. For any of them, where understanding is realized and whether it has entered S's epistemic situation are to be asked separately.

What this chapter has brought out is that different theories require different evidence, and that a property granted to one bearer does not pass to another without argument. Part IV takes up questions related to whether an artificial system can literally believe, represent content, or understand: norm formation and epistemic self-government in the analysis of autonomy over inherited standards (Chapter 7, Section 4.3), and, in Chapter 8, artificial knowledge bearers and societies (Section 1) and what would let an artificial knower's checks count as evidence, its states be about a world, and its commitments remain answerable to that world (Section 2).

7. What understanding is valued for and what it may enable across time

Section 4 distinguished an attempt's being directed at understanding from a requirement that research, or each of its operations, bring understanding about; the characterization imposes no such requirement for any achievement. This leaves the value of understanding and its place in sustained inquiry open to substantive accounts. The value in question is that of understanding as an epistemic status: what it is valued for, in itself or for what it may enable in continuing inquiry. Chapter 9, Section 3 counts such a status as one possible object of value; the question that section mainly pursues, which of S's questions, practices, and distributions of results matter and to whom, belongs to the value and governance level of Chapter 1, Section 1 and is not taken up here. One answer concerns understanding's value in itself or its place as an aim of inquiry (Section 7.1). Another concerns how it constitutes, evidences, enables, or promotes further capacities in continuing inquiry (Sections 7.2–7.4). The strong predictive case of Section 4 puts the question of what understanding enables sharply: what would be lost, beyond any single validated result, if a research system brought about knowledge that neither it nor those for whom it inquires understood, whoever, if anyone, held that knowledge? The subsections are arranged accordingly. Section 7.1 takes up understanding valued for its own sake or as an aim. Sections 7.2–7.4 take up what understanding may enable as inquiry continues beyond one validated result, divided by what is grasped or made available: a grasp of how a target would differ if what it depends on were different (Section 7.2), a grasp of how a domain hangs together (Section 7.3), and the availability of understanding to others (Section 7.4). This division is the book's own, drawn along strands in the literature on understanding rather than taken from a classification that literature offers, and it does not claim to be exhaustive.

7.1 Understanding valued for its own sake or as an aim

Several epistemologists hold that the value of understanding is not exhausted by what it enables. Kvanvig argues that the value of knowledge is exhausted by the value of some of its constituents, such as true belief and subjective justification, whereas understanding has value beyond that of such parts. On this account understanding requires grasping explanatory and other coherence-making relations within a large body of information, and grasping them organizes and systematizes one's thinking on a subject matter in a way that goes beyond adding more true beliefs, or even more justified true beliefs. Organized thinking lets one reason from one item of information to related items that can serve as a basis for action, and it gives inquiry a satisfying closure, a sense of having grasped the subject matter as a whole; the value beyond the parts is the value of this organization (Kvanvig 2003, 185, 188, 192, 202, 205). Pritchard argues that understanding why something is so typically, if not universally, involves a cognitive achievement in a demanding sense, one that demands overcoming a significant obstacle or exercising significant cognitive ability, and that achievements of this kind are finally, that is non-instrumentally, valuable (Pritchard 2016, 9–10). In the same article Pritchard grounds this value in the way such achievements exercise one's agency on the world and in the intellectual autonomy that understanding manifests: a grip on things that is one's own even when it is gained with the help of experts (Pritchard 2016, 9–12).

Riggs is among those who hold that the really valuable things from an epistemic point of view are higher-grade cognitive accomplishments such as understanding. As Grimm reports the view, we do not by nature seem to have any desire to acquire trivial pieces of information, such as the name of a particular person listed in an old phone book, whereas any instance of understanding may seem worth pursuing, and Riggs writes that any understanding, even of a subject matter we may consider trivial or mundane, contributes to the epistemic value of one's life (Grimm 2021, §3.1). As Gordon reports it, Riggs holds that understanding a subject matter requires an appreciation of how its parts fit together and of the role each plays in the whole, and he distinguishes from understanding what he calls intelligibility, which also implies a grasp of order, pattern, and connection but does not seem to require a substantial connection to truth (Gordon n.d., §§2b, 3).

Zagzebski, among others, has argued that an epistemology focused on knowledge alone is one-sided, since it neglects other epistemic goods such as understanding and wisdom (Grimm 2021, §1.2). Reporting the history behind this neglect, Grimm notes that the ancient term episteme has been argued to be better rendered as understanding than as knowledge, since for Plato and Aristotle it involved a systematic grasp of how things are connected or of their causes, and that epistemology's later focus on isolated propositional knowledge has been explained as a response to the rise of skepticism in Hellenistic philosophy, an explanation Grimm finds in Burnyeat and in Zagzebski, or, as Pasnau suggests, to the religious wars of early modern Europe (Grimm 2021, §1.1). As Gordon reports Zagzebski's view, not all understanding requires true belief: the belief that objects fall in a vacuum at a fixed rate, which ignores the attraction of everything but the earth, yields more understanding for most purposes than the vastly more complicated truth, since grasping the truth can come at too high a cognitive cost (Gordon n.d., §2b).

Hills, writing on aesthetic understanding, holds that awareness of the reasons why a work is or is not valuable is likely to help one make better judgments in the future, and that such understanding is an essential component of aesthetic virtue, so that the ideal way to make aesthetic judgments is through one's own understanding. Part of her case is an idea of mirroring value. True beliefs mirror the world in virtue of their content; a judgment based on a grasp of the reasons that make it true also mirrors the world in its form, since the dependence of one belief on others matches a dependence in the world. When someone judges a novel bad because they recognize that it is inept, lifeless, and badly written, their belief that it is bad depends on their belief that it is inept just as its lack of merit depends on its ineptness, and they would have judged differently had the novel had different qualities (Hills 2022, 21, 28–29). Hills suggests that this explanation generalizes to moral understanding (Hills 2022, 22).

Not every account of the value of understanding, however, appeals to value beyond what understanding enables. Grimm traces much of the special value of understanding to the position it gives one to predict, and possibly control, how the world will unfold, while granting that this may not exhaust the intuitions in its favor (Grimm 2017). Grimm's earlier survey keeps both kinds of value in view, and it shows that valuing understanding for its own sake need not depend on denying that understanding is a kind of knowledge. Grimm, who counts himself among those who take understanding why to be knowledge of causes, recasts the question why understanding is more valuable than knowledge as the question why it is better than propositional knowledge, treating knowledge as a genus whose species differ in their objects. He holds that objective understanding is plausibly desired both for its own sake and for the promise it offers of controlling the world, and argues that if a more profound mirroring of reality is epistemically better, every item of understanding is more valuable than the corresponding item of propositional knowledge (Grimm 2012, 4, 11, 15).

Related positions treat understanding as an aim. Pritchard has suggested that understanding, rather than knowledge, may be the goal of inquiry. On this account, someone who learns from a reliable source that their house burned down because of faulty wiring, but who has no conception of how faulty wiring could do this, has not yet reached the goal of their inquiry (Pritchard 2008, §§10–12). In later work Pritchard restricts the claim. Inquiries that seek an explanation of why something is so are legitimately closed only by the kind of knowledge involved in understanding, whereas an inquiry into whether, say, an animal in a zoo is a genuine zebra can usually be closed by knowledge from a trusted informant. Pritchard calls the resulting view a complex knowledge account of inquiry: it is always knowledge that legitimately closes a well-conducted inquiry, but in some inquiries knowledge of a specific sort (Pritchard 2016, 6–7). Kelp, who defends knowledge as the aim of inquiry into specific questions, takes understanding to be the aim of inquiry into a general phenomenon, so that such inquiry succeeds if and only if one understands the phenomenon. On this account such an inquiry is not completed by knowing each truth about the phenomenon piecemeal, for example each on the word of a different informant; it also requires that one's beliefs be based on one another in a way that reflects one's knowledge of the explanatory and support relations among those truths. On Kelp's account, maximal understanding is maximally comprehensive and well-connected knowledge of the phenomenon, and lesser understanding is a matter of degree (Kelp 2021b, S1583–S1584, S1588; Kelp 2015, 16, 18). Set side by side, Pritchard's later view and Kelp's both make what properly ends an inquiry depend on what the inquiry is into, and both allow that more than isolated knowledge can be required, but they draw the line in different places: Pritchard between inquiries that seek an explanation and others, Kelp between inquiry into specific questions and inquiry into phenomena, such as the life of Napoleon, inquiry into which can progress through knowledge that is not explanatory, such as that Napoleon was French (Kelp 2021b, S1583, S1589). On such views, taking knowledge as the orientation of inquiry does not by itself settle whether understanding is required; what an inquiry requires depends on the question it pursues, in line with the question-relativity noted in Section 2.

In the philosophy of science, Elgin argues that truth is not the paramount epistemic objective, since an epistemology centered on truth cannot account for the epistemic standing of a science that relies on models and idealizations known not to be true (Section 3.4). Elgin argues further that the cognitive achievement good science standardly yields is understanding rather than knowledge. A scientific account is not a collection of separately supported truths: its claims support one another, their conjunction is apt to be falsified by some anomaly, and the anomalous parts cannot be excised without unravelling the rest; knowledge requires truth, and the accounts we admire do not come out true, whereas understanding, which on this account answers to the facts without being factive, can advance through strictly false accounts. Because devices such as metaphor, fiction, and exemplification figure in scientific as well as artistic understanding, Elgin holds that scientific understanding cannot be done justice while denying that the arts and their devices function cognitively (Elgin 2004, 1–2; Elgin 2006, 1, 3–5; Elgin 2007, 2–5; Elgin 2002, 1). De Regt treats understanding phenomena as one of the central epistemic aims of science and distinguishes views on which understanding is bound up with the explanatory aim, is an additional aim, or takes the place of traditional aims (de Regt 2020, 921, 923, 932). Dellsén's account, discussed in Section 4, belongs to this family. So does Potochnik's, introduced in Section 3.4, on which understanding, not truth, is the ultimate epistemic aim of science, and truth and knowledge matter as routes to it: idealized representations can represent accurately the causal patterns they depict, and science, on Potochnik's account, generates understanding of phenomena by way of knowledge of those patterns (Potochnik 2020, 13, 16). It follows that, on this account, where an attempt is directed at knowledge, its target is valuable chiefly as a route to understanding; the working sentence, which does not specify the kind of achievement, can accommodate this ranking without adopting it.

These positions differ from one another, and each is contested. Critics point to easy cases of understanding that seem to involve no significant achievement (Grimm 2021, §3.1). Boyd, who defends the acquisition of understanding by testimony, argues by contrast that understanding that is easy for an expert can still count as a strong achievement, because the expertise that makes it easy was itself hard won (Boyd 2017, 37–38). The demanding sense of achievement in this exchange is narrower than the general term epistemic achievement in Chapter 1, which by itself requires neither overcoming a significant obstacle nor exercising significant cognitive ability. Whether easy understanding is an achievement in Pritchard's sense therefore does not decide whether it can be an epistemic achievement new to S. DePaul and Grimm turn Kvanvig's own reasoning against Kvanvig's positive proposal. Kvanvig had argued that knowledge has no value beyond that of some of its constituents because any condition that excludes Gettier cases will be gerrymandered and so not itself worth satisfying, and further held that understanding is compatible with such luck and so needs no such condition. Against this, they describe a case in which a fabricating reporter's account of why a goal was scored happens to be true and the reader grasps the explanatory connection it describes; on their account the reader does not understand why the goal was scored, any more than the reader knows that it was, since such a reader would have grasped a different story just as readily. If so, understanding too requires a non-accidental relation between the grasping and the connection grasped, and by Kvanvig's own reasoning it would lose the value claimed for it. Because they already reject a premise of Kvanvig's argument about knowledge, they suggest taking this as a further reason to doubt that argument (DePaul and Grimm 2007, 510–513). DePaul and Grimm do not discuss artificial understanders, but applied to one, the requirement their case supports gives the shortcut problem of Section 3.3 a definite form: what an evaluation has to exclude includes a grasp that would have fastened just as readily on a different explanation had that one been supplied, so that the question is whether the system's account follows the explanatory connection itself or only the explanation it was given (compare the anti-luck conditions on knowledge in Chapter 2, Section 4).

Which of these positions is adopted changes what is required of a research system. If, as on Pritchard's later view and Kelp's compared above, understanding is what properly closes an explanation-seeking inquiry, or an inquiry into a phenomenon, a system that delivers validated results leaves such inquiries unfinished, whatever its record of knowledge, until the understanding they seek is realized in the bearer they target: the system itself, relevant members of the community for which it inquires, or, on accounts of collective understanding, that community (Section 6), and, where the inquiry is for S and that bearer lies outside S, until the understanding has also entered S's epistemic situation on the adopted account (Sections 6 and 9). On Kelp's account, the understanding that closes such an inquiry need meet only a contextual threshold, short of the maximal understanding that is the ultimate aim of inquiry (Kelp 2021b, S1588). Under the working characterization, the activity can still count as research, and under the assumptions of the strong predictive case in Section 4 its results can count as knowledge. This does not make an inquiry that specifically sought explanatory understanding complete. Whether an activity is research and whether it has answered its particular question are different judgments; an aim-centered account adds a further claim about which achievement properly closes inquiries of that kind.

In whom is the value these accounts claim realized? Read with this question in mind, several of them locate it in an understander. Pritchard locates it in an achievement creditable to the understander's own cognitive ability (Pritchard 2008, §§10–11), and Zagzebski, as Gordon reports her view, ties the epistemic value of understanding to its transparency: one cannot, she holds, understand without understanding that one understands (Gordon n.d., §5a). On such accounts, the value is realized where someone understands, not merely where an explanation is available. It therefore attaches to an individual's understanding, which Section 6 distinguished from understanding credited to science in the sense of a communicable explanation. These accounts state their grounds for persons, through such things as the epistemic value of a life (Riggs), the satisfying closure that organized thinking gives inquiry (Kvanvig), and an achievement creditable to one's own cognitive ability (Pritchard). Applied to an artificial understander, which none of them discusses, whether its understanding has such value turns on whether those grounds hold of it, and the grounds raise different questions. Kvanvig's closure comes with a sense of having grasped the subject matter as a whole, and so meets the question Section 6 raised for Potochnik's felt sense of understanding; Pritchard's asks whether the understanding is the system's own achievement, which for artificial systems is disputed (Chapter 7, Section 3.3); and Riggs's, the epistemic value of a life, asks whether the system has a life to whose epistemic value its understanding could contribute. The question of whose understanding has such value has also been answered directly for research done with AI tools, by a claim about what basic science is for rather than by an account of what understanding is. Botvinick and Gershman, in their perspective in a joint article that collects several perspectives with responses, asking of basic science done with such tools "'whose' understanding matters?", answer that human understanding is to remain a core goal of science: "We cannot cede understanding to artificial systems." They would keep this goal, together with the choice of problems to work on, with human scientists even in a scenario in which technical limitations presented no barrier, while allowing that, because of limits on human cognition, AI systems may someday represent aspects of nature that humans cannot; even then, on their view, as much human insight as possible is to be extracted from such systems (Binz et al. 2025, 6–7). Their answer fixes the bearer: in basic science, they hold, the understanding whose value counts is that of humans, whatever an artificial system may represent. Read against Chapter 1, Section 2, where neither A nor S settles who bears an achievement and, on Humphreys's account, science's being done for humans does not by itself require that what it comes to know lie within their current understanding, the answer can be read as adding to a human S a requirement on the bearer that does not follow from S's being human.

Two further points matter for reading Sections 7.2–7.4, which follow. First, the claim that understanding is valuable for its own sake, or is an aim of inquiry, does not follow from a list of what understanding enables, and it is not refuted by showing that some of those effects can be obtained in other ways. Second, it follows that the relations traced in those sections are not offered as exhausting the value of understanding; on the positions above that ascribe final value to understanding, they do not. They record the part of it that becomes visible when one asks what a continuing research system would lose without it. The two kinds of value need not compete. Kvanvig's explanation of the value of understanding appeals both to the way organized thought supports reasoning toward action and to the satisfying closure it gives inquiry (Kvanvig 2003, 202). On ability accounts such as the one Hills favors, moreover, the grasp that understanding involves is itself a kind of ability or know-how, which, as Hills puts it for moral understanding, includes abilities to explain and to draw conclusions about new cases (Hills 2020, 12), so describing what the abilities discussed below make possible need not treat understanding as a mere means.

The first of these points can be seen in an account that treats the separation of understanding from what it enables as a historical change. Koichi Takahashi, writing about AI-driven science, holds that what joined science and technology in the modern period was understanding: laws of nature were understood, and that understanding was turned into technique. Takahashi holds that prediction which does not pass through understanding is emerging, citing structure prediction by AlphaFold2, deep-learning weather models, and the screening of candidate materials by AI, and that if prediction and control become possible without passing through understanding, the reason for the marriage of science and technology, in Takahashi's phrase, disappears and the two head toward a divorce. What is then lost, on this account, is not understanding itself but understanding as a means. The understanding that remains once how to reach results is handed to AI becomes an end in itself, as with the question why the universe began, which Takahashi calls technically useless but essential to human intellectual activity (Takahashi 2026, 184–186). Whose understanding such prediction bypasses is left unstated, although in the example from materials science the physical explanation is supplied afterwards by humans. Takahashi also allows that AI prediction and scientific understanding may form a new kind of coupling rather than simply separating, as when researchers take predicted structures as the starting point for new hypotheses and understanding (185). On Grimm's account, which traces much of the special value of understanding to the position it gives one to predict and control, the separation Takahashi describes would make much of that value obtainable without understanding. On the accounts above that ascribe final value to understanding, it would leave the value they ascribe in place, as the first point says. Takahashi's description of what remains, understanding that has become an end in itself, can be read along these lines, although it does not draw on these accounts.

7.2 Grasping how things would differ: transfer, intervention, diagnosis

The dependency accounts of Section 3.2 and the ability accounts of Section 3.3 disagree about what understanding consists in: the former place it in grasping a model of dependence relations, the latter in what a subject can do. This book nevertheless reads them as sharing a concern with one modal competence, one that concerns what would be or would have been the case and not only what is: grasping a structure of dependence well enough to tell how a target would differ if the factors on which it depends were different. The reason is that what each account names as the content or the signs of understanding involves this competence. The dependence relations that dependency accounts ask a subject to grasp are relations of how a target varies with the factors on which it depends. The abilities that ability accounts list, drawing conclusions about relevantly similar cases, answering what-if questions, and modifying a representation to support new inferences, all reach beyond the cases actually given (Sections 3.2 and 3.3).

The following descriptions bear this reading out. Explanations on Woodward's interventionist account, as Lauren Ross and Woodward present it, answer what-if-things-had-been-different questions, telling how the explanandum would have been different under changes in the factors cited (Ross and Woodward 2023, §3). Grimm describes the dependency maps that understanding takes up as mobile, and the understanding mind as able to anticipate how varying the value of one variable will lead, or fail to lead, to changes in the values of others (Grimm 2017). Hills's cognitive control includes drawing conclusions about relevantly similar cases (Hills 2020, 12), and Kuorikoski and Ylikoski take understanding to be constituted by the ability to make correct inferences about what would have happened had things been different, what would happen if certain things were changed, and how a desired change could be brought about (Kuorikoski and Ylikoski 2015, §2). Le Bihan's modal view extends this beyond a single structure. On this view, understanding a phenomenon consists in knowing how to navigate a space of possible dependency structures that would give rise to it, and this is called modal understanding because it concerns how the phenomenon could arise in other possible worlds as well as how it arises in the actual one. Le Bihan's aim is to explain how theories and models known to misrepresent the world can still yield understanding of phenomena. The ideal gas model, on which molecules exert no forces on one another, and the van der Waals model, which adds attraction between molecules and their size, describe different possible dependency structures for the behaviour of gases. On this account, knowing how each structure gives rise to the behaviour it recovers, knowing how the structures relate to one another and where they differ, and knowing which constraints, such as the laws of thermodynamics, hold across all possible structures are three levels of such understanding (Le Bihan 2017).

Accounts disagree about the status of this competence: some treat it as constitutive of understanding, others as a manifestation or evidence of it, and some deny that the abilities involved are special to understanding (Grimm 2021, §2.2). Le Bihan, for instance, takes knowing how to navigate such a space to be constitutive of modal understanding, but counts the abilities to infer, transfer, and answer what-if questions as manifestations of it rather than as constitutive of it (Le Bihan 2017). Whether the competence constitutes understanding or only manifests it, a system that lacks it lacks one resource on which the situations below can draw, so this subsection can ask what a continuing research system would lose without understanding without first choosing among these accounts.

This subsection takes up three situations in which a research system that continues over time uses this competence: carrying what it has learned into a new context (transfer), deliberately changing something (intervention), and finding that an expectation has failed (diagnosis). Prediction under new conditions falls under transfer and intervention. It is not listed separately because the question of this subsection is what understanding adds to validated prediction: the strong predictive case of Section 4 already grants such prediction where no human member of the community understands why the target regularity holds, so prediction alone cannot show what would be lost without understanding.

The first use is transfer and generalization, in the sense in which what was learned from some cases continues to hold beyond them, close to the sense the word has in machine learning. A representation of relevant dependencies can indicate which regularities would survive changes in context. It can expose why a proxy worked and where it will fail. Understanding does not guarantee generalization, and robust empirical methods can transfer without it. It can nevertheless make the proposed basis of transfer available for criticism rather than leaving extrapolation to a single performance history. The accounts of Section 3 would explain differently why such transfer can evidence or follow from understanding. On a dependency account such as Dellsén's, transfer would rest on the dependence relations that the grasped model represents continuing to hold in the new context (Dellsén 2020). On de Regt's account, as he and Boge restate it, scientists who have constructed explanations that produce understanding of phenomena may go on to apply, extend, and refine their knowledge of the target systems using the same skills, so transfer is one such extension (Boge and de Regt 2025, 420). On Hills's ability account, cognitive control includes drawing conclusions about relevantly similar cases, so transfer is an exercise of abilities that partly make up understanding (Hills 2020, 12). Khalifa's reductive account, introduced in Section 3.1, does not deny that understanding and transfer go together; it explains the connection without positing abilities special to understanding. On this account, understanding why something is the case is a matter of knowing an explanation of it, and the abilities that understanding involves are, in Khalifa's phrase as Grimm reports it, "especially unspecial" (Grimm 2021, §2.2): they are those exercised in considering and comparing potential explanations and in explaining (Khalifa 2019, 10, 31). On this account, too, understanding improves with the amount of explanatory information grasped, so that someone who grasps both why something holds and how what explains it brings it about understands better than someone who grasps only the first (Khalifa 2019, 33).

It was said above that understanding can state the reason for expecting a result to hold in a new context, the proposed basis of transfer, in a form open to criticism, rather than leaving extrapolation to a past performance history. Woodward's account offers one way of stating such a reason: this dependence holds unchanged within a certain range of interventions and background circumstances, and the new context falls within that range. This account brings out at least three things about a claim of transfer stated in this way. First, the claim needs support for its extension beyond the original setting. On Woodward's account, a causal generalization, in a sense different from the one above, namely a general claim that states how one variable depends causally on another, holds within a range of interventions and background circumstances, and whether it holds for other subjects and circumstances is a question of what the literature on experimental design calls external validity, analytically distinct from whether it held in the original experiment. As Woodward notes, however, the two assessments need not use wholly separate evidence: evidence of stability across contexts can also support a local causal claim (Woodward 2026, 5–6). Second, that support does not require knowing every boundary of the range. To use such a generalization to explain the behavior of a system, Woodward argues, one must know that the system falls within the generalization's domain of invariance, the range within which the dependence holds unchanged, though not the exact boundaries of that domain (Woodward 2000, 233–234). Third, whether a claim of transfer succeeds can depend on what is carried over. Li and colleagues report Woodward's distinction using structural equation models: quantitative claims can be population-specific even where qualitative claims about what can cause what hold more widely (Li et al. 2018, §2). A claim of transfer stated in this way can therefore be met with definite questions: does the new context really fall within the range, and can only the qualitative relationship be carried over to it, or the quantitative one as well? That is what it means for the basis of transfer to be open to criticism.

The second use is intervention and construction. Prediction can guide action, but intervention can require distinguishing causes, constraints, mechanisms, and manipulable variables. A predictor may fail when its inputs are themselves changed by policy or experiment. One example Woodward discusses is the Lucas critique in macroeconomics, which, on Woodward's account, turns on whether the generalizations on which economic models rely are invariant under changes in, for example, the incentives, relative prices, or information available to economic agents (Woodward 2018a, §4). Explanatory or causal understanding can reveal intervention points and possible side effects. Engineering understanding can similarly connect an artifact's behavior to what can be changed, repaired, or built differently.

Listing intervention as a use of the competence does not restrict the competence to causal dependence. Woodward's interventionist account, discussed in Section 4 and earlier in this section, ties explanatory information to manipulation: to explain is to show how an outcome would change if one intervened on the factors cited. But Woodward restricts that account to causal explanation, and allows that a derivation can answer what-if-things-had-been-different questions where the question cannot be read as one about an intervention, and may then be a noncausal explanation of some sort. One example discussed is the argument that the stability of planetary orbits depends mathematically on the dimensionality of space, since no stable planetary orbits are possible in a space of four or more dimensions; the derivation tells how the possibility of stable orbits would change as the dimensionality of space changed, but the idea of an intervention that changes the dimensionality of space is unhelpful, perhaps even unintelligible (Woodward 2018b, §§2–3). Woodward's account therefore does not imply that all understanding is causal, and neither does this subsection's use of it.

The third use is anomaly diagnosis and revision. When an experiment conflicts with a prediction, the outcome bears on a bundle of hypotheses, auxiliary assumptions, instruments, preprocessing choices, and environmental conditions. It does not identify its own target of revision. An organized account of dependencies can help investigators decide whether to revise the focal hypothesis, a measurement model, a boundary condition, or the test itself. This is one reason understanding can matter to self-correction even when a single result is warranted without it. Duhem-style underdetermination, discussed in Chapter 2, Section 5, is the point that an adverse result by itself does not settle which of these is to be revised; Duhem's thesis does not itself supply a procedure for locating the error, so locating it calls for a capacity of this kind. Elgin argues that although a failed expectation shows only that something in a constellation of commitments is wrong, the commitments are not all equally vulnerable: those independently supported by other well-confirmed constellations are less likely to be the locus of error, so the better supported the background, the more precisely a mistake can be located (Elgin n.d., 17–18). Among the abilities in Hills's cognitive control (Section 3.3), as Gordon lists them, two run in opposite directions: drawing the conclusion that p from the information that q, which runs from the explaining factor to what it explains, as prediction does, and giving q as the explanation when given p, which runs back from what is to be explained to what explains it (Gordon n.d., §3c). Diagnosis takes the second direction: it starts from a failed expectation and works back to what went wrong. And Wilkenfeld's examples of understanding include being able to notice and correct inconsistencies or mistakes in one's own representation (Wilkenfeld 2013, 10). Neither Hills's ability to work back from what is to be explained nor the ability Wilkenfeld describes to notice and correct mistakes guarantees that the revision chosen is the right one.

7.3 Connecting a domain: retention, reuse, and further questions

Where Section 7.2 drew on accounts that focus on grasping a structure of dependence, another strand of the literature locates understanding in a grasp of how items of information hang together. Kvanvig, as seen in Section 7.1 and as Grimm reports, takes understanding to require grasping the explanatory and conceptual connections between the pieces of information involved in a subject matter, combined into a unified body (Grimm 2021, §§2.1, 2.3). Elgin characterizes an understanding as an epistemic commitment to a comprehensive, systematically linked body of information that is grounded in fact, responsive to evidence, and enables nontrivial inference, argument, and perhaps action regarding its topic (Elgin 2018, 8). Dellsén's account, which concerns understanding a phenomenon rather than understanding why, locates understanding in grasping a model of the dependence relations in which a phenomenon stands. A model here is an information structure interpreted so as to represent its target, as the Lotka–Volterra equations become a model of predation once their variables are read as the sizes of predator and prey populations. The model understanding requires represents what the phenomenon depends on, how, and what it does not depend on. Such a model, Dellsén argues, can fail in two ways: by misrepresenting a dependence or by not representing it at all. The account therefore measures a model by two criteria, accuracy, which asks whether it misrepresents, and comprehensiveness, which asks whether it represents what it should. Each is met more or less rather than simply met or not, so understanding too is a matter of degree: one understands a phenomenon to the degree that one grasps an accurate and comprehensive model of its dependence relations. Comprehensiveness also covers what does not depend on what, just as a causal graph shows not only which elements cause which but also which are not causally connected. Learning that two factors that seemed related are in fact independent therefore adds to understanding, as when Galileo's thought experiment shows that an object's acceleration in free fall does not depend on its mass (Dellsén 2020, §§3, 7).

How does such connecting relate to the competence of Section 7.2, the competence to tell how a target would differ if what it depends on were different? It could be a further use of that competence, or a distinct achievement that supports it, and the accounts point in different directions. Ylikoski and Kuorikoski give a reason to link the two. They argue that an explanation well integrated into a larger body of theory yields more understanding than the two bodies of knowledge taken separately, because integration widens the range of what-if questions that can be answered, in two ways. First, through inferential connections to the existing theory, dependencies between factors in that theory and aspects of the phenomenon can open dimensions, not foreseen before, along which what-if questions about the phenomenon can be answered. Second, the explanation can bridge gaps within the existing theory, so that new what-if questions about other phenomena can be answered. Integration in their sense is therefore more than formal consistency or conceptual coherence: it must allow new relevant inferences about the phenomenon (Ylikoski and Kuorikoski 2010, §4.4). That connecting widens the range of answerable questions does not by itself settle which of the two it is, however, since a distinct achievement could have the same effect. On accounts that, like Kvanvig's, count coherence-making relations other than explanatory ones, or that, like Kelp's, let knowledge that is not explanatory add to understanding (Section 7.1), what is grasped in connecting a domain can include relations other than dependence. On such accounts, connecting may be an achievement that is not exhausted by the competence to grasp dependence.

This subsection takes up two relations, under such connecting, that matter to research continuing over time: retention and reuse, and opening further questions. The first is retention and reuse: keeping what has been obtained over time, and using and extending it in later inquiry. Kvanvig holds that grasping explanatory relations organizes and systematizes thinking about a subject matter in a way that goes beyond adding further true beliefs. Such organization is useful, on this view, because it lets one reason from one piece of information to other related information that can serve as a basis for action, whereas unorganized thinking provides no such basis for inference (Kvanvig 2003, 202); this bears on reuse. Among the abilities of Hills's cognitive control, as Gordon lists them, is an ability to draw from the information that q′ the conclusion that p′, or that probably p′ (Gordon n.d., §3c); this too bears on reuse. Taken together, on these accounts an organized body of results can be extended to new cases by inference from what it contains, whereas a collection of isolated answers offers no inferential links among its answers, so an answer has to be obtained afresh for each new case. Retention has a precedent in the Meno, where Socrates compares true opinions to the statues of Daedalus, which run away unless they are fastened: true opinions are of little value until they are "fastened by the tie of the cause", and once bound they are abiding, which is why knowledge is more honorable than true opinion (Plato, Meno 97e–98a). Grimm reports that a case has been made that understanding is a better translation than knowledge of Plato's and Aristotle's episteme (Section 7.1); read in that way, the passage ties being kept to grasping the cause. Wilkenfeld, on whose account understanding is a matter of compressing information about the understood so that it can be used, gives a modern case: a student who had memorized a soundness proof would have been lost had he forgotten one step, whereas a logician who understands the proof can reconstruct it from simpler representations (Wilkenfeld 2019, 7). Educational research states a parallel claim. Novak and Cañas report that knowledge learned by rote, with little integration into existing knowledge, tends to be quickly forgotten unless much rehearsed, whereas meaningful learning supports the retention of knowledge over long periods (Novak and Cañas 2008, 6–7). These points bear on retention: they suggest that connections to grounds, or an organization that permits reconstruction, can help preserve or recover what would otherwise be lost.

The second is opening further questions. Understanding can reorganize a domain and reveal new contrasts, anomalies, and interventions. A predictive system can also generate new questions by discovering patterns or failures. The difference is not that only understanding creates novelty. It is that a representation of relations can make the space of possible questions navigable in ways an isolated answer does not; Ylikoski and Kuorikoski's account of integration states one version of this claim. Elgin holds that an understander should be able to use what she understands, perhaps as a source of working hypotheses about related matters (Elgin 2007, 5), and that reconfiguring a domain, as a metaphor does, equips us to raise new questions that could not otherwise have been framed or motivated (Elgin 2002, 5, 9, 12). The relation also runs the other way. As noted in Section 7.1, Kvanvig says that organized understanding gives inquiry satisfying closure, and Pritchard holds that an inquiry seeking an explanation is not legitimately closed until the understanding it seeks is reached (Kvanvig 2003, 202; Pritchard 2016, 6–7). On their accounts, understanding closes inquiry. This seems to sit uneasily with the claim of this subsection that understanding opens further questions. The two claims can, however, be read as concerning questions of different scope: what understanding closes is the question that prompted an inquiry, and what it opens are new questions beyond it. Grasping, through Galileo's thought experiment, that an object's acceleration in free fall does not depend on its mass closes the question whether heavier objects fall faster, and at the same time raises the question of what that acceleration does depend on.

7.4 Making understanding available to others: communication, criticism, and memory

An explanation can compress relations into a form others can examine, teach, contest, and connect to existing knowledge. Articulation may expose an ambiguity that remained invisible while a practice went unarticulated. It can also mislead: standardized explanations may create an illusion of shared grasp, while some expertise remains partly tacit. Whether understanding itself can be passed on is disputed. One tradition, which Grimm reconstructs in order to dispute it, holds that grasping how things are connected is something each person does at first hand: one can be told that a connection holds without thereby grasping it oneself (Grimm 2019, §II); Hills argues that understanding why involves abilities that testimony alone does not normally pass on (Hills 2020, 5, 12–13). Others argue that testimony can bring understanding when the recipient already has the background needed to take it up; Section 8 sets out these positions, together with a distinction of Hills's between ways of learning from others, and what they imply for a research system that relies on artificial outputs. De Regt treats scientific understanding as a community achievement and holds that a recipient acquires understanding from another's explanation by following and reproducing its line of reasoning, in more or less detail and with a correspondingly varying level of understanding, and concludes that the intelligibility underlying the explainer's understanding appears to be a requirement for the recipient's as well (de Regt 2017, 91, 99–100). Kuorikoski and Ylikoski, who regard scientific understanding as essentially collective, argue that external representations such as formal models can improve it partly by making assumptions explicit and so easier to evaluate (Kuorikoski and Ylikoski 2015, §§2–3). What matters, then, is whether recipients actually come to have the grasp that understanding requires, not whether a document shaped like an explanation was produced. Boge, Schuster, and Stoll, whose distinction Section 6 discussed, make explanation central here: on their account, the explanation is the medium of scientific understanding, and it can be inspected in a canonical, communicable way (Boge, Schuster, and Stoll 2026, 5–6, 11).

Criticism and memory depend on this availability. A representation that others can follow can be checked by someone other than its producer, and a record that others can follow can be returned to after those who produced it have moved on. Of the reasons given in this subsection why making understanding available to others supports criticism and memory, two rest on features of human research: that those who produce a result move on, and, on de Regt's account, that a recipient understands by following and reproducing the reasoning. Where S is human, the need for a representation its human members can follow remains whatever produced the result. Where the producing system persists and the recipients are artificial members of S, checking that does not share the producer's ways of going wrong is still needed, as a matter of independence (Chapter 11, Section 2), while what availability requires changes form (Section 5.4). Hills adds a limit, argued for moral judgement: someone who takes an expert's word is responsive to the reasons for taking that word rather than to the reasons that make the judgement right, and taking the word does not give them the ability to draw different conclusions when the situation differs (Hills 2020, 12–13). If Hills's account is adopted, a community that acts on an artificial system's outputs without that ability would be guided by the system rather than by the dependencies the system tracks.

Sections 7.2–7.4 thereby bring into view an answer to the question raised at the start of this section, what would be lost beyond any single validated result if no one understood: the competence to state a basis for transfer open to criticism, to intervene, and to diagnose failures; the retention and reuse of results and the opening of further questions; and the availability of results to others for criticism and memory, unless these are supplied by other means. These are candidate relations, not a definition of understanding, and this section does not show that every research act realizes them. Some can be supplied by modular verification, redundant measurements, robust search, specialized agents, or institutional organization. A simple explanation may itself fail under shift. In evaluating a research system, the question they raise is which capacity a given purpose requires and whether the system has it; relabeling every desirable capacity as understanding would not answer that question. Nor would supplying these capacities by other means settle whether understanding is valuable for its own sake or an aim of inquiry (Section 7.1).

This yields the following conclusion: on the working characterization, which epistemic achievement research aims at is left open, yet particular inquiries and sustained research systems may require capacities associated with understanding.

If the working characterization is adopted, which epistemic achievement research aims at, knowledge or understanding, is not fixed by the characterization but left open to particular attempts, and attaining it is not made a condition of each research act. Whether understanding is required depends on the achievement an attempt seeks. Positions that value understanding for its own sake or take it as an aim of inquiry can therefore be accommodated by taking understanding as the achievement aimed at, and on them what is required is set by that value or aim. Particular inquiries and durable autonomous research systems may nevertheless require capacities that important theories associate with understanding, even where understanding is not what they aim at, and what those capacities have to serve differs with whether S is human or artificial (Section 7.4).

This conclusion may also give a reason to look again at the working characterization itself. The capacities said to be needed may turn out to be obtainable without understanding, or the characterization may not fully capture the place understanding has in research (Introduction, Section 4).

Whether those capacities jointly constitute understanding remains a philosophical question. Whether a system actually possesses them is an empirical and engineering question. The two questions are distinct, but each informs the other.

8. Why a local achievement does not settle continuing inquiry capacity

The preceding sections asked about understanding mostly with a single result or a single inquiry as the unit, which this section calls local: whether a result can be warranted without understanding, and whether understanding is needed to close a given inquiry. This section changes what is assessed and over what span. What is assessed is no longer one result but the system or community that repeatedly produces and uses such results, and the span is no longer one inquiry but inquiry as it continues over time. The change matters because verdicts at the two levels can come apart in either direction. A particular opaque result can be warranted while the system that repeatedly produces and uses such results gradually loses important epistemic capacities. Conversely, an opaque component can belong to a robust system whose other agents, instruments, records, and institutions supply reliable checks and repair, so that the component's opacity does not become a problem for the system.

Messeri and Crockett describe one form of the risk that a system loses epistemic capacities as illusions of understanding, in which scientists believe they understand more about the world than they actually do. On their account, because AI tools are expected to make research more productive and more objective, scientists are apt to trust them as collaborators, much as researchers rely on one another's expertise, and someone who relies on understanding located elsewhere can mistake it for their own. Moreover, the simple, quantitative answers such tools give tend to produce a sense of understanding that need not match actual understanding. The tools' efficiency can also foster monocultures in which questions and methods suited to AI, and the standpoints AI can represent, crowd out other ways of proceeding, which would leave science more vulnerable to error (Messeri and Crockett 2024, 49–53). Their analysis is a risk framework rather than evidence that every AI-supported field already exhibits these effects. It nevertheless supplies a direct reason to evaluate continuing epistemic capacity separately from local output volume. Neither risk shows up in the quality of any single result: the first lies in what those who rely on such tools take themselves to understand, and the second emerges as reliance extends across a field and over time, so together they concern both what is assessed and over what span. An observational study of papers in six natural sciences reports a pattern consistent with the risk of monoculture, without establishing it as an effect of the use of AI methods, and Chapter 11, Section 8 discusses it (Hao et al. 2026); it does not bear on the risk of overestimating understanding. Messeri and Crockett write about human scientists. Of the two risks, monoculture concerns how inquiry is organized and can arise for any S whose members come to share questions, methods, and ways of going wrong; the illusion of understanding, as they describe it, turns on features of human cognition, trust in tools modelled on reliance on colleagues and a sense of understanding that need not match understanding, so that whether an artificial member of S is open to a counterpart of it depends on whether anything in it plays the role of that sense (compare Section 6).

The change in what is assessed can be seen in an ordinary feature of contemporary research. Contemporary research projects can depend on divisions of cognitive labor in which participants rely on instruments, software, procedures, or specialist claims they do not each understand in full. As Chapter 2, Section 6 discussed, even where cognition is described as distributed across such a project, as on Giere's account, which Brown reconstructs, that does not by itself settle whether the organized system also knows (M. J. Brown 2015), and collective production does not by itself settle who possesses the resulting knowledge. Such divisions of labor rule out a demand that every participant understand everything in full. They do not show that any additional opacity is harmless. What they leave open is how dependence is organized, a question asked of the organization of the project as a whole rather than of any single result: where reliability is established, how correlated failures are detected, who can answer challenges, and how reliance changes when conditions fail.

Evaluation therefore divides into two levels: the level of a single contribution, which the preceding sections mostly addressed, and the level of a continuing system, which this section addresses. At the contribution level, we ask what question was addressed and whether the resulting claim or other achievement is true or adequate, warranted, or explanatory, or amounts to understanding, in the claimed sense. At the continuing-system level, we ask whether its organization of research preserves the capacities for diverse search, independent criticism, memory, dependency tracking, correction, further question formation, and the reproduction of the competence with which members of S do and evaluate research, among others. A collection of locally warranted outputs does not by itself answer the question at the level of the continuing system. The two evaluations can come apart in either direction, so neither can be inferred from the other: a result can be warranted while the organization of research loses capacities, and capacities can be preserved while a particular result fails. For example, a laboratory that comes to rely on a predictor whose outputs it checks case by case may accumulate warranted results while losing the ability to diagnose anomalies without the predictor (the loss to which Humphreys's further worry in Section 4 points), and if neighboring groups rely on the same model, a failure common to all of them could escape the checks that each group applies to its own results. The first loss appears only when the laboratory is followed over time, the second only when the assessment extends beyond one group.

The last capacity in the list for the continuing system, that for reproducing the competence with which members of S do and evaluate research, can be lost in a way that appears only across cohorts of researchers. Castellacci and coauthors, in a preprint that grew out of a roundtable on generative AI in research, call this capacity depletion: it arises where the tasks AI absorbs are the same tasks through which research capability is acquired, so that AI may, on their account, democratize access to the artifacts of research without democratizing the capability to produce them. They present it as a risk of present adoption, distinct from the information asymmetry that undisclosed AI use creates for evaluators and from negative externalities on a shared knowledge base, and they read the studies of learning they cite as pointing to the mode of engagement with a tool, rather than its use as such, as what matters (Castellacci et al. 2026, §§1, 2.4). Bender, Bergstrom, and West, in a response in the joint article by Binz and colleagues discussed in Section 7.1, make a related point: science produces the scientists themselves as well as the results published in papers (Binz et al. 2025, 8). Both write about human researchers; where S is mixed or artificial, the corresponding question is whether the members on whose judgments S's evaluation depends continue to be formed with the competence to make them. A count of warranted results registers this loss no better than the two above. Several later arguments presuppose the competence: direct calibration of a source requires independent opinions on some of its claims (Chapter 8, Section 3.4), if artificial configurations that carry out research come to gather and assess more evidence than any member of S across many fields, S as a whole can come to stand to them as a layperson, unable to check their judgments and able only to rely on them (Chapter 11, Section 6), and contestation requires parties with the competence to contest (Chapter 12, Section 7).

Whether members of such a division of labor gain understanding from others' outputs bears on the continuing-system level, and here accounts of testimony and understanding disagree. Hills's account of understanding bears on the division of cognitive labor described above. Hills distinguishes two ways of learning from what others say. In transmission, the hearer takes the speaker's word as the reason for belief; this permits a massive division of epistemic labor, but what results is second-hand knowledge rather than understanding, since understanding why requires cognitive control, the ability to draw conclusions and give explanations about new cases, which, like most abilities, comes from practice. In propagation, what is said prompts and frames the hearer's own inquiry; this is a division of labor of a different kind, and through it understanding can be passed on. The argument concerns moral understanding, but Hills presents the distinction as general (Hills 2020, 2–5, 8, 10–13, 18). If this account is adopted, and if reliance on artificial outputs is testimony, which differs across accounts (Chapter 8, Section 3.4; Chapter 11, Section 5.1), and takes the form of transmission, members of a research system who rely on those outputs could come to know more without coming to understand more, and a count of warranted results would not register the difference.

Hills does not treat this as a reason to pursue understanding on every occasion. On her account of moral testimony, the reasons to favor propagation over transmission hold whenever propagation is available, that is, when the learner has the time and ability to develop her own understanding; and even a morally ideal agent will take others' word on other matters, such as experiences she has not shared, that can supply vital non-moral information (Hills 2020, 14).

Others dispute the asymmetry on which Hills's conclusion rests, that knowledge can be passed on by testimony while understanding cannot easily be. Boyd argues that understanding can be acquired directly from testimony when what is said is easy for the recipient to understand, including when it is easy only for an expert, because the recipient can fit the new information into relations already grasped (Boyd 2017, 23–34). Grimm argues that, as with propositional knowledge, passing on understanding by testimony is usually easy when the recipient has been suitably prepared and usually difficult, perhaps impossible, when not, although the work the recipient does differs in kind, since for understanding it is grasping connections (Grimm 2019, §§IV–VI). Hu argues, as Grimm reports in his encyclopedia entry on understanding, that knowing that one thing caused another already brings a rudimentary understanding of why, so that in whatever sense knowledge can be passed on by testimony, such understanding can be too (Grimm 2021, §3.2). Malfatti sorts the arguments for the claim that testimony cannot transmit understanding into three, and argues that each can be resisted. First, gaining knowledge from testimony can also require exercising one's own understanding of the subject to interpret what is said, so a difference in the effort required cannot separate the two. Second, transmission does not always require fully deferring to the speaker. Third, the abilities that grasping is said to involve can sometimes be acquired by being told (Malfatti 2020, 56–70).

Brought to bear on a count of warranted results, these positions agree that it does not by itself show what understanding members have gained, but they locate what it misses differently. If Hills's account is adopted, it misses whether members take artificial outputs as grounds for belief or as prompts for inquiry they then carry out themselves. If Boyd's or Grimm's account is adopted, it misses whether members keep the background through which testimony can bring understanding at all, a background that, in expert cases, Boyd describes as the product of the recipients' own earlier work (Boyd 2017, 38–39). If Hu's account is adopted, it misses the degree of the understanding gained rather than its presence (Hu 2021, 5–7). What members gain or fail to gain in this way also bears on the level of the continuing system, since it affects what the system can still do later: whether members can diagnose failures without the outputs, for example, and whether they keep the background through which later testimony can bring understanding. These positions concern learning from what others say or produce. Where a representation or ability can instead be copied or shared directly among artificial members, whether the recipient thereby understands turns on further features of the account adopted: on ability accounts (Section 3.3), what matters may be whether the recipient now has the relevant abilities, whereas on accounts on which understanding typically involves an achievement creditable to the understander's own cognitive ability, such as Pritchard's (Section 7.1), whether a copied state is the recipient's own achievement is a further question.

Evaluation at the continuing-system level is not another condition silently added to every research act. Some projects will be valuable despite contributing little to system-level capacity, and some institutions will remain fragile while producing many valuable local results. Part V takes up the problems that arise at this level when the relations surrounding inquiry, now carried in part by parties outside the research, can come to be carried by the artificial configurations that carry out the research: allocation, independent criticism and trust, and authority. The present chapter needs only the narrower conclusion: understanding can matter to the health of an inquiry over time even when it is not required for the warrant of each local result.

9. What accounts of understanding require of artificial research

This section applies the chapter's distinctions to situations in which artificial systems conduct research. The consequences are not uniform. They change with four things: which achievement is claimed (predictive performance, knowledge, understanding, and so on), in whom it is claimed to be realized (the system itself, its users, an organized whole, an artificial community), which account of that achievement is adopted, and what it is to be used for. Using constructed cases, the section takes up in turn a predictive case set against a formally checked proof, requests for transparency and the functions they serve, the evidence that bears on a claim that a system understands, what long-run autonomous research is assessed for, and the distinction between the reference society S and the bearer of an achievement. The aim is to apply the accounts introduced in Sections 3 to 6 and show how the consequences differ with the claim, the account, and the use.

First, two cases in each of which an achievement is clearly attained can be contrasted. One is the strong predictive case of Section 4. A system reliably predicts a property within a stated range, but its human users cannot explain the mechanism that produces the property. Its reliability is established by evidence not merely inferred from agreement among its own outputs. In this case the system can be credited with scoped predictive performance, and on accounts that permit knowledge without explanatory understanding the users can also acquire knowledge (Section 4). Neither, however, shows that anyone understands why the property holds.

Who, if anyone, understands why the property holds receives different verdicts on different accounts. On explanation-based accounts, the users do not. On Khalifa's reductive account, if someone later comes to know the explanation, that knowledge is the understanding; an attempt at understanding then becomes an attempt to acquire knowledge of the explanation, and who holds that knowledge, and whether it has entered the epistemic situation of S, are the questions Chapter 2 asked about knowledge (Section 3). On de Regt's criterion, the regularity remains scientifically ununderstood unless there is an explanation based on an intelligible theory, and by the argument of de Regt and Dieks about an oracle that produces perfect predictions, this predictive success does not count as a great scientific success either. If the predictor is a theory in de Regt's sense, however, its successful use presupposes that its users understand that theory; even then, understanding why the regularity holds still requires, on this account, an explanation based on the theory (Section 4). On Woodward's account, the predictor explains to the extent that it also supports correct answers about what would happen under interventions and that this information is accessible to its users (Section 4).

By contrast, on Dellsén's earlier formulation, grasping how to predict correctly across varied circumstances counts as partial understanding even without an explanation, and on Beisbart's account a scientist who, by running the predictor repeatedly, has learned to anticipate how its outputs change with its inputs has some objectual understanding. If the scientist has to run the predictor itself to draw those inferences, however, Beisbart's account assigns the understanding to the coupled system of human and computer, not to the unaided human (Section 4). On Gijsbers's view of the understanding that classification gives, the question becomes, further, whether the features that support the predictor's classifications are available in a graspable form (Section 3.2). Where an artificial system conducts the research and S is a human society, as here, whether the system enabled human understanding thus depends on the account. On explanation-based accounts it did not. On Dellsén's earlier formulation and Beisbart's account, it did to the extent that the users themselves can anticipate the predictor's behavior across varied circumstances.

Contrast a generated proof accepted by a sound formal checker, a program that verifies mechanically that each step of a proof follows the rules. Here the route by which the proof was generated may remain opaque, because what the check establishes, that the formally stated claim has been proved, does not weaken when that route is hidden. Two things are not thereby settled. One is whether the formal statement correctly expresses the question originally asked. The other is whether those who hold the proof grasp its explanatory dependencies, that is, why the theorem holds (Sections 3 and 5.1; Chapter 6, Section 3).

The Liquid Tensor Experiment shows what the first point involves in practice. Scholze found the formal definitions and theorem statements surprisingly readable but could not read the proofs at all, and the formalizers added formally proved results about the objects involved as evidence that the checked statement concerned the intended objects (Section 5.1). Judging the first point thus requires being able to read the statement and the results that support reading it as intended, not the proof. Where an artificial system generates the proof and S is a human society, this judgment can remain with humans even when the proof is unreadable to them, provided the statement is readable to them (Section 5.1).

On the second point, understanding, the verdicts differ by account. Hills's account requires, for understanding why the theorem holds, the abilities to follow the explanation, to put it in one's own words, and to draw conclusions in relevantly similar cases, so human users who merely hold a proof no human can survey may know the theorem but do not understand in this sense. Scholze's report shows, on the other hand, that people who take part in a formalization can come to understand why a proof's route works, although in Scholze's case without a feel for the surrounding terrain (Section 4). For whether the generating system itself understands the proof, Wilkenfeld's account supplies a concrete test. Unlike a merely memorized proof, an understood proof can be adapted to a slightly different system, so the evidence on this account is whether the system can itself adapt the proof, without anyone rewriting its internal states from outside (Sections 3.3 and 6).

Each case thus contains an achievement to credit, scoped predictive performance in the first and the proof of a formal statement in the second. The cases differ in whose abilities are tested for understanding beyond that, and how. In the predictive case, the question is whether the users themselves can anticipate the predictor's behavior or must keep running it to do so. In the proof case, the questions are whether human users can follow the proof's explanation and whether the system can itself adapt the proof.

Second, a request for transparency alone does not say what is being asked for. A request for transparency becomes informative when it states what the transparency is for, and different functions are served by different things. A process trace, recording which steps were carried out, supports reproduction and debugging. An evidential record supports assessment of how far a result is warranted. A model of the target may support explanation. A statement of scope and uncertainty supports judging how far to rely on a result. A presentation suited to its audience supports communication. A single generated rationale therefore cannot stand in for all of them.

Even for the function of explanation, what serves differs with the account. On Sullivan's account, for a model that, like the deep networks Sullivan discusses, is not opaque at the highest level, what chiefly limits the understanding it can give is not the opacity inside it but link uncertainty, the lack of evidence connecting the model to the phenomenon. What serves understanding of the phenomenon is then less an internal record than evidence from outside the model supporting that link, and the greater the harm of error, the higher the standard both for that evidence and for checking that dependencies extracted from the model are faithful to how it works (Section 5.2). On Beisbart's account, what is missing is an informative description of what the network does in terms of the variables and processes of the target system, and however detailed a record of the computation's execution, it does not by itself supply this (Section 5.2). On Fleisher's account, a post hoc explanatory model that computes a different function from the classifier can still contribute to the understanding of why the classifier reached its verdict, for its developers, its operators, and those affected, if its departures bear the marks of idealization and it agrees well with the original model near the input explained (Section 5.4).

Where the model is a deep-learning model, rendering its internal reasoning in human concepts may face a further limit. As Section 5.4 discussed, Otsuka compares interpreting the internal representations of a deep-learning model with radical translation, translating an unknown language from its speakers' behavior alone. If that comparison is right, a rendering in human concepts may be only one of several interpretations that fit equally well, and however fully such a rendering is recorded, the record could not settle whether it is the correct translation, since there may be no single correct one. How much this limit matters depends on who is to understand what. For a human S, understanding has to be brought about in a form its human members can use; but, as Section 5.4 noted, where understanding of the phenomenon is sought, the route through a model of the phenomenon need not wait for the rendering of the internal reasoning to be settled. Where the recipient is an artificial system able to work with the model's representations directly, rendering them in human concepts may not be needed at all.

What a record needs to contain also changes where models are idealized or purpose-relative (Section 3.4). For such models, accuracy as a representation and adequacy for a particular prediction, explanation, intervention, or pedagogical use come apart, so a record that is to support assessment for a particular use needs to distinguish the two. What it has to distinguish also becomes specific on particular accounts (Section 3.4). On Potochnik's account, each posit's departure from the truth must be negligible given its role in the representation and the aims of the research, so the record needs to say what was idealized and for which aim. On Strevens's account, an explanation that contains idealizations is correct when its claims about what makes a difference and what does not are true, so the record needs to state which factors were left out as making no difference. Applying Weisberg's taxonomy, a system with far greater computational capacity than its human counterparts has reason to undo Galilean idealizations, introduced for tractability, but no such reason to undo minimalist or multiple-models idealizations. Greater computational capacity is therefore not a reason to undo every idealization. Undoing a minimalist idealization would obscure the explanation obtained by keeping only the factors that make a difference, and merging multiple-models idealizations into one model would obscure the trade-offs among desiderata such as generality, accuracy, and simplicity. Extending the positions of Section 3.4 this far, if the record is also to show what the evidence still leaves open, competing models that remain compatible with the evidence would remain in it even after one has been selected for the current task.

Third, what evidence bears on a claim that a system understands can be specified only once the claim identifies who understands, its bearer, and which account of understanding it adopts. The following, for example, are different hypotheses, to be checked in different ways: the AI enabled human understanding, the AI enabled another artificial system to understand, the AI understands, the organized human–AI system understands, and the artificial community understands. The bearer named in such a claim need not be the society for which the understanding is available or new (see the final item). Performance on transfer, intervention, counterfactual, scope-recognition, or anomaly-diagnosis tasks can provide evidence. But, as Section 3.3 noted, performance can also be reached through shortcuts such as memorization or retrieval, so it is evidence of the claimed abilities only to the extent that the evaluation discriminates them from the shortcuts that matter on the account the claim relies on.

Which performance counts as evidence, and which shortcuts matter, can be worked out account by account (Sections 3.3 and 6). Here the case considered is the one in which the system itself is named as the bearer; the verdicts on a claim that the system enabled human understanding were given for the predictive case, and those on a claim that an organized whole understands are given under long-run autonomous research below. On Hills's account, the tests are whether the system can follow explanations others give, give explanations itself, and draw conclusions and give explanations in relevantly similar cases. On Wilkenfeld's account, the test is whether the system can itself modify its representations so as to enable new valid inferences, without its internal states being rewritten from outside; lucky performance and the application of a memorized procedure are excluded from understanding on that account from the start. Barman and colleagues propose testing the degree of understanding by how widely and correctly the subject answers what-, why-, and what-if questions. On Moody and de Regt's account, the question is whether the system can recognize qualitatively characteristic consequences of a theory without exact calculation, and they credit current language models with a fragile but nontrivial degree of understanding on the indirect evidence of accurate answers to a wide range of out-of-distribution scientific questions. On these accounts, performance can support a claim of understanding if the evaluation discriminates the shortcuts. On Potochnik's account, by contrast, understanding requires the sense of understanding that a representation induces, so however good the performance, the question whether that sense is present remains. Accounts on which acceptance rather than belief suffices for understanding also differ in what they ask. On Dellsén's account, understanding requires acceptance and enough mastery of the subject to explain it correctly, but not belief; if belief is a disposition to feel that p is true, understanding is then closer than knowledge for a system to which feeling cannot be attributed, though whether using p as a premise in explanation amounts to adopting a policy in Dellsén's sense remains a question. On the functional and dispositional accounts of belief, by contrast, acceptance put to work in explanation may itself count as evidence of belief, so that this route is not separate from belief. On Elgin's account, the acceptance that understanding requires is voluntary and undertaken for epistemic ends, so the question becomes whether the system has epistemic ends and accepts in that sense (Section 6).

Fourth, what long-run autonomous research is assessed for depends on how research is characterized. On characterizations that place understanding at the center of research, all such research is assessed for understanding, and the account adopted determines what that involves, including whose understanding counts: the system's, that of its recipients, or that of a collective (Section 6). Suppose, for example, that research is characterized by an account that places understanding at the center of science and its progress (Sections 4 and 7.1). On Dellsén's noetic account, progress lies in publicly available information that enables the relevant members of a society to increase their understanding (Sections 4 and 6). Assessed this way, a system's acquiring a good model of dependencies is not enough by itself; the question is whether the information has become available to the members of S, and, if S is a human society, available in a form its human members can use. Assessed by de Regt's account, the question is whether the research has given explanations based on intelligible theories, and research that only produces perfect predictions does not count as a great scientific success (Section 4). On the working characterization, by contrast, which epistemic achievement research aims at is left open (Section 7). Long-run autonomous research is then assessed by the achievement its attempts aim at, and Dellsén's and de Regt's criteria apply as criteria of success only to attempts that aim at understanding.

Separately, such research can be assessed for the capacities that its autonomy itself requires. The more of an inquiry is left to the system, the more capacities the system itself has to supply (Chapter 7, Section 4.4). Can it recognize when a regularity no longer transfers? Can it distinguish a failure of the focal claim from a failure of an instrument or auxiliary assumption (Chapter 6, Sections 2 and 4.2)? Can it generate and compare alternative representations (Chapter 5, Section 3)? Can it expose its evidence to criticism and propagate corrections (Chapter 11, Sections 2 and 8)? Can it revise the standards by which it assesses results without becoming insulated from the world (Chapter 6, Section 5; Chapter 7, Section 4.3)? Some accounts tie some of these capacities to understanding itself. Recognizing that a regularity no longer transfers is, on Woodward's account, recognizing that a new context falls outside the domain of invariance of a dependency, or that only its qualitative relationship carries over (Section 7.2); generating alternative representations is close to the modification of representations that, on Wilkenfeld's account, manifests understanding (Section 3.3). Such accounts may therefore interpret an integrated realization of these capacities as understanding. Whether the capacities are concentrated in one system or distributed across agents and institutions is, however, a separate question from whether their realization constitutes understanding. Depending on the account, either arrangement may supply them without constituting understanding (Section 7.4). For a distributed arrangement, the consequences differ by account. Extending Beisbart's account, seen in the predictive case, where a human draws inferences by running the system, the understanding belongs to the coupled whole of human and system, not to the unaided human (Section 4). On accounts that ground group understanding in members' understanding, the arrangement has yielded understanding only when some member, human or artificial, understands. On an account that extends Bird's group-functional account of knowledge to understanding, the organized whole can be the bearer even if no member holds the whole (Section 6).

Finally, the reference society S, relative to which an achievement is new, is distinct from the achievement's bearer, the subject in whom it is realized; the two coincide in a claim that S itself understands. Because they are distinct, a member's new understanding, collective understanding, and a newly available explanation are different claims, and which of them amounts to entry into the epistemic situation of S differs by account (Section 6). On accounts that ground group understanding in members' understanding, it is the relevant members' understanding; on an account that extends Bird's to understanding, it is the society's organization realizing the understanding as a whole. On the account of Boge, Schuster, and Stoll and on Dellsén's noetic account, what is asked is whether a communicable explanation or public information has become available; whether such availability already amounts to entry into the epistemic situation or only puts the society in a position to understand remains open, as it does for knowledge (Chapter 2, Section 7). Where an artificial system conducts the research and S is a human society, an artificial system's understanding, if it understands, could be new to that society without the society itself understanding. Whether this describes the intended research depends on the claim and the activity, not on choosing S to suit. Describing such work as research for that society also presupposes that the society's epistemic situation could come to include understanding of the kind sought, for instance through an explanation its members can follow (Chapter 1, Section 2). For a human S, this presupposition comes into question where the organization of dependencies that an artificial system grasps cannot be made intelligible to humans (Section 6); for a mixed or artificial S, it may be met through artificial members to whom that organization can be communicated. Applying the distinction of Boge, Schuster, and Stoll to the human case, an artificial system's understanding would correspond to what they call scientists' understanding and would not yet be scientific understanding, which on their account requires an explanation communicable to a sufficiently broad scientific audience. In terms of their example, the system would stand where Feynman stood before Dyson's proofs gave other physicists an explanation they could follow (Section 6). Boge and de Regt's proposal to bridge the divide by testing whether an AI can communicate its understanding to human experts addresses this case.

Because what is required changes with use, these contrasts do not form a single ladder on which the most human-like system counts as the most advanced. Human-facing explanation, for example, or, on accounts that allow understanding without explanation, another vehicle of understanding usable by humans (Section 3.2), is essential where S is human and the understanding is meant to enter the epistemic situation of S, but may be unnecessary where the understanding serves only the system's own inferences or is communicated to artificial members of S (Section 6). And on accounts that do not require a felt sense of grasp or other forms of experience (compare Section 6 and Chapter 8, Section 1.3), such as that of Barman and colleagues, who treat understanding as an ability that can be realized by mechanisms unlike human ones, or Wilkenfeld's, which does not require representations to be symbolic, artificial representations could support genuine nonhuman understanding without resembling human introspection. How far that possibility is supported on such accounts depends on how far the alternative realization can be shown to bear the relation to its object that the adopted account requires, which for worldly targets includes its states being about them at all (Chapter 8, Section 2.2). Whether it would also remain corrigible through further contact with the world is a separate question, about the continuing capacities of Section 8 and the world-answerability examined in Chapter 8, Section 2.3. On Potochnik's account, by contrast, understanding requires a sense of understanding, and what promotes understanding depends on features of human cognition, so on this account the possibility turns first on whether such a sense is possible for an artificial system (Section 6).

Returning to the chapter's question, when understanding is achieved and by whom, the answer is fixed by which achievement is claimed, whom it names as bearer, and which account is adopted. Where artificial systems conduct research, the question "by whom" becomes a question in its own right: unlike in human research, what produced a result cannot be presumed to be what understands it (Section 6). On the working characterization, which epistemic achievement research aims at is left open. For an attempt that aims at understanding, whether understanding is reached bears on whether the attempt succeeds; for one that does not, continuing research may still require capacities associated with understanding (Sections 7–8). Many of the capacities discussed here, transfer, diagnosis, further questions, criticism, and memory, depend not on the properties of a single result but on how inquiry is organized (Section 8). The next part, Chapters 4 to 6, therefore moves from achievement to the organization of inquiry, asking from three sides of the same inquiry what it means for a machine to ask, how candidates and representations become available, and what results bear on and what they revise. Chapter 7 then asks where in that organization conduct and capacity can be attributed.