Abstract
The literature on the nature of understanding can be divided into two broad camps. Explanationists believe that it is knowledge of explanations that is key to understanding. In contrast, their manipulationist rivals maintain that understanding essentially involves an ability to manipulate certain representations. The aim of this paper is to provide a novel knowledge based account of understanding. More specifically, it proposes an account of maximal understanding of a given phenomenon in terms of fully comprehensive and maximally well-connected knowledge of it and of degrees of understanding in terms of approximations to such knowledge. It is completed by a contextualist semantics for outright attributions of understanding according to which an attribution of understanding is true of one just in case one knows enough about it to perform some contextually determined task. It is argued that this account has an edge over both its explanationist and manipulationist competitors.
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Notes
Lipton (2009, p. 47). I take it that Lipton’s theses (i) that explanations must offer direct answers to the relevant why questions and (ii) that explanations by showing necessity require constructive arguments constitute constraints that any satisfactory account of explanation (by showing necessity) will have to satisfy. As a result, his argument will go through on any viable account of explanation.
(Lipton 2009, pp. 47–48). Note, first, that Lipton argues that the situation is analogous in the case of mathematical proofs which also allows for a distinction between explanatory and non-explanatory proofs. Here, too, Lipton is attracted by the idea that proofs by reductio are not explanatory. Second, those who are not convinced by this particular case may recall that Lipton offers three other cases of understanding without explanation. To those who remain unmoved by all of them, I’d say that the onus is on them to show why. Finally, third, for the purposes of this paper, I can in principle allow that understanding requires knowledge of explanations. What does matter is that non-explanatory knowledge can improve one’s understanding of a given phenomenon (why will become clear in Sect. 5.).
I take it that there is little mileage in the idea that Galileo’s understanding of the independence of gravitational acceleration and mass is not scientific, if only because Lipton’s example is taken from the history of science.
(Wilkenfeld 2013, p. 1003). It has been argued that the very notion of mental representation is problematic (e.g. van Fraassen 2008). Of course, it will be bad news for Wilkenfeld if there is a problem already with the central notion of his account. However, for present purposes, I will not take a stance on this issue and so will not pursue this line against Wilkenfeld.
If this isn’t immediately obvious, suppose \(T\) is also a biology professor and goes on to include her new theory in her lecture on the Indian elephant, if only as an alternative to the standard theory. If her story did advance her own understanding of the evolution of the Indian elephant, we may suppose that it will position students to advance their understanding of this phenomenon as well. Since it is plausible that a central aim of biology lectures is to position students to advance their understanding of various biological phenomena (cf. Sect. 1), her including her theory in the lecture contributes towards attaining a central aim of the lecture. As a result, we should have no qualms about her including her new theory in the lecture. However, this is not the case. On the contrary, we would find it entirely unacceptable for her to include her new theory in her lecture. Why? The plausible answer is that her theory does not contribute towards attaining any of the aims of a biology lecture because it simply does not position anyone to improve their understanding of the evolution of the Indian elephant.
When I use the term ‘outright’ in ‘outright attribution of understanding’ and similar constructions, I mean ‘not involving degrees’. For instance, assertions of statements of the form ‘\(S\) understands \(P\)’ are outright attributions of understanding. In contrast, assertions of statements of the form ‘\(S\) understands \(P\) to degree \(d\)’, ‘\(S_1\) understands \(P\) better than \(S_2\)’ are not.
Compare also Kripke’s dogmatism paradox:
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(1)
\(\Phi \)
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(2)
If \(\Phi \), then any future evidence against \(\Phi \) is misleading.
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(3)
Hence, any future evidence against \(\Phi \) is misleading.
It is now widely acknowledged among epistemologists that even if one knows \(\Phi \), one need not therefore also believe that any future evidence against \(\Phi \) is misleading. After all, acquisition of new evidence concerning \(\Phi \) changes one’s epistemic position towards \(\Phi \), which might undermine one’s knowledge of \(\Phi \), even if this evidence is in fact misleading. The same is true of explanations. Even if one now knows that \(e\) explains \(P\), this does not require one to believe that any alternative explanation of \(P\) that future scientific research may produce is incorrect.
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(1)
Note that the same goes for knowledge. It is widely agreed that knowledge is a relation between an agent and a proposition. As a result, there is no reason to think that a uniform account of knowledge about metaphysically diverse phenomena will be problematic.
It is common practice in the epistemology literature to distinguish between two types of understanding, to wit, propositional understanding, which takes individual propositions as its objects and objectual understanding the objects of which are “bodies of information” (Kvanvig 2003, p. 191). Given the above characterisation of phenomena, it is easy to see that the proposed account of understanding phenomena qualifies as an account of objectual understanding.
Note that the point about different languages does not play any substantive role in this argument. It is simply meant to make perspicuous the possibility of having unconnected knowledge.
Since the account is stated in terms of knowledge, it presupposes that understanding is a form of knowledge (U = K). It may be worth noting that, for the purposes of this paper at least, this presupposition is inessential. To see this, notice, first, that the central aim of this paper is to argue that my account is preferable to its two most prominent competitors in the philosophy of science literature (explanationism and manipulationism) as it can steer clear of the problems they encounter. Notice, next, that this aim can be achieved even on variants of my account that do not presuppose U=K. Consider, for instance, the following two variants of Max-U:
Max-U \(^{\prime }\)
If one has fully comprehensive and maximally well-connected justified beliefs about a phenomenon \(P\), then one has maximal understanding of \(P\). (The variants of Deg-U and Out-U (see below) are as expected.)
Max-U \(^{\prime \prime }\)
If one has fully comprehensive and maximally well-connected justified true beliefs about a phenomenon \(P\), then one has maximal understanding of \(P\). (The variants of Deg-U and Out-U (see below) are as expected.)
Neither Max-U \(^{\prime }\) nor Max-U \(^{\prime \prime }\) presupposes U = K. Max-U \(^{\prime }\) construes understanding as a form of justified belief (U = JB), Max-U \(^{\prime \prime }\) as a form of justified true belief (U = JTB). At the same time, it is easy to see that both variants enjoy the benefits of my account vis-à-vis explanationism and manipulationism. The paper’s central aim can thus be achieved just as well if my knowledge based account is abandoned in favour of either variant. For that reason the presupposition of U = K is inessential for the purposes of this paper. Finally, note that most epistemologists who reject U = K accept either some version of U = JB or of U = JTB. As a result, there is reason to believe that my presupposition of U = K is not epistemologically problematic.
Note if \(O\)’s knowledge is not maximally well-connected it is not clear that \(O\) will also be maximally understanding. If \(O\)’s beliefs are minimally well-connected in the way \(A\)’s beliefs were in the above case, it would seem that \(O\), too, understands little to nothing at all. That said, it is actually not clear that \(O\) could be both omniscient and yet fail to have maximally well-connected knowledge. To see this, consider a proposition \(p\) such that, let’s suppose, \(O\) knows that \(p\) based on testimony from \(T\). Since \(O\) is omniscient, \(O\) would also know that he knows that \(p\) based on testimony from \(T\). Now suppose that \(T\) knows that \(p\) because \(T\) saw that \(p\). Since \(O\) is omniscient, \(O\) would also have to know that \(T\) saw that \(p\). However, it is not clear that \(O\) could know that \(p\) based only on testimony from \(T\), when he also knows that \(T\) saw that \(p\). After all, \(O\)’s state would then be irrational in a way that is not evidently compatible with his omniscience.
It is tempting to think that degrees of understanding depend on degrees of breadth and depth of understanding and that approximations to fully comprehensive knowledge measure breadth of understanding and approximations to maximally well-connected knowledge measure depth of understanding. That said, I will not pursue the project of offering a precise account of degrees of understanding in any more detail here. Fortunately, I don’t have to, at least not for the purposes of this paper. Recall that the main aim here is to offer an account that compares favourably with its rivals on both the manipulationist and the explanationist side. Now notice first that, while everyone agrees that understanding comes in degrees and allows for evaluation in terms of depth and breadth, no one has offered anything that comes even close to a detailed account of degrees of understanding. For that reason, my account is not at a disadvantage vis-à-vis its explanationist and manipulationist rivals on this front. Second, as will become clear in due course, my account can avoid the problems that beset its rivals without recourse to a precise account of degrees of understanding. In consequence, I can arguably claim an advantage over both manipulationism and explanationism for my account.
I don’t mean to suggest that there might not be a minimal threshold for understanding. Again, even if there is one, for the purposes of this paper, it won’t be necessary to specify it.
It might be thought that the subjunctive conditional here is problematic. After all, as Shope (1978) has argued at length, biconditionals featuring a subjunctive are prone to what he calls “the conditional fallacy”. In the simplest case, the biconditional is of the form ‘\(p \leftrightarrow (q \Box \!\!\rightarrow r)\)’. In one version of the fallacy (V1), \(p\) is true and \(q\) is not, but if \(q\) were true, \(q\)’s being true (and/or \(r\)’s being true) would lead to \(p\)’s no longer being true. In another version of the fallacy (V2), \(p\) is true and \(q\) is not, but if \(q\) were to be true, this would lead to \(r\)’s no longer being true. Fortunately, there is reason to think that Out-U does not fall prey to the conditional fallacy. Concerning V1, note that we can add further conditions to the antecedent of the subjunctive such that they entail that the left-hand side of the biconditional is true. A biconditional of the form ‘\(p \leftrightarrow ((p \wedge q) \Box \!\!\rightarrow r)\)’ will evidently be safe from V1. In the case of Out-U, we can require that the context remains the same and \(S\) approximates fully comprehensive knowledge to the same degree and in the same way. Since whether or not an agent surpasses the threshold depends only on the context and the degree and way of approximation to fully comprehensive knowledge, adding the above conditions to the antecedent guarantees that if the antecedent of the subjunctive is true, the left-hand side of Out-U is true also. Concerning V2, note that if the corresponding conditional is necessarily true, again there is no need to worry: ‘\(p \leftrightarrow ((p \wedge q) \Box \!\!\rightarrow r)\)’ will evidently be safe from V2 when ‘\(p \leftrightarrow \Box ((p \wedge q) \rightarrow r)\)’ is true also. In Out-U, the addition of the proviso that conditions be suitably favourable arguably ensures that the corresponding conditional is necessarily true. That said, it is in principle possible to avoid stating Out-U in terms of a subjunctive conditional. One alternative strategy appeals to the notion of an epistemic duplicate and claims that ‘\(S\) understands \(P\)’ is true in a context just in case some epistemic duplicate of \(S\) would successfully perform the tasks determined by context. (Thanks to Catherine Elgin for pointing this out to me.) I decided to opt for the subjunctive version because it strikes me as most intuitive and more elegant certainly than the “epistemic duplicate” version.
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Acknowledgments
Thanks to the audiences of the following events for helpful feedback on this paper or the material presented in it: ‘Towards an Epistemology of Understanding: Rethinking Justification’ at the University of Berne, the ‘Explanatory Power II: Understanding through Modelling’ at Ruhr Universität Bochum, EPSA 2013 at the University of Helsinki, GAP8 at the University of Konstanz, ‘Epistemology Meeting: Doxastic Attitudes’ at the University of Ghent and ‘Philosophy Colloquium’ at University of Duisburg-Essen. Special thanks to Anna-Maria Eder for a thoughtful commentary that I hope I will be able to address in a more satisfactory way in the future. Finally, thanks to the members of the Leuven Epistemology Group for helpful discussion of the paper and related issues.
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Kelp, C. Understanding phenomena. Synthese 192, 3799–3816 (2015). https://doi.org/10.1007/s11229-014-0616-x
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DOI: https://doi.org/10.1007/s11229-014-0616-x