What reasoning might be

The philosophical literature on reasoning is dominated by the assumption that reasoning is essentially a matter of following rules. This paper challenges this view, by arguing that it misrepresents the nature of reasoning as a personal level activity. Reasoning must reflect the reasoner’s take on her evidence. The rule-following model seems ill-suited to accommodate this fact. Accordingly, this paper suggests replacing the rule-following model with a different, semantic approach to reasoning.

1. What does it mean to say that reasoning, or any other activity, fundamentally consists in \(\varPhi \)-ing? Consider what the activity of playing basketball consists in. One might answer this question on many different levels, including the anatomic/physiological level, the level of individual movements, and the level of strategy and tactics. But there is a sense in which more fundamental than all of those is an abstract specification of what the game is all about: roughly, two teams competing against each other, scoring points by getting the ball through hoops mounted on poles. This level of description is fundamental in the sense that descriptions at all other levels are intelligible by reference to this one: they are further specifications of how one does what is specified at this level of description. This is the sense in which, according to the rule-following model, reasoning is fundamentally a matter of following rules.

2. It is impossible to give an exhaustive list of philosophers who endorse the rule-following model of reasoning, since the model is so often simply taken for granted. For a sampling of authors—in addition to Boghossian and Broome—who are more or less explicit on the issue, see Winters (1983), Van Cleve (1984), Brandom (1998), Wedgwood (2002), Wright (2004a, 2014), Hlobil (2014), and Miller (2015). This is not to say that the rule-following model has gone entirely unchallenged in philosophy. Rumfitt (2008, 2011), for one, proposes an alternative that is in many ways similar to my own.

3. The “mental models” theory (Johnson-Laird 1983, 2001, 2008; Johnson-Laird and Byrne 1991) in the psychology of reasoning is also often advertised as “semantic”, and is specifically developed in reaction to rule-based accounts such as Rips (1994). However, care is needed in interpreting this claim (I will briefly return to this in Sect. 5). For now, I just want to note that my aim is to answer a rather different question from the one that mental model theory aims to answer: my concern is what you do when you reason, rather than how reasoning is carried out at the computational level. Of course, the two questions are not simply independent of each other: an account of what we do when we reason must be sensitive to much of the same empirical data as an account of how reasoning is carried out at the computational level, while the latter sort of account can benefit from a clearer conceptual characterization of the phenomenon it seeks to explain.

4. An anonymous referee asks how this distinction relates to the “System 1/System 2” distinction, made famous by Kahneman (2011). I think there is no simple answer to this, as Kahneman’s System 1 is a very mixed bag—bundling together things like the processing that underlies depth perception with “intuitive” responses to logical or mathematical puzzles (Kahneman himself, of course, recognizes that he abuses terminology in his labeling). But while depth perception is quite plausibly handled by an informationally encapsulated and cognitively impenetrable system, our intuitive responses to, e.g., the Linda the bank-teller case are not—witness the fact that, once you see the right answer it no longer seems to you that the wrong answer is correct (though, strikingly, this does not seem to immunize you from similar mistakes in the future). This sort of difference suggests that we should not expect a theory of reasoning to treat both of these processes on a par.

5. That is, Tom reasons directly from the premiss that the relevant pattern of spots is present on Bob’s face to the conclusion that Bob will soon die. Tom’s crazy theoretical beliefs are part of the background of his inference, not among his premisses. Tucker (2010) questions this distinction, but I think it is essential for understanding inference.

6. This way of presenting matters presupposes that rules of reasoning are schemas of truth-evaluable statements, so that their substitution-instances can figure as premisses in reasoning. But this is not essential to the argument. What matters is just that the subject’s grasp of the rule manifests itself in a higher-order belief like (a)—regardless of whether this is conceived as a substitution step or not.

7. The history of arguments in this vicinity traces back at least to Carroll’s (1895) story of Achilles and the Tortoise. Variations are given by Winters (1983), Van Cleve (1984), Johnston (1988), Brewer (1995), Fumerton (1995), Boghossian (2003, 2008, 2014), Railton (2006), Broome (2013), Wedgwood (2006), and others. For some replies, see Leite (2008) and Valaris (2014). Worries about rule-following are famously also at the core of Kripke’s (1982) reading of Wittgenstein (1958). While the two sets of worries are not unrelated, Kripke’s primary focus is on meaning or content, not reasoning as such.

8. I thank a referee for pointing out mistakes in my earlier reading of Broome’s account.

9. Broome also suggests that sometimes checking can simply consist in repeating the same process. But, surely, repeating the same process and getting a different result should not just brutely cause me to change my assessment of my earlier result. The divergence may well give me reason to reconsider that assessment, but that would be a case of further reasoning, not just a brute disposition.

10. There is a tradition, stemming from a reading of Wittgenstein’s (1958) remarks on rule-following, that seeks to avoid this dilemma by introducing a way of following a rule that does not rest on interpretation, i.e., a way of following a rule that is not mediated by the application of any further rules (McDowell 1984; Miller 2015). On Miller’s (2015) view, for example, reasoning in accordance with the rule (MP) may require no more than an intentional state with the rule as (part of) its content, and which combines with your beliefs that if Socrates is human then Socrates is mortal and that Socrates is human to cause you, in the right way, to believe that Socrates is mortal. Now, the challenge for any such view will be to spell out what “the right way” of causing beliefs is. Proponents of such views, following Wittgenstein himself, appeal to things like “practice”, “custom”, “training” and so on. Let us say that such a transition counts as reasoning just in case it is the manifestation of a certain kind of (perhaps socially scaffolded) cognitive skill by the reasoner. As it happens, I have much sympathy with this sort of view; I just wonder whether the appeal to a rich enough concept of cognitive skill does not render appeal to rules superfluous. Consider the inference from “roses are red” to “roses are colored”. How should we explain a normal English speaking subject’s capacity to reason in this way? As will become clearer below, my view is this: her understanding of these two statements enables her to see that there is no way for the former to be true while the latter is not. Her reasoning is explained by cognitive skills—specifically, skills of semantic evaluation. It is not clear that there is any need to appeal to rules of inference at all. Of course, some of those who appeal to rule-following in their account of reasoning also hope to explain the cognitive skills involved in understanding in terms of rule-following (e.g., Brandom 1998; Boghossian 2003). For them, the appeal to rules is not redundant. But if we do not share this ambition it is not clear we should follow them on this. I thank an anonymous referee for pressing me on this point.

11. This is not intended as a reductive account of belief in terms of ruling out possibilities. The point, rather, is to draw upon our intuitive grasp of belief to introduce some quasi-technical vocabulary that will be useful in what follows.

12. Taking epistemic space to extend beyond the space of logical possibility is a relatively familiar way of treating deductive ignorance and error. See, for example, Rumfitt (2008) and Jago (2014). Any account of reasoning will need some way to represent deductive ignorance, and this approach seems natural if one wishes to avoid syntactic approaches.

13. This is consistent with propositional accounts of “knowing wh-” (see Stanley 2011, Chap. 2 for an illuminating overview). My knowing who Barack Obama is, for example, might consist in my knowing the relevant range of demonstrative propositions of the form “this is Barack Obama”, in the right perceptual contexts. A similar account is plausible for a subject’s knowing what things have to be like for a statement to be true: it consists in knowing, upon considering a relevant possibility that makes the statement true, that this possibility makes the statement true. One may wonder whether it is plausible that ordinary understanding involves knowledge of meta-linguistic propositions of this sort; but the charge of over-intellectualizing ordinary skills is one that propositionalists about “knowing wh-” have to address in any case.

14. It bears noting that taking p to follow from R on the present approach is not just an input to a causal process that leads one to believe p by reasoning from R. On the contrary, it is coming to believe reasoning from R. One might wonder whether this makes my account incompatible with familiar causal theories of action, thereby undermining its claim to capture the sense in which reasoning is active. I return to this point in Sect. 5.

15. Bird (2005) denies this for cases of abductive inference. It would take us too far afield to consider Bird’s objections.

16. I thank an anonymous referee for pressing me on this.

17. For a theory of mental action that attempts to reproduce something like the structure found in the standard story, see Proust (2009). Proust’s account is intended to apply not just to reasoning, but also to things like actively searching one’s memory. In this latter case it is not implausible that we really do have a process (searching one’s memory) which is controlled or guided by distinct mental states (e.g., your desire to remember someone’s name). By the same token, however, it seems doubtful that this external guidance shows that the process of remembering itself is an action: it is more natural to say that I actively bring it about that I remember than that I actively remember (Mele 2009 makes the same point). But then this structure cannot give us what we want in the case of reasoning: we want a sense in which reasoning itself is active, not simply a sense in which I can actively bring it about that I reason.

18. Boghossian (2014, pp. 17–18) recants his own earlier inferentialist leanings on similar grounds.

19. Much of the evidence for such “content effects” comes from research with the Wason selection task paradigm. For example, subjects perform much better with versions of the Wason selection task (Wason 1968) which are about familiar topics than with versions that involve either meaningless symbols or unfamiliar content (Wason and Shapiro 1971; Pollard 1981). Such content effects show that our reasoning capacities are, at the very least, not purely formal—they are not insulated from background knowledge and processes of semantic evaluation.

20. This is a familiar complaint, made by a number of participants in an Open Peer commentary on Deduction (Johnson-Laird and Byrne 1991) in Behavioral and Brain Sciences (Andrews 1993; Bundy 1993; Stenning and Oberlander 1993; Ter Meulen 1993).

I would like to thank three reviewers for their generous and constructive comments. Earlier versions of this paper were presented at the philosophy seminar at the University of Adelaide and the Minds Online 2015 conference. On the latter occasion I benefitted from written comments from Matt Boyle, Zoe Jenkin and Chris Tucker. I would like to thank the participants of both events for many insightful comments and suggestions.

Authors and Affiliations

1. University of New South Wales, Sydney, NSW, Australia

   Markos Valaris

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Correspondence to Markos Valaris.

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