Synthese DOI 10.1007/s11229-017-1535-4

Reasoning without regress Luis Rosa1

Received: 2 May 2017 / Accepted: 12 August 2017 © Springer Science+Business Media B.V. 2017

Abstract In this paper I explore alternative ways of answering the infinite regress problem of inference, as it was depicted in Lewis Carroll’s ‘What the Tortoise said to Achilles’. Roughly put, the problem is that if a claim to the effect that one’s premises give support to one’s conclusion must itself be part of one’s premises, then an infinite regress of reasons ensues. I discuss some recent attempts to solve that problem, but I find all of them to be wanting. Those attempts either require the reasoner to believe that her premises give support to her conclusion, or to take her premises to give support to her conclusion, where taking is not a doxastic attitude. I conclude that, on the face of the failure of those attempts to solve the problem, there is a strong prima facie case for allowing inference to be blind (in which case reasoners need not believe or take it that their premises give support to their conclusions). Keywords Reasoning · Regress of reasons · Taking condition · Lewis Carroll

1 Introduction Call a reasoned state-transition from a positive attitude toward ϕ to a positive attitude toward ψ ‘doxastically blind’ when the reasoner performs that transition without so much as believing that ϕ gives support to ψ (that ψ follows from ϕ, or that ϕ makes it likely that ψ). The relevant attitudes need not be belief attitudes or even highcredence attitudes. They may be suppositional attitudes or hypotheses. Just as one can inferentially believe that ψ on the basis of one’s belief that ϕ, so one can derive the conclusion that ψ under the scope of one’s supposition that ϕ. The premises and

B 1

Luis Rosa [email protected] University of Cologne, Albertus-Magnus-Platz 1, D-50923 Köln, Germany

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conclusions are identical in these two cases, but the reasoner’s attitudes towards them are not. Assume that no piece of reasoning is doxastically blind: if there is reasoning at all, then the reasoner believes that her premises give support to her conclusion (or the reasoner holds a ‘bridge-belief’ for short). Now consider a subject S who infers that ψ on the basis of her belief that ϕ. According to our initial assumption, S also believes that ϕ gives support to ψ. Presumably, then, that belief was also part of S’s pool of premises, and S’s inferential belief is actually based on both S’s belief that ϕ and S’s belief that ϕ gives support to ψ. But then our initial assumption says again that that piece of reasoning must not be doxastically blind, and so the reasoner must also believe that premises ϕ and ϕ gives support to ψ themselves give support to ψ. Therefore, the content of that belief was also part of S’s pool of premises, and so on ad infinitum: it turns out that reasoning is impossible (for S would need to draw her conclusion on the basis of infinitely many beliefs). This is of course reminiscent of Lewis Carroll’s ‘What the Tortoise said to Achilles’ (1895), and it is a problem that epistemologists are well aware of (e.g. see Boghossian 2003 and Railton 2006). There are three ways to respond to this argument: (1) to require the reasoner to have some non-doxastic or non-propositional attitude towards the support relation between premises and conclusion, (2) to still require the reasoner to hold bridge-beliefs, but in such a way that they are not part of the reasoner’s pool of premises, or (3) not require any bridge-attitude on the part of the reasoner at all. According to (1), even though reasoned state-transitions may occur in the absence of bridge-beliefs, they are nonetheless not completely blind: the reasoner in some sense still takes her premises to give support to her conclusion, where taking is a non-doxastic type of bridge-attitude (see Boghossian 2014 for a defense of this approach, and also for different characterizations of the taking attitude). (2) says that the requirement of bridge-beliefs can be made in such a way as to prevent the regress argument to go through. In contrast to (1) and (2), (3) says that reasoning can occur in total blindness, no bridge-beliefs or other taking attitudes required (see Wright 2014 for a defense of this view). In this paper I will explore some recent defenses of strategies (1) and (2). In Sect. 2 I present Markos Valaris’s (2014; 2016a) defense of a proposal of type (2). In Sect. 3 I give reasons to think that Valaris’s account of reasoning does not after all constitute a good solution to the regress problem. In Sect. 4 I discuss two very similar approaches of type (1), by BonJour (2014) and Fumerton (2015) respectively. I argue that their proposals either fail to solve the regress problem or they boil down to a proposal of type (3). In Sect. 5 I discuss yet another strategy of type (1): Boghossian’s (2014) recent defense and interpretation of the ‘taking condition’ for inference. I argue that his arguments in support of that condition are inconclusive. In the last section I suggest that a solution of type (3) is our best choice.

2 Valaris’s account Valaris (2014) argues that reasoning, understood as a conscious, person-level activity, is not just a type of causal process. According to him, we should not think of bridge-

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beliefs—which in Valaris’s view are beliefs about what follows from what—as being part of a causal chain that characterizes the process of reasoning. He thinks that it is that account of the nature of reasoning which, together with the requirement of bridge-beliefs, is liable to the infinite regress argument. Suppose again that bridge-beliefs are necessary for reasoning, and that S deduces that ψ on the basis of her belief that ϕ. The bridge-belief that ψ follows from ϕ—or so the causal account of reasoning would have it—needs to be involved in the causation of S’s belief that ψ, as formed on the basis of S’s belief that ϕ. To say that the bridgebelief is one of the contributing causes of S’s belief that ϕ, and thus plausibly also that the inferential belief that ψ is based on that bridge-belief, is to embark on the relevant infinite regress. The bridge-belief is not a necessary, enabling condition for S’s belief that ϕ to cause S’s belief that ψ either—for surely one could cause the other even without that bridge-belief (Valaris 2014, p. 108). And, furthermore, it is also problematic to claim that the bridge-belief contributes causally to the formation of the inferential belief by causing another, this time a higher-order belief to the effect that the reasoner ought to believe the conclusion of her inference. For in this case two other questions need to be answered: (i) How does the bridge-belief contribute to the formation of the higher-order belief? (ii) How does the higher-order belief contribute to the reasoner’s belief in the conclusion? If (i) and (ii) are themselves pieces of reasoning, then an infinite regress of beliefs looms yet again. If they are not then, first, it is not clear what they are exactly; second, there is now a pressure to explain why this type of process is not after all available to get one directly from one’s premises to one’s original conclusion (Valaris 2014, pp. 108–109). So taking bridge-beliefs to be necessary for reasoning does not seem to be compatible with the causal account of reasoning. According to Valaris, however, bridge-beliefs do play a constitutive role in reasoning, as opposed to a causal one—and that in itself does not lead to a Carrollian regress. His view is that there are two general types of reasoning: non-basic reasoning and basic reasoning, both of which are constituted by bridge-beliefs. The difference between these two types of reasoning is that in nonbasic reasoning the subject’s bridge-belief itself involves reasoning, whereas in basic reasoning it does not. Non-basic reasoning just is believing that a certain conclusion follows from one’s premises (Valaris 2014, p. 112). So the bridge-belief here does not figure in reasoning as a link in a causal chain (for the bridge-belief and the reasoning are the same thing), and therefore its content is not an additional premise in one’s inference. In the case of basic reasoning Valaris proposal is that, by reasoning from one’s premises to one’s conclusion, one already counts as believing that one’s conclusion follows from one’s premises. That would be so at least assuming that the reasoner has a certain capacity for self-reflection (Valaris 2014, p. 113), and that she believes that she believes the conclusion on the basis of her premises (or: she believes that she believes the conclusion for those reasons, where ‘those’ makes reference to the reasoner’s premises). And so in neither case reasoning is made impossible by the requirement of a bridgebelief—for the bridge-belief is constitutive of the activity of reasoning, instead of being a premise-belief on the basis of which the subject draws the conclusion. This is a very brief summary of Valaris’s view (further details will be explored below). His take on the Carrollian regress problem is therefore a response of type (2) as described above, in

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that it says that ‘we should simply deny that the role of the belief that one’s conclusion follows from one’s premises is to provide one with an extra premise’ (2014, p. 107). I turn next to Dogramaci’s challenge to Valaris’s view. 2.1 Dogramaci’s challenge Dogramaci (2016) argues that Valaris’s view lacks the generality required from an account of reasoning: it would not be able to properly characterize inferences whose output beliefs are themselves grounded on pieces of suppositional reasoning, as opposed to a set of premise-beliefs. (From now on, every mention of Dogramaci refers to his 2016 paper). As an example of this type of inference consider the following process: I hypothesize that Some feminists are men; under the scope of that supposition, I conclude that Some men are feminists; I then finally infer (inferentially believe) that If some feminists are men then some men are feminists. It would appear that I do not end up believing that conditional claim on the basis of any believed premises. I.e. my inferential belief appears to be grounded on a process or activity of reasoning with suppositions, as opposed to being grounded on previous beliefs. There are many other examples of this kind, and the power (if a power it is) of this type of process to generate new knowledge has already been explored elsewhere in the literature (e.g. see Balcerak Jackson and Balcerak Jackson 2013).1 Dogramaci’s view is that cases of this sort give support to the view that there is blind reasoning (by ‘blind’ reasoning Dogramaci just means what I am calling ‘doxastically blind’ reasoning here). In Valaris’s view reasoning is a process of believing something for a reason (2014, p. 105). The reasoner must believe that her conclusion follows from her reasons. The question, then, is: for which reasons does one believe e.g. a proposition of the form If ϕ then ψ when that belief is formed through a piece of suppositional reasoning that goes from the supposition that ϕ to the conclusion (drawn under the scope of that supposition) that ψ? Valaris’s account requires there to be a proposition or claim that plays the role of a reason for the subject to believe that If ϕ then ψ here. And so Valaris must (so to speak) put the reasoner’s state-transition from her supposition that ϕ to her conclusion that ψ in the ‘space of reasons’. Assuming that the target inferential process does indeed generate knowledge or justified belief, the relevant reason better not be (the subject’s belief toward) the proposition that If ϕ then ψ, for in that case we would just have a case of objectionable circularity: the subject uses If ϕ then ψ as a reason to believe that If ϕ then ψ. What about the proposition that ψ follows from ϕ—could not it be the reason for which the reasoner believes that If ϕ then ψ? If what Valaris says about reasoned state-transitions involving beliefs applies also to reasoned state-transitions involving 1 Some authors—-e.g. see Williamson (2007, p. 162) and Rumfitt (2008, p. 63)—have characterized the

power we have to know logical truths be means of processes of suppositional reasoning of this type as some sort of byproduct of our more down-to-earth competence to handle doxastic input (to extract more information about the world from the information we already have). That we are equipped to infer that Some As are Bs on the basis of our belief that x is A and x is B means that we are also equipped to infer that If x is A and x is B then some As are Bs by going offline and exploring the consequences of our assumptions.

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suppositional or hypothetical attitudes, he could take the subject’s piece of reasoning from her assumption that ϕ to her conclusion that ψ to be/to be constituted by the subject’s belief that ψ follows from ϕ. And so this construal of the subject’s reason to believe the conditional If ϕ then ψ here seems to cohere with Valaris’s view. As Valaris uses the notion in his (2014) paper, however, ‘ψ follows from ϕ’ means that ϕ is conclusive evidence for ψ—and Dogramaci rightly points out that this relation does not obtain between the contents of some (competent, epistemically good) pieces of suppositional reasoning. In his example, Dogramaci pictures himself as believing that He is a monkey’s uncle if the Liar is and is not true. He believes that claim on the basis of an episode of suppositional reasoning that goes roughly as follows: he assumes that The Liar is and is not true; under that assumption he concludes that The Liar is true (by conjunction–elimination); he then derives from that intermediary conclusion that Either the Liar is true or he is a monkey’s uncle (by disjunction–introduction); as he also derives The Liar is not true under the scope of the initial assumption (also by conjunction–elimination), he concludes that He is a monkey’s uncle, again under the scope of the initial assumption (by disjunctive syllogism). Finally, he ends up inferring that He is a monkey’s uncle if the Liar is and is not true (conditional proof), thus discharging the initial assumption. But that The Liar is and is not true is not conclusive evidence that Dogramaci is a monkey’s uncle (it is not evidence for anything). But perhaps Valaris could avoid that objection by adopting a more inclusive notion of consequence, in such a way that bridge-beliefs would not necessarily be about evidential relations.

2.2 Valaris’s response Valaris (2016a) thinks that his account of the nature of reasoning can accommodate cases of inferential beliefs that are formed as a result of suppositional reasoning. According to him, the view that in these cases our beliefs are not based on any reasons is ‘hard to accept’ (2016a, p. 3). To use the example from above, even though it looks as if I come to know that If some men are feminists then some feminists are men purely on the basis of a process of suppositional reasoning—and therefore not on the basis of any previously held belief—that would not actually be so. His suggestion seems to be that what entitles me to believe such a thing is my recognition of the fact that Some feminists are men can be derived from my supposition that Some men are feminists (2016a, p. 3). That fact or proposition is therefore my reason to believe that If some men are feminists then some feminists are men. A similar view was held by Crispin Wright (2014, p. 29), who in this case would have me ground my judgment that If some men are feminists then some feminists are men on my anterior judgment that I have validly derived the conclusion that Some feminists are men from my supposition that Some men are feminists. Later on in the same article Valaris (2016a, p. 6) equates recognition of the fact that ψ can be derived from the supposition that ϕ with recognition of the fact that ψ follows from ϕ—where this again is a belief-state: it consists (perhaps among other things) in believing that ψ follows from ϕ. His final explanation is, then, that in cases

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of suppositional reasoning one first recognizes (ergo believes) that ψ follows from ϕ, and then one also recognizes (ergo believes) that If ϕ then ψ follows from ψ follows from ϕ. If this is to be a successful response to Dogramaci’s challenge, it is precisely because this time Valaris is embracing a more inclusive notion of consequence, as suggested above. Indeed, he now seems to subscribe to the idea that ψ follows from ϕ when there are no real possibilities in which ϕ is true and ψ is false (Valaris 2016a, b). Since there are no real possibilities in which ϕ is true and ψ is false not only when ϕ is conclusive evidence for ψ, that would seem to be a way out of Dogramaci’s objection. Valaris can now grant that The Liar is and is not true is not conclusive evidence that Dogramaci is a monkey’s uncle; still, there is no real possibility in which it is true that The Liar is and is not true and false that Dogramaci is a monkey’s uncle (if only because there is no real possibility in which the Liar is and is not true). But what more exactly does recognizing that ψ follows from ϕ involve, over and above believing that ψ follows from ϕ? According to Valaris it consists in ‘ruling out’ the ways for things to be in which ϕ is true and ψ is not true (2016a, b). Of course, one would now want to hear more about what it is to ‘rule out’ possibilities. But let me sidestep this issue and look at the way in which Valaris uses the notion of ruling out. He says roughly the following (see Valaris 2016a, p. 5). If I believe that ϕ, all the ways for things to be that are open to me are such that ϕ is the case, and so I have already ruled out all possibilities in which ϕ is not true. When and how will I come to believe of a certain ψ that it follows from ϕ? Valaris says that believing that ψ follows from ϕ in this situation just is coming to believe that ψ—for in this case I am precisely ruling out all the ways for things to be in which ϕ is true and ψ false. Now, in this explanation Valaris makes use of the fact that I believe both ϕ and ψ to account for the fact that I come to recognize that ψ follows from ϕ. But surely this cannot be the explanation of how I come to recognize that fact when ϕ is the content of a supposition of mine—a supposition under the scope of which I derive ψ. Still, to recognize that ψ follows from ϕ in this case is also to rule out those possibilities in which ϕ is true and ψ false. And so we should tell a similar story as the one we told about reasoning with belief-attitudes. When I suppose or hypothesize that ϕ, I rule out all the ways for things to be in which ϕ is not true—where this is of course a different sort of ruling out from the one involved in the attitude of belief (for I may rule out scenarios in which ϕ is not true in the hypothetical sense while at the same time actually believing that not-ϕ). And here we can ask again: given my act of supposing that ϕ, when and how will I believe of a certain ψ that it follows from ϕ? We would then expect Valaris to answer this question in a similar way as he did in the case of reasoning that involves transitions between belief-states: believing that ψ follows from ϕ in this situation just is drawing the conclusion that ψ under the scope of the initial assumption that ϕ, in that the reasoner is again ruling out the ways for things to be in which ϕ is true but ψ is not. Since I do believe that ψ follows from ϕ when I conclude that ψ under the scope of my assumption that ϕ (because I rule out the possibilities in which ϕ is true and ψ is not), that is again my reason to believe that If ϕ then ψ in a case of suppositional reasoning. And so Valaris would seem to avoid Dogramaci’s objection by embracing a more inclusive (and kosher) interpretation of what it is for a proposition to follow from another.

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3 Objections In this section I will raise further challenges to Valaris’s account of reasoning. These problems will remain even if Valaris can successfully respond to Dogramaci’s objection, perhaps along the lines suggested above. Valaris’s explanation of how reasoners come to hold bridge-beliefs is presumably incomplete. It cannot be that I believe that ψ follows from ϕ whenever I rule out the ways for things to be in which ϕ is true but ψ is not. I may believe that John loves Mary and that We are in the year of 2017 at the same time, and so I rule out all the ways for things to be in which John still loves Mary but we are not in the year of 2017 (if only because I rule out all the ways for things to be in which we are not in the year of 2017). I may analogously suppose both things at the same time, so that I can rule out the relevant possibilities in the suppositional sense of ‘ruling out’ as well. But surely I do not believe that We are in the year of 2017 follows from John loves Mary in either scenario. What is it that is missing in this case but is satisfied in those cases in which I do indeed believe that ψ follows from ϕ by ruling out all the ways for things to be in which ϕ is true but ψ is not? One possible answer is: the cases in which my ruling out the relevant possibilities constitutes my believing that ψ follows from ϕ are those cases in which I reason from ϕ to ψ (or: I reason deductively from ϕ to ψ). That is perhaps a good answer, but those who embrace Valaris’s account of reasoning will be caught in a (non-virtuous) circle by endorsing it. First one makes use of the notion of a bridge-belief to describe the nature of reasoning—and then one uses the notion of reasoning to explain how the relevant bridge-belief comes into existence. Another possibility is: the cases in which my ruling out the relevant possibilities constitutes my believing that ψ follows from ϕ are those cases in which there is a certain type of causal relation between my attitude towards ϕ and my attitude towards ψ. That type of causal relation occurs precisely when one reasons from ϕ to ψ, and so one does not count as believing that ψ follows from ϕ merely because one believes both ϕ and ψ at the same time. There is no problem of circularity here, insofar as it is the notion of causation that is used to set the two kinds of ruling-out apart (the ones that do and the ones that do not constitute bridge-beliefs), and not the very notion of reasoning. Sure enough, we are assuming that the relevant type of causation occurs precisely in those cases in which one does reason—but here the notion of causation serves to individuate both at the same time, bridge-beliefs and reasoning. Given Valaris’s overt rejection of the causal account of reasoning, however, this move is also not open to him. And so we are left wondering what makes it the case that certain types of ruling out constitute bridge-beliefs whereas others do not, as Valaris’s account does not yet tell us how to set these apart. Furthermore, those more or less intuitive ways of drawing the relevant distinction turn out to be incoherent with Valaris’s account of reasoning. It might be suggested that Valaris’s account could be amended in the following way: when a reasoner considers whether ψ follows from ϕ during a process of reasoning or inference, she considers only the ways for things to be in which ϕ is the case, thus

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setting aside the ways for things to be in which her other beliefs are true.2 And so the fact that one has ruled out the possibilities in which ϕ is the case but ψ is not just because one happens to believe ϕ and ψ respectively does not make it the case that one believes that ψ follows from ϕ; in order for that to be the case, one must have considered only the possibilities that are ruled out by ϕ. That might as well be true, but notice that if performing this procedure were a necessary condition for reasoning, then reasoning would become way more difficult and less pervasive a cognitive process than it actually is. In order to count as reasoning subjects would have to constantly perform this ‘surgical process’ of isolating the contents of their premise-beliefs from the rest of their knowledge and checking which ways for things to be are ruled out by those premises. The problem with this requirement becomes more or less evident when we consider the fact that ordinary reasoners can draw inferences on the basis of many premisebeliefs in quite an effortless manner; if they had to consider each premise in isolation and check which possibilities are ruled out by them—and presumably also check which possibilities are ruled out by those premises combined with each other—that would in some cases squander their cognitive resources and make inferences that are actually easy to perform very difficult. E.g. I know that World War II (WWII) ended in 1945 and that 1945 is before 1953, and now I learn that Einsenhower only served as the President of the United States from 1953 to 1961; I then infer on that basis that Einsenhower did not play a role in WWII as the President of the United States. But I do not really set my other beliefs about Eisenhower or WWII apart when I perform that inference—e.g. I still keep my beliefs that Eisenhower served as an Army general of the Allied forces during WWII, that the United States were part of the Allied forces, etc., and thus my cognitive state continues to eliminate the possibilities in which those propositions do not hold. If I had to isolate my premise-beliefs from the rest of my knowledge and check which ways for things to be are ruled out by them only, my reasoning would not go through with the naturalness and effortlessness it actually went through. Here is another objection to Valaris’s account. An obvious problem with any account that takes bridge-beliefs to be necessary for reasoning is that it excludes agents who clearly seem to be performing inferences but do not have the concept of consequence from the class of reasoners. There is no good reason to think that children or even adult thinkers who lack a concept of consequence cannot engage in the practice of reasoning—even in the more specific sense of a conscious, person-level activity (see Boghossian 2014, §6 for a similar observation). E.g. consider a six-year old child who was told that Her toy is either in the top drawer or in the one below it; she opens the top drawer and thereby realizes that The toy is not in the top drawer; instead of asking her mother again where her toy is, she infers that The toy is in the drawer below the top one and acts accordingly: she opens it and gets her toy. That piece of inference may have been easy, but the child did give it a thought; she was consciously thinking about those contents, and she was representing information in an explicit way (we may even suppose that the child has repeated what

2 I thank an anonymous reviewer for calling my attention to this possible reply.

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her mother said originally: ‘Either in the top drawer or in the one below it’, and that she explicitly said out aloud, or she was mumbling, or maybe using her internal voice to say: ‘It is not in the top drawer’). The six-year old does not have a concept of consequence, however. She does not yet ‘go second-order’ in such a way as to think about certain propositions following from others. Yet, this is as good an example of reasoning as any. But if one does not have a concept of consequence, one cannot have bridge-beliefs, and so one does not count as a reasoner according to Valaris’s account (the same would apply to human adults who do not have a concept of consequence). Perhaps Valaris would want to say that, despite appearances to the contrary, these people do have a concept of consequence. And so he must give us good reasons to believe that that is the case. But he cannot simply say something like ‘Those people do have a concept of consequence, because they are clearly engaging in the practice of reasoning’. He must give us independent reasons to think that the child (or the human adult) has a concept of consequence, without using the very theory of reasoning he is trying to defend.

4 Non-doxastic taking: awareness and insight In the first section we saw that there are three ways of addressing the infinite regress problem of inference: (1) to require the reasoner to take her premises to give support to her conclusion, where the taking-attitude is not a belief-attitude, (2) to require the reasoner to believe that her premises give support to her conclusion, but in such a way that the content of that bridge-belief is not included in the reasoner’s pool of premises, or (3) to allow reasoning to be blind and not require any bridge-attitude at all. The reflections above suggest that Valaris’s defense of strategy (2) does not after all constitute a good answer to the problem. First, it does not tell us how to distinguish between the type of ruling out that does and the one that does not constitute a bridgebelief, and some plausible ways of drawing the relevant distinction (the ones we have considered above) are not coherent with Valaris account of reasoning. Second, his account seems to exclude some reasoners from the class of reasoners, simply because they lack a concept of consequence. It would appear, then, that we are left again with strategies (1) and (3). Here is one way of pursuing strategy (1): even though the reasoner is not supposed tobelieve that her conclusion follows from her premises, she mustbe aware of the consequence relation that holds between the premises and the conclusion. That state of awareness would be a non-propositional state, so that its content is not a further premise to be added to the reasoner’s pool of premises. Fumerton (2015) proposes something along these lines as a condition for inferential justification. A similar proposal—defended by BonJour (2014)—is that the reasoner must have aninsight into the way in which the premises are related to the conclusion. Again, that mental state would be nonpropositional in character. Both Fumerton and BonJour are not so much as offering necessary conditions for reasoning or inference, but rather for inferential justification. I.e. their theses are not about the nature of inference—they are about what makes a belief justified when it is formed through inference. But they could also be thought of as accounts of the nature of inference.

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The idea is, then, that a state of awareness or insight puts a stop to the Carrollian regress. Are those purported states of awareness or insight indeed non-propositional in character? There is reason to suspect that if there are states of awareness or insight of the relevant kind, then they do possess propositional content. For since they are supposed to establish a positive connection between the premises and the conclusion, they must be about how those propositions are logically related to each other. But it is hard to see how that could be so without positing a propositional content for those states—e.g. they are states of awareness that something follows from something else, or states of ‘seeing’ (with the mind’s eye, as it were) that something follows from something else. In that case, however, it would not be correct to say that those propositional contents are not part of the reasons on the basis of which the subject believes the conclusion [see also Boghossian (2014, p. 9), Wright (2014, p. 31) and McHugh & Way (2016, p. 320)]. For the defenders of the awareness/insight view presumably do not want those states of awareness or insight to occur vacuously: those states are supposed to constitute a basis for, or to give support to one’s inferential beliefs—that is their role in inference. But if those states do have propositional content, and one also relies on them in drawing inferences, then their contents are as much a part of one’s reasons as the contents of one’s premise-beliefs. Here is perhaps a good way of making this point. Let A1 , . . . , An represent types of mental states or attitudes of taking it that something is the case, where possibly Ai = A j for i = j. So when a subject S is in state Ai ϕ, S takes it that ϕ is the case. We might call those states or attitudes ‘assertive’ states or attitudes, since they consist in taking a positive stance—as opposed to, say, an agnostic stance—towards a proposition. In the special case where Ai is a belief-state, to say that S is in state Ai ϕ or that S has attitude Ai towards ϕ is just to say that S believes that ϕ. But Ai ϕ can also be e.g. a state of insight or awareness that ϕ (let us leave aside for now the question of whether the fact that ‘S has an insight that/is aware that ϕ’ entails ‘S believes that ϕ’—the point I want to make here would seem to hold either way). Now consider the following conjunction: ‘S infers that ψ on the basis of S’s states or attitudes A1 ϕ1 , . . . , An ϕn , but ϕi (with i ∈ {1, . . . , n}) is not a reason for which S believes that ψ’. Call that a ‘basis-but-no-reason conjunction’. A relevant instance of this is: S believes that Some Fs are Gs on the basis of her belief that x is an F and a G and her awareness that Some Fs are Gs follows from x is an F and a G; but that Some Fs are Gs follows from x is an F and a G is not part of the reasons for which S believes that Some Fs are Gs. Conjunctive assertions that fall under this pattern sound false, for the simple reason that they seem to take away with one hand (‘ϕi is not a reason for which S believes that ϕ’) what they gave with the other (‘S infers that ψ on the basis of A1 ϕ1 ,…, An ϕn ’, ergo ‘S infers that ψ also on the basis of Ai ϕi ’ with i ∈ {1, . . . , n}). The defender of the awareness/insight approach could reply at this point: “The contents of one’s state of awareness or insight are indeed reasons on the basis of which one holds one’s inferential belief; but they are not part of the premises that are used by one in the inference. Not all reasons are premises”. The latter claim might as well be true, insofar as we do form beliefs on the basis of reasons in a non-inferential way. E.g. that Betty told me that she is busy may be a reason for me to believe that

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Betty is busy; but it might also be argued that if I do believe that Betty is busy on the basis of Betty’s testimony in this way I am not so much as performing an inference—it is some other type of process that is going on. And so that Betty told me that she is busy is a reason for me to believe that Betty is busy, and I do believe that proposition on the basis of that reason; but the former is not a premise of an inference (there is no inference happening here). But even if we grant that not all the reasons on the basis of which a subject believes that ϕ are premises from which that subject infers that ϕ, it does not follow that those reasons that are postulated by the awareness/insight view should not count as premises (given the role that they are supposed to play in inference). For the reasoner would not only need to be aware that Some Fs are Gs follows from x is an F and a G, but also to make use of that proposition in order to transition from one’s belief that x is an F and a G to one’s belief that Some Fs are Gs—otherwise, one’s state of awareness/insight would again be vacuous. That movement of thought would not count as an inference (according to this view) if the subject had reached the conclusion that Some Fs are Gs without relying on it being the case that this follows from x is an F and a G. So why should not the proposition that Some Fs are Gs follows from x is an F and a G count as part of the premises of one’s inference? It seems arbitrary to say that it is not. (Notice that one cannot make the “it is not an inferential process” move here—for inference is the very topic of this discussion). On the face of this prima facie case for including the contents of purported states of awareness/insight in the set premises from which a subject draws her inference, defenders of the awareness/insight approach need to explain why we should not do so. And the reasons they have to give us in this regard must be independent of their take on the Carrollian regress problem (e.g., their answer better not be: “We should not include those contents in the subject’s set of premises because that is how the regress comes to its end”). It would appear, then, that the defender of awareness or insight as conditions for inference must either: (a) embrace the existence of infinitely many states of awareness/insight of ever increasing complexity (if they accept our considerations in favor of including the propositional contents of those states in the subject’s set of premises), or (b) claim that the regress does not ensue, because the point at which the reasoner ‘stops’ and draws the inference is simply when she believes the conclusion on the basis of her premise-beliefs plus her awareness/insight that the premises give support to the conclusion. But (a) is a version of the very problem we were trying to solve, and (b) simply boils down to saying that reasoning is blind—only the reasoner’s set of premises now includes a proposition about the relevant support relation.

5 Boghossian and the taking condition Another strategy of type (1) can be found in Boghossian (2014): to take one’s premises to give support to one’s conclusion is to follow an inferential rule when deriving the conclusion from the premises. He considers different interpretations of what it is to follow a rule and finds all of them to be problematic (see his 2014, Sections 9–13): when we analyze the notion of rule-following, it becomes difficult or impossible to see

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how inference could be a rule-governed activity. The solution he finds most plausible is that of taking the notion of rule-following to be a primitive, unanalyzable notion. Otherwise we would need to dispense with the concept of inference (or reasoning in general) altogether. But this dilemma presupposes that inference must involve a taking-attitude. And if that presupposition is false, then this is a false dilemma. So the question is, then: what reasons are there to think that the taking condition is a necessary condition for inference? The type of cognitive process that Boghossian has in mind when he talks about inference is a conscious, person-level mental act. According to him, what underwrites the taking condition is that inference consists in “an attempt to arrive at a belief by figuring out what, in some suitably broad sense, is supported by other things one believes” (2014, p. 5). This is what sets inference apart from mere causation among doxastic states. That one must have such an aim in order to count as inferring (even in Boghossian’s sense) is controversial, however. As McHugh & Way (2016, p. 325) rightly point out, the aim of inference is better construed as simply the aim of finding out what is true. One may consciously deliberate about a certain issue and make an inference on the basis of one’s available reasons without so much as aiming to find out what those reasons give support to. One just wants to make up one’s mind about what is the case. E.g. the detective is not trying to decide whether John is the murderer is supported by John was at the scene of the crime, The victim had an affair with John’s wife, etc. The detective is just trying to find out whether John is the murderer. She then concludes that John is the murderer after all, and she does so on the basis of the evidence available to her. (The detective is not doing logic or confirmation theory, she is just doing a criminal investigation). Yet it is not clear what the detective is doing but performing an inference. Of course, one could weaken Boghossian’s claim about the aim of inference and say that the reasoner can be interpreted as someone who is trying to figure out what is supported by what she believes. But obviously that is just too weak to underwrite the taking condition. As it stands, Boghossian’s claim about the aim of inference is vague between stronger and weaker interpretations, and so it is not clearly true. And if the taking condition is supposed to be underwritten by that claim, then there better be something else to be said in support of the taking condition. (One might point out that arriving at the truth should not be taken to be the aim of reasoning in general, since one might perform suppositional reasoning with the aim of arriving at a necessary falsehood instead.3 But presumably what motivates one to try to derive a necessary falsehood from a supposition is to find out whether that supposition itself is necessarily false, in which case its negation would be necessarily true. If one in fact derives a necessary falsehood from one’s supposition, one can then accordingly infer that that supposition is false and its negation true, thereby accomplishing one’s goal.)

3 I thank an anonymous reviewer for this observation.

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5.1 Deduction and induction Boghossian offers two additional considerations in support of the taking condition. According to the first one, the taking condition allows us to distinguish between deductive and inductive inference. Presumably what this means is that, when a reasoner performs a deductive inference, she takes her conclusion to validly follow from her premises (or something along these lines), whereas when the reasoner performs an inductive inference, she takes her conclusion to be made probable by, or to better explain the truth of her premises. Now to the extent that there is indeed such a distinction between deductive and inductive inferences (it cuts inferential phenomena at its joints), it must be a distinction between two different types of cognitive processes. For we are not just talking about arguments in this case, but rather about something that goes on in the minds of agents like you and me (about the danger of conflation between argument and inference, and the possible mistake in the use of the term ‘deductive inference’, see Harman 1986, Ch. 2). But one does not need to make use of the taking condition in order to individuate those types; and it is not clear that this is the best way of doing so. E.g., one could individuate deductive and inductive inferences by means of their functional profiles: if one has deduced that ψ on the basis of one’s belief that ϕ, then learning that ψ is false will prompt one to revise one’s attitude toward ϕ (e.g. learning that There are no pollution-free cities will prompt one to revise one’s belief that Calgary is a pollution-free city); but if one has inferred that ψ on the basis of ϕ by means of an inductive process, then learning that ψ is false will not prompt one to revise one’s attitude toward ϕ (e.g. learning that Not all ravens are black will not prompt one to revise one’s belief that All raven’s that were observed so far were black). Alternatively (or in addition to that) one could say that, when the inferential process is deductive, the reasoner is at least as certain about ψ (the conclusion) as she is about ϕ (the premise); but when the inferential process is inductive, the reasoner is less certain (if only slightly so) about ψ than she is about ϕ. Both characterizations can be generalized to inferences with n premises in more or less natural ways, and further cognitive features may be added to those characterizations (e.g. number of inferential steps). These ways of drawing the relevant distinction do not by themselves imply that one’s deductive or inductive inferences are good deductive or inductive inferences. One may have the wrong functional profile towards a pair of premise- and conclusionbeliefs. E.g., suppose I have inferred that Mary is not going to make it to the meeting on the basis of my belief that If Mary took the train at 8am, she is going to make it to the meeting, and Mary did not take the train at 8pm; if I learn now that Mary is going to make it to the meeting, that will prompt me to revise my premise-belief—I have deduced the former from the latter. But of course this tie between my premisebelief and my conclusion-belief is unwarranted, given the alethic relations among those claims (all of the following can be true at the same time: Mary is going to make it to the meeting, Mary did not take the train at 8pm, If Mary took the train at 8pm then she is going to make it to the meeting). Still, the fact that my inference is a bad deduction does not imply that it was not a deduction at all.

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The point here is not that those are the ways of drawing the distinction between deductive and inductive inferences (or that those are the only ones that are extensionally correct). But they are strong alternatives to the one that makes use of the taking condition. And so it is not clear that a taking attitude is needed here. (McHugh & Way (2016, p. 326) also seek to undermine Boghossian’s use of the distinction between deduction and induction in support of the taking condition—but their criticism rests on the claim that that distinction is primarily a normative one, as opposed to a psychological one).

5.2 Impossible inferences The second argument Boghossian offers in support of the taking condition is as follows. Consider a person who believes Fermat’s Last Theorem (FLT) directly on the basis of her belief that the Peano axioms (PA) are true—she does so without going through any intervening deductions or using the testimony of reliable mathematicians. According to Boghossian, an explanation is needed why we have the ‘considerable feeling’ (2014, p. 6) that such a transition does not consist in an inference. The taking condition would provide the required explanation: an ordinary person like the one in the example could not take it that PA gives support to FLT. But this line of argument is problematic in two ways. First, it is not clear that the target doxastic transition is not an inference. Maybe what drives Boghossian’s and perhaps other people’s intuitions here is that that transition is not a good inference, or that it is not an instance of a good type of reasoning. Of course, that transition does preserve truth as a matter of necessity—but the epistemic goodness of a type of inference is not only a function of the fact that one of its conclusions follows from one of its premises (a type of inference has many tokens). Accordingly, Boghossian’s subject may be executing a bad type of inference that (luckily in this case) outputs a conclusion that follows from the premise. But it is an inference nonetheless. In inference, as much as anywhere else, one may get things right in the wrong way.4 Second, why could not the subject of Boghossian’s example take it that PA gives support to FLT? Using Boghossian’s very notion of taking, why could not she follow a rule in deriving FLT from PA, even though we would perhaps call it a defective rule? Maybe Boghossian thinks that it only counts as taking when the reasoner follows a non-defective rule—but then how can he make sense of the fact that there are bad inferences? So he must grant that the subject in question may be following a rule when she derives FLT from PA (in which cases she does take PA to give support to FLT according to Boghossian’s preferred interpretation of taking). So Boghossian’s second argument in support of the taking condition is equally inconclusive. All things considered, his case for the taking condition does not establish that it is a necessary condition for inference (here I join Wright (2014) and McHugh and Way (2016), even though we attack Boghossian’s proposal from different angles).

4 See Turri (2010, p. 317) for an example of a belief whose content is entailed by the reasons it is directly

based on, but where the subject’s mode of reasoning is epistemically bad.

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6 Conclusion To recap, there are three ways of trying to solve the regress problem of inference: (1) to require the reasoner to take her premises to give support to her conclusion, where the taking-attitude is not a belief-attitude, (2) to require the reasoner to believe that her premises give support to her conclusion, but in such a way that the content of that bridge-belief is not included in the reasoner’s pool of premises, or (3) to allow reasoning to be blind and not require any bridge-attitude at all. I have argued that some recent proposals of type (1) are unsatisfying in different ways, and so is Valaris’s recent defense proposal of type (2). Since I did not submit theories of type (3) to the same scrutiny that I submitted theories of types (1) and (2) to, however, the considerations I have made above do not yet warrant me to boldly conclude that (3) is the alternative we should opt for.5 There is nonetheless a strong prima facie case for that conclusion. There seems to be on the one hand a lack of good grounds for thinking that the taking condition is a necessary condition for inference; on the other hand, the interpretation according to which the taking attitude is a state of awareness/insight does not really solve the Carrollian regress problem (the contents of those states would also be included in the reasoner’s pool of premises or reasons), whereas the interpretation according to which it is an attitude of belief gives rise to other problems (as we saw in the case of Valaris’s account, we would exclude some unsophisticated reasoners from the class of reasoners, and we would also have troubles establishing the conditions under which the ruling out of possibilities amounts to bridge-beliefs). In the absence of versions of (1) and (2) that do better than the ones we have considered, it appears that we are left with (3). Perhaps that is one of lessons to be learned from Lewis Carroll’s ‘What the Tortoise Said to Achilles’: reasoning must be allowed to be blind—otherwise it won’t ever happen.6

References Balcerak Jackson, Magdalena, & Balcerak Jackson, Brendan. (2013). Reasoning as a source of justification. Philosophical Studies, 164(1), 113–126. Boghossian, Paul. (2003). Blind reasoning. Proceedings of the Aristotelian Society, Supplementary, 77, 115–248. Boghossian, Paul. (2014). What is inference? Philosophical Studies, 169(1), 1–18. BonJour, Laurence. (2014). In defense of the a priori. In M. Steup, J. Turri, & E. Sosa (Eds.), Contemporary debates in epistemology (2nd ed., pp. 177–184). Malden: Wiley. Carroll, Lewis. (1895). What the tortoise said to achilles. Mind, 4, 278. Dogramaci, Sinan. (2013). Intuitions for inferences. Philosophical Studies, 165(2), 371–399. Dogramaci, Sinan. (2016). Reasoning without blinders: A reply to valaris. Mind, 125(499), 889–893. Fumerton, Richard. (2015). What the internalist should say to the tortoise. Episteme, 12(2), 209–217. Harman, Gilbert. (1986). Change in view. Cambridge: MIT Press. McHugh, Conor, & Way, Jonathan. (2016). Against the taking condition. Philosophical Issues, 26(1), 314– 331. 5 I thank an anonymous reviewer for pointing that out to me. 6 See Dogramaci (2013) for an example of a blind-reasoning view that would seem to receive support from

the considerations I made here. Notice, however, that the way in which Dogramaci understands the notion of intuition (as a conscious temptation to believe something, which occurs also in perceptual experience) is very different from the way BonJour (2014) and other rationalists do.

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Synthese Railton, Peter. (2006). How to engage reason: The problem of regress. In R. Wallace, P. Pettit, S. Scheffler, & M. Smith (Eds.), Reason and value: Themes from the Moral philosophy of Joseph Raz (pp. 176–202). Oxford: Oxford University Press. Rumfitt, Ian. (2008). Knowledge by deduction. Grazer Philosophische Studien, 77, 61–84. Turri, John. (2010). On the relationship between propositional and doxastic justification. Philosophy and Phenomenological Research, 80(2), 312–326. Valaris, Markos. (2014). Reasoning and regress. Mind, 123(489), 101–127. Valaris, Markos. (2016a). Supposition and blindness. Mind, 125(499), 895–901. Valaris, M. (2016b). What reasoning might be. Synthese, 194(6), 2007–2024. doi:10.1007/s11229-0161034-z. Williamson, Timothy. (2007). The philosophy of philosophy. Malden: Blackwell Publishing. Wright, Crispin. (2014). Comment on Paul Boghossian’s “What is inference?”. Philosophical Studies, 169(1), 27–37.

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