CHAPTER FORTY-SEVEN Skepticism about A Priori Knowledge OTÁ VIO BUENO 1 INTRODUCTION A priori knowledge is, roughly, knowledge that does not depend on experience (except perhaps for whatever experience that may be needed to acquire the relevant concepts). This is a rough formulation since, when analyzing the notion of a priori knowledge, some care is needed to characterize the independence-from-experience condition so that what is taken to be known independently of experience (such as mathematical and logical results) turns out to be known a priori (according to the proposed analysis of a priori knowledge), and what is taken to be known based on experience, and thus is dependent on experience (such as particular physical traits of the world), is not known a priori (according to the relevant account). The challenge is then to secure that the proposed analysis is extensionally adequate. Two questions then emerge: (a) Can we have a priori knowledge? (b) Can we know that—or, at least, determine whether—we have such knowledge? Corresponding to these two questions, there are two forms of skepticism regarding the a priori : (aʹ ) One can provide arguments to the effect that, despite appearances to the contrary, one doesn’t have knowledge of the a priori , such as mathematical claims and claims about the validity of arguments. This is a priori skepticism (see Beebe 2011 ). Alternatively, (bʹ ) one can provide arguments to the effect that conceptual analyses (characterizations, defi nitions) of a priori knowledge (see, for instance, Kitcher 1980 , 2000 ; and, for an account of a priori justifi cation, Casullo 2003 ) are ultimately problematic. This is skepticism about a priori knowledge . And if it is unclear what a priori knowledge ultimately is, it is similarly unclear how we can determine whether we have any such knowledge. In this chapter, I will consider both forms of skepticism regarding the a priori , focusing in particular on skepticism about a priori knowledge. After all, by challenging the very concept of a priori knowledge, it seems to me that this form of skepticism is more basic. Given the centrality of a priori knowledge to so many cognitive endeavors (from mathematics and logic to philosophy), the presence of SSkepticism.indbkepticism.indb 668585 110/24/20170/24/2017 99:37:42:37:42 PPMM 686 SKEPTICISM these forms of skepticism highlights a central issue that needs to be addressed by those who claim to have the corresponding knowledge. 2 A PRIORI SKEPTICISM Most people think they know several mathematical claims, including simple arithmetical results, such as that 71 is the sum of 13 and 58. Most people think they also know whether a given conclusion follows logically from certain premises, such as that q follows logically from p and if p then q . Since such mathematical and logical results are arguably instances of what is known a priori , most people think they have a priori knowledge (although, unless they have some philosophical training, they are unlikely to describe that knowledge in these terms). A priori skepticism challenges such knowledge claims, and any others that are based on a priori considerations ( Beebe 2011 ). The form of the argument for it is the same as the familiar brain-in-a-vat or evil-demon arguments, in which, fi rst, a necessary condition for knowing something about the world is that one knows that one’s experiences are not being generated in a brain-in-a-vat scenario or by an evil demon. Support for this premise is provided by the closure principle, according to which (roughly) one knows what follows logically from things that are already known and that are established on the basis of that knowledge. Second, it turns out that one is unable to know that one is not in such skeptical scenarios. After all, one’s perceptual experiences are insensitive to such scenarios: one would believe that one is experiencing the world even if one weren’t (as the case would be if one were in such skeptical situations). The result is that one doesn’t know anything about the world. The argument for a priori skepticism is entirely analogous. In fact, it is an application of the familiar evil-demon argument to a priori knowledge claims, such as knowing the validity of modus ponens . As James Beebe notes: (P1 ) If I know that modus ponens is correct, then I know that my belief that modus ponens is correct is not based on faux intuitive experiences induced in me by a bumbling evil demon. (P 2 ) I don’t know that my belief that modus ponens is correct is not based on faux intuitive experiences induced in me by a bumbling evil demon. (C) Therefore, I don’t know that modus ponens is correct ( Beebe 2011 : 590; the numbering of the premises and the conclusion of this argument has been changed; of course, nothing hangs on this). Interestingly, the argument above does not depend on establishing the invalidity of modus ponens . Those who take this form of inference to be valid would insist on the impossibility of demonstrating the inference’s invalidity: on their view, any such attempt would inevitably lead one into a contradiction. Rather, the argument is meant to challenge one’s knowledge that modus ponens is valid (or correct) on the grounds that one’s belief in the validity of this inference could be based on a bumbling evil demon. Whether modus ponens is ultimately valid or not, one cannot know that it is valid. SSkepticism.indbkepticism.indb 668686 110/24/20170/24/2017 99:37:42:37:42 PPMM SKEPTICISM ABOUT A PRIORI KNOWLEDGE 687 There is also a different route to a priori skepticism ( Beebe 2011 : 593–594). It emerges from the consideration of alternative logical and mathematical practices, in which established mathematical and logical truths may not hold. This route surfaces from Ludwig Wittgenstein’s work (see Wittgenstein 1956 , as understood by Stroud 1965 ; for a discussion, see Beebe 2011 : 593–594). From the perspective of those who adopt the traditional view regarding logical and mathematical truths—according to which these truths are metaphysically necessary—one may not understand under what conditions mathematical and logical truths would be false. However, one’s inferential and calculation practices, which shape the relevant logical and mathematical results, could differ signifi cantly from the traditional ones. This would generate genuine alternatives to these practices, so that despite the agreement that modus ponens is valid, one would not agree that from p and if p then q , it would follow that q ; one could also follow the rule “adding 2” in such a way that after reaching 1,000, the rule continues as 1,004, 1,008, etc. It is ultimately a contingent fact that we developed the mathematical and logical concepts we currently have. Had the history of our species been different, we could have developed correspondingly different concepts. As Wittgenstein points out: I am not saying: if such-and-such facts of nature were different people would have different concepts (in the sense of a hypothesis). But: if anyone believes that certain concepts are absolutely the correct ones, and that having different ones would mean not realizing something that we realize—then let him imagine certain very general facts of nature to be different from what we are used to, and the formation of concepts different from the usual ones will become intelligible to him. ( Wittgenstein 1956 : I 141; quoted in Beebe 2011 : 594) It is possible then, in light of the contingency of the way in which mathematical and logical concepts have been developed, that these concepts could have evolved differently, thus resulting in different logical and mathematical practices (see also Stroud 1965 : 513, and Beebe 2011 : 594). As a result, one doesn’t know the correctness of one’s current mathematical and logical practices. It seems to me that a priori skepticism provides a signifi cant challenge to those who claim to know mathematical and logical results. But the challenge depends on the version of the challenge that is advanced. The second, contingency-based, formulation of this skeptical challenge seems to me more effective. The concern about the fi rst, brain-in-a-vat or evil-genius-based formulation, is that it invites a particular sort of Moorean response. One could easily complain that we have more reason to believe in the truth of the relevant mathematical and logical results than we have to believe in the truth of the second premise, (P2 ), of the argument for a priori skepticism, according to which we don’t know that our relevant logical or mathematical beliefs are not based on experiences induced by an evil demon (or that emerge from a brain-in-a-vat scenario). Of course, as a principled response to skepticism, this move blatantly begs the question, since it assumes that we know precisely those items that the skeptical argument challenges. From this point of view, the response is clearly ineffective. But one can think of it as expressing a particular attitude: one that dismisses the entire skeptical argument as being so general, so SSkepticism.indbkepticism.indb 668787 110/24/20170/24/2017 99:37:42:37:42 PPMM 688 SKEPTICISM detached from the particular mathematical and logical issues under consideration, that it verges on being irrelevant. The response reinforces the point that, due to its generality, there is very little in the fi rst argument for a priori skepticism that engages with the content of logical or mathematical beliefs per se. The fact that the argument is a particular instance of the usual brain-in-a-vat or evil-demon argument clearly illustrates this point.