Can We Be Skeptical About A Priori Knowledge?∗ Sherif Salem† Abstract In this paper, we present a dialectical argument for a priori skepticism (i.e. the thesis that it is possible to be skeptical about a priori knowledge). Our argument is based on two types of a priori skepticism: Cartesian and Kantian. The former questions the possibility of knowing a priori propositions (viz. logical and mathematical propositions), while the latter challenges the soundness of the proposed epistemic conditions for a priori knowledge. Then, we propose a specific understanding of a priori propositions that combines elements from inferential contextualism and logical conventionalism to offer a weak transcendental argument against a priori skepticism. 1 Introduction Audi (2008) classifies a priori propositions into at least four categories: 1) logical and mathematical propositions, 2) relational propositions between universals, 3) simple philosophical propositions (e.g. a belief is not a process), and 4) intuitive moral principles (e.g. killing is, prima facie, wrong). A priori knowledge is defined as knowledge of a priori propositions. In this essay, we take category (1) of Audi's classification as a paradigm case for a priori propositions. Hence, "a priori knowledge" is used to solely indicate knowledge of "logical and mathematical" propositions. That said, we can define our central concept: • A Priori Skepticism: is the thesis that it is possible to be skeptic about a priori knowledge. One can fairly say that a priori skepticism1 is not well investigated in skepticism studies, and this for some good reasons. One of these rationales is that it is difficult to conceive the possibility of a priori skepticism due to Putnam's centrality argument, which basically says that it is hard to doubt the laws of logic because they are presupposed by "so much of the activity of argument itself that it is no wonder that we cannot ∗I would like to thank Alessandro Topa, Robert McIntyre, Duncan Pritchard, Georg Meggle, Johannes Brandl, Hamid Vahid, Thomas Grundmann, Bernhard Weiss, Tamer Nawar, and other members of the Universities of Edinburgh, Cape Town, and Salzburg for their helpful comments and suggestions. †Email: gamalsalem.sherif@gmail.com 1This term is used as opposed to a posteriori skepticism, which is concerned with external-world skepticism. 1 envisage their being overthrown [. . .] by rational argument2". Some philosophers take the centrality argument as decisive against a priori skepticism3. Nevertheless, a priori skepticism can still be found, in one way or another, in the work of some influential twentieth-century philosophers like Von Neumann (1937a and b), Quine (1953), and Putnam (1979, 1983) who argue that some logical rules can be, revised for empirical considerations (e.g. Quantum mechanics' experimental results). Recently, and contra the aforementioned empirically motivated to a priori skepticism, Beebe (2011) presents a rational approach to a priori skepticism. He primarily argues that it is possible to construct a syllogistic argument- à la external-world skeptical arguments- that challenges the alleged priori knowledge4. In this paper, we propose a third approach to conceive a priori skepticism, namely from a dialectical perspective. But before proceeding, let us first discuss the notion of epistemic justification. Initially, the received (analytic) views about epistemic justification (e.g. reliabilism and evidentialism) are essentially individualistic ones. This led to the general understanding that epistemic disagreement has no skeptical significance whatsoever since social aspects are irrelevant to justification. Nonetheless, there is merit to the intuition that disagreement among epistemic peers5 around whether P should undermine their beliefs about their justifications for whether P . Yet, Lammenranta (2011) points out that the individualist account of justification cannot explain this intuition6 , and he suggests that we should conceive epistemic justification as a dialectical process. Wieland (2013) defines dialectical justification as follows: • Dialectical justification: S is (dialectically) justified in believing P only if S can defend P to (possible) opponents7in a non-question begging way. For Lammenranta, dialectical justification can explain our intuitions about why disagreement can lead to epistemic skepticism. The reason is that we are now required 2Putnam (1983, 110) 3Steup (2005) writes: "There is skepticism about knowledge of the external world, other minds, and the past. Skepticism about a priori propositions, however, is rarely pursued. Indeed, considering that knowledge of a priori propositions includes knowledge of the laws of logic, and more specifically, knowledge of an argument's validity, it is hard to see how a skeptical argument for anything could get off the ground without the prior assumption that knowledge of a priori propositions is indeed possible" (pp. 10–11) 4Our aim here is not to evaluate Beebe's argument as it needs a separate paper to do so. Yet, it is worth noting that Vahid (2013) argues that Beebe's claim does not pose any skeptical threat to first-order a priori knowledge, and that it undermines, at most, second-order a priori knowledge. 5Christensen (2007) and Lackey (2010) recognize two conditions for epistemic peers: evidential equality and cognitive equality. 6In short, he basically thinks that the individualist epistemic justification account cannot explain the significance of epistemic disagreement because the disagreeing parties will always have asymmetric access to the beliefs of their opponents, and hence will not be able to assess their credence. For instance, consider the case where there is perceptual disagreement between S1and S2 about whether P. Although both subjects acknowledge each other as epistemic peers, each subject has access only to his/her perceptual evidence, and hence cannot check the validity of the other's evidence. There are possible objections to this analysis, yet a full examination of Lammenranta's argument is beyond the scope of this paper. 7These opponents are taken to be epistemic peers. 2 to defend our beliefs against potential defeaters proposed by other subjects, and if we can't defend these beliefs, then they are not properly justified8.Given this dialectical understanding of epistemic justification, we can define the following notion of epistemic disagreement: • Dialectical disagreement: Two subjects (or more) are in a situation of dialectical disagreement on whether P if they cannot produce a dialectical justified belief for (or against) P. To avoid Putnam's centrality argument, we propose dialectical skepticism as a gateway to a priori skepticism. The way we approach this is by employing Conant's (2004) distinction between two types of skeptical questions: the Cartesian and the Kantian skeptical questions. The former is concerned with the knowledge of P , while the latter is concerned with the conditions of the knowledge of P . The Cartesian skeptic is worried about the possibility of knowing P , while the Kantian skeptic is worried about the possible grounds that can generate the legitimate claim to know that P 9. By applying Conant's distinction to a priori knowledge, we end up with two forms of a priori skepticism: Cartesian a priori skepticism, and Kantian a priori skepticism. The former type questions the possibility of knowing a priori propositions, while the latter challenges the soundness of the proposed epistemic conditions for a priori knowledge. In response to the a priori skeptic, we suggest, in section 4, a specific (epistemic and metaphysical) understanding of logic that blocks her skeptical arguments. According to this understanding, the epistemic nature of logic should be understood from the lens of epistemic contextualism, whereas the metaphysical nature of logic should be conceived in terms of logical conventionalism. We spend some time defending this position by arguing that the rules of logic can be dialectically justified if we apply (i) the epistemic framework of inferential contextualism and (ii) the metaphysical structure of logical conventionalism to the rules of logic10. We call this model, the contextual-conventionalist thesis about logic. In section 5, we argue that the contextual-conventionalist thesis can offer a weak transcendental solution to a priori skepticism in its two forms, the Cartesian and the Kantian. Finally, some terminal thoughts are provided in section 6. 8Williamson (2004; 2007, 238–41) rejects dialectical justification as it might lead to a global suspension of beliefs in case we met a radical skeptic who does not accept anything as cogent evidence. But this presumption is too strong since a radical skeptic will not be usually considered an epistemic peer in normal circumstances. 9If we take the case of Cartesian skepticism about language as an illustrative case, Conant asks: how do I know that my interpretation of a sign is the correct interpretation of the sign? For the skeptic, there will be always an epistemic gap between our interpretation of the sign, and what the sign really means. In that way, there is an extra-linguistic epistemic element (viz. an interpretation) that must be added to the string of physical signs in order to outweigh one of the large possibilities of linguistic meaning(s). The question now for the Cartesian skeptic is how can we be sure that the extra-linguistic epistemic element that we picked for P is the correct one. On the other hand, Kantian skepticism about language is concerned with a more fundamental question, namely: what are the necessary conditions for the existence of such extra-linguistic epistemic element(s) for a string of signs to have a meaning? 10We defend (ii) by providing a reflective equilibrium argument for implicit logical conventionalism. 3 2 Cartesian A Priori Skepticism If we go back to the domain of a posteriori skepticism, we notice that our perceptual experience is not epistemically superior to any radical skeptical hypothesis (e.g. the statement that "I am a brain-in-a-vat"). The reason is that the subject's quotidian experiences are subjectively indistinguishable from her experiences in the brain-in-a-vat case. In that sense, we can say that a subject's rational support for her perceptual beliefs is epistemically underdetermined by the skeptical hypothesis11. A similar dialectical argument can be constructed in the case of Cartesian a priori skepticism. Consider the Kripkean example of the quus function12. When we say that two subjects (or more) dialectically disagree on whether the "+" in "x+ y = z" means "plus" or "quus", the Cartesian skeptic will conclude that there exists no way to settle this dispute. In other words, the Cartesian skeptic will argue that, in case of dialectical disagreement, our knowledge of the true meaning of "+" is underdetermined by the multiplicity of potential interpretations of "+". This thesis can be formulated as follows: • The Epistemic Underdetermination Skeptical Thesis (EUST): When two (or more subjects) dialectically disagree on the interpretation of an a priori sentence P , then there exists no method to know which interpretation is the correct one. When thinking more about EUST, it becomes tempting to ask: how is Cartesian a priori skepticism possible at all? Is it the case that Cartesian a priori skepticism is merely an illusory form of epistemic disagreement over the interpretation of a given P? Or is it the case that these epistemic disagreements are more genuine and fundamental? In the next part, we defend a strong reading of EUST by proposing that Cartesian a priori skepticism is a fundamental epistemic problem that is rooted in a linguistic phenomenon, namely the open-texture of language. An argument for EUST can be traced to Friedrich Waismann's (1945) notion of open-texture. Originally, Waismann used open-texture to refute the doctrine of verificationism. For him, there exists no set of rules that can govern the use of empirical propositions in all possible situations. In other words, there exists nothing in the established use (or the non-linguistic facts) of an empirical proposition P that dictates the correct usage of P in future scenarios13. In a Possible Worlds notation, a proposition 11Pritchard (2016) 12Quss is defined as in Kripke (1982) 13Waismann's notion of open texture is a mere extension of Wittgenstein's ideas about rule-following for empirical propositions. Waismann (1945) writes: Suppose I have to verify a statement such as 'There is a cat next door'; suppose I go over to the next room, open the door, look into it and actually see a cat. Is this enough to prove my statement?. . .What. . . should I say when that creature later on grew to a gigantic size? Or if it showed some queer behavior usually not to be found with cats, say, if, under certain conditions it could be revived from death whereas normal cats could not? Shall I, in such a case, say that a new species has come into being? Or that it was a cat with extraordinary properties?. . . The fact that in many cases there is no such thing as a conclusive verification 4 P is open-textured if there exists at least one possible world where the application of P is indeterminate14. The phenomenon of open-texture is a serious epistemic problem disguised in a semantic form. After all, terms are introduced to be applied for specific objects, and to exclude other objects. Yet, Waismann argues that such simple requirement fails even for natural kind terms15 The relevant question now is: can logical/mathematical expressions be open-textured, too? After all, logical/mathematical expressions are precisely defined without any chance of ambiguity. Interestingly, Shapiro (2006) argues that this not the case. He gives many examples of mathematical and logical notions that we might take for granted as rigorously defined without ambiguity, and shows that our intuition is wrong. For example, the foundational concept of a "number" is a subject of philosophical dispute. Similarly, the elementary notion (at least in computational mathematics) of "computable function" is subject to open-texture, too. In set theory, George Boolos (1989) argues that the notion of a "set" in ZC is not unique; rather it combines a fuzzy mixture between two notions. Moving to logic, Shapiro rightly argues that logical connectives, if studied without explicit stipulations or conversational context, are subject to open-texture. Connectives like "and", "or", "there exists" are completely subject to open-ended interpretations according to differentiated contexts. One objection to the open-texture analysis of logical/mathematical propositions is that it is inconceivable for some terms like a "prime natural number" to be subject to novel interpretations. Truly, EUST does not imply that all logical/mathematical notions are subject to opentexture; yet it is a laborious task to find the a priori notions that are not subject to it. 3 Kantian A Priori Skepticism The Kantian a priori skeptical argument proceeds by asking: what are the epistemic conditions required for a proposition P in order to be a priori? The Kantian skeptic notices that the two classical criteria proposed, at least since Kant's time, are necessity and universality16. Yet, the Kantian skeptic sees that these two criteria fail to act as successful epistemic conditions for a priori knowledge. On one hand, necessity fails is connected to the fact that most of our empirical concepts are not delimited in all possible directions. (121–2) 14See Margalit (1979) for more discussion. 15"The notion of gold seems to be defined with absolute precision, say by the spectrum of gold with its characteristic lines. Now what would you say if a substance was discovered that looked like gold, satisfied all the chemical tests for gold, whilst it emitted a new sort of radiation? 'But such things do not happen.' Quite so; but they might happen, and that is enough to show that we can never exclude altogether the possibility of some unforeseen situation arising in which we shall have to modify our definition . . . In short, it is not possible to define a concept like gold with absolute precision; i.e., in such a way that every nook and cranny is blocked against entry of doubt. That is what is meant by the open texture of a concept." (Waismann 1945, 122–3) 16See for example, section B3 of Kant's Critique of Pure Reason. 5 as a condition mainly due to Kripke's (1971, 1980) convincing distinction between the nature of necessary propositions as belonging to the metaphysical realm, and the nature of a priori propositions as belonging to the epistemological realm. On the other hand, universality also fails in case of the existence of dialectical disagreement. To elaborate, note that universality can be interpreted from a reliabilist framework as suggested by Kitcher (1983). In that sense, a reliable process that produces universal a priori knowledge must satisfy the following conditions: i) it must be accessible independently of experience, ii) it must produce warranted beliefs, and (iii) it must produce true beliefs. If these conditions are satisfied, then a subject can assure the existence of a warranted process that generates true a priori knowledge, even in counterfactual situations. This account of universality rules out the possibility of having fallible or defeasible a priori knowledge. The backdrop of Kitcher's analysis of a priori knowledge can be cashed out in his unrevisability thesis (UT)17. • Unrevisability Thesis (UT): If subject S is justified in believing that P a priori, then P is (rationally) unrevisable in light of any future evidence18. Does the Kantian skeptic accept UT? The answer is no19 based on the following pessimistic inductive argument: • The Kantian Pessimistic Inductive Argument (KPIA): 1. At time t1, assume all priori propositions were considered to be unrevisable. 2. At time t2 > t1,some a priori propositions are found to be revisable. 3. Then by induction, some a priori propositions are going to be revisable in the future. KPIA's second premise can be defended based on Priest's (2014) distinction between three senses of the word 'Logic': logica docens , logica utens , and logica ens20. First, logica docens is logic as claimed by logicians (i.e. what logicians teach about logic in their textbooks). Second, logica utens is logic as practiced, for reasoning, by people. Finally, 17This position regarding the universality of a priori knowledge was also defended by Putnam (1983). 18Casullo (1988) 19Casullo (1988, 193) presents Mary's thought experiment to undermine UT. Suppose Mary is a well-trained student of logic who can discern between valid and invalid inferences. At time t, Mary is convinced that (a)" 'P → Q' entails '¬P → ¬Q' " is a valid inference. Nevertheless, after time t, Marry realized upon reflection that her belief was wrong, and she formed a new belief that (b) " 'P → Q' entails '¬Q → ¬P ' " instead. The question now is whether Mary's knowledge of (a) can be considered a priori? Casullo's response is yes. His argument is that (a) was justified by a reliable process despite the fact that (a) is false. The flaw of UT, for Casullo, is that it confuses between the strength and the nature of justification. So despite the fact that Mary's justification for (a) is based on an error, this is by itself does not rule out its a priority as it overlooks the "fact that revision can take place on the basis of a priori considerations. Thus, it is possible for Casullo to have a priori knowledge that this is based on a defeasible and/or self-correcting process. See also Field (1998) for a defense of the possibility of defeasible a priori claims. 20Given this classification, we are only interested in logica docens as it represents the epistemic aspect of logic as opposed to its practical or metaphysical aspects. 6 logica ens is logic in-itself (i.e. what is the real metaphysical notion of validity?, and so on). Priest maintains that it is not only possible for logica docens to be revised, but it was de facto revised21. Priest stresses that the process of revising logica docens was not a mere extension of logical systems over a continuum. For example, the Darapti – which is a valid Aristotelian syllogism – cannot be validated within first-order logic22. Moreover, it cannot be validated within first-order logic without debunking other principles of Aristotelian logic. In addition, other philosophers such as Birkhoff and von Neumann (1936), and Putnam (1979) argued that it is plausible to revise logical principles (or rules) due to empirical considerations. Another defense of KPIA's second premise can be found of Bueno and Colyvan (2004) adoption of a "theory change" model23 to explain changes in logical theories. For Bueno and Colyvan, the basic idea is that at any given point in time there are common core assumptions that are shared by the philosophical community, which can be represented in three groups: (i) shared logical theories (i.e. logical principles and rules), (ii) shared views about the aims of logic, and (iii) shared methodological principles (i.e. shared metalogical principles). Usually, the philosophical community shares at least one of these sets, which can be used to debate the other sets. This process definitely leads, at some point, to the revisability of logical rules. It is worth mentioning that the aforementioned defenses of KPIA can be generally understood as a product of dialectical disagreement. This is hard to conceive unless one accepts the dialogical nature of logic24. To sum up, if KPIA is true then the Kantian skeptic is in a strong position by deflating the available two meta-epistemic conditions for a priori knowledge: necessity and universality. 4 Rethinking A Priori Skepticism The aim of this section is to argue for a particular characterization of logic, which we call the contextual-conventional view of logic The basic idea is to propose an epistemological view of logic that is derived from inferential contextualism and combine it with a conventionalist metaphysical view of logic to open the possibility for a form of pluralism regarding the nature of the logical enterprise. 21"At any rate, one needs only a passing acquaintance with logic texts in the history of Western logic to see that the logica docens was quite different in the various periods. The differences between the contents of Aristotle's Analytics, Paul of Venice's Logica Magna, the Port Royale Logic, or the Art of Thinking, Kant's Jäsche Logik, and Hilbert and Ackermann's Principle's of Mathematical Logic would strike even the most casual observer. It is sometimes suggested that, periods of oblivion aside, the development of logic was cumulative. That is: something once accepted, was never rejected. Like the corresponding view in science, this is just plain false." (213) 22"But it might well be suggested that the adoption of classical logic did not revise Aristotelian logic in any interesting sense: Aristotelian logic was perfectly correct as far as it went; it was just incomplete. Classical logic simply extended it to a more complete theory. Such a suggestion would be false. It is a well-known fact, often ignored by philosophers (though not, perhaps, historians of philosophy) that Aristotelian logic is incompatible with classical logic in just the same way that non-Euclidean geometries are incompatible with Euclidean geometry." (2006, 164 -165) 23Developed first by Laudan (1984). 24A thesis that we advocate in section 4. 7 4.1 Inferential Contextualism In recent decades, contextualist approaches to epistemic problems have gained special prominence. Particularly, they have been used to target a posteriori skepticism. Yet, the term "contextualism" has been used as an umbrella term for a large group of views about the nature of knowledge (and epistemic justification). To put things loosely, the basic common thesis is that the truth-value of knowledge (and epistemic justification) ascription is context-dependent. Pritchard (2002) classifies epistemic contextual theories into two genres: The first one is semantic contextualism which is the view that truth-value of a proposition like "S knows that P " is dependent on some features of the conversational context in which such a proposition was uttered. The second genre is inferential contextualism as found in the work of Michael Williams (1991), which we are going to focus on for reasons described later25. Williams's version is characterized by three main features: 1) It is subject-based contextualism which means the standards that S should meet in order to know P are determined by the context of S ; 2) The context of S is mainly determined by its inferential structure (which in turn depends on S 's practical interests and his background knowledge); 3) It rejects the idea that epistemic standards can be anchored by a fixed scale that is context-independent. Hence, the difference between quotidian and skeptical contexts, according to inferential contextualism, does not lie in the different epistemic standards imposed by the skeptic on each of these contexts 26; rather, it lies in the subject matter that the skeptic is investigating. In the latter case, the skeptic is no longer studying ordinary knowledge, but knowledge as such27. In that way, inferential contextualism rejects the customary totality condition which states that all our beliefs can be rationally evaluated at once28. On the contrary, Williams thinks that for each domain of inquiry there are some "methodological necessities" which act as reference points for rationally evaluating our beliefs, but these methodological necessities are not themselves subject to rational evaluation29. If these methodological necessities shift from one epistemic context to another, then there are no epistemically prior methodological necessities, which is the case for Williams. What is interesting for us here is that Williams' understanding of inferential contextualism is based on a dialectical form, which Grundmann (2004) refers to as Williams' "default and challenge" model of justification and knowledge. This model can be reformulated as a sequential game between a proponent and an opponent in a given context with specified methodological necessities (MN): • The proponent is entitled to hold a belief p (which is consistent with the given 25As found in the work of David Lewis (1996), Stewart Cohen (1988), and Keith DeRose (1995). 26As claimed by semantic contextualism. 27In other words, "the skeptic doesn't just raise the standards of knowledge but completely changes the subject" (Brendel and Jäger 2004) 28Williams (1991, 90) 29Pritchard (2002) notes that Williams' thesis is explicitly based on the Wittgensteinian notion of hinge propositions. 8 MN) in case the opponent does not justifiably challenge it. • If the opponent challenges the validity of p, the proponent has to state the evidence that supports p (and rebuts the opponent's challenge). If not, the proponent loses his entitlement in believing p. Williams thinks that these MN set up the direction of inquiry in each context as they specify the inferential status of each belief/proposition in that context (i.e. is it a basic non-inferential belief/proposition or not?). So, for history scholars, for instance, one has to reject the Russellian hypothesis that earth came into existence five minutes ago and accept the authenticity of historical records as a methodological necessity for historical inquiry (which indicate that earth, surely, existed more than 5 minutes ago). If one starts accepting the Russellian hypothesis, then she is no longer engaged in the domain of inquiry called history; rather, she is doing epistemology. This kind of understanding of contextualism leads to a form of relativism about knowledge, which might end up assigning the same epistemological status to astronomy and to astrology. Yet, Williams does not accept this kind of relativistic implication as he states we should not think of "contexts of justification as insulated from external criticism30." The way he cashes out this thought is by requiring an externalist understanding of the conditions of justification to be in act. Thus, it is not enough for a belief p to be justified to remain dialectically unchallenged in the sequential game; it has to be reliably formed in an "objective" way. This is the way through which Williams refrains from the alleged relativistic conclusions of his inferential contextualism31. Williams' inferential contextualism can be applied to a priori knowledge as well. So, for instance, we can think of different inferential structures and methodological necessities (say, paraconsistent v.s. classical logical structures) where the truth-value of some logical propositions shifts when we move between contexts. Does this imply that all a priori inferential structures are equally (epistemically) justified? The answer is no. As there are inferential contexts that were formed in more dialectically reliable ways than others, and this is the subject of our next subsection. 4.2 Logical Conventionalism Conventionalism is, briefly speaking, the thesis that some truths (e.g. logical and mathematical truths) are true by convention or in virtue of meaning. This thesis gained momentum due to the support of logical positivists, especially Carnap (1934), but failed to keep its status after that. Logical conventionalism can be defined as follows: 30(Williams, 2001, p. 227). 31Grundmann (2004) argues that Williams anti-relativistic position clashes with his commitment to the epistemological anti-realistic nature of inferential contextualism. 9 • Logical Conventionalism: given a logical system L, for any logically true sentence α in L, our linguistic conventions C fully explain why α is true32. Two versions of logical conventionalism need to be distinguished. The first is explicit conventionalism where logical truths are roughly understood as a series of explicit linguistic stipulations concerning these truths. Quine (1936) presents a Carrollesque regress argument to show the implausibility of this form of conventionalism33. His criticism is generally accepted by many contemporary philosophers as a powerful argument against explicit conventionalism34. Notwithstanding, there is another version of logical conventionalism that Quine was aware of and also criticized, namely implicit conventionalism. The primary idea of implicit conventionalism is that logical truths can be fully explained by the implicitly followed rules governing the use of logical connectives. Quine also attacks this line of reasoning since we cannot distinguish between specific behaviors that act according to these implicit rules and those which do not. More specifically, Quine's first criticism is that we cannot infer any general implicit rule by mere observation as this allows for a large space of conventions that can explain the same set of rule-following behavior depending on how we conceive these conventions to be violated. A second issue for Quine is that implicit conventionalism risks being reduced to mere behavioristic statements that are firmly accepted, and hence conventionalism becomes an empty label with no explanatory power whatsoever. Despite Quine's criticisms, implicit conventionalism is alive and kicking 35, and here we propose another defense of implicit conventionalism that is motivated from a dialogical perspective36. Interestingly, historical logic was certainly tied to dialectical practices to the extent that Lloyd (1996) claims the emergence of the deductive method of logic was conditioned by the Greek sociocultural structure, especially their practice of debating37. To illustrate, Hintikka (1995, 1997) argues that Aristotle's ideas about logic were shaped by his ideas on dialectic which is, for Hintikka, a dialogical game in the strict sense (viz. starts with a status quo position, players can depart from the status quo position 32Warren (2016). 33Other arguments, which are different from the Quineian spirit, against logical conventionalism can be found in Yablo (1992), Boghossian (1996), and Sider (2003). See also Warren (2015) for a consistent defense of logical conventionalism against these attacks. 34For instance, Scott Soames (2005) writes: "This, in a nutshell, was one of the central arguments of Quine's paper, "Truth by Convention," . . . Although not fully appreciated right away, it eventually became a classic, and is now widely known for its powerful critique of the program of grounding a priori knowledge in knowledge of meaning" (p.265) Also, Paul Boghossian expresses the same thought: "In his classic early writings on analyticity in particular, in "Truth by Convention," "Two Dogmas of Empiricism," and "Carnap and Logical Truth" Quine showed that there can be no distinction between sentences that are true purely by virtue of their meaning and those that are not. In so doing, Quine devastated the philosophical programs that depend upon a notion of analyticityspecifically, the linguistic theory of necessary truth." (p.360) 35See Azzouni (2014) and Warren (2015) for an extensive defense of this position 36We do not aim here to lay down a full-blooded defense of logical conventionalism as it is a tremendous task that certainly goes beyond our limited scope. We just aim to sketch a brief strategy about how to conceive implicit conventionalism from a dialogical aspect. 37See also Castelnerac and Marion (2009) for more on this point. 10 by making rule-governed moves, etc38). This historical connection between logic and dialogical practices can also be found in other philosophical traditions like the Islamicate tradition39, and is also present in medieval logic40. Nevertheless, Novaes (2015) correctly points that this dialogical import of logic was forgotten (or rejected) due to the Cartesian discovery of subjective logic, which meant logic should be mainly thought of as normative for individual thinking and not for argumentation. Based on the previous historical analysis, and if we take the dialogical origins of logic seriously, then we can construct a dialectical story about the development of implicit logical conventionalism. The story frames implicit logical conventionalism as a process of reflective equilibrium where the following stages take place: • Stage 1: Let S be the set of all relevant subjects, P the set of all relevant logical propositions, and B sp the set of all initial beliefs of S about P . We can think of B sp as contextualized by exogenous conditions like history, language, culture, educational institutions, and others. Then, we have the n-tuple C (S , P , B sp) as the set of all conventional claims concerning B sp. • Stage 2: Let T be the set of all theoretical principals used to systematize B sp, and TB be the set of all background theories adopted by S when reasoning about T . Then, we have the n-tuple C (S , P , TB , T ) as the set of all conventional claims concerning T . • Stage 3: Probably, there will be a form of outer incoherence between C (S , P , B sp) and C (S , P , TB , T ), or even an inner incoherence in C (S , P , B sp) or in C (S , P , TB , T ). The goal of S is to follow a Maxmin strategy with respect to these outer/inner inconsistencies. • Stage 4: The final state resulting from this procedure is called Wide Reflective Equilibrium, WRE [C (S , P , B sp), C (S , P , TB , T )]. This process can be repeated in case of a new generated set B∗sp due to changes in the relevant exogenous conditions. If this argument works, then we have a plausible explanation (that avoids Quine's criticisms) for the emergence of implicit logical conventions, which is what we need to complete our argument against a priori skepticism. 4.3 Contextual-Conventionalism Now, we are going to compile inferential contextualism with logical conventionalism as two complementary theses regarding the nature of logic. We start by defining our main 38See Lorenzen and Lorenz (1978) for another formulation of these dialogical games. 39As found in Rahman and Iqbal (2018). 40Stump (1989). 11 notations: let the set of knowing subjects41 be S : s1, s2, . . . , sn, and the set of known logical propositions for subject si be P : p1, p2, . . . , pm. Similarly, we can define the set of all possible times as T : t1, t2 . . . , tl. Also, the set of all possible contexts is denoted by C = c1, c2, . . . , cv; note that C denotes only the contexts which are epistemically relevant to the knowing subject. Finally, we define the set of all possible conventions by Co = co1, co2, . . . , coy. Now take the ordered n-tuple K(si, pm, tl, cv, con) to denote that subject si knows proposition pm at time tl given a specified context cv and a specified convention con42. Given our framework, the last two parameters–cv and con–are the most decisive variables in judging the epistemic status of a logical proposition pm. By changing the context cv, the convention formed con might change, and consequently the epistemic status of pm might vary, too. To see this, contrast the utterance of the following two statements: • K(s1, p1, t1, c1, co1). • ¬K(s1, p1, t1, c2, co2). Given t1, c1 and co1, subject s1 knows p1. While given t1, c2 and co2, the same subject s1 does not know the same proposition p1. This synthesis between inferential contextualism (as an epistemological view of logic) and logical conventionalism (as a metaphysical view of logic) allows us to construct a pluralistic view about the nature of logic as a deductive inferential mode of reasoning. In that sense, we can have different Logics depending on the adopted conventions and the context of inference. As Shapiro (2014) puts it when defending logical pluralism: Whether we say that the logical terms have the same meaning, or different meanings, in the different structures or theories, depends on what is salient in a conversation comparing the structures or theories. For some purposes-in some conversational situations-it makes sense to say that the classical connectives and quantifiers have different meanings than their counterparts in intuitionistic, paraconsistent, quantum, etc. systems. In other situations, it makes sense to say that the meaning of the logical terminology is the same in the different systems. (128) 41Knowing subjects are treated in first person, and not as third person attributions. 42Similar descriptions can be used for other epistemic notions like 'justification'. In that case, take the ordered n-tuple J(si, pm, tl, cv , con) to denote that subject si is justified to belief proposition pm at time tl given a specified context cv and a specified convention con. 12 5 A Transcendental Argument against A Priori Skepticism In this section, we present a weak transcendental argument43 against a priori skepticism with its twofold structures: Cartesian and Kantian. Stern (2007) identifies two significant features of transcendental arguments: a) they have a self-evident starting point Y that the skeptic is expected to accept (e.g. that we have specific undeniable subjective experiences), and b) show that for Y to obtain there has to exist a necessary condition X , that is doubted by the skeptic, and therefore rebut the skeptical argument against X 44. We call this type of argument a strong transcendental argument. In contrast, we propose a weak transcendental argument as a plausible response to a priori skepticism. The weak version differs from the strong version in the following: a) The starting point Y is not self-evident, yet it is a conceivable view about Y that the skeptic can accept, and b) X is just a sufficient condition for Y to obtain. Granting this, let us proceed with the details of the argument by defining two types of contextual-conventionalism. Given a specific framework (e.g. a framework of propositions, a framework of real numbers, etc.), Carnap (1950) distinguishes between two classes of ontological questions: internal and external questions. Internal questions are those questions asked concerning the ontological status of some entities within a framework. Conversely, external questions are those asked concerning the ontological status of a framework as a whole. In a similar spirit, contextual-conventionalism can be divided into two general categories: internal and external contextual-conventions. The main difference between internal and external contextual-conventions is that in the former case the truth value of a specified P does not shift when changing the context (and fixing the language), while in the latter case the truth value of a specified P does not shift when changing the language itself. More specifically, • Internal contextual-convention: For any language L and a context cv, we say that there is an internal contextual-convention in L if it is the case that all theorems Tn in (L, c1) can be obtained, salva veritate, given another context (L, c2). As an example, we can see this by examining the notion of logical validity in classical logic. Beall and Restall (2006) generalize the Tarskian validity notion as follows: • Generalized Tarski Thesis: An argument is validx if and only if, in every casex in which the premises are true, so is the conclusion. 43Transcendental arguments as an anti-skeptical strategy have a long history in philosophy. Prominent examples include Aristotle's elenctic response to those who are skeptical of the law of non-contradiction, Descartes's argument for the cogito, Kant's transcendental deduction of the categories, Putnam's argument against external world skepticism, and Davidson' argument against skepticism of other minds. 44There is a huge debate which started by Stroud's (1968) criticism against the strategy of transcendental arguments. He basically claimed that all a transcendental argument can show is that we must believe that X is necessary for Y (or it appears to us that X is necessary for Y ), without having the necessity relation being actually true. Nevertheless, I will abstain from engaging in this debate here as the structure of the transcendental argument proposed here is different from the one that Stroud is attacking. 13 Then Beall and Restall argue that all results of classical logic (our L) can be obtained given two different cases of validity: one is the possible worlds case, the other is the Tarskian model case. We take Beall and Restall's notion of cases to a be an expression of different contexts c1 and c2. In that way, we can see that there is an internal contextualconvention in classical logic about the notion of validity between the possible worlds context and the Tarskian model context. On the contrary, a lack of internal convention can be found in Sambin (2011) discussion of the notion of "function" in constructive mathematics. Their argument is that we can find two inconsistent, yet correct understandings of functions in the language of constructive mathematics. The first is the computational understanding, which identifies a function as a series of computational instructions. The second is the geometric understanding, which identifies a function by its behavior 45. Therefore, we have a case in which two different contextual treatments of the notion of the function (i.e. the computational and the geometric) within the same language (of constructive mathematics) are lacking any internal convention about the truth-value of their output theorems. External contextual-conventions can be differently defined as follows: • External contextual-convention: For any languages L1, L2 and contexts c1, c2, we say that there is an external contextual-convention between L1 and L2 if it is the case that all theorems Tn in (L1, c1) can be obtained, salva veritate, given another language and context (L2, c2). External contextual-conventions can be thought of as metaconventions . In other words, we have an external contextual-convention in case we have a convention about how we should form our conventions in a diverse range of possible languages and contexts. As an example, Gödel (1969) and Tarski (1948) showed that any intuitionistic logic-based language (viz. (L1, c1)) can be translated into a classical language supplemented with modal operators (viz. (L2, c2)), in this case we have an external contextual-convention between (L1, c1) and (L2, c2). Conversely, an example of the lack of external contextualconventionalism can be found in a branch of mathematics called smooth infinitesimal analysis as compared to classical analysis. In smooth infinitesimal analysis there is an infinitesimal (number) nilsquare ε that behaves in a non-classical way46. This seeming contradiction can be worked out by relying on intuitionistic logic (i.e. denying the law of excluded middle47). By shifting the context from classical analysis to smooth infinitesimal analysis, there was a meaning-shift of concepts like "not", "for all" and even 45The two approaches are different in a significant way as the computational approach treats a version of the axiom of choice as a logical principle, while the geometric approach denies that possibility. 46On one hand, not every nilsquare is identical to zero: ¬(∀ε) (ε2 = 0→ ε = 0). On the other hand, it is not the case that there exists another nilsquare that is different from zero: (∀ε) (ε2 = 0→ (¬(ε 6= 0)). 47See Shapiro (2014) and Hellman (2006). 14 "identity". In that way, "there exists another nilsquare that is different from zero" does not follow from the case that "not every nilsquare is identical to zero". Given the aforementioned conceptual schemes, we can claim now the following: • Claim 1: We have a weak transcendental solution to Cartesian A Priori Skepticism in case we have an internal-contextual convention. • Claim 2: We have a weak transcendental solution to Kantian A Priori Skepticism in case we have an external-contextual convention. Concerning claim 1, recall that EUST resulted from a dialectical disagreement regarding the knowledge of the correct interpretation (or context) of P. Now given the proposed contextual-conventional understanding of logic, if we have an internal-contextual convention, then there is an agreement on the truth value of P . This means that a dialectical disagreement over the relevant interpretation (or context) of P can be settled by an internal-contextual convention, which is sufficient to refute the Cartesian skeptic. Also, recall that the essence of the Kantian skeptical argument is the impossibility of knowing the conditions of a priori knowledge. Thus, it is not possible to know whether P is a priori or not since the two proposed conditions (i.e. necessity and universality) for a priori knowledge fail. Put differently, what the Kantian skeptic claims is that there will always be a dialectical disagreement on the conditions of a priori knowledge. Now notice that if we have an external-contextual convention (as in claim 2), then we have an agreement on the truth value of P 48, and hence on the conditions required for P to be true. This means that we can construct a wide-ranging agreement on the conditions49 of the truth value of P, which is sufficient to counter the Kantian skeptic. 6 Agreeing to Disagree: The Philosophers' Case So far, we proposed a twofold skeptical problem, which we labeled a priori skepticism as it casts our concern over the epistemic validity of the whole deductive enterprise. All being well, contextual-conventionalism offers a weak transcendental solution to our epistemic angst. Interestingly, the core insight of the contextual-conventionalist solution was mentioned at the beginning of the conversation between Achilles and the tortoise in Carroll (1895): -"So you've got to the end of our race-course?" said the Tortoise. "Even though it does consist of an infinite series of distances? I thought some wiseacre or other had proved that the thing couldn't be done?" -"It can be done," said Achilles. "It has been done! Solvitur ambulando. You see the distances were constantly diminishing; and so-" (278) 48Even if we change the language and context used to express P. 49These conditions do not have a specific essence as they are subject to contextual-conventional formation. 15 Here, Achilles seems to stumble upon an easy rebuttal of the tortoise's theoretical reasoning: solvitur ambulando (viz. the problem of finishing the race is solved by walking). If both Achilles and the tortoise agree that the former succeeded in ending the race-course, then Achilles surpassed the challenge. Nevertheless, if the tortoise has a good reason to be convinced that Achilles did not finish the race, then Achilles' solviturambulando response will not work. To see this, we have to think of the conversation from a contextual-conventional perspective. Given the conversational context of Achilles and the tortoise, the disagreement stems from the absence of any convention between Achilles and the tortoise on what exactly does it mean to "finish the race". On one hand, the tortoise is seeking a theory-based solution. On the other hand, Achilles accepts an action-based solution. We call this: a situation of absence of an external contextualconvention. In this sense, a priori skepticism is the product of a genuine prior disagreement about the choice of a conventional language in a specified context. This is a more radical disagreement from modest disagreements about which methods/rules/axioms we should adopt within any specific framework. Shapiro (2014) thinks that this radical disagreement is a kind of intrinsic feature of our subjective epistemic structure when thinking about logic in general: There is no consensus concerning how logical terms, when used in the wild, get the meanings they have (if, indeed, they have determinate meanings). Indeed, there is no consensus on what meaning is, even when attention is focused on so called logical terminology. (127) In short, the way to eliminate a priori skepticism is by blocking any absence of internal and external contextual conventions. Whether this is a feasible goal or not is a different question beyond the scope of this paper. References Audi, Robert. "Skepticism about A Priori Justification: Self-Evidence, Defeasibility, and Cogito Propositions." In The Oxford Handbook of Skepticism, edited by John Greco. Oxford: Oxford University Press, 2008. Azzouni, Jody. "A Defense of Logical Conventionalism." In The Metaphysics of Logic, edited by Penelope Rush. Cambridge University Press, 2014. Beall, Jeffrey C., and Greg Restall. Logical pluralism. Oxford University Press, 2006. Beebe, James R. "A Priori Skepticism." Philosophy and Phenomenological Research 83, no. 3 (2011): 583-602. 16 Birkhoff, Garrett, and John Von Neumann. "The logic of quantum mechanics." Annals of Mathematics (1936): 823-843. Boghossian, Paul Artin. "Analyticity reconsidered." Noûs 30, no. 3 (1996): 360-391. BonJour, Laurence. Epistemology: Classic Problems and Contemporary Responses . Rowman & Littlefield Publishers, 2009. Boolos, George. "Iteration again." Philosophical Topics 17, no. 2 (1989): 5-21. Brendel, Elke, and Christoph Jäger. "Contextualist Approaches to Epistemology: Problems and Prospects." In Contextualisms in Epistemology , edited by Elke Brendel and Christoph Jäger. Dordrecht: Springer, 2004. Bueno, Otávio, and Mark Colyvan. "Logical Non-Apriorism and the Law of NonContradiction." In The Law of Non-Contradiction: New Philosophical Essays, edited by Graham Priest, Jeffrey C. Beall, and Bradley Armour-Garb. Oxford: Oxford University Press, 2004. Carnap, Rudolf. "Empiricism, Semantics, and Ontology." Revue Internationale de Philosophie 4, no. 11 (1950): 20-40. ---.The Logical Syntax of Language. Translated by A. Smeaton. London: Routledge and Kegan Paul, 1934. Castelnérac, Benoît, and Mathieu Marion. "Arguing for Inconsistency: Dialectical Games in the Academy." In Acts of Knowledge: History, Philosophy and Logic, edited by G. Primiero and S. Rahman. London, College Publication , 2009. Carroll, Lewis. "What the Tortoise said to Achilles." Mind 4, no. 14 (1895): 278-280 Casullo, Albert. "Revisability, Reliabilism, and A Priori Knowledge." Philosophy and Phenomenological Research 49, no. 2 (1988): 187-213. Cohen, Stewart. "How to be a Fallibilist." Philosophical Perspectives 2 (1988): 91-123. Conant, James. "Varieties of Scepticism." In Wittgenstein and Scepticism, edited by Denis McManus. Routledge, 2004. Christensen, David. "Epistemology of Disagreement: The Good News." Philosophical Review 116, no. 2, (2007): 187-217. DeRose, Keith. "Solving the Skeptical Problem." The Philosophical Review 104, no. 1 (1995): 1-52. Field, Hartry. "Epistemological Nonfactualism and the A Prioricity of Logic." Philosophical Studies 92 (1998): 1-24. 17 Gödel, Kurt. "An Interpretation of the Intuitionistic Sentential Logic." In The Philosophy of Mathematics , edited by J. Hintikka. Oxford, Oxford University Press, 1969. Grundmann, Thomas. "Inferential Contextualism, Epistemological Realism and Scepticism: Comments on Williams." Erkenntnis 61, no. 2-3 (2004): 345-352. Hellman, Geoffrey. "Mathematical Pluralism: The Case of Smooth Infinitesimal Analysis." Journal of Philosophical Logic 35, no. 6 (2006): 621-651. Hintikka, Jaakko. "Commentary on Allen." In Proceedings of the Boston Area Colloquium in Ancient Philosophy 11, no. 1, (1995): 206-215. ---. "What was Aristotle doing in his Early Logic, Anyway? A reply to Woods and Hansen." Synthese 113, no. 2 (1997): 241-249. Kant, Immanuel. Critique of Pure Reason. Translated by Norman Kemp Smith. London: MacMillan and Co., Limited, 1929. Kitcher, Philip. The Nature of Mathematical Knowledge. Oxford University Press on Demand, 1983. Kripke, Saul. "Identity and Necessity." Perspectives in the Philosophy of Language (1971): 93-126. ---. Naming and Necessity . Cambridge: MA: Harvard University Press, 1980. ---. Wittgenstein on Rules and Private Languages . Cambridge: MA: Harvard University Press, 1982. Lackey, John. "A Justificationist View of Disagreement's Epistemic Significance." In Social Epistemology, edited by Adrian Haddock, Alan Millar, and Duncan Pritchard. Oxford University Press, 2010. Lammenranta, Markus. "Skepticism and Disagreement." In Pyrrhonism in Ancient, Modern, and Contemporary Philosophy , edited by D. Machuca. Dordrecht: Springer, 2011. Laudan, Larry. Science and values: The Aims of Science and their Role in Scientific Debate. University of California Press, 1984. Lewis, David. "Elusive Knowledge." Australasian Journal of Philosophy 74, no. 4 (1996): 549-567. Lloyd, Geoffrey. "Science in Antiquity." In Modes of Thought: Explorations in Culture and Cognition, edited by D. Olson and N. Torrance. Cambridge: Cambridge University Press, 1996. 18 Lorenzen, Paul, and Kuno Lorenz. Dialogische Logik . Wissenschaftliche Buchgesellschaft, 1978. Margalit, Avishai. "Open Texture." In Meaning and Use, edited by Avishai Margalit. Springer Science+Business Media Dordrecht, 1979. Mates, Benson. The Skeptic Way: Sextus Empiricus's Outlines of Pyrrhonism. Oxford: Oxford University Press, 1996. Novaes, Catarina Dutilh. "A Dialogical, Multi-Agent Account of the Normativity of Logic." Dialectica 69, no. 4 (2015): 587-609. Priest, Graham."Revising Logic." In The Metaphysics of Logic, edited by P. Rush. Cambridge: Cambridge University Press, 2014. Pritchard, Duncan. "Two Forms of Epistemological Contextualism." Grazer Philosophische Studien 64 (2002): 19–55. ---. Epistemic Angst: Radical Skepticism and the Groundlessness of our Believing . Princeton University Press, 2016. Putnam, Hilary. "The Logic of Quantum Mechanics." In Mathematics, Matter and Method: Philosophical Papers 1, second edition. Cambridge: Cambridge University Press, 1979. ---. Philosophical Papers: Volume 3, Realism and Reason. Cambridge: Cambridge University Press, 1983. Quine, Willard van Orman. "Truth by Convention." In Readings in Philosophical Analysis , edited by H. Feigl and W. Sellars. NY: Appleton-Century-Crofts, Inc., 1936. ---. "Two Dogmas of Empiricism." In From a Logical Point of View , 20–46. Cambridge, Massachusetts: Harvard University Press, 1953. Rahman, Shahid, and Muhammad Iqbal. "Unfolding Parallel Reasoning in Islamic Jurisprudence: Epistemic and Dialectical Meaning in Abū Ish. āq al-Shırāzı's System of Co-Relational Inferences of the Occasioning Factor." Arabic Sciences and Philosophy 28, no. 1 (2018): 67-132. Sambin, Giovanni. "A Minimalist Foundation at Work." In Logic, Mathematics, Philosophy, Vintage Enthusiasms , edited by D. Devidi, M Hallett, and P. Clark. Dordrecht: Springer, 2011. Shapiro, Stewart. "Computability, Proof, and Open-texture." In Church's Thesis after 70 Years , edited by Adam Olszewski, Jan Woleński, and Robert Janusz. Frankfurt: Ontos Verlag, 2006. 19 ---. Varieties of Logic. Oxford: Oxford University Press, 2014. Sider, Theodore. "Reductive Theories of Modality." In The Oxford Handbook of Metaphysics , edited by M.J. Loux and D.W. Zimmerman. Oxford: Oxford University Press, 2003. Soames, Scott. Philosophical Analysis in the Twentieth Century: Volume I, The Dawn of Analysis . Princeton University Press, 2005. Stern, Robert. "Transcendental Arguments: A Plea for Modesty." Grazer Philosophische Studien 74 (2007): 143-161. Steup, Matthias. "Knowledge and Skepticism: Introduction." In Contemporary Debates in Epistemology , edited by M. Steup, and E. Sosa. Malden: Blackwell, 2005. Stroud, Barry. The Significance of Philosophical Skepticism. Oxford: Oxford University Press, 1984. ---. "Transcendental Arguments." The Journal of Philosophy 65, no. 9 (1968): 241256. Stump, Eleonore. Dialectic and its Place in the Development of Medieval Logic. Cornell University Press, 1989. Vahid, Hamid. "Skepticism, A Priori Skepticism, and the Possibility of Error." International Journal for the Study of Skepticism 3, no. 4 (2013): 235-252. von Neumann, John. "On Alternative Systems of Logics." In Manuscript, von Neumann Archives , Library of Congress, Washington, DC. 1937a. ---. "Quantum Logics (Strict-and Probability-Logics)." In Unfinished Manuscript, John von Neumann Archive, Libarary of Congress, Washington, DC, reviewed by AH Taub in: von Neumann (1962/IV), 195-197. 1937b. Waismann, Friedrich. "Verifiability." Proceedings of the Aristotelian Society , Supplementary Volume 19 (1945); reprinted in Logic and Language, edited by Antony Flew. Oxford: Basil Blackwell, 1968. Warren, Jared. "The Possibility of Truth by Convention." The Philosophical Quarterly 65, no. 258 (2015): 84-93. ---. "Revisiting Quine on Truth by Convention." Journal of Philosophical Logic 46, no. 2 (2016): 119-139. Wieland, Jan . "Is Justification Dialectical?." International Journal for the Study of Skepticism 3, no. 3 (2013): 182-201. 20 Williams, Miachel. Unnatural Doubts: Epistemological Realism and the Basis of Scepticism. Oxford: Basil Blackwell, 1991. ---. Problems of Knowledge: A Critical Introduction to Epistemology . Oxford: Oxford University Press, 2001. Williamson, Timothy. "Philosophical 'Intuitions' and Skepticism about Judgment." Dialectica , no.58 (2004): 109–53. ---. The Philosophy of Philosophy . Oxford: Blackwell. Wright, Crispin. "Scepticism and Dreaming: Imploding the Demon." Mind 100, no. 1 (1991): 87-116. Yablo, Stephen. "Review of Alan Sidelle, Necessity, Essence, and Individuation." Philosophical Review 101, no. 4 (1992): 878-881.