The Counterexample Method and Armchair Philosophy Peyman Pourghannad Davood Hosseini Tarbiat Modares University Abstract. According to a bedrock assumption in the current methodology of armchair philosophy, we may refute a theory aiming at analyzing a concept by providing a counterexample in which it intuitively seems that a hypothetical or real situation does not fit with what the theory implies. In this paper, we shall argue that this assumption is at most either untenable or otherwise useless in bringing about what is commonly expected from it. 0. Introduction According to a bedrock assumption in the current methodology of armchair philosophy, we may refute a theory aiming at analyzing a concept by providing a counterexample in which it intuitively seems that a hypothetical or real case does not fit with what the theory implies. In this paper, we shall argue that this assumption is, at most, either untenable or otherwise useless in bringing about what is commonly expected from it. This paper is not going to assert anything affirmatively about this method. We deliberately restricted ourselves to disprove a widely-accepted idea around the role of the counterexample method in armchair philosophy without going further to discuss what other functions the counterexample method may alternatively have. (Before starting the main discussion, it is worth contemplating a methodological point relevant to this paper, which can hardly be overemphasized. We, authors, do acknowledge that the conclusion of the main argument of this paper, if plausible, denies a widely accepted principle of philosophy methodology. However, no compelling counterargument against this paper may essentially appeal to the fact that a great amount of philosophical practices is at odds with the conclusion of the argument. Generally speaking, to undermine a theory or argument by appealing to what allegedly happens in an area, rather than what epistemically and justifiedly ought to happen or what actually happens there, from a methodological point of view, is just a begging the question against skepticism about the area. In fact, a methodologically plausible objection against our argument must be premise-sensitive rather than conclusion-sensitive. The latter sort is of little evidential interest, as it merely trivially repeats the negation of the conclusion as an objection to the argument; while the former takes pains to undermine the argument by committing itself to rationally question and refute a premise; and probably bears plausibility. Moreover, if anyone objects to this argument on the ground that philosophers apply the counterexample method extensively, or that such and such premises of our argument lead to a conclusion inconsistent with what supposedly happens within philosophy community, or that there are such and such (merely logically) possible alternatives to our premises or conclusion, we are happy for one read what we said, but we are sad because of hearing from the critic nothing beyond his or her mere disagreement expression.) First, suppose we have a target theory T that analyzes the concept C as follows: T: x is an instance of C if and only if x satisfies conditions K1, K2, ... Next, suppose it is asserted that we have found a good counterexample against T. The critic attempts to challenge the theory by describing a case e in which it intuitively seems that what has been described satisfies all Ks but not C (or vice versa).1 This provides the critic with a counterexample E against the target theory: 1 This qualification will be dropped in the following, of course without loss of generality. E: e satisfies all Kis, yet it is not an instance of C2. That is a widespread general form of undermining philosophical theories whose paradigmatic instance is Gettier's proposed counterexamples (Gettier, 1963). In his paper, Gettier first (re)formulates a theory of knowledge according to which to know that P is to have a justified true belief that P ( henceforth we call it "JTB-theory"); and in order to undermine it, he constructs hypothetical scenarios in which intuitively the protagonist satisfies the three conditions above, though he lacks knowledge3. 1. Epistemic and Semantic Requirements for the Method Concerning this pattern, there are two clearly necessary requirements, one epistemic and the other semantic, for the validity of such counterexamples: (1) The philosophical intuition must be a justifiable or reliable source of evidence; and more significantly (2) the predicate "C" in E must refer to a concept, say Ce; otherwise E would not express an evidence at all. 1.1. Semantic Requirement Let us concentrate first on the semantic demand. Suppose a critic of T, intuits that e although satisfies all Kis, is not an instance of C. The critic truly intuits this proposition only if he considers relevant features of the case e and possesses the concept Ce. Now we may ask what is the concept possessed4 by the critic, Ce, which is designated by the predicate 2 Goldman (2007) and Goldman et al. (1998) claims this form as the general form of intuitive evidence in philosophical analysis. To my knowledge, no one explicitly has challenged this form so far. Although one may find this form uneasily applicable to particular cases especially in philosophy of language, I assume that all singular evidence in philosophy more or less straightforwardly reducible to this from. 3 We merely used Gettier's cases as example throughout this paper. We did so because (1) it is widely taken as a successful attempt to undermine a theory; and (2) it is widely taken as a paradigmic instance of using intuitive counterexamples in philosophy. However, the conclusion of this paper can be extended more or less straightforwardly to many other instances such as Chalmers' zombie argument (Chalmers, 1996) or Cohen's lottery case (1988). 4 The notion "concept possession" is a term originated from Bealer's works on intuition and a priori knowledge. We will focus on this notion as we proceed. "C" in E? Is it the same concept as designated by "C" in T? Regarding this question, we face a dilemma: either "C" refers equivocally to C, that is to say, the concepts designated by "C" in the theory is different from the concept possessed by the critic as he intuits E, or they are identical. First, suppose the concept of the critic constituting his evidence is different from the concept designated in the theory. In such a case, the evidence, even if true, does not refute the theory, simply because the critic's evidence involves possessing a concept about which the proposed theory asserts nothing. To illustrate this possibility, imagine that a critic, who is fully informed about the hypothetical cases constructed by Gettier's paper intuits that "the case described in the paper is not an instance of knowledge, though is an instance of a justified true belief." If "knowledge" here refers not to the concept Knowledge that is designated by "knowledge" in the JTB-theory, but for example to Knowledge*, then clearly the proposed evidence, even if true, does not refute the theory, because the JTB-theory does not assert anything about the concept of Knowledge*; the theory is supposed to analyze Knowledge rather than Knowledge*. Second, suppose the critic's concept is the same as the concept designated in the theory. That is to say, "C" occurred in theory and evidence refers unequivocally. For example, it is widely held by philosophers that as one reflects on the Gettier's scenarios, one intuits that the cases described do not instantiate the very concept that the JTB-theory aims to analyze. Hence, according to the critic, the JTB-theory was supposed to analyze the concept Knowledge designated by the general term "knowledge" (or the verb "know)"5; and the JTB-theory's proposed analysis is to identify Knowledge with Justified-true-belief. But afterward, the critic, by reflecting on the Gettier's scenarios, comes to the belief that JTB-theory fails to capture the concept designated by "knowledge" because he thinks, the hypothetical protagonist has a justified true belief but, contrary to the JTB-theory's 5 It seems clear that we use the general term "knowledge" just to identify the concept involved, that is the concept referred to by the term. We are not committed to the idea that to have a concept such as knowledge, it is necessary to apply its corresponding term in natural language. We return to this issue in short. proposal, does not present an instance of the concept of Knowledge which is designated in natural language by "knowledge". What already mentioned was a methodic doctrine widely accepted by many, but under careful scrutiny, its hidden implausibility may be revealed. As cited before, the critic has good counterexample against T only if he has already possessed the analysandum concept, or at least possesses it at the moment of intuiting E. But if so, a question immediately arises: What epistemic role is the counterexample expected to play then? If the critic already possesses the analysandum concept, then why on earth does he need the alleged counterexample at all in order to discover that the theory is not true? In other words, the critic acknowledges the falsity of the theory as merely upon understanding the theory and possessing the analysandum concept. The moment one understands the false theory, by comparing the analysis proposed by the false target theory with what was already possessed by him as the concept C, one can readily and justifiedly conclude that what theory proposes as the true analysis of the analysandum C, in fact, fails to capture the very same concept already designated by the predicate "C". Particularly, if the reader of the Gettier's cases has already possessed the concept of Knowledge as designated by "knowledge" in natural language, then having been sufficiently informed of the JTB-theory, he can compare the compound concept of Justified-true-belief suggested by the JTB-theory with the already-possessed concept of Knowledge to determine whether the JTB-theory's account is the true one, that is to say whether knowledge = justified true belief. In such a case, therefore, determination of the falsity of the theory occurs needlessly of essential and genuine cognitive reliance on the counterexamples provided by Gettier's cases. Moore's argument as to why true analysis of a concept is not anything beyond a trivial identity concerns the situation just mentioned. Briefly speaking, he maintains that regarding the conceptual identity C = C*, either "C" and "C*" mean the same in which case the identity is trivial or they do not mean the same in which case the identity is not true at all. However, it may be claimed that the preceding argument does not exhaust all possibilities. Particularly, an advocator may claim that it is consistent that one possesses the concept of Knowledge and fully understands the JTB-theory while he is not able to correctly and justifiedly decide, independently of intuitive counterexamples, whether the possessed concept of Knowledge is the same as the theory's proposal, that is Justified-truebelief. In other words, it is possible, therefore, that not having considered Gettier's cases, one, who possesses the concept of Knowledge, is not able to correctly decide whether or not the concept-identity-proposition "Knowledge = Justified true belief" is true. Such a circumstance occurs, the advocator says, when for example the critic possesses the concept of knowledge inexplicitly. However, the advocator continues, one may still justifiedly intuit that the Gettier's cases are not instances of knowledge, though one would not able to correctly decide on the truth value of concept-identity proposition "Knowledge = Justified true belief" merely in virtue of possessing the concept of Knowledge plus understanding the JTB-theory. We may reply by saying that it is embodied in the notion of "concept possession" that if one cannot correctly intuit whether concept-identity-proposition involving the concept C, such as "C = F", is true, then he does not possess the concept C. According to this response, by definition, concept possession entails somehow correct decision on truthvalues of such concept-identities. As an instance of a definition of "concept possession", we may refer to Bealer's account. Bealer isolates two senses in which a subject is said to possess a concept: First, one possesses a concept at least nominally iff the subject has a propositional attitude toward some propositions which contain the concept. In this sense, concept possession is compatible with incomplete understanding of the concept or misunderstanding a concept such as Burge's (1979) case (Bealer 1999, p. 37). But he, as we assume throughout this paper, acknowledges that in natural language by "concept possession" we mean a much stronger sense. He calls the stronger sense "determinate concept possession"(Bealer 1999, p. 38). According to him "X determinately possesses a given concept iff, for associated test property-identities p: x would have intuitions which imply that p is true iff p is true." (Bealer 1999, p. 41; Bealer 1998, p. 223-230) However, it is not clear how to analyze "imply" in Bealer's account. By the way, at least one of his examples suggests that we may interpret it as support: Suppose a woman, x, determinately possesses the concept multigon; and suppose that the property of being a multigon = property of being a closed straight-sided plane figure. According to this definition "X determinately possesses the concept of being a multigon iff: x would have the intuition that it is possible for a triangle or a rectangle to be a multigon iff it is true that it is possible for a triangle or a rectangle to be a multigon." (ibid, p. 41) Here x's intuition that it is possible for a triangle or a rectangle to be a multigon seems to support the concept-identity multigon = being a closed straight-sided plane figure. But, contrary to the initial assumption, it seems dubious that x is said to possess the concept determinately, since her intuition that it is possible for a triangle or a rectangle to be a multigon, indeed, also implies many other clearly false conceptidentities, namely multigon = being a figure made of more than two lines. In other words, the concept-identity implied is underdetermined by the intuitive evidence. Therefore it is not straightforwardly answered which identity, among mutually exclusive concept-identity, implied by the intuition. It seems the problem arises due to the fact that Bealer's account of concept possession is not strong enough, for it is consistent with inability to recognize true and only true concept-identities involving the concept in question. As the account suggests it is sufficient for possessing the concept to have intuition implying the true conceptidentities, which is much weaker a condition than to grasp the implied identity "multigon = being a closed straight-sided plane figure" itself. Thus, it seems we require a much stronger definition of the notion. We are not to propose another account for the notion; rather, for our discussion, suffice it to mention the necessary condition discussed above. That is as follows: (CP) X (determinately) possesses concept C only if x would have true intuitions which presuppose that concept-identities in the form of C = F is true iff C = F is true6. To illustrate this, we can say, to have true and only true intuitions which presuppose that the concept-identity (property-identity) "Knowledge = Justified true belief" is false is necessary for determinately possessing the concept of Knowledge. What is at issue for us is that, as CP also implies, to (determinately) possess a concept it is necessary to be able to have correct intuitions which constitutively presupposes the relevant concept-identities. Here we acknowledge that presupposition is not a precisely-defined relation, but nevertheless, it adequately captures what we need for further discussions. But it is worth giving a relatively precise definition for the relation. It might be said: X's intuition that P presupposes Q iff X's intuition that P is based upon the assumption that Q is true (or to assume Q is cognitively and essentially prior to Pintuitions). Therefore up to now, we have seen that the having an intuitive counterexample against a theory requires that (1) "C" in both evidential proposition E and theory refers unequivocally to the concept C, the concept in question, since otherwise the evidence, at best, would be irrelevant to the assessing the target theory; (2) C is possessed by the subject determinately enough; and (3) determinate concept possession entails true intuitions which presupposes that the concept-identities are true. (Also throughout this paper by "concept possession" we mean the stronger sense of it which is incompatible with misunderstanding, that is to say, using Bealer's terminology, by "concept possession" we actually mean "determinate concept possession".) 6 However, We leave it open whether or not this account truly capture the sufficient condition for determinate concept possession. 1.2. Epistemic Requirement Now let us return to the second requirement, that is, the epistemic requirement. If intuition is to be a reliable or justifiable source of evidence, then one necessary condition for the subject who intuits on a case is that the subject possesses the concept in question. This requirement seems uncontroversial. It seems that one who is to reliably and intuitively judge cases had to already possess the concept in question. If not so, we may intelligibly ask based on what ground does one intuit that a case e is (not) an instance of C and not otherwise? Clearly, having been fully informed of the case, though necessary, is not sufficient for reliability of case-intuition. Rather, besides the satisfying requirement discussed above and being fully informed of the relevant properties of the case intuited, one has to possess, or using Bealer's terminology "determinately possess", the concept about which he is making intuitive judgment. In considering a case, we should already know of what concept the case allegedly is (not) an instance. Otherwise, intuitions on particular cases, either hypothetical or real, would be baseless, and thereby unreliable and probably flawed, since there would be no criterion to say which properties of the case are (ir)relevant to the instantiation of the concept under discussion. The truth is that in virtue of possessing the concept we know which property of the case is (ir)relevant to the instantiation of the concept. Therefore, we may formulate this requirement as follows: (JS) X's Intuition on particular cases involving the concept C is a reliable source of evidence only if X possesses C. Moreover, from JS and CP it follows that one's intuition on particular cases involving the concept C is a reliable source of evidence only if one would have true intuitions presupposing corresponding concept-identities. Thus, so far, the moral is that to possess a concept it is necessary to have the true supporting concept-identity proposition; otherwise, our intuitions on the case would be unreliable. 2. Objections and Clarifications 2.1. Sarch's Objection to CP Against CP, we may highlight Sarch (2010) argument based on the possibility of genuine conflict on a wide range of cases. Accordingly, if CP were true, then it would be impossible for there to be genuine conflict on intuitions on particular cases between two people who possess the very same concept. The reason is that if two people both possess the very same concept, then according to the above-mentioned condition, they both have true intuitions presupposing that the corresponding identities are true (false), if true (false); and thereby they apply the same concept-identities to all relevant particular cases. So, the resultant intuitive judgments on a wide range of particular cases would be the same, assuming that both people are fully informed about the cases. According to him, for example, even a much weaker account such as Bealer's entails that if a person with Kantian morality and a person with Utilitarian morality both possess the very same concept of Moral Rightness, they would not disagree on a wide range of particular moral cases, since they both agree on the underlying concept-identities. But, he objects, "it clearly does seem possible for two people to determinately possess the same concept of moral rightness while in ideal cognitive conditions and still have intuitions that genuinely conflict on a wide range of particular cases." (p. 469) This possibility entails that it is possible for two people to possess the same concept while at least one of them intuits incorrectly in some particular cases. But if we take this possibility seriously, we are left with a mystery: How may two people both possess a concept at all in a way that is compatible with genuine conflict on intuitions on some instances of the concept? If the first possesses the concept in question as the second does, then what cognitive diversity prevents either one from correctly intuiting on relevant particular cases at all, provided that they both are also fully informed of the case? If we take this objection seriously, it is left unanswerable how and why these two genuinely disagree on a wide range of cases, despite the facts that they possess (determinately, using Bealer's terminology) the very same concept and that they captured the relevant features of the cases in question. Despite Sarch, it seems the natural explanation for conflict on intuitions on particular cases is that the more diverse intuitions the two people have on particular cases, the more difference is there between the two people regarding possession of the concept in question. Wide range of disagreement is much more significant than Sarch supposes to be: It is a symptom of difference between the concepts possessed by the two, or it indicates that at least one of them does not possess the concept as determinately as the other does, assuming of course, that both sides have fully understood the controversial cases. We see no explanation for genuine conflict on particular cases as straightforward as the one given above. Appealing to maneuvers such as inability to apply the possessed concept to particular cases sounds more like a disappointing ad hoc attempt, rather than a unifying and genuine explanation for apparent disagreement. Unless there appears a good explanation, which it is not clear to us what it can be, it is more plausible to adhere to the conclusion that conflicting subjects do not possess the very same concept. 2.2. In Support of CP and JS In this sub-section, we are going to provide some further support for the necessary condition for concept possession and reliability of intuition as mentioned in CP and JS. 2.2.1. In what follows CP and JS are illustrated and supported more through examples in which to intuit justifiably on particular cases we see first, as JS implies, it is necessary to possess the corresponding concept; and moreover to possess the concept, as CP implies, it is necessary to presuppose the corresponding concept-identities. (1) Suppose someone justifiedly intuits that 6 is an even number. We may ask "In virtue of what does he justifiedly intuit this singular proposition?" Partly in virtue of understanding the concepts constituting the proposition among which is the concept Evenness. To justifiedly judge that 6 is an even number, it is necessary to know that Evenness = Being-divisibleby-2. It seems too odd to claim that one may justifiedly or reliably judge on evenness of many even numbers without possessing that the concept of Evenness is identical to the concept of Being-divisibleby-2. Clearly facing the question why to put 6 but not 5 under the category of even numbers, the natural (not artificial) response would be "because being an even number is just being divisible by 2 and 6 but not 5 possesses the property of being divisible by 2; and thereby 6 but not 5 is an even number." A crucial point, however, is that knowing that Evenness is identical to Divisibility-by-2 does not necessitate being able to utter the corresponding concept-identity-sentence. In other words, it is one thing to understand and intuit the proposition that 6 is an even number as presupposing that Evenness = Being-divisibleby-2, and it is another to have the disposition or to be able to utter the sentence "Evenness = Being-divisibleby-2" as required. One may grasp the proposition involving the concept Evenness while he does not know to which concept the term "even" refers (this caveat also applies to subsequent examples). (2) As another example, let us take another look at Bealer's example of multigon: A woman introduces the term "multigon"7 and applies it to various closed plane figures while she possesses the concept of Multigon. Suppose that either multigon = being a closed straight-sided plane figure, or multigon = being a closed straight-sided plane figure with five or more sides. (Bealer 1999, p. 39). Considering the question whether a given triangle is a multigon, she would have intuition that the triangle is a multigon only if he had already introduced the term "multigon" so that being a multigon = being a closed straight-sided plane figure; but would have intuition that triangle is not a multigon only if for example multigon = being a closed straight-sided plane figure with five or more sides. Again as mentioned in the previous example, she may fully understand the term and has a definite concept of Multigon corresponding to the term while she is not well-prepared to explicate or verbalize the corresponding concept-identity statement 7 "Multigon" is the hypothetical terms used by Bealer as the counterfactual counterpart for "polygon". The definition referred in the text is adapted from Webster. (3) A person, upon mentally constructing one of Gettier's cases, intuits the case is not an instance of Knowledge. A natural account for her intuitive judgment, we think, is to say that she intuits so partly because she understands the term "knowledge" so that Knowledge ≠ Justified-true-belief. In a counterfactual situation, if she had, no matter for which reason, taken for granted that Knowledge = Justified-true-belief, she would have, upon fully understanding Gettier's hypothetical cases, intuited otherwise. Essentially, there is no fundamental difference between the three examples above. Each example contains intuition on a particular case and a supporting concept-identity. Common among all three examples is that justified particular intuition involves possessing the corresponding concept (Evenness, Multigon, Knowledge) and the latter involves presupposition of a concept-identity-proposition. Therefore, we see that only by satisfying JS and CP the subject's intuitions on relevant particular cases are deemed justified. Of course, we do admit that in philosophical practice, as in the last example, the necessity of the presence of the concept-identity in the background of intuitive-philosophical judgment is not as obvious and as clear as in the mathematical cases (otherwise the present paper would be totally redundant!). That we may readily admit that in the mathematical examples above concept-identities support particular-case-intuitions while we are not so sure in the epistemological case, can be explained away by appealing to the fact that concepts in mathematics, or at least basic and simple ones such as "polygon" (or its counterpart "multigon" in Bealer's scenario) and "evenness", are considerably more definite than philosophical concept such as Knowledge, Causation etc. and thereby such mathematical concepts are relatively well-defined and well-phrased. To possess the concept of Polygon, one has to possess relatively definite concepts such as Closed, Straight-sided and Plane-figure as normally understood; however to possess the concept of Knowledge involves possessing at least the concepts of Belief, Truth, and Justification, clearly none of which is as clear as mathematical ones. (Otherwise, there would not be such huge literature through the history of philosophy published on analysis of these concepts!). No one can understand the content of the predicate "knowledge" if one cannot understand the content of the predicate "truth", where the latter is clearly not as clear as those simple and definite mathematical concepts.8 2.2.2. We may reach the same conclusion by appealing to another line of argument. Suppose, on Friday night when Smith is wearing a yellow shirt he knows there is a table before him. We may ask ourselves why does this case intuitively satisfy Knowledge? The natural response would include highlighting some relevant properties of the case, namely the fact that he believes that there is a table before him, the fact that actually there is a table before him, and the fact that he is perceptually aware of the table being before him, among other things; but would not include irrelevant facts such as his weight, his eyes' color, the day of the week etc. Why do we pick out particular properties of the case, but not others, as relevant? Because we presuppose a background and perhaps implicit theory prior to intuiting that such and such a case is (not) an instance of Knowledge. In Smith's example about knowledge, the background theory implies, among other things, that for being knowledge of P, it is necessary to truly believe that P. Suppose for the sake argument, that the JTB-theory is our presupposed theory at the time of intuiting that Smith knows there is a table before him and that JTB-theory, in fact, is true. It does not matter us, say, whether he is wearing a yellow shirt or a black one because the presupposed theory generally excludes these properties as irrelevant to having knowledge; but it does matter us whether Smith is in a good cognitive condition or not because the JTB-theory implies so. Or in the Gettier's second case, the reason we, along with Gettier, do not care whether or not the Jones and Smith are brothers but do care whether Jones, in fact, owns a Ford is that our presupposed theory excludes the former but somehow includes the latter9. To include some property as relevant and exclude others as irrelevant is nothing but to assume a background theory, maybe of course still an 8 Here it is assumed for the sake of example that Knowledge entails truth. 9 Our response to this objection may also bring about challenges to the supposed role of philosophical theories: If for reliable intuitions, which provide us with evidence for or against theories, it is necessary to presuppose a true concept-identity-proposition and this proposition itself proposes an analysis of the concept in question, then it seems we are bounded in a epistemic circle: There must be a theory to support our particular intuitions while the intuition is supposed to provide us with evidence for or against theories in return. It is a complicated subject and we do not intend to enter it. implicit one. Therefore it is the background theory in the form of a concept-identity C = F that dictates us, implicitly or explicitly, which properties to exclude and which properties to include. Other attempts to explain (away) the profound distinction between the class of relevant and the class of irrelevant properties of a given case, such as appealing to the thought that it is merely the concept possessed itself, independent of any theory, that dictates us which case-property to include and which to exclude, sound nothing more than a verbal manipulation of our argument above. To include the properties F-ness and G-ness and only these properties as relevant to a case being an instance of C is, in fact, nothing beyond presupposition of an analyzing theory in the form "C = F & G" while intuiting on a case of C. 3. Conclusion We can review the argument as follows: 1. If intuition is not a reliable source of evidence, then the counterexample method is not tenable; for in armchair methodology it heavily and unavoidably relies on intuitive evidence. (Epistemic Requirement) 2. If intuition is a reliable source of evidence, then having intuitive evidence involves (determinately) possessing the concept C, the concept under discussion. (JS) 3. If having intuitive evidence involves (determinately) possessing the concept C, then either it is the same as the concept designated by the "C" in the to-becriticized theory or not. (Semantic Requirement) 4. If the concept C constituting the intuitive evidence is not the same as the concept designated by "C" in the theory, then even if the evidence is true, it is irrelevant. 5. If the concept C constituting the intuitive evidence is the same as the concept designated by "C" in the theory, then if the critic possesses the concept C determinately enough, there is no epistemic need to rely on counterexample evidence to assess the theory; because one already know the concept-identity of the form "F = G" or its negation. (From CP) 6. If one already knows the true corresponding concept-identity, then the counterexample method is needless. Therefore, the counterexample method is either epistemologically untenable or needless, if not irrelevant to the subject. As an initial guess, the most the counterexample method may serve is to reveal that perhaps our verbalization of our presupposed theory is not proper. Of course, it is still a naïve guess requiring more contemplation. References Bealer, G. (1999). A theory of a priori. Philosophical Studies , 13, 29-55. Bealer, G. (1998). Intuition and autonomy of philosophy. In M. R. DePaul, & W. 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