Forthcoming in Graham Priest on Dialetheism and Paraconsistency, Can Başkent and Thomas Ferguson (eds.), Dordrecht: Springer Priest's Anti-Exceptionalism, Candrakırti and Paraconsistency Koji Tanaka School of Philosophy Research School of Social Sciences Australian National University Koji.Tanaka@anu.edu.au 1 Anti-Exceptionalism In the context of the philosophy of logic, anti-exceptionalism is the view that logic does not have any special status in relation to empirical sciences and that the methodology for theorising about logic is the same as that for the theorisation of empirical sciences.1 According to this view, logic is not exceptional: it is revisable and not a priori, just like the theories of empirical sciences. This view is often associated with Quine.2 Priest also accepts anti-exceptionalism about logic (Priest (2006, 2014, 2016)). Ironically, Priest's anti-exceptionalism is part of his argument against Quine's position on non-classical logic. Quine held that someone who denies classical logic and subscribes to non-classical logic is only changing the subject (Quine (1986)). For him, someone who disagrees with the classical account of propositional connectives and quantifications means different things by 'not', 'if... then...' and so on. It is in response to this position of Quine that Priest develops his anti-exceptionalism in the service of defending paraconsistent logic (see also Priest (1979)). In this paper, I will examine Priest's anti-exceptionalist view of logic. He has taught me that the best respect you can pay to a philosopher is to take their work 1See Hjortland (2017). 2Quine's ultimate view on this issue might be complicated. Shapiro (2000), for instance, casts doubt on this interpretation of Quine. seriously by having a critical stance towards it. I will do exactly that. First, I will present what I take to be his anti-exceptionalist view. Second, I will show that the anti-exceptionalist view that Priest presents requires further specification. Third, I will fill a gap in Priest's presentation of his view by appealing to the Buddhist Madhyamaka philosopher Candrakırti. I will then pose a problem for Priest's anti-exceptionalism. Fourth, I will suggest a way out of the problem for Priest. Whether or not he accepts my solution, I will let him decide. 2 Priest's Anti-Exceptionalism Priest's anti-exceptionalism is part of his arguments for paraconsistent logic. A logic is said to be paraconsistent iff its consequence relation does not validate ex contradictioone quodlibet (ECQ): A,¬A |= B for any A and B. An argument for paraconsistent logic is, thus, an argument against the classical principle ECQ. Priest (1979) argues against ECQ by claiming that logic is a normative subject: [T]he notion of validity that comes out of the orthodox [classical] account is a strangely perverse one according to which ... any rule whose premises contain a contradiction [ECQ] is valid. By a process that does not fall far short of indoctrination most logicians have now had their sensibilities dulled to these glaring anomalies. However, this is possible only because logicians have also forgotten that logic is a normative subject: it is supposed to provide an account of correct reasoning. When seen in this light the full force of these absurdities can be appreciated. (Priest (1979): 297) Let's agree that logic provides 'an account of correct reasoning'.3 What exactly this amounts to is a controversial issue. For the sake of this paper, let's understand the claim that 'logic is normative' in the sense that it serves as the standard for evaluating one's reasoning as correct or incorrect.4 It follows that reasoning is correct if it meets the standard sets by logic. For instance, if logic declares the following inference as valid: A round square is round. A round square is not round. The moon is made of blue cheese. reasoning to the conclusion on the basis of the premises counts as correct. 3This is, in fact, a controversial view. For an opposing view, see Harman (1986). 4According to MacFarlane (2000, 2002), this is Frege's view about the normativity of logic. 2 But how could the normative nature of logic be a reason for rejecting ECQ? How could it entail that the account of correct reasoning is paraconsistent? In order to answer these questions, Priest (1987) invites us to think of logic analogously to the theorisation of dynamics: [J]ust as with dynamics, so with logic, one needs to distinguish between reasoning or, better, the structure of norms that govern valid/good reasoning, which is the object of study, and our logical theory, which tries to give a theoretical account of this phenomenon. (p. 257) Priest's analogy between dynamics and logic can be explained as follows. In the case of dynamics, we must make a distinction between the physical structure that governs the movement of physical objects and a theory about this structure. We theorise about the physical structure by first observing the movement of physical objects and then systematising the data we acquire through our observations. It is possible that an observation of the movement of an object does not match the prediction made by a theory. This is possible even in the case of a theory that has been largely accepted by a scientific community. If there is such a discrepancy, there are at least two options: reject the data (i.e., our observation) or modify (or dispose of) the theory. It is this second option that is important for Priest. When an anomaly is discovered, there must be an option to modify or reject the theory we currently have. How exactly this can be done is a matter of debate. Nevertheless, the important point is that the second option cannot be a priori ruled out in the case of dynamics or in any empirical science. For Priest, this must be the case for logical theorisation too. When our observation does not match the system of logic, understood as a theory of the norms of correct/valid reasoning, we currently accept, we cannot always reject our observation as irrelevant or redescribe it so that it is no longer anomalous with one's logical theory (which is equivalent to a priori rejecting the data). For Priest (2016), we must consider such factors as adequacy to the data, simplicity, consistency, explanatory power, and avoidance of ad hoc elements. Putting aside the details of these factors, the important point for Priest is that the criteria for logical theorisation are basically the same as those of empirical sciences. In particular, just like the case of dynamics, rejecting or modifying one's logical theory in response to data cannot be ruled out a priori. There must be a possibility of modifying or disposing of one's logical theory based on new data. By inviting us to understand the nature of logical theorisation analogously to the theorisation of empirical sciences, Priest places logic on the same footing as empirical science. In other words, logic has no exceptional status in relation to empirical science. This is Priest's anti-exceptionalism. 3 3 Logical 'Data' Crucial to Priest's anti-exceptionalism as analysed above is the existence of 'data' that can force revision of logical theory. What exactly is the kind of data that is capable of inciting logical revision? In the case of dynamics, it is easy to specify the kinds of data that might place a theory in doubt. If a moving object does not display the behaviour that is prescribed or predicted by the theory, we need to consider rejecting the data as an anomaly or modifying (or disposing of) the theory. But what can be the equivalent data in the case of logic? What could the data be which might lead to rejecting a logical theory? What kind of observation can undermine ECQ? An observation of someone simply reasoning badly cannot be a counter-example. As Priest claims, logic is normative: it is 'an account of correct reasoning' (ibid.). So we must be able to observe not only how we do in fact reason but how we ought to reason. What kind of observation could that be? Priest (2016) answers this question in the following way. Consider the following vernacular inferences: John is in Rome. If John is in Rome he is in Italy. John is in Italy. If John is in Rome he is in Italy. John is not in Rome. John is not in Italy. Priest tells us that the inference on the left 'strike[s] us as correct' and the one on the right 'strike[s] us as invalid' (p. 355). The inferences we just looked at are particular ones expressed vernacularly. What about inferential forms such as A If A then B B where A and B are meta-variables for any formulas? Priest reminds us that we must be careful about the relationship between inferential forms and their particular instances. For instance If he were here he would be hopping mad. He were here. He would be hopping mad. does not 'strike us as valid' (p. 356) even though it has the form of modus ponens. Or consider any Sorites argument. It involves multiple modus ponens even though it is paradoxical and the validity of particular Sorites argument may be in doubt.5 5In the case of Sorites argument, one may reject the premises instead of rejecting the inference in order to resolve the paradox. I am here raising a possible reaction one can have in response to Sorites arguments. 4 There is a lot that can be said about the relationship between an inferential form and its instances. Despite this concern, Priest tells us that the form modus ponens as such 'strikes us as intuitively correct' (p. 356). So, for Priest, the data that logical theorisation needs to accommodate are 'our intuitions'. As he writes: In the criterion of adequacy to the data, what counts as data? It is clear enough what provides the data in the case of empirical sciences: observation and experiment. What plays this role in logic? The answer, I take it, is our intuitions about the validity or otherwise of vernacular inferences [and inferential forms]. (p. 355) For Priest, it is our observation of how people make intuitive judgements about inferences that provides data to be considered in logical theorisation. Thus, logic, as a theory, has to accord with our intuitions about the validity of various inferences: what should be accepted as valid/invalid is assessed against our intuitions. However, an appeal to intuition is exactly what the defenders of the a priori nature of logic, such as Bealer (2000) and BonJour (1998), specify as the data that a theory of validity must be responsive to. They take our immediate intuitive judgements about validity as evidence for the validity/invalidity of inferences. Priest may not believe in the 'faculty' of rational intuitions to which they appeal. Nevertheless, for Priest as well as for Bealer and BonJour, the data that serves as evidence for establishing the validity/invalidity of inferences are our intuitions.6 They both appeal to intuitions as evidence for logical theorisation. How different is Priest's view about logical data from the view of the a priori defenders? Priest rejects the views of Bealer and BonJour (and others who defend the a priori nature of logic) (Priest (2016): §3). However, he does not explain how different his position is from that of the a priori defenders with respect to the data that logical theorisation must accommodate. Without any elaboration on the notion of intuitions that Priest appeals to, it is hard to understand the difference between his view and the views of those who subscribe to the a priori nature of logic. In what way, then, is Priest's view anti-exceptionalist? How different is his notion of intuitions from that used by the a priori defenders? In the next section, I will present one way to understand Priest's view and show that it is indeed antiexceptionalism when it is construed in a certain way. 6Bealer and BonJour do not discuss our intuitions invalidating the currently accepted logic. That is, they are not anti-exceptionalists. Nevertheless, it is still the case that they as well as Priest appeal to intuitions as doing the groundwork for logical theorisation. 5 4 Candrakırti's Take On Priest's Anti-Exceptionalism I suggest that the best way to make sense of Priest's anti-exceptionalism is to appeal to the Buddhist philosopher Candrakırti. Candrakırti is one of the most, if not the most, influential philosophers in the Madhyamaka tradition after the 'founder' of the tradition Nāgārjuna. The Madhyamaka school is often considered to be the most influential school in the Buddhist philosophical traditions, especially in Tibet.7 It is to this school that contemporary scholars are often drawn in bringing Buddhist material to contemporary philosophical discussions.8 What exactly Candrakırti meant or even said is a matter of scholarly debate amongst Buddhist scholars. In this paper, I will largely follow the analysis of Tillemans (2011) who presents Candrakırti as interpreting the notion of truth and knowledge in terms of what the people on the street accept. According to this analysis, Candrakırti reduces truth and knowledge to mere opinions and beliefs. Truth is nothing more than what people on the street assent to and knowledge is nothing more than what they think. This is the case no matter whether they are opinions or beliefs about plumbing, empirical science or mathematics. Because of this, there is not much more to science than what can be expressed by ordinary notions like 'When wood, strings, and manual effort are present, sounds arise from musical instruments' (p. 155). I refer to this account of truth and knowledge as the lokaprasiddha (what is acknowledged by the world) account. The lokaprasiddha account implies that theorising about what is true and what should count as knowledge requires investigating the opinions and beliefs of people on the street. What investigation must take place and how the results of the investigation should be understood are also matters of opinions and beliefs. But there is nothing special about how truth and knowledge should be expressed. They are expressible by ordinary notions. This account is not as absurd as it might first appear, at least from a Mādhyamika point of view.9 Crucial to Māhyamikas is the thought that anything that exists is empty of essential, intrinsic and independent property (svabhāva), i.e., the doctrine of emptiness. If an object does not possess this property, it may be said to exist but only because other things exist. For instance, a chariot might be said to exist only because of the existence of the wheels, the poles, the wheels, the body flag-staff, the yoke, the reins and the goad. A flame may be said to exist only 7While this is true in Tibet, it is actually not clear what the level of Madhyamaka's influence has been in China, Korea and Japan. Also, as contemporary scholars agree, Candrakırti was a minor figure in India until his texts went to Tibet where he became an important thinker. I am here following the conventional wisdom of contemporary scholarship. 8For instance, the Cowherds (2011). 9I follow the contemporary convention of using 'Madhyamaka' as referring to the school of thought and 'Mādhyamika' as referring to the thinker who belongs to the school. 6 because there is a certain amount of oxygen, fuel, etc. The main Madhyamaka thought is that everything whatsoever that can be said to exist is like that. If a chariot can be said to exist only because of the existence of the wheels, the poles and so on, it may 'disappear' when one theorises about what a chariot is. For instance, a chariot may be 'reduced' to the wheels, the poles, etc. Opponents of Mādhyamikas, at least those of Nāgārjuna, employed reductive analyses to claim that a chariot and other macro-level objects do not really exist. Mādhyamikas follow such reductive analyses to their logical end and argue that no reductive analyses can bottom out because everything, not just macro-level objects, can be analysed away. If there is no end to a reductive analysis, however, employing such analyses to work out what is true cannot ultimately bear fruit. Assuming that reductive analysis is the only mode of analysis in town,10 there is not much point in engaging in analysis. Any attempt to work out why something is the way it is is unproductive as there is really nothing that can be analysed. In claiming to have truth or knowledge, an appeal to people's opinions and beliefs may be as good as anything else. Now, Candrakırti's lokaprasiddha account of truth and knowledge can be extended to the validity of inferences.11 Following his lokaprasiddha account of truth and knowledge, we might think that whether or not an inference is valid is also just a matter of what the people on the street would accept. For instance, presented with an inference such as John is in Rome. If John is in Rome he is in Italy. John is in Italy. we might say that it is valid. In so doing, we might be understood as simply expressing our opinions. We may not have any sustained reasons for why we believe it is valid. The only reason we can say to account for our response is simply that it strikes us as valid. Or, if there are additional reasons, they are merely additional opinions and beliefs. According to this line of thought, in order to adjudicate which inference is valid, we just need to find out the opinions and beliefs of people on the street. This is not to say that we need to find out how people do, in fact, reason in order to 10Later Mādhyamikas seem to have developed different kinds of analyses based on different semantic accounts. See Tanaka (2014). But early Mādhyamikas seem to recognise only reductive analyses. In fact, without making this assumption, Nāgārjuna's argument for emptiness and Candrakırti's lokaprasiddha account of truth and knowledge are implausible. 11In fact, Candrakırti has an elaborate discussion of logical principles based on his lokaprasiddha account of truth. See Tillemans (2016). That discussion goes in a different direction from the current discussion about Priest's anti-exceptionalism. Here I deviate from Candrakırti's thought about logical matters expressed in his writings. 7 work out what inferences are valid. That would be to confuse how people reason with how people ought to reason. What we need to find out is what people accept as 'an account of correct reasoning': what inferences should count as valid. On this account, there is no need to analyse logical concepts, the notion of validity or anything. All there is to logic is what can be expressed by things like 'This inference looks good to me' or 'That inference strikes me as valid'. If all there is to science is what can be expressed by ordinary notions like 'When wood, strings, and manual effort are present, sounds arise from musical instruments' (ibid.), all there is to logic can be expressed by ordinary notions like 'When you reason to the conclusion that John is in Italy from the premises that John is in Rome and that if John is in Rome he is in Italy, your reasoning strikes us as good'. According to the lokaprasiddha account of inference, there is nothing exceptional about validity in relation to empirical science. This lokaprasiddha account fits nicely with Priest's view of logical data. In theorising about what inferences count as valid/invalid, Priest appeals to our intuitions. For him, what does the work of establishing an inference as valid or invalid is our intuition: what strikes us as valid or invalid. It is our pre-reflective judgements about inferences that provide us with data for logical theorisation. For him, these judgements are expressed as 'this inference strikes us as valid'. If we redescribe these pre-reflective judgements as opinions and beliefs that are expressible in ordinary notions, Priest's account boils down to a lokaprasiddha account. Once Priest's account is redescribed as a lokaprasiddha account, we can show that his account is anti-exceptionalist and, thus, can be distinguished from a priori views as such Bealer's and BonJour's. If the data which we must account for in logical theorisation is people's opinions and beliefs, it is an empirical question what counts as valid inference. We need to survey what people think about various inferences. According to the lokaprasiddha account, how to conduct surveys and how to interpret the result of surveys are also empirical questions. So we have to investigate not only the opinions and beliefs of people about what inferences should count as valid but also those about the way to conduct surveys and to interpret the result of the surveys. However to be analysed, the result of such survey is unknown a priori. According to the lokaprasiddha account the data for logical theorisation is something that is not simply given to us; it is something that we must observe. The data revealed by a survey may overturn an established logical theory if the survey contains a new statistic of opinions and beliefs about certain inferences. When a survey reveals that enough people reject an inference that is prescribed as valid according to a current logical theory or a theory that is hypothesised, we can either revisit and question the survey (i.e., reject the data) or reject the theory. People's opinions and beliefs may change in which case the currently accepted 8 logical theory needs to be revised to take new survey into account. So if the result of survey is what logical theorisation is responsive to, the lokaprasiddha account provides an anti-exceptionalist methodology that can make sense of the kind of data that can be used as evidence for logical theorisation. Hence, once we redescribe Priest's view of logical data in terms of lokaprasiddha, we can show that his account is anti-exceptionalist. As is shown above, the data for logical theorisation under this account is available empirically in the way that the data for theorisation of dynamics is. Also, the lokaprasiddha account can make sense of revisability of logic. Priest's account as a lokaprasiddha can, thus, be shown to be an anti-exceptionalist view of logic. 5 Dismal Slough The lokaprasiddha account of inferences was developed in analogy to (empirical) sciences. It is hard to imagine, however, that this account accommodates the opinions and beliefs people have about (empirical) sciences. It is very unlikely that the majority of people think of sciences as being expressible only in ordinary terms like: 'When wood, strings, and manual effort are present, sounds arise from musical instrument' (ibid.) at least in these modern days. It is more likely that people believe in the mechanisms underlying the sounds that arise from musical instrument and they think that the study of those mechanisms requires more than ordinary notions. In fact, it is important for Priest that logical revision is triggered in a principled manner. The need for logical revision arises when certain criteria are met. And those criteria must be chosen carefully and they need to be examined thoroughly. It is most likely that Priest would not be happy to think of logical revision as simply a matter of the change of opinions and beliefs people happen to have at the time of survey. These considerations suggest that Priest requires something more than lokaprasiddha. Tillemans' description of the lokaprasiddha account of truth and knowledge on which the lokaprasiddha account of inference is based may leave us wondering what is left of sciences and logic. The picture Tillemans (2011) paints of Candrakırti's view is a 'dismal' one. As he puts it aptly, it entails a dismal slough.12 I think that there is another way to understand the lokaprasiddha account.13 Candrakırti reduces truth and knowledge to mere opinions and beliefs. He reaches such a view by following through the doctrine of emptiness to its logical end as he sees it. If there is nothing that ultimately exists, there is not really anything 12See also Tanaka (2015). 13In fact, Tillemans (2011) seems to acknowledge this. See also Tillemans (2016). 9 that we must accommodate in claiming to have truth and knowledge. But this is compatible with the idea that people accept there being a mechanism underlying the sounds of musical instruments. What is incompatible is the idea that there is an ultimate answer to what that mechanism is. For Candrakırti, what that mechanism is is a question that can be answered only by appealing to the opinions and beliefs of people. If we understand it this way, the lokaprasiddha account of truth and knowledge is not dismal. There is nothing in the account to redescribe what the sciences are or should be. It accepts what people think them to be. Similarly, the lokaprasiddha account of inference is not dismal. It does not radically redescribe what logic is or should be. All it does is opens up the possibility of revision in relation to the data that can be observed. It is this feature that makes it an account of antiexceptionalism. And this feature of the account is not what is described as dismal. 6 Anti-Exceptionalism and Paraconsistency As mentioned before, Priest has developed his anti-exceptionalism in the service of defending paraconsistent logic. How does anti-exceptionalism help him argue for paraconsistent logic? In order to answer this question, we must remember that an argument for paraconsistent logic is an argument against classical logic. In particular, a case for paraconsistent logic can be made by showing that ECQ (A,¬A |= B for any A and B) is invalid. Priest's typical strategy to argue against ECQ is to provide counter-examples. For instance, Priest (2008) writes: Not only is this [ECQ] highly counterintuitive, there would seem to be definite counter-examples to it. There appear to be a number of situations or theories which are inconsistent, yet in which it is manifestly incorrect to infer that everything holds. (pp. 74-75) A counter-example to ECQ is a situation where not everything is true even when a contradiction obtains. One of the counter-examples is about visual illusions such as the waterfall effect where something stationary appears to move after seeing constant motion. [A] point in the visual field, say at the top, does not appear to move, for example, to revolve around to the bottom. Thus, things appear to move without changing place: the perceived situation is inconsistent. But not everything perceivable holds in this situation. For example, it is not the case that the situation is red all over. (pp 75-76) 10 For Priest, a perceptual experience of waterfall effect is a counter-example to ECQ. The perceived situation is a contradictory one: things are perceived as moving without changing place. Yet not everything is perceived in such a situation. So a perception of waterfall effect is an instance where the premise of ECQ is affirmed but the conclusion is rejected. Thus, it provides the data in terms of which classical account of reasoning must be rejected. Because of the existence of such situations functioning as counter-examples, so Priest argues, ECQ and, thus, classical logic do not specify correct reasoning. This strategy is, in fact, not available to Priest under the lokaprasiddha account. According to the lokaprasiddha account, there is no deadlock that we can all appeal to in theorising about what should count as valid/invalid. There may be no further reason that can be given for why an inference should count as valid. If so, the judgements about vernacular inferences may not depend on the judgements about inferential forms. For instance, the judgement that John is in Rome. If John is in Rome he is in Italy. John is in Italy. is valid may not depend on accepting modus ponens as valid. If this vernacular inference strikes one as valid, no further explanation, other than further opinions and beliefs, may be given for why it appears as valid. Under the lokaprasiddha account, this vernacular inference may be valid but not necessarily in virtue of its form. Similarly, the reason why modus ponens strikes us as valid may not be because of its instances. If modus ponens strikes us as valid, that validity does not necessarily spill over to its instances. According to the lokaprasiddha account, judgements about the validity of vernacular inferences may come apart from those about the validity of their forms.14 One may reject the conclusion that the situation is red all over while accepting that things move without changing place; yet accept ECQ as a valid inferential form. Under the lokaprasiddha account, there is no such a thing as counter-example that can invalidate an inferential form. In order to argue against ECQ and, thus to argue for paraconsistency, Priest would have to show directly that ECQ, as an inferential form, is not accepted as valid according to the conventional wisdom of people. So, under the lokaprasiddha account, in arguing for paraconsistent logic, one needs to show that people do not accept ECQ as valid. This is an empirical issue and requires a survey. All of the empirical studies in support of paraconsistency in the literature have been conducted with particular cases and with the assumption that a counter-example can show ECQ as invalid. In the above passage, Priest 14Many thanks go to an anonymous referee who brought out this feature of the lokaprasiddha account of validity. 11 conducts an experiment on himself and describes a situation in support of paraconsistency. Ripley (2009) reports an experiment that shows that people accept contradictions in some situations. But, again, the experiment is conducted in relation to particular situations. The only 'experiment' I know of that supports paraconsistent logic is my own experience. I have taught large logic classes (sometimes 700+ students) to first year university students at various places.15 After presenting the classical definition of validity in terms of truth-preservation, I ask them whether various inferential forms as well as vernacular inferences are valid or invalid. Except those students who have taken the definition to heart or those who have followed the lecture material carefully, most students consider ECQ to be invalid. It takes me some time and effort to explain to them that the (classical) definition of validity implies that ECQ is valid. My experience may not 'prove' anything on its own. However, it is possible (and I think that it is very likely) that people on the street do not accept ECQ as valid. Thus, under the lokaprasiddha account, anti-exceptionalism allows paraconsistent logic to be a live option. 7 Conclusion Priest holds anti-exceptionalism about logic. That is, he holds that logic, as a theory, does not have any exceptional status in relation to the theories of empirical sciences. Priest's anti-exceptionalism is connected to his argument for paraconsistent logic. He claims that the classical principle ECQ is not adequate to the data. But what is the data that can lead to revision or overturning of logical theories? Priest claims that the data is our intuitions about the validity of inferences. In order to make sense of this claim, I appealed to the Madhyamaka Buddhist philosopher Candrakırti. I applied Candrakırti's lokaprasiddha account to Priest's view about the data that logical theories must respect. I have then shown the problematic nature of Priest's anti-exceptionalism as construed in terms of the lokaprasiddha account. I have, however, presented a way out for Priest. I have shown that Priest would have a coherent account of anti-exceptionalism that can be used to argue for paraconsistent logic if he accepted the lokaprasiddha account. Whether or not Priest is happy with my redescription of his view and my suggested solution, I will leave it to him to answer. References Bealer, George (2000) 'A Theory of the A Priori', Pacific Philosophical Quarterly, Vol. 81, 1-30. 15My teaching experiences are limited to Australia and New Zealand. There might be some cultural differences but I am putting aside that issue from consideration for now. 12 BonJour, Laurence (1998) In Defence of Pure Reason: A Rationalist Account of A Priori Justification, Cambridge: Cambridge University Press. Cowherds, The (2011) Moonshadows: Conventional Truth in Buddhist Philosophy, Oxford: Oxford University Press. Harman, Gilbert (1986) Change in View, MIT Press, Cambridge, MA. Hjortland, Ole T. (2017) 'Anti-Exceptionalism About Logic', Philosophical Studies, Vol. 174, 631-658. MacFarlane, John G. (2000) What Does It Mean To Say That Logic Is Formal?, Ph.D Dissertation, University of Pittsburgh. --– (2002) 'Frege, Kant, and the Logic in Logicism', Philosophical Review, Vol. 111, 25-65. Priest, Graham (1979) 'Two Dogmas of Quineanism', Philosophical Quarterly, Vol. 29, 289-301. --– (1987) In Contradiction, Dordrecht: Martinus Nijhoff Publishers, Expanded Edition published by Clarendon Press, Oxford, 2006. --– (2006) Doubt Truth To Be A Liar, Oxford: Oxford University Press. --– (2008) An Introduction to Non-Classical Logic (Second Edition), Cambridge: Cambridge University Press. --– (2014) 'Revising Logic', The Metaphysics of Logic, P. Rush (ed.), Cambridge: Cambridge University Press, 211-223. --– (2016) 'Logical Disputes and the A Priori', Logique et Analyse, Vol. 59, 347-366. Quine, W. V. (1986) Philosophy of Logic (Second Edition), Cambridge, MA: Harvard University Press. Ripley, David (2009) 'Contradictions at the Borders', Vagueness in Communication, R. Nouwen et al. (eds.), Dordrecht: Springer, pp. 169-188. Shapiro, Stewart (2000) 'The Status of Logic', New Essays on the A Priori, P. Boghossian and C. Peacocke (eds.), Oxford: Clarendon Press, pp. 333-366. Tanaka, Koji (2014) 'In Search of the Semantics of Emptiness' J-L. Liu and D. Berger (eds.), Nothingness in Asian Philosophy, Routledge. pp. 55-63. --– (2015) 'The Dismal Slough', Moonpaths: Ethics and Emptiness, The Cowherds, Oxford: Oxford University Press, 43-53. Tillemans, Tom (2011) 'How Far Can a Mādhyamika Buddhist Reform Conventional Truth?', Moonshadows, The Cowherds, Oxford: Oxford University Press, 151165. --– (2016) How Do Mādhyamikas Think?, Boston: Wisdom Publications.