The Value of Apparently Incoherent Positions Mark Ressler March 13, 2013 Abstract Incoherence arguments are intended to demonstrate that some philosophical position should be rejected because it is fatally flawed. I review the kinds of fatal flaws targeted in incoherence arguments, and argue that such arguments are not conclusive against the position they target, but merely pose challenges that require greater imagination. Furthermore, I claim that apparently incoherent positions have an instrumental value in expanding the intellectual resources of philosophy. I have become increasingly suspicious of incoherence arguments – those arguments that purport to demonstrate that a particular philosophical position or theory should be rejected because it is ultimately incoherent in some way. I am not convinced that any incoherence argument demonstrates that an apparently incoherent position should be rejected. I suspect that such arguments merely pose challenges to be solved with regard to the position. It is the nature of those challenges that lead me to suspect that there is a peculiar instrumental value in apparently incoherent positions. In short, I propose not only that apparently incoherent positions should not be rejected on the grounds of their putative incoherence, but that such positions should become the focus of increased research, since they represent opportunities for philosophy to expand. The target of the charge of incoherence in these arguments is certain philosophical positions or theories, rather than speech, behavior or beliefs, which are also sometimes considered to be incoherent. If incoherence is supposed to be a fatal flaw in a theory, then coherence would seem to be a general virtue of theories, and it is important at the beginning of this discussion to consider why it should be a virtue. The root meaning of the word 'coherence' expresses a quality of sticking together. Why should this stickiness be a virtue? I think the virtue lies in the sense of unity that coherence implies, as suggested by G. F. Stout in an early response to the coherence theory of truth: "Coherence as a test of truth rests (1) on the Law of Contradiction, and (2) on the Unity of the Universe" (Stout 1908, pp. 30-31). Since the universe as a unified whole seems to hold together, so should any adequate theory purporting to describe or explain that universe or any part thereof, and according to Stout, one way that theories stick together is by avoiding contradictions. So coherence as a virtue represents the unity both in the subject matter to be explained and in the theory that explains it. It would seem in a sense that a theory that does 1 not stick together and therefore flies apart is ultimately not a theory at all, at least after it has fallen apart. Of course, British Idealists such as Harold Joachim to whom Stout was responding made it clear that mere logical consistency or validity was not sufficient for the kind of coherence that they considered vital to the nature of truth (Joachim 1906, pp. 73-75). As F. H. Bradley argued, truth requires both coherence and comprehensiveness (Bradley 1914, pp. 202-203, 214). However, the notion of coherence that figures into incoherence arguments need not be strong enough to establish truth according to some formulation of a coherence theory of truth. It would certainly be a strong virtue of a theory that it be a true theory, but not all false theories are thereby incoherent, so the kind of coherence needed to demonstrate the coherence of theories need not be the same as the the kind of coherence in the coherence theory of truth. It appears to be some weaker notion of coherence that incoherent positions lack, such that incoherence arguments seek to establish not only that those positions are false, but also that they are not even candidates for truth since the positions cannot hold themselves together. I think there are two conceptions of coherence upon which incoherence arguments typically rely: (1) argumentative consistency, and (2) systematicity. My claim for these two rests on the basis of an examination of various conceptions of coherence that figure in philosophical arguments, and a determination of which of these conceptions yield sufficiently feasible conceptions of incoherence by their negations that could conceivably support a rejection of an apparently incoherent position by means of an incoherence argument. Some conceptions merely indicate that the argument for a position is inadequate or incomplete, for example, not that a position cannot hold itself together. I omit this preparatory study here in the interest of avoiding tedium. Consider first the conception of incoherence as a failure of argumentative consistency. This conception is linked strongly to the notion of self-refutation. If a coherent position is one that supports a consistent argument on its behalf, an incoherent position would be one that refutes itself. Indeed the charge of self-refutation often features strongly in incoherence arguments. Although the notion of self-refutation seems to represent an insuperable obstacle to the establishment of a viable philosophical position, I nevertheless have doubts concerning whether such self-refutation arguments ultimately succeed. John Passmore identifies three kinds of self-refutation: absolute, pragmatic, and ad hominem. Ignoring the last kind, which is directed against individual people, rather than positions or accounts, there remain two ways to show that a position refutes itself: "Formally, the proposition p is absolutely self-refuting, if to assert p is equivalent to asserting both p and not-p" (Passmore 1961, p. 61). Pragmatic self-refutation occurs when ". . . somebody has put forward a thesis while at the same time apparently engaging in a procedure which, according to his thesis, is impossible, e.g. he appears to speak the words 'I cannot speak'" (1961, p. 80). Furthermore, John Mackie has provided a formal analysis of these kinds of self-refutation, showing how the refutation can be 2 logically demonstrated and identifying the formal conditions under which each kind of self-refutation applies (Mackie 1964). Given these analyses and others that have followed them, it might seem that there are no grounds for doubting the success of incoherence arguments based upon self-refutation. Nevertheless, I do indeed have doubts. Passmore's account of absolute self-refutation, like Stout's conception of coherence, rests upon the principle of non-contradiction. The appearance of internal contradictions within a philosophical position may indeed be an unwelcome discovery. However, it seems that at least some philosophical positions accused of being incoherent deliberately countenance the kind of contradictions that characterize absolute self-refutation according to Passmore. Contradictions in these cases are not awkward, unwelcome consequences of a poorly considered position. Rather, the contradictions are precisely part of what is being claimed in the position. To hold contradictions to be fatal to these sorts of philosophical positions would seem to beg the question against them. With regard to Mackie's formal analysis, comparable considerations apply. Mackie's formal analysis relies upon classical formal logic. So if the results of this analysis are applied to philosophical positions that explicitly reject classical logic, positions that might advocate intuitionist or relevance logics, for example, the claim of self-refutation would thus seem to beg the question, since the claim of self-refutation is based upon logic that the position explicitly rejects. Interpretive charity requires imputing to a position interpretations according to which most of its statements come out true, including interpretations of the logic according to which the position operates. Even if a position does not explicitly reject classical logic, it might be shown later that the position would seem more viable under an alternative, non-classical logic. Furthermore, even if an existing non-classical logic is not available according to which a philosophical position might seem sensible, it may be the case that a new logic might later be devised to make sense of the position. These considerations point to one reason for suspicion of incoherence arguments. If an incoherence argument proceeds on the basis of a classical logical analysis, for example, but there is an existing non-classical logic that makes sense of the position that is the target of such an argument, then it seems to me that the fault lies with the failure of the incoherence argument to apply existing resources to the problem, not with the apparently incoherent position. Suppose however that no existing system of logic was available to make sense of an apparently incoherent position. In this case the incoherence argument would appear to be justified. Yet what if a new system of logic were developed later according to which the apparently incoherent position would not seem incoherent at all? I suggest that in this case, the problem lies with the lack of imaginative resources deployed in the incoherence argument, the lack of imagination to devise an adequate system of logic that could make the apparently incoherent position seem more coherent, not with the apparently incoherent position itself. It would be premature to claim at this point that these suspicions apply to all incoherence arguments, that they all represent a failure of imagination, since the previous considerations apply primarily to what Passmore calls absolute self3 refutation and to a formal analysis of pragmatic self-refutation. There are other approaches to pragmatic self-refutation that do not rely specifically upon purely logical considerations that must be considered. I think two general strategies for demonstrating pragmatic self-refutation can be identified: (1) the position undermines its own foundations, and (2) the position fails to meet its own standards. As an example of a position undermining its own foundations, consider a reductio ad absurdum argument against relativism offered by Harvey Siegel, who notes that according to radical relativism, there is no neutral framework for theory evaluation. Yet if relativism is correct, then there must be some justification for the position and therefore some neutral framework according to which it can be judged to be correct. So if relativism is correct, the means by which it can be established as being correct effectively undermine the foundations of relativism itself, and therefore "relativism of the sort we have been considering collapses into incoherence" (Siegel 1984, p. 367). One problem with this argument as given and with arguments of this sort in general, it seems to me, is establishing precisely what is to count as foundational in any given philosophical position. I have already appealed earlier to interpretive charity in attributing a logical system to a position. The application of interpretive charity in this case would require that if a position seems incoherent on the attribution of a certain foundational claim, then perhaps that apparently foundational claim should not be attributed to the position. If relativism seems incoherent on the assumption that there is no neutral framework for theory evaluation, then interpretive charity would suggest that relativism may not require this assumption. Perhaps some particular proponent of relativism may explicitly have made such an assumption, but the incoherence argument would then merely address this careless assumption on the part of one individual, not necessarily the tenability of relativism itself. The problem then becomes how to understand a form of relativism, even radical relativism, in which there might indeed be a neutral framework of theory evaluation. The incoherence argument does not examine this possibility, but merely accepts the problematic assumption as given. Another problem lies in working out the consequences of the position, assuming that the foundational assumptions are correct. If relativism does indeed require there to be no neutral framework for theory evaluation, then does the assertion of the correctness of relativism really require such a neutral framework? It would appear so if correctness is understood in an absolute sense, but a proponent of radical relativism would not accept a conception of correctness in this absolute sense. Interpretive charity would thus appear to require the rejection of the understanding of correctness as absolute correctness. The problem then becomes how to understand how a position can be only relatively correct in some meaningful way. Again, the incoherence argument just stated does not examine this possibility, but merely accepts the problematic understanding of correctness. Both problems point to a common pattern according to which incoherence arguments of this form rely on certain assumptions that are not further explored, 4 where the position in question might be understood to be coherent upon further exploration. However, there are indeed stronger self-refutation arguments than the one I cited from Siegel that attempt to close this gap by posing destructive dilemmas for a philosophical position. According to this pattern of argument, either the position under evaluation accepts one alternative or another, but either alternative leads to incoherence. Therefore, the position is incoherent. Indeed, Siegel himself has already presented such a stronger destructive dilemma against relativism in an earlier argument than the one previously cited. Stated briefly, the argument is as follows: "In short, to defend relativism is to defend it nonrelativistically, which is to give it up; to 'defend' it relativistically is not to defend it at all" (Siegel 1968, p. 231). Yet here too I think the same kinds of problems resurface. Perhaps there are ways of understanding the position such that one or more alternatives are viable, ways that the argument does not consider. Perhaps the assumption that the alternatives are exhaustive is mistaken, and that there is some other alternative according to which the position is coherent. Even if the dilemma is framed in terms of a direct contradiction, such as that either relativism requires neutral frameworks or it does not, further distinctions may show that there is an alternative understanding of the position that may require neutral frameworks in some sense and not in another, or a relativistic defense of relativism in one sense and not in another. The incoherence argument only works when such alternatives are no longer explored, and the deployment of an incoherence argument seems to indicate the limits of imagination in failing to identify such alternatives, not necessarily the absolute failure of the apparently incoherent position. So again, an incoherence argument seems to pose a challenge, but it is not clear that such arguments always demonstrate that the challenge cannot be met. The other strategy for demonstrating pragmatic self-refutation that I noted earlier is to show that a position fails to meet its own standards. This pattern might be seen as a species of the previous strategy of undermining the foundations of a position, where the foundations in question are not necessarily substantive assumptions, but epistemic standards that the position applies. Perhaps the most notorious instance of this strategy is the argument against logical positivism, which relies upon the principle of verifiability to determine the meaningfulness of statements. Someone eventually noted that the positivist statement asserting the principle of verifiability was not verifiable according to any formulation presented by logical positivism and therefore was meaningless according to its own standards. More importantly for a discussion of incoherence, consider an example from J. M. Fritzman in an article entitled "Against Coherence" in which he argues that the coherence theory of justification is incoherent. Briefly, he states his argument as follows: "Coherentism claims that it is impossible to criticize, evaluate, or justify beliefs from a perspective external to the belief set. Not only is it possible to adopt an external point of view, but it is also necessary. Since coherentism denies this, it is incoherent" (Fritzman 1992, p. 186). One reason that Fritzman gives for the necessity of an external point of view is that 5 the evaluation of beliefs occurs at a metalinguistic level, which is by definition outside of the level of the linguistic system that it discusses (1992, p. 187). This strategy for demonstrating incoherence may seem more secure than the strategy of showing that a position undermines its own foundational assumptions, at least insofar as a position explicitly outlines the standards that it applies. Of course, if those standards are merely extrapolated by whomever deploys the incoherence argument as being inherent in the position criticized, then there is a question whether that position truly entails those standards used against it in the argument. Again, interpretive charity would suggest that if the extrapolated standards lead to incoherence, then perhaps those standards should not properly be attributed to the position. Yet even if a position explicitly states the standards that it demands and that are not met by the position itself, it is not clear whether the position has merely been formulated carelessly, or whether the position is simply untenable under any formulation. What emerges from the incoherence argument is a challenge to reformulate the apparently incoherent position. The apparent failure of a position to meet its own standards may pose a more difficult challenge than that posed by the apparent undermining of a position's own foundations. For example, Fritzman's argument seems to pose the challenge of formulating a coherence theory of justification that spans metalinguistic levels. Yet it is not clear to me that the incoherence argument demonstrates that the problem cannot be solved. Rather, the argument seems to take the very existence of the problem itself to be conclusive against the target position. For these reasons, incoherence arguments by self-refutation seem suspicious to me, since the positions they target appear to pose challenging philosophical problems to be solved, but the incoherence arguments merely take those problems to be fatal to the position, rather than exploring ways to meet those challenges. In this context, consider the argument of Michael Stack against certain self-refutation arguments, in particular, arguments that claim that a position is false because it argues on the basis of something that the position itself rejects. One example that he gives is the case of the skeptic who denies rational belief. As the self-refutation argument typically proceeds, if the skeptic fails to argue for his position, then he can safely be ignored, but if he argues for his position, he relies on the possibility of rational justification for beliefs and therefore refutes himself (Stack 1983, p. 328). Stack notes that most selfrefutation arguments of this sort are deployed to preserve traditional doctrines, such as the intuition that there is knowledge and justification. His claim is that tradition-preserving arguments on the basis of self-refutation misconstrue positions that challenge traditional doctrines by failing to recognize that the arguments that seem to refute themselves in this way are in fact reductio ad absurdum arguments against the traditional positions. If the skeptic argues for his position, it is because he aims to convince someone who does accept rational argument as valid, and if rational argument can be used effectively to challenge rational argument, then the problem would seem to lie with rational argument, not with skepticism. Once the problems with rational argument are noted by means of the argument, the skeptic can discard the argument for skepticism and 6 its presumption of the validity of rational argumentation, as in Sextus Empiricus' metaphor of the ladder that is discarded once it is used to ascend (Sextus Empiricus, 2005, p. 183). Stack's suspicions concerning self-refutation arguments align very well with mine against incoherence arguments. Tradition tends both to constrain imagination as well as enable it. Imagination seems to require a pre-existing stock of images, concepts, and ideas as a source on which to operate. The various techniques of imagination operate by playing with, modifying, and even flatly denying existing ideas, as described by Nelson Goodman as ways of worldmaking (1978, pp. 7-17), for example, rather than producing new ideas from the void. Yet that very tradition can also constrain imagination when those ideas become so entrenched that some thinkers refuse even to suppose that the ideas could possibly be denied coherently. It seems to me that a blunt refusal to play with certain ideas lies at the heart of incoherence arguments in general. I think the question of philosophical imagination likewise underlies suspicions concerning the second conception of incoherence, namely lack of systematicity. The conception of coherence involved in this case seems to derive from Hegel through the British Idealists, for whom the notion of a system was vitally important. If a position is so disorganized or is dependent on such a fragile foundation that no system can even be assembled, then it would indeed appear to be an incoherent position. The problem is not that the system falls apart, but that it cannot even come together in the first place, which would certainly be a serious criticism of a position. I think a good example of this kind of incoherence argument can be found notably in Richard Fumerton's article "The Incoherence of Coherence Theories". Fumerton points out two conceptual regresses faced by the coherence theory of truth. The first concerns the relata of coherence, namely what must cohere with what. According to Fumerton, what makes a proposition true according to coherentism is that it coheres with a set of propositions that is believed. Yet what makes it true that this set of propositions is believed? Presumably that it coheres with some other set of propositions that is believed, and so forth, falling into a regress (Fumerton 1994, p. 94). The second regress concerns the facts about the coherence relations themselves that hold between propositions. What makes the propositions about the coherence relations true? Presumably it will be their coherence with other propositions. Yet there are propositions about this new coherence relation that will likewise be true on the basis of other coherence relations, and so forth (1994, p. 96). These conceptual regresses indicate that a coherence theory of truth cannot even get off the ground, that it cannot properly be systematized in order to provide an explanatory account of truth. Of course, incoherence of this sort is properly directed against any possible systematization of a position, not merely a particular actual systematization. If one proposed systematization fails, that failure by itself does not show that all systematizations must fail. Yet here again I think the same basic considerations about failure of imagination apply as those noted with regard to self-refutation. The charge of incoherence by failure of systematicity can be refuted most ef7 fectively by producing a system. For example, with regard to another kind of argument, the core of the argument for intelligent design is that certain living species are irreducibly complex, meaning that they are too complex for the process of natural selection to explain them. In my terms, the claim seems to be that certain species cannot be explained by any system of natural forces that does not include intentionality of design. The response from evolutionary biologists is that they already have such an explanatory system, but that proponents of intelligent design neither bother to learn the system in its entirety nor to understand the evidence for that system. With regard to incoherence arguments in philosophy, I think the most notable recent example of a challenge to a charge of failure of systematicity is Graham Priest's dialethic logic (Priest 2006). Because the principle of noncontradiction is so firmly embedded in human thought, it has been thought incoherent to deny the principle, particularly in such a way as to suggest that there might be true contradictions. This incoherence would seem to be grounded in a failure of systematicity, according to which it might be thought that no system that allowed that there might be true contradictions could even get off the ground, let alone hold together, since contradictions are precisely the sort of thing that tear systems apart, as suggested by Stout's comment cited earlier. Priest's response is to produce such a system and to show how it can hold together. Regardless of what one might think of Priest's arguments for his claims that specific contradictions hold true in the world, I think the formulation of his dialethic system shows that the idea is not completely incoherent, where incoherence is understood as failure of systematicity, and where the charge of incoherence seems ultimately grounded in an inability to imagine or to understand a dialethic system. With regard to Fumerton's argument, then, there seems to be inherent in his argument a challenge to provide a system for the coherence theory of truth, one that can be formulated in such a way as to avoid the kinds of regresses that he points out. Though Fumerton claims that the first kind of regress is effective against any formulation of the coherence theory of truth (1994, pp. 9596), I am not convinced. It may be effective against coherence theories of truth that make the same assumptions that Fumerton makes in his analysis, particularly the assumption that a coherence theory must talk about the relata of coherence (1994, p. 96), but I am not certain that there can be no formulation of a coherence theory of truth on different assumptions that still counts as a coherence theory of truth. What Fumerton's argument seems to rely on is a foundationalist pattern of reasoning, though not necessarily an explicit foundationalist theory of truth. The pattern is that the coherence of any single proposition is established on the basis of something else that is already established. With this assumed pattern of argument, Fumerton's conceptual regresses may seem compelling. However, the problem with this assumption seems to me to be that a coherence theory of truth should properly reject this foundationalist pattern of reasoning in favor of a more consonant holistic pattern. The truth or coherence of any single proposition is not separately established on the basis of something already 8 established, but rather, every true proposition is established as coherent together and at once. The systematicity of coherentism would be established by the existence of a set of propositions that is a coherent set, according to some operative conception of coherence. So the coherence theory need not eventually address coherence in terms of relata, as a relational property held between individual propositions and something else, as Fumerton claims, but rather, coherence should be understood as a property of an entire set of propositions. There may be an epistemic or practical problem in how to identify such a set, a problem that Nicholas Rescher attempts to address (Rescher 1973), but it is not clear that there is a metaphysical problem with coherentism in the way that Fumerton claims. The two conceptual regresses he poses are problems only for formulations of a coherence theory of truth that are formulated explicitly using a foundationalist approach, whereas I have suggested that coherence theories should more properly adopt a holistic approach. I doubt that anyone is fully persuaded by my discussion thus far, and may not likely be persuaded by what I have to say next. Firstly, my arguments have a distinctly ad hominem flavor, by suggesting that the plausibility of incoherence arguments is grounded in the failure of imagination of the individual philosophers who offer them. Of course, I have attempted to be careful to phrase my argument in terms of suspicions and grounds for suspicion, rather than claiming to have demonstrated that incoherence arguments are always faulty or even incoherent. Yet it might be thought that these kinds of suspicions do not even represent a proper subject for philosophical discussion. Secondly, and perhaps more importantly, none of my criticisms here seem to extend any farther than effectively pointing out the fallibility of incoherence arguments. Yes, any given incoherence argument or any other kind of argument may fail to imagine alternatives that might undermine the argument. The history of philosophy and science is filled with such cases, and it seems unreasonable to demand of any philosopher to see beyond the horizon of one's abilities, so to speak. All that we philosophers can do is simply to offer arguments as honestly as possible according to our best available conceptual resources. Our philosophical descendents will be in a better position to evaluate our arguments, given their expanded resources. And to this I agree. In fact, my arguments here may be fallible on precisely the same grounds that I use to criticize incoherence arguments, as some readers likely have been eager to point out. Perhaps I have not been able to imagine a conception of coherence and incoherence beyond those that I have discussed earlier that would make incoherence arguments decisive. Perhaps I have not been able to imagine how self-refutation and failure of systematicity can be deployed to defeat any possible reformulation of the incoherent position. In short, this discussion is just as fallible as any of the incoherence arguments to which I direct my suspicion, and therefore should seem equally suspect. Of course, pointing out that all arguments are fallible does not tend to increase confidence in any of them, whether in incoherence arguments or my suspicions against them. What I would point out here, though, is a difference in 9 attitude between those who are satisfied with incoherence arguments and those who may be suspicious of them. If I am satisfied with an incoherence argument, I will not continue to explore the incoherent position to seek alternatives to make the position work. After all, if the position is indeed incoherent, then such exploration would be senseless. If I do continue with the exploration, then this would suggest that I am not satisfied with the incoherence argument after all. By contrast, if I am suspicious of the incoherence argument, I would tend to understand the apparent incoherence as simply posing a problem to be solved, a problem requiring more philosophical imagination than had been applied in the incoherence argument itself. The charge of incoherence leveled by the incoherence argument would thus represent an incentive to further research. Yet an incoherence argument might still be understood to indicate that the target of the argument is a conceptual dead end such that further research might be a waste of time. Why spend valuable time trying to fix an apparently incoherent position when there are more promising positions available to be patched up? To the contrary, I suggest that apparently incoherent positions have a particular instrumental value over putatively more coherent positions, and this value lies precisely in requiring greater imagination applied to the solution of the philosophical problems they aim to address, greater imagination than what is required for more traditional, coherent, and comfortable positions. I am not the first to make such a suggestion. Fritzman himself, after arguing for the incoherence of coherence, argues against coherence as a general virtue, framing his argument in a historical context: "Beliefs which now are incoherent may be made coherent by the introduction of a new idea, or perspective, which reconciles or synthesizes them" (Fritzman 1992, p. 188). Furthermore, Fritzman cites Paul Feyerabend, who contends notoriously in Against Method that knowledge does not converge toward some ideal final theory, but represents an expansion of incompatible competing theories (Feyerabend 2010, pp. 15-16). Of course there is an uncomfortable tension in Fritzman's arguments, since if new ideas can make apparently incoherent beliefs coherent, then Fritzman's own incoherence argument may suffer the same fate, with the result that coherence is reaffirmed as a virtue. Comparable tensions have been noted with Feyerabend's position when applied to itself. So it is at the risk of falling into similar problems myself that I proceed to argue for the instrumental value of apparently incoherent positions. I think nevertheless that I can make a good case. I will frame this discussion against the background of a particular conception of the nature of philosophy. The success of science led to what Daniel Wilson calls "a crisis of confidence" (Wilson 1987, p. 235) in philosophy during the late nineteenth and early twentieth centuries, at least in the United States. The issue was whether philosophy should become more like the sciences in its methodologies and in the specialization of its concerns. Of course, if philosophy and the sciences were to share methodologies, then it would seem that only the subject matters of the two disciplines could properly distinguish them, which would raise the question of what the proper subject matter of philosophy is or should be. The traditional broad classification of philosophical subject divides its matters into 10 ethics, metaphysics and epistemology. However, if philosophy were to adopt the methods of the sciences, some of the traditional concerns that fall under these classifications would need to be abandoned, notably much of metaphysics, since these concerns could not be addressed by the scientific method. Yet other conceptions of the subject matter of philosophy have arisen to prominence over the last century, under the ascendancy of linguistic approaches to philosophy, such as the conception that philosophy is concerned with a priori or necessary statements. I do not share these conceptions of philosophy, and I think that it is somewhat misleading to seek the subject matter of philosophy in contradistinction to the subject matter of the sciences in the first place. I tend toward a different conception of philosophy, one grounded in its history or even pre-history, an older conception held by William James (James 1911, pp. 3-28), among others. It might seem that what follows should be accounted more as a mythology or fairy tale about philosophy, but such mythologies can serve a useful role in directing and motivating a discipline. It has been a long time since anyone has called philosophy the queen of the sciences, at least not with a straight face. The image of philosophy ruling over the sciences seems ludicrous now, and given the ascendancy of science in modern society, this demotion in rank and prestige for philosophy would seem to justify a crisis of confidence. Yet if not queen of the sciences, philosophy is surely the mother of the sciences, since the early history of philosophy included what is now recognized as the subject matter of the sciences, as seen most notably in the work of Aristotle. At one time, the sciences were known as natural philosophy before becoming functionally independent of philosophy. Psychology only became independent of philosophy in the late nineteenth century. This independence again raises the question of what should be the proper relation of philosophy to the sciences, if indeed philosophy has any role to play beyond understanding and articulating what science is doing. I suggest understanding the break of the sciences from philosophy in terms of the model of specialization within the sciences. As sciences progress, the increasingly detailed problem sets that need to be solved make it impractical for individual scientists to work in the whole of science, or even the whole of a broad field of science such as physics. Therefore physics becomes specialized as thermodynamics, fluid dynamics, quantum physics, and so forth. This does not mean that physics itself is nothing more than an aggregate of specializations, though. The role of physics in general lies in unifying the results of the specialized branches of physics. Sometimes those results across specializations are unified quite easily, but other times they raise conflicts or anomalies, which pose further problem sets in the affected specializations. Insofar as an individual physicist working in a specialized field seeks to unify those specialized results with results in other specializations, that physicist practices general physics, in addition to any primary specializations. I suggest that philosophy and the sciences can be understood comparably in terms of specialization. What is the subject matter of philosophy? Since the sciences and other rational disciplines seem historically to branch off from 11 philosophy, I suggest that the subject matter of philosophy is anything subject to rational inquiry. When a field of philosophy gains sufficient unity in terms of its methods and range of concerns, it specializes as an independent branch of study, as a science or other discipline. What is the role of philosophy, then? It seems that philosophy must study everything not specialized into a separate science or discipline, as well as unifying that study with the results from the specialized disciplines, and unifying the results from the specialized disciplines with each other. Insofar as an individual scientist seeks to unify the results of a branch of science with disciplines other than science, that scientist engages his subject as a philosopher, not as a specialized scientist. After all, where this unifying function extends beyond the sciences, it thereby extends beyond the methods of the sciences and therefore cannot be considered strictly part of scientific practice. This conception of philosophy does not reinstate philosophy as the queen of the sciences, since science remains autonomous in its specialization. However, it identifies a function that philosophy serves in relation to the sciences and other disciplines in terms of unifying and reconciling these disciplines. Yet what is relevant here to the discussion of apparently incoherent positions is not this unifying function of philosophy, but rather what remains out of the totality of what is subject to rational inquiry once the subject matter of the sciences and other disciplines has been subtracted. I have argued that this remnant falls to philosophy to study, since other disciplines delineate and restrict their subject matter and their methods as a result of specialization in order to gain productivity by focusing on specific problems in specific ways. Philosophy in general is not subject to such restrictions. Of this remnant that falls to philosophy, some fields have been fairly clearly defined, such as the traditional philosophical concerns with ethics, metaphysics, and epistemology, and of course these fields themselves have become further specialized just as individual sciences have become specialized. Yet what I would ask here is whether these previously identified philosophic fields and the scientific and other disciplines together exhaust the totality of what is subject to rational inquiry? Can one merely enumerate all the known disciplines and sciences and philosophical fields and claim that all knowledge falls into one of these categories? Or are there unexplored recesses of the remnants out of the totality of knowledge once these known disciplines are subtracted? If there are unexplored recesses, the sciences and other disciplines will not discover them, since by definition they fall outside of their delineated subject matters and methodologies. Therefore, philosophy would seem to be the only discipline in which these recesses could be explored. Yet insofar as philosophy itself has delineated particular subject matters such as ethics and epistemology, focusing strictly on these pre-existing subject matters would seem likewise to fail to discover any new subject matter. Here is where I would claim that apparently incoherent positions gain their instrumental value. Sensible solutions to traditional philosophical problems gain their sensibility by remaining within comfortable intellectual boundaries. Challenging solutions test those boundaries. Yet apparently incoherent solutions 12 tend to break those boundaries completely. If there is any new intellectual discipline to be discovered, I propose that it will be discovered by focusing on these apparently incoherent positions and by attempting to make sense out of apparent nonsense. The rationale behind this proposal derives precisely from my suspicions concerning incoherence arguments, namely that they seem to represent a failure to imagine what would be required to make a putatively incoherent position seem perfectly coherent. The imaginative demands of philosophers researching apparently incoherent positions may need to extend far beyond the comfortable intellectual boundaries that characterize putatively more sensible positions, possibly thereby extending into intellectual regions not encompassed by any existing discipline. In order to explore such regions, new methodologies would need to be devised, methodologies different from those of any existing scientific or philosophical discipline. By contrast, by holding to more sensible positions, a philosopher would likely remain within very comfortable intellectual boundaries, use methodologies that are already well known, and remain firmly within the bounds of existing disciplines. An initial problem may have been framed within an existing field of science or philosophy, but a solution may require the recognition of a new field altogether, with new ways of thinking and new methodologies. And here is where I think philosophy stands to gain value with regard to other disciplines. The philosophical function of unifying disparate branches of knowledge certainly has an important role to play in the overall scheme of knowledge, but more importantly, new philosophical ideas have the potential to revolutionize any number of other disciplines as well as the sciences. Such is the power of good ideas. Rather than aping the methods of the sciences and envying their success and prestige, I would suggest that philosophy should recognize its unique position with regard to knowledge as a whole and aim beyond its current bounds in search of something radically new. My suggestion is that apparently incoherent positions represent a unique locus for study whereby the limits of knowledge can be tested and possibly expanded. Those positions themselves may not turn out to be feasible in the end, but my proposal is that exploring those positions beyond the current bounds of common sense has an instrumental value in enabling new philosophical ideas and discoveries. In closing, let me cite one example of an apparently incoherent position that was later recognized not only as coherent, but as important. The example is well known and perhaps well worn, but I think it bears repeating in this context. It comes not from within philosophy, but from mathematics and geometry. The status of Euclid's parallel postulate as a postulate had bothered geometers for centuries. Part of what bothered them was that it seemed so incoherent that two lines should intersect if the interior angles formed by another line crossing these two were equal to two right angles. If that were so, then it seemed as though space would either explode hyperbolically or implode elliptically. Because of this seeming incoherence, some geometers thought that the parallel postulate could be proved as a theorem from the remaining postulates and axioms of Euclid's system. Yet in the early nineteenth century, Bolyai and Lobachevsky published treatises based on a denial of the parallel postulate and 13 thereby opened up the field of non-Euclidean geometry. Here, as with my previous discussion of the conception of coherence as systematicity, the clearest way to challenge the perception that denying the parallel postulate was incoherent was to produce a system denying it. The new field of non-Euclidean geometry became significant enough as a theoretical branch of geometry, but it became much more important with the application of a non-Euclidean geometry within relativity physics. What this new field of geometry required was someone with sufficient imagination to see how an apparently incoherent idea could work after all.1 References Bradley, F. H. (1914). Essays on Truth and Reality. Oxford: Oxford University Press. Feyerabend, Paul. (2010). Against Method. 4th ed. London: Verso. Fritzman, J. M. (1992). Against Coherence. American Philosophical Quarterly 29, no. 2: 183-191. Fumerton, Richard. (1994). The Incoherence of Coherence Theories. Journal of Philosophical Research 19: 89-102. Goodman, Nelson. (1978). Ways of Worldmaking. Indianapolis: Hackett Publishing Company. James, William. (1911). Some Problems of Philosophy. London: Longman, Green, and Co. Joachim, Harold H. (1906). The Nature of Truth. Oxford: Oxford University Press. Mackie, John L. (1964). Self-Refutation - A Formal Analysis. The Philosophical Quarterly 14, no. 56: 193-203. Passmore, John A. (1961). Philosophical Reasoning. New York: Basic Books. Priest, Graham. (2006). In Contradiction. 2nd ed. Oxford: Oxford University Press. Rescher, Nicholas. (1973). The Coherence Theory of Truth. Oxford: Oxford University Press. Sextus Empiricus. (2005). Against the Logicians. (R. Bett, Ed.). Cambridge: Cambridge University Press. Siegel, Harvey. (1968). Relativism, Truth, and Incoherence. Synthese 68, no. 2: 225-259. -. (1984). Goodmanian Relativism. Monist 67, no. 3: 359-375. Stack, Michael. (1983). Self-Refuting Arguments. Metaphilosophy 14, no. 3: 327-335. Stout, G. F. (1908). Immediacy, Mediacy and Coherence. Mind 17, no. 65: 20-47. 1This essay will be expanded and incorporated into a forthcoming book, tentatively entitled The Method of Perspectival Reduction. 14 Wilson, Daniel J. (1987). Science and the Crisis of Confidence in American Philosophy, 1870-1930. Transactions of the Charles S. Peirce Society 23: 235-262. http://www.markressler.com/doc/Value-of-Apparently-Incoherent-Positions.pdf