A Virtue-Based Defense of Mathematical Apriorism

Mathematical apriorists usually defend their view by contending that axioms are knowable a priori, and that the rules of inference in mathematics preserve this apriority for derived statements—so that by following the proof of a statement, we can trace the apriority being inherited. The empiricist Philip Kitcher attacked this claim by arguing there is no satisfactory theory that explains how mathematical axioms could be known a priori. I propose that in analyzing Ernest Sosa’s model of intuition as an intellectual virtue, we can construct an “intuition–virtue” that could supply the missing explanation for the apriority of axioms. I first argue that this intuition–virtue qualifies as an a priori warrant according to Kitcher’s account, and then show that it could produce beliefs about mathematical axioms independent of experience. If my argument stands, this paper could provide insight on how virtue epistemology could help defend mathematical apriorism on a larger scale.     

Necessity and Apriority

The classical view of the relationship between necessity and apriority, defended by Leibniz and Kant, is that all necessary truths are known a priori. The classical view is now almost universally rejected, ever since Saul Kripke and Hilary Putnam discovered that there are necessary truths that are known only a posteriori. However, in recent years a new debate has emerged over the epistemology of these necessary a posteriori truths. According to one view – call it the neo-classical view – knowledge of a necessary truth always depends on at least one item of a priori knowledge. According to the rival view – call it the neoempiricist view – our knowledge of necessity is sometimes broadly empirical. In this paper I present and defend an argument against the neo-empiricist view. I argue that knowledge of the necessity of a necessary truth could not be broadly empirical.     

Meaning‐Theories and the Principle of Humanity

In this paper, I briefly outline the notion of a truth‐conditional meaning‐theory and introduce two prominent problems it faces. The “extensionality problem” arises because not all correct specifications of truth‐conditions are meaning‐giving. The “explanatory problem” concerns the extent to which truth‐conditional meaning‐theories can contribute to the task of clarifying the nature of linguistic meaning. The “principle of humanity” is supposed to resolve both issues simultaneously. I argue that it fails to do so.     

On Moderate Pluralism About Truth and Logic

According to moderate truth pluralism, truth is both One and Many. There is a single truth property that applies across all truth-apt domains of discourse, but instances of this property are grounded in different ways. Propositions concerning medium-sized dry goods might be true in virtue of corresponding with reality while propositions pertaining to the law might be true in virtue of cohering with the body of law. Moderate truth pluralists must answer two questions concerning logic: (Q1) Which logic governs inferences concerning each truth-apt domain considered separately? (Q2) Which logic governs inferences that involve several truth-apt domains? This paper has three objectives. The first objective is to present and explain the moderate pluralist’s answers to (Q1) and (Q2). The second objective is to argue that there is a tension between these answers. The answer to (Q1) involves a commitment to a form of logical pluralism. However, reflection on the moderate truth pluralist’s answer to (Q2) shows that they are committed to taking logic to be topic neutrality. This, in turn, forces a commitment to logical monism. It would seem that the moderate truth pluralist cannot have it both ways. The third objective is constructive in nature. I offer an account of what moderate truth pluralists should say about logic and how they might resolve the tension in their view. I suggest that, just like moderate truth pluralists distinguish truth proper and “quasi-truth,” they should endorse a distinction between logic proper and “quasi-logic.” Quasi-truth is truth-like in the sense that instances of quasi-truth ground instances of truth. Quasi-logic is logic-like in the sense that it concerns arguments that are necessarily truth-preserving but are not generally so in a topic neutral way. I suggest that moderate truth pluralists should be monists about truth proper and logic proper but pluralists about quasi-truth and quasi-logic. This allows them to say that logic proper is topic neutral while still accommodating the idea that, for different domains, different arguments may be necessarily truth-preserving.     

Is open-mindedness truth-conducive?

What makes an intellectual virtue a virtue? A straightforward and influential answer to this question has been given by virtue-reliabilists: a trait is a virtue only insofar as it is truth-conducive. In this paper I shall contend that recent arguments advanced by Jack Kwong in defence of the reliabilist view are good as far as they go, in that they advance the debate by usefully clarifying ways in how best to understand the nature of open-mindedness. But I shall argue that these considerations do not establish the desired conclusions that open-mindedness is truth-conducive. To establish these much stronger conclusions we would need an adequate reply to what I shall call Montmarquet’s objection. I argue that Linda Zagzebski’s reply to Montmarquet’s objection, to which Kwong defers, is inadequate. I conclude that it is contingent if open-mindedness is truth-conducive, and if a necessary tie to truth is what makes an intellectual virtue a virtue, then the status of open-mindedness as an intellectual virtue is jeopardised. We either need an adequate reliabilist response to Montmarquet’s objection, or else seek alternative accounts of what it is that makes a virtue a virtue. I conclude by briefly outlining some alternatives.

     

Necessity and Language: In Defence of Conventionalism

Kalhat has forcefully criticised Wittgenstein's linguistic or conventionalist account of logical necessity, drawing partly on Waismann and Quine. I defend conventionalism against the charge that it cannot do justice to the truth of necessary propositions, renders them unacceptably arbitrary or reduces them to metalingustic statements. At the same time, I try to reconcile Wittgenstein's claim that necessary propositions are constitutive of meaning with the logical positivists’ claim that they are true by virtue of meaning. Explaining necessary propositions by reference to linguistic conventions does not reduce modal to non‐modal notions, but it avoids metaphysical accounts, which are incapable of explaining how we can have a priori knowledge of necessity.     

On the Reduction of Necessity to Essence

In his influential paper ‘‘Essence and Modality’’, Kit Fine argues that no account of essence framed in terms of metaphysical necessity is possible, and that it is rather metaphysical necessity which is to be understood in terms of essence. On his account, the concept of essence is primitive, and for a proposition to be metaphysically necessary is for it to be true in virtue of the nature of all things. Fine also proposes a reduction of conceptual and logical necessity in the same vein: a conceptual necessity is a proposition true in virtue of the nature of all concepts, and a logical necessity a proposition true in virtue of the nature of all logical concepts. I argue that the plausibility of Fine's view crucially requires that certain apparent explanatory links between essentialist facts be admitted and accounted for, and I make a suggestion about how this can be done. I then argue against the reductions of conceptual and logical necessity proposed by Fine and suggest alternative reductions, which remain nevertheless Finean in spirit.     

Supervenience,Repeatability, & Expressivism

Expressivists traditionally explain normative supervenience by saying it is a conceptual truth. I argue against this tradition in two steps. First, I show the modal claim that stands in need of explanation has been stated imprecisely. Classic arguments in metaethics for normative supervenience and those that rely on it as a premise presuppose a constraint on the supervenience base that is rarely (if ever) made explicit: the repeatability of the non-normative properties on which the normative supervenes. Non-normative properties are repeatable when it is possible for numerically distinct individuals to share them. Second, I show if the modal truth that stands in need of explanation entails that there are individuals exactly alike in repeatable non-normative respects that cannot normatively differ, then standard expressivist accounts of normative supervenience as a conceptual truth are unsuccessful. Expressivist metasemantics for normative terms, together with constitutive facts about the non-cognitive attitudes essentially involved in normative thought, strongly suggest that repeatable supervenience could not be a conceptual truth. I argue, finally, that although repeatable supervenience bears the marks of a conceptual truth, expressivists should be content to treat it as an ordinary normative truth, and to explain it the same way they explain other normative truths.     

Kantian Moral Retributivism: Punishment,Suffering, and the Highest Good

Against the view of some contemporary Kantians who wish to downplay Kant's retributivist commitments, I argue that Kant's theory of practical of reason implies a retributive conception of punishment. I trace this view to Kant's distinction between morality and well‐being and his attempt to synthesize these two concerns in the idea of the highest good. Well‐being is morally valuable only insofar as it is proportional to virtue, and the suffering inflicted on wrongdoers as punishment for wrongdoing is morally good so long as it is proportional to the wrongdoing. According to Kantian retributivism, punishment is warranted as a means to promote proportionality between well‐being and virtue.     

Agency,Thought, and Language: Analytic Philosophy Goes to School

I take as my starting point recent concerns from within educational psychology about the need to treat the conceptual and philosophical underpinnings of empirical research in the field more seriously, specifically in the context of work on the self, mind and agency. Developing this theme, I find such conceptual support in the writings of P. F. Strawson and Donald Davidson, two giants of analytic philosophy in the second half of the Twentieth Century. Drawing particularly on Davidson’s later work, in which he seeks to integrate key claims about subjectivity, objectivity, belief, truth and knowledge, within what he refers to as a triangular framework of two speakers and a common world, I find support for pedagogic and classroom organizational structures based on collaborative thinking and dialogue. While Davidson did not write about education, I argue that his framework has much to offer, most particularly in view of the priority it affords language and dialogue as the necessary and sufficient conditions for reason, belief and thought—in short, for being a person in the world.     

Leave Truth Alone: On Deflationism and Contextualism

Abstract: According to deflationism, grasp of the concept of truth consists in nothing more than a disposition to accept a priori (non‐paradoxical) instances of the schema: (DS) It is true that p if and only if p. According to contextualism, the same expression with the same meaning might, on different occasions of use, express different propositions bearing different truth‐conditions (where this does not result from indexicality and the like). On this view, what is expressed in an utterance depends in a non‐negligible way on the circumstances. Charles Travis claims that contextualism shows that ‘deflationism is a mistake’, that truth is a more substantive notion than deflationism allows. In this paper, I examine Travis's arguments in support of this ‘inflationary’ claim and argue that they are unsuccessful.     

Default reasonableness and the mathoids

In this paper I will argue that (principled) attempts to ground a priori knowledge in default reasonable beliefs cannot capture certain common intuitions about what is required for a priori knowledge. I will describe hypothetical creatures who derive complex mathematical truths like Fermat’s last theorem via short and intuitively unconvincing arguments. Many philosophers with foundationalist inclinations will feel that these creatures must lack knowledge because they are unable to justify their mathematical assumptions in terms of the kind of basic facts which can be known without further argument. Yet, I will argue that nothing in the current literature lets us draw a principled distinction between what these creatures are doing and paradigmatic cases of good a priori reasoning (assuming that the latter are to be grounded in default reasonable beliefs). I will consider, in turn, appeals to reliability, coherence, conceptual truth and indispensability and argue that none of these can do the job.     

AN ARCHIMEDEAN POINT FOR PHILOSOPHY

Abstract: According to an orthodox account of meaning and translation, meaning is a property of expressions of a language, and translation is a matching of synonymous expressions across languages. This linguistic account of translation gives rise to well‐known skeptical conclusions about translation, objectivity, meaning, and truth, but it does not conform to our best translational practices. In contrast, I argue for a textual account of meaning based on the concept of a text‐type that does conform to our best translational practices. With their semantic function in view, text‐types are Archimedean points for their respective disciplines. The text‐type of philosophy is no exception. Culture‐transcendent conceptual analysis can proceed on firm footing without having to deny the reality of radical cultural and linguistic difference by treating components of text‐types as the concepts to be analyzed. Analyses of central philosophical concepts are provided as a means of adjudicating philosophical controversy.     

Play, agreement and consensus

In this paper I employ the analysis of play to clarify the distinction between an agreement and a consensus, and I argue that it is the conditions supplied by the playful process that enable us to partake in the recognition and creation of truth. Gadamer's hermeneutical truth, unlike propositional truth, speaks of the interpretive act whereby meaning is recognized. This interpretive recognition of meaning is described by Gadamer as an occurrence of interpretive play orgenuine understanding. Regarding Gadamer's conception of truth as modelled on agreement rather than consensus, I demonstrate that it is in the process of play that we achieve the making and maintaining of the conditions that are necessary for agreement, and that the nature of understanding is most clearly revealed by viewing it as a playful process.     

James Fodor's Christian Theory of Truth: Is it Christian?

The 'task confronting contemporary theology', says James Fodor, 'is that of the rehabilitation or recovery of a distinctively Christian vision of truth' ( Christian Hermeneutics [Oxford, 1995] p. 72). In this paper I examine Fodor's attempt to construct a Christian or transformational theory of truth. I argue that his analysis of truth in terms of transformation leads to a concept of truth which is both subjective and relative. I argue further that Fodor's truth theory is either committed to a version of creative anti-realism, according to which the existence of basic structure of the world is determined by our linguistic activities, or it implies that although our language doesn't correspond to the world, we should go on making our theological truth claims anyway. I conclude that Fodor's Christian theory of truth is in most crucial respects not Christian at all.     

Modal rationalism and the demonstrative reply to the scrutability argument against physicalism

According to the scrutability argument against physicalism, an a priori gap between the physical and conscious experience entails a lack of necessitation and the falsity of physicalism. This paper investigates the crucial premise of the scrutability argument: the inference from an a priori gap to a lack of necessitation. This premise gets its support from modal rationalism, according to which there are important, potentially constitutive, connections between a priori justification and metaphysical modality. I argue against the strong form of modal rationalism that underwrites the scrutability argument and suggest a more moderate rationalist view. I offer a novel demonstrative reply to the scrutability argument, according to which demonstratives play a vital role in the generation of meaning for our representations of conscious experience. This connection between conscious experience and demonstratives, rather than a metaphysical gap generated by the truth of dualism, is the source of the epistemic gap between consciousness and the physical.

     

Play,agreement and consensus

In this paper I employ the analysis of play to clarify the distinction between an agreement and a consensus, and I argue that it is the conditions supplied by the playful process that enable us to partake in the recognition and creation of truth. Gadamer's hermeneutical truth, unlike propositional truth, speaks of the interpretive act whereby meaning is recognized. This interpretive recognition of meaning is described by Gadamer as an occurrence of interpretive play orgenuine understanding. Regarding Gadamer's conception of truth as modelled on agreement rather than consensus, I demonstrate that it is in the process of play that we achieve the making and maintaining of the conditions that are necessary for agreement, and that the nature of understanding is most clearly revealed by viewing it as a playful process.     

Intensional Specifications of Truth-Conditions: ‘Because’, ‘In Virtue of’, and ‘Made True By…’

Although a number of truth theorists have claimed that a deflationary theory of ‘is true’ needs nothing more than the uniform implication of instances of the theorem ‘the proposition that p is true if and only if p’, reflection shows that this is inadequate. If deflationists can’t support the instances when replacing the biconditional with ‘because’, then their view is in peril. Deflationists sometimes acknowledge this by addressing, occasionally attempting to deflate, ‘because’ and ‘in virtue of’ formulas and their close relatives. I examine what I take to be the most promising deflationist moves in this direction and argue that they fail.     

C. I. Lewis,Kant, and the reflective method of philosophy

ABSTRACT

If it seems unquestionable that C. I. Lewis is a Kantian in important respects, it is more difficult to determine what, if anything, is original about his Kantianism. For it might be argued that Lewis’ Kantianism simply reflects an approach to the a priori which was very common in the first half of the twentieth century, namely, the effort to make the a priori relative. In this paper, I will argue that Lewis’ Kantianism does present original features. The latter can be detected by focusing on Lewis’ account of the method of philosophy in the first chapter of Mind and the World Order. In that context, Lewis argues that the method of philosophy should be reflective and critical. It will be my contention that this understanding of philosophy involves a therapeutic perspective, which bears important resemblances to Kant’s account of transcendental reflection in the Amphiboly of the Critique of Pure Reason. I will illustrate how this therapeutic application of reflection works in Lewis’ metaphysics. In this context, reflection can correct errors of reasoning that occur when we are operating within a particular conceptual scheme and use the criteria of reality that are appropriate in another.