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.     

The defeater version of Benacerraf’s problem for a priori knowledge

Paul Benacerraf’s argument that mathematical realism is apparently incompatible with mathematical knowledge has been widely thought to also show that a priori knowledge in general is problematic. Although many philosophers have rejected Benacerraf’s argument because it assumes a causal theory of knowledge, some maintain that Benacerraf nevertheless put his finger on a genuine problem, even though he didn’t state the problem in its most challenging form. After diagnosing what went wrong with Benacerraf’s argument, I argue that a new, more challenging, version of Benacerraf’s problem can be constructed. The new version—what I call the Defeater Version—of Benacerraf’s problem makes use of a no-defeater condition on knowledge and justification. I conclude by arguing that the best way to avoid the problem is to construct a theory of how a priori judgments reliably track the facts. I also suggest four different kinds of theories worth pursuing.     

Philosophy Upside Down?

Philip Kitcher recently argued for a reconstruction in philosophy. According to him, the contemporary mainstream of philosophy (in the English‐speaking world, at least) has deteriorated into something that is of relevance only to a few specialists who communicate with each other in a language nobody else understands. Kitcher proposes to reconstruct philosophy along two axes: a knowledge axis (with a focus on the sciences) and a value axis. The present article discusses Kitcher's diagnosis as well as his proposal of a therapy. It argues that there are problems with both, and it ends with an alternative view of what some core problems of the profession currently are.     

Dummett's intuitionism is not strict finitism

Michael Dummett's anti-realism is founded on the semantics of natural language which, he argues, can only be satisfactorily given in mathematics by intuitionism. It has been objected that an analog of Dummett's argument will collapse intuitionism into strict finitism. My purpose in this paper is to refute this objection, which I argue Dummett does not successfully do. I link the coherence of strict finitism to a view of confirmation — that our actual practical abilities cannot confirm we know what would happen if we could compute impracticably vast problems. But to state his case, the strict finitists have to suppose that we grasp the truth conditions of sentences we can't actually decide. This comprehension must be practically demonstrable, or the analogy with Dummett's argument fails. So, our actual abilities must be capable of confirming that we know what would be the case if actually undecidable sentences were true, contradicting the view of confirmation. I end by considering objections.I especially want to thank Alex George and Philip Kitcher for their help on this paper. I'd also like to thank the members of the Propositional Attitudes Task Force, Jane Braaten, Jay Garfield, Lee Bowie, Murray Kitely and Tom Tymoczko. My thanks also to Peter Godfrey-Smith and the anonymous reviewers of Synthese, one of whom was particularly helpful.     

THE MODAL ARGUMENT FOR A PRIORI JUSTIFICATION

Kant famously argued that, from experience, we can only learn how something actually is, but not that it must be so. In this paper, I defend an improved version of Kant's argument for the existence of a priori knowledge, the Modal Argument , against recent objections by Casullo and Kitcher. For the sake of the argument, I concede Casullo's claim that we may know certain counterfactuals in an empirical way and thereby gain epistemic access to some nearby, nomologically possible worlds. But I maintain that our beliefs about metaphysical necessities still cannot be justified empirically. Furthermore, I reject Casullo's deflationary thesis about the significance of such justification. Kitcher's most troublesome objection is that we can gain any modal justification whatsoever through testimony , i.e. in an experiential way. This can be countered by distinguishing between productive sources of justification, like perception, and merely reproductive sources, like testimony. Thus, some productive a priori source will always be needed somewhere. ¹     

The Fragility of Moral Principles

According to a widely accepted conceptual model, principles play essential roles in moral reasoning: it is asserted that they hold universally and cannot be avoided in the justification of human action and belief. This paper challenges that view. It argues that, though some principles play such substantive roles, most do not. They can be characterized instead as being fragile or defeasible, i.e., they are capable of being weakened, voided or undone. The claim is made that it is the pressures exerted by particular cases of moral dilemmas that are the sources of such fragility. The paper contains detailed examples illustrating how the process of defeasibility, including a retreat into moral vacuity, arises from such pressures.     

Practical success and the nature of truth

Philip Kitcher has argued for a causal correspondence view of truth, as against a deflationary view, on the grounds that the former is better poised than the latter to explain systematically successful patterns of action. Though Kitcher is right to focus on systematically successful action, rather than singular practical successes, he is wrong to conclude that causal correspondence theories are capable of explaining systematic success. Rather, I argue, truth bears no explanatory relation to systematic practical success. Consequently, the causal correspondence view is not in a better position to explain success than the deflationary view; theories of truth are the wrong place to look for explanations of systematic practical success.     

Kagan on Speciesism and Modal Personism

Shelly Kagan argues in his ‘What's Wrong with Speciesism?’ for four provocative claims: 1. speciesism is not necessarily a mere prejudice; 2. most people are not speciesists; 3. ‘modal personism’ more closely reflects what most people believe, and 4. modal personism might be true. In this article, I object to Kagan's account of what constitutes a ‘mere prejudice’, and I object to the sort of argument he uses to show that most people are not speciesist. I then attempt to motivate, and defend what I take to be the best version of modal personism; answer several problems for the view; and raise other problems that I think are harder to answer.     

Truth, Warrant and Superassertibility

In a recent paper on Truth, Knowability and Neutrality Timothy Kenyon sets out to defend the coherence of a putative anti-realist truth-predicate, superassertibility, due to Wright (1992, 1999), against a number of Wright’s critics. By his own admission, the success of Kenyon’s defensive strategies turns out to hinge upon a realist conception of absolute warrant which conflicts with the anti-realist character of the original proposal, based, as it was, on a notion of defeasible warrant. Kenyon’s potential success in resisting Wright’s critics brings a pyrrhic victory: either way, realism wins. Here I argue that the link between superassertibility and defeasible warrant can be restored in a way which clarifies the consistency of the pair, provided that the notion of inference to superassertibility is properly understood in logical terms. As one might expect, the requisite notion is not classical in character. As one might not expect, the notion cannot be properly construed in intuitionist terms either. Hence, I propose an alternative logical framework which, I believe, is at least formally adequate to the representation of superassertibility on the basis of defeasible warrant. The price to be paid for rejecting the ‘third way’ proposed here in favour of either of the two more traditional logical options is precisely that indicated by Kenyon’s discussion.     

Take If from Me: The Epistemological Status of Testimony

Testimony consists in imparting information without supplying evidence or argument to back one's claims. To what extent does testimony convey epistemic warrant? C. J. A. Coady argues, on Davidsonian grounds, that (1) most testimony is true, hence (2) most testimony supplies warrant sufficient for knowledge. I appeal to Grice's maxims to undermine Coady's argument and to show that the matter is more complicated and context‐sensitive than is standardly rocognized. Informative exchanges take place within networks of shared, tacit assumptions that affect the scope and strength of our claims, and the level of warrant required for their responsible assertion. The maxims explain why different levels of warrant are transferred in different contexts.     

Explaining dubious assertions

David Sosa argues that the knowledge account of assertion is unsatisfactory, because it cannot explain the oddness of what he calls dubious assertions. One such dubious assertion is of the form ‘P but I do not know whether I know that p.’ Matthew Benton has attempted to show how proponents of the knowledge account can explain what’s wrong this assertion. I show that Benton’s explanation is inadequate, and propose my own explanation of the oddness of this dubious assertion. I also explain what’s wrong with other dubious assertions mentioned by Sosa.     

Williamson on Knowledge and Psychological Explanation

According to many philosophers, psychological explanation canlegitimately be given in terms of belief and desire, but not in termsof knowledge. To explain why someone does what they do (so the common wisdom holds) you can appeal to what they think or what they want, but not what they know. Timothy Williamson has recently argued against this view. Knowledge, Williamson insists, plays an essential role in ordinary psychological explanation.Williamson's argument works on two fronts.First, he argues against the claim that, unlike knowledge, belief is``composite' (representable as a conjunction of a narrow and a broadcondition). Belief's failure to be composite, Williamson thinks, undermines the usual motivations for psychological explanation in terms of belief rather than knowledge.Unfortunately, we claim, the motivations Williamson argues against donot depend on the claim that belief is composite, so what he saysleaves the case for a psychology of belief unscathed.Second, Williamson argues that knowledge can sometimes provide abetter explanation of action than belief can.We argue that, in the cases considered, explanations that cite beliefs(but not knowledge) are no less successful than explanations that citeknowledge. Thus, we conclude that Williamson's arguments fail both coming andgoing: they fail to undermine a psychology of belief, and they fail tomotivate a psychology of knowledge.     

Kant’s “I think” and the agential approach to self-knowledge

ABSTRACT

This paper relates Kant’s account of pure apperception to the agential approach to self-knowledge. It argues that his famous claim ‘The I think must be able to accompany all of my representations’ (B131) does not concern the possibility of self-ascribing beliefs. Kant does advance this claim in the service of identifying an a priori warrant we have as psychological persons, that is, subjects of acts of thinking that are imputable to us. But this warrant is not one to self-knowledge that we have as critical reasoners. It is, rather, an a priori warrant we have, as thinkers, to prescribe to given representations their conformity to principles of thinking inherent in our capacity of understanding itself.     

Transmission of warrant-failure and the notion of epistemic analyticity

In this paper I will argue that Boghossian's explanation of how we can acquire a priori knowledge of logical principles through implicit definitions commits a transmission of warrant-failure. To this end, I will briefly outline Boghossian's account, followed by an explanation of what a transmission of warrant-failure consists in. I will also show that this charge is independent of the worry of rule-circularity which has been raised concerning the justification of logical principles and of which Boghossian is fully aware. My argument comes in two steps: firstly, I will argue for the insufficiency of Boghossian's template which is meant to explain how a subject can acquire a warrant for logical principles. I will show however that this insufficiency of his template can be remedied by adopting what I call the Disquotational Step. Secondly, I will argue that incorporating this further step makes his template subject to a transmission of warrant-failure, assuming that certain rather basic and individually motivated principles hold. Thus, Boghossian's account faces a dilemma: either he adopts the Disquotational Step and subjects his account to the charge of a transmission of warrant-failure, or he drops this additional step leaving the account confronted with explaining the gap that has previously been highlighted. I will then suggest various rejoinders that Boghossian might adopt but none of which—I will argue—can resolve the dilemma. Lastly, I will raise and briefly discuss the question whether this worry generalizes to other accounts, such as Hale and Wright's that aim to explain our knowledge of logic and/or mathematics in virtue of implicit definitions.     

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.     

Testimonially based Knowledge from False Testimony

I provide an example to illustrate the contention that there are cases in which a recipient can acquire testimonially based knowledge from false testimony. The example involves a case in which the proposition believed by the recipient, though derived in a testimonially based way, is not identical with the proposition attested to. I conclude by suggesting that if we are to make sense of such cases as cases of testimonially based knowledge, we need to make some revisions both in our conception of the ways in which testimonially-grounded warrant can accrue to a belief and in our conception of what 'testimonial authority' can apply to.     

Contextualism and the Knowledge Norms

Epistemic contextualism is widely believed to be incompatible with the recently popular view that knowledge is the norm of assertion, practical reasoning, or belief. I argue in this article that the problems arising for contextualism from the mentioned normative views are only apparent and can be resolved by acknowledging the fairly widespread phenomenon of non‐obvious context‐sensitivity (recently embraced by even some of contextualism's most ardent former critics). Building on recent insights about non‐obvious context‐sensitivity, the article outlines an independently attractive contextualist account of the mentioned epistemic norms and provides a solution to the puzzles they give rise to in a contextualist framework.     

"Two Concepts of Liberty" Through African Eyes

In "Two Concepts of Liberty" Berlin notes the protean nature of the word "freedom" and then systematically proceeds to narrow its range of meanings. In the process, Berlin eliminates much of what most people, in everyday communication, regard as freedom, believing that this is in the best interest of intellectual clarity. As he puts it:
[N]othing is gained by a confusion of terms. To avoid glaring inequality or widespread misery I am ready to sacrifice some, or all, of my freedom: I may do so willingly and freely: but it is freedom that I am giving up for the sake of justice or equality or the love of my fellow men. I should be guilt-stricken, and rightly so, if I were not, in some circumstances, ready to make this sacrifice. But a sacrifice is not an increase in what is being sacrificed, namely freedom, however great the moral need or the compensation for it. Everything is what it is: liberty is liberty, not equality or fairness or justice or culture, or human happiness or a quiet conscience. (Emphasis added).
Berlin's other, perhaps overarching, aim is to show how inattention to the specificity of the meanings of concepts might have potentially dangerous political repercussions. He implicitly argues that the intellectuals who promoted the idea of positive freedom as opposed to that of negative freedom contributed to the emergence of totalitarianism and fascism in Europe.     

Wittgenstein,Theories of Meaning,and Linguistic Disjunctivism

This paper argues that Wittgenstein opposed theories of meaning, and did so for good reasons. Theories of meaning, in the sense discussed here, are attempts to explain what makes it the case that certain sounds, shapes, or movements are meaningful linguistic expressions. It is widely believed that Wittgenstein made fundamental contributions to this explanatory project. I argue, by contrast, that in both his early and later works, Wittgenstein endorsed a disjunctivist conception of language which rejects the assumption underlying the question that such theories seek to answer—namely, the assumption that the notion of a meaningful linguistic expression admits of non‐circular analysis. Moreover, I give two arguments in favor of the view I ascribe to Wittgenstein: one based on later Wittgenstein's discussion of meaning skepticism and one based on considerations concerning the identity of linguistic expressions.