The semantics of knowledge attributions

The basic idea of conversational contextualism is that knowledge attributions are context sensitive in that a given knowledge attribution may be true if made in one context but false if made in another, owing to differences in the attributors’ conversational contexts. Moreover, the context sensitivity involved is traced back to the context sensitivity of the word “know,” which, in turn, is commonly modelled on the case either of genuine indexicals such as “I” or “here” or of comparative adjectives such as “tall” or “rich.” But contextualism faces various problems. I argue that in order to solve these problems we need to look for another account of the context sensitivity involved in knowledge attributions and I sketch an alternative proposal.     

Contextualism on a pragmatic,not a skeptical,footing

Contextualism is supposed to explain why the following argument for skepticism seems plausible: (1) I don’t know that I am not a bodiless brain-in-a-vat (BIV); (2) If I know I have hands, then I know I am not a bodiless BIV; (3) Therefore, I do not know I have hands. Keith DeRose claims that (1) and (2) are “initially plausible.” I claim that (1) is initially plausible only because of an implicit argument that stands behind it; it is not intuitively plausible. The argument DeRose offers is based on the requirement of sensitivity, that is, on the idea that if you know something then you would not believe it if it were false. I criticize the sensitivity requirement thereby undercutting its support for (1) and the skeptical data that contextualism is meant to explain. While skepticism is not a plausible ground for contextualism, I argue that certain pragmatic considerations are. It’s plausible to think that to know something more evidence is required when more is at stake. The best way to handle skepticism is to criticize the arguments for it. We should not adopt contextualism as a means of accommodating skepticism even if there are other pragmatic reasons for being a contextualist about knowledge.     

Why contextualists cannot know they are right: Self-refuting implications of contextualism

Conversational contextualism in epistemology is characterized by four main theses: 1. the indexicality of knowledge claims thesis; 2. the attributor contextualism thesis; 3. the conversational contextualism thesis, and 4. the main thesis of contextualism according to which a knowledge claim can be true in one context and false in another context in which more stringent standards for knowledge are operant. It is argued that these theses taken together generate problems for contextualism. In particular, it is shown that there is no context in which the contextualist can truthfully claim to know her theory is true. Since these results were obtained only with principles the contextualist cannot give up—like the principle of epistemic closure and the principle that knowledge implies truth—it seems that contextualism is in need of a thoroughgoing revision if it is to become a successful epistemic theory.     

Contextualist theories of knowledge

Contextualist theories of knowledge offer a semantic hypothesis to explain the observed contextual variation in what people say they know, and the difficulty people have resolving skeptical paradoxes. Subject or speaker relative versions make the truth conditions of “S knows that p” depend on the standards of either the knower’s context (Hawthorne and Stanley) or those of the speaker’s context (Cohen and DeRose). Speaker contextualism avoids objections to subject contextualism, but is implausible in light of evidence that “know” does not behave like an indexical. I deepen and extend these criticisms in light of recent defenses by contextualists (including Ludlow). Another difficulty is that whether certain standards are salient or intended does not entail that they are the proper standards. A normative form of contextualism on which the truth of a knowledge claim depends on the proper standards for the context is more promising, but still unsatisfactory whether the view is speaker or subject relative. I defend alternative explanations for the observed linguistic and psychological data: a pragmatic account for some cases and a cognitive account for others.¹ I presented this paper at the 2004 Bled Conference on Contextualism, sponsored by Mirabor and Northern Illinois Universities.     

Is Believing at Will ‘Conceptually Impossible’?

In this paper I discuss the claim that believing at will is ‘conceptually impossible’ or, to use a formulation encountered in the debate, “that nothing could be a belief and be willed directly”. I argue that such a claim is only plausible if directed against the claim that believing itself is an action-type. However, in the debate, the claim has been univocally directed against the position that forming a belief is an action-type. I argue that the many arguments offered in favor of the ‘conceptual impossibility’ of performing such actions fail without exception. If we are to argue against doxastic voluntarism we are better off by resorting to more modest means.

In Defense of Epistemic Circularity

In this paper I defend epistemic circularity by arguing that the “No Self-Support” principle (NSS) is false. This principle, ultimately due to Fumerton (1995), states that one cannot acquire a justified belief in the reliability of a source of belief by trusting that very source. I argue that NSS has the skeptical consequence that the trustworthiness of all of our sources ultimately depends upon the trustworthiness of certain fundamental sources – sources that we cannot justifiably believe to be reliable. This is a problem, I claim, because if the trustworthiness of all of our sources depends upon sources that we should not believe to be reliable, then a reflective individual should not trust any of his sources at all. The hidden cost of rejecting epistemic circularity is thus the unacceptable skeptical thesis that reflective individuals like you and I have no justified beliefs whatsoever.     

A Priori knowledge contextualised and Benacerraf’s dilemma

In this article, I discuss Hawthorne’s contextualist solution to Benacerraf’s dilemma. He wants to find a satisfactory epistemology to go with realist ontology, namely with causally inaccessible mathematical and modal entities. I claim that he is unsuccessful. The contextualist theories of knowledge attributions were primarily developed as a response to the skeptical argument based on the deductive closure principle. Hawthorne uses the same strategy in his attempt to solve the epistemologist puzzle facing the proponents of mathematical and modal realism, but this problem is of a different nature than the skeptical one. The contextualist theory of knowledge attributions cannot help us with the question about the nature of mathematical and modal reality and how they can be known. I further argue that Hawthorne’s account does not say anything about a priori status of mathematical and modal knowledge. Later, Hawthorne adds to his account an implausible claim that in some contexts a gettierized belief counts as knowledge.     

Understanding, Integration, and Epistemic Value

Understanding enjoys a special kind of value, one not held by lesser epistemic states such as knowledge and true belief. I explain the value of understanding via a seemingly unrelated topic, the implausibility of veritism. Veritism holds that true belief is the sole ultimate epistemic good and all other epistemic goods derive their value from the epistemic value of true belief. Veritism entails that if you have a true belief that p, you have all the epistemic good qua p. Veritism is a plausible and widely held view; I argue that it is untenable. I argue that integration among beliefs possesses epistemic value independent from the good of true belief, and so has value veritism cannot account for. I argue further that this integration among beliefs comprises the distinctive epistemic value of understanding.     

Coherentism,Truth, and Witness Agreement

Coherentists on epistemic justification claim that all justification is inferential, and that beliefs, when justified, get their justification together (not in isolation) as members of a coherent belief system. Some recent work in formal epistemology shows that “individual credibility” is needed for “witness agreement” to increase the probability of truth and generate a high probability of truth. It can seem that, from this result in formal epistemology, it follows that coherentist justification is not truth-conducive, that it is not the case that, under the requisite conditions, coherentist justification increases the probability of truth and generates a high probability of truth. I argue that this does not follow.     

The modality principle and work-relativity of modality

Davies argues that the ontology of artworks as performances offers a principled way of explaining work-relativity of modality. Object oriented contextualist ontologies of art (Levinson) cannot adequately address the problem of work-relativity of modal properties because they understand looseness in what counts as the same context as a view that slight differences in the work-constitutive features of provenance are work-relative. I argue that it is more in the spirit of contextualism to understand looseness as context-dependent. This points to the general problem—the context of appreciation is not robust enough to ground modal intuitions about objective entities. In general, when epistemology dictates ontology there is always a threat of anti-realism, scepticism and relativism. Davies also appeals to the modality principle—an entity’s essential properties are all and only its constitutive properties. Davies understands essentiality in a traditional way: a property P is an essential property of an object o iff o could not exist and lack P. Kit Fine has recently made a convincing case for the view that the notion of essence is not to be understood in modal terms. I explore some of the implications of this view for Davies’ modal argument for the performance theory.     

Relevance and Relationalism

This paper will provide support for relationalism; the claim that the identity of objects is constituted by the totality of their relations to other things in the world. I will consider how Kit Fine’s criticisms of essentialism within modal logic not only highlight the inability of modal logic to account for essential properties but also arouse suspicion surrounding the possibility of nonrelational properties. I will claim that Fine’s criticisms, together with concerns surrounding Hempel’s paradox, show that it is not possible to provide a satisfactory account of certain properties in abstraction from their place within a wider context. Next, we will shift attention to natural kinds and consider the notion that relevance plays in metaphysical accounts of identity, by examining Peter Geach’s notion of relative identity. I will argue that the intensional relation between subject and object must be included in a satisfactory account of metaphysical identity.     

The Leibniz’s Law Problem (For Stage Theory)

Stage theorists invoke the idea of counterpart relations to make sense of how objects are able to persist despite their claim that an object is identical with a single instantaneous stage. According to stage theorists, an object persists if and only if it has a later counterpart that bears the appropriate counterpart relation of identity to it. Whilst objects can and do persist, stages cannot and do not. This seems to amount to a refutation of Leibniz’s law. Stage theorists think that the nature of the counterpart relation invoked depends on how it is that the object is referred to. In this paper, I argue that the context sensitivity that they invoke here gives stage theorists a response to the Leibniz’s Law Problem.     

Contextualism and conceptual disambiguation

I distinguish between Old Contextualism, New Contextualism, and the Multiple Concepts Theory. I argue that Old Contextualism cannot handle the following three problems: (i) the disquotational paradox, (ii) upward pressure resistance, (iii) inability to avoid the acceptance of skeptical conclusions. New Contextualism, in contrast, can avoid these problems. However, since New Contextualism appears to be a semanticized mirror image of MCT, it remains unclear whether it is in fact a genuine version of contextualism.     

Epistemological Skepticism, Semantic Blindness, and Competence-Based Performance Errors

The semantic blindness objection to contextualism challenges the view that there is no incompatibility between (i) denials of external-world knowledge in contexts where radical-deception scenarios are salient, and (ii) affirmations of external-world knowledge in contexts where such scenarios are not salient. Contextualism allegedly attributes a gross and implausible form of semantic incompetence in the use of the concept of knowledge to people who are otherwise quite competent in its use; this blindness supposedly consists in wrongly judging that there is genuine conflict between claims of type (i) and type (ii). We distinguish two broad versions of contextualism: relativistic-content contextualism and categorical-content contextualism. We argue that although the semantic blindness objection evidently is applicable to the former, it does not apply to the latter. We describe a subtle form of conflict between claims of types (i) and (ii), which we call différance-based affirmatory conflict. We argue that people confronted with radical-deception scenarios are prone to experience a form of semantic myopia (as we call it): a failure to distinguish between différance-based affirmatory conflict and outright inconsistency. Attributing such semantic myopia to people who are otherwise competent with the concept of knowledge explains the bafflement about knowledge-claims that so often arises when radical-deception scenarios are made salient. Such myopia is not some crude form of semantic blindness at all; rather, it is an understandable mistake grounded in semantic competence itself: what we call a competence-based performance error.     

Assertibility and Sensitivity

Epistemologists have proposed various norms of assertion to explain when a speaker is in an epistemic position to assert a proposition. In this article I propose a distinct necessary condition on assertibility: that a speaker should assert only what she sensitively believes, where a subject's belief is sensitive just in case the subject would not hold it if it were false. I argue that the Sensitivity Rule underwrites simple explanations for three key features of assertibility that pose explanatory challenges to other prominent proposals: the fact that assertibility is open under known entailment, the general impropriety of assertions that a lottery ticket has lost made purely on the basis of the speaker's knowledge of the odds, and the fact that assertibility varies widely with features of the conversational context. I close by considering three distinct roles the Sensitivity Rule might play in the overall theory of assertibility.     

RESEARCH IN MATHEMATICS EDUCATION: SOME ISSUES AND SOME EMERGING INFLUENCES

In this article, I introduce a typology of forms of algebraic thinking. In the first part, I argue that the form and generality of algebraic thinking are characterised by the mathematical problem at hand and the embodied and other semiotic resources that are mobilised to tackle the problem in analytic ways. My claim is based not only on semiotic considerations but also on new theories of cognition that stress the fundamental role of the context, the body and the senses in the way in which we come to know. In the second part, I present some concrete examples from a longitudinal classroom research study through which the typology of forms of algebraic thinking is illustrated.     

Problems for Broome’s Cognitivist Account of Instrumental Reasoning

In this paper, I examine an account of instrumental reasoning recently put forth by John Broome. His key suggestion is that anyone who engages in reasoning about his intentions also believes that he will do what he intends to do and that combined with a belief about necessary means this creates rational pressure towards believing that one will take the necessary means. I argue that Broome’s model has three significant problems; his key premise is false—the sincere expression of an intention does not entail the belief that one will successfully execute that intention; his account yields a model of instrumental reasoning that is uncomfortably reflective; he seems unable to explain the rational pressure towards taking necessary means that arises directly from having an end and an instrumental belief. All three problems, I argue, are a consequence of Broome’s inadequate position on what it is to intend to do something.     

Rethinking common belief,revision, and backward induction

Whether rationality and common belief in rationality jointly entail the backward inductive outcome in centipede games has long been debated. Stalnaker’s compelling negative argument appeals to the AGM belief revision postulates to argue that off-path moves may be rational, given the revisions they may prompt. I counter that the structure of common belief and the principles of AGM justify an additional assumption about revision. I then prove that, given my proposed constraint, for all finite, n-player, extensive form, perfect information games with a unique backward inductive solution, if there is initial common belief in rationality, then backward induction is guaranteed.     

Alethic Functionalism,Manifestation, and the Nature of Truth

Michael Lynch has recently proposed an updated version of alethic functionalism according to which the relation between truth per se and lower-level truth properties is not the realization relation, as might be expected, and as Lynch himself formerly held, but the manifestation relation. I argue that the manifestation relation is merely a resemblance relation and is inadequate to properly relate truth per se to lower-level truth properties. I also argue that alethic functionalism does not justify the claim that truth per se exists, or that truth per se is a functional property. Finally, I suggest a replacement for the manifestation relation. I argue that the resulting theory is a strict improvement over alethic functionalism on two counts, but that the improved theory does not justify the claim that truth per se exists. Since no further improvements to the theory are apparent, the prospects for alethic functionalism are dim.