Indefinite Divisibility

Some hold that the lesson of Russell’s paradox and its relatives is that mathematical reality does not form a ‘definite totality’ but rather is ‘indefinitely extensible’. There can always be more sets than there ever are. I argue that certain contact puzzles are analogous to Russell’s paradox this way: they similarly motivate a vision of physical reality as iteratively generated. In this picture, the divisions of the continuum into smaller parts are ‘potential’ rather than ‘actual’. Besides the intrinsic interest of this metaphysical picture, it has important consequences for the debate over absolute generality. It is often thought that ‘indefinite extensibility’ arguments at best make trouble for mathematical platonists; but the contact arguments show that nominalists face the same kind of difficulty, if they recognize even the metaphysical possibility of the picture I sketch.     

Externalism and Authoritative Knowledge of Content: A New Incompatibilist Strategy

Philosophical Studies -     

Communicating quantities: a review of psycholinguistic evidence of how expressions determine perspectives

The way in which information about proportions, amounts, frequencies, probabilities, degrees of confidence, and risk is portrayed in natural language is not neutral, but reflects presuppositions and assumed norms. In this paper we present a review of evidence in support of this position. We show that the choice of expressions for communication depends in a systematic way on the kinds of inferences communicators draw. We go on to discuss the consequences of this for attribution phenomena, aspects of reasoning, the portrayal of uncertainty, and responses to questionnaires. We also suggest that communicator preferences for using language rather than numbers may have to do with human reasoning being argument‐based, rather than with a preference for vagueness, as has been commonly claimed. Copyright © 2000 John Wiley & Sons, Ltd.     

Monitoring and Anti-Reductionism in the Epistemology of Testimony

One of the central points of contention in the epistemology of testimony concerns the uniqueness (or not) of the justification of beliefs formed through testimony–whether such justification can be accounted for in terms of, or 'reduced to', other familiar sort of justification, e.g. without relying on any epistemic principles unique to testimony. One influential argument for the reductionist position, found in the work of Elizabeth Fricker, argues by appeal to the need for the hearer to monitor the testimony for credibility. Fricker (1994) argues, first, that some monitoring for trustworthiness is required if the hearer is to avoid being gullible, and second, that reductionism but not anti-reductionism is compatible with ascribing an important role to the process of monitoring in the course of justifiably accepting observed testimony. In this paper we argue that such an argument fails.