Gideon Rosen

A Subject with No Object: Strategies for Nominalistic Interpretation of Mathematics

Numbers and other mathematical objects are exceptional in having no locations in space or time or relations of cause and effect. This makes it difficult to account for the possibility of the knowledge of such objects, leading many philosophers to embrace nominalism, the doctrine that there are no such objects, and to embark on ambitious projects for interpreting mathematics so as to preserve the subject while eliminating its objects. A Subject With No Object cuts through a host of technicalities that have obscured previous discussions of these projects, and presents clear, concise accounts, with minimal prerequisites, of a dozen strategies for nominalistic interpretation of mathematics, thus equipping the reader to evaluate each and to compare different ones. The authors also offer critical discussion, rare in the literature, of the aims and claims of nominalistic interpretation, suggesting that it is significant in a very different way from that usually assumed.

Culpability and ignorance

When a person acts from ignorance, he is culpable for his action only if he is culpable for the ignorance from which he acts. The paper defends the view that this principle holds, not just for actions done from ordinary factual ignorance, but also for actions done from moral ignorance. The question is raised whether the principle extends to action done from ignorance about what one has most reason to do. It is tentatively proposed that the principle holds in full generality.

Worldly indeterminacy: A rough guide

This paper defends the idea that there might be vagueness or indeterminacy in the world itself--as opposed to merely in our representations of the world--against the charges of incoherence and unintelligibility. First we consider the idea that the world might contain vague properties and relations ; we show that this idea is already implied by certain well-understood views concerning the semantics of vague predicates (most notably the fuzzy view). Next we consider the idea that the world might contain vague objects ; we argue that an object is indeterminate in a certain respect (colour, size, etc.) just in case it is a borderline case of a maximally specific colour (size, etc.) property. Finally we consider the idea that the world as a whole might be indeterminate; we argue that the world is indeterminate just in case it lacks a determinate division into determinate objects.

Yablovian ‘If-Thenism’

ABSTRACT The paper explores Stephen Yablos suggestion that ‘If-Thenism’ in the philosophy of mathematics is best formulated as the thesis that the real content of a mathematical claim C is the result of subtracting the potentially problematic metaphysical commitments of mathematics (numbers exist) from C [Yablo 2017]. Yablos proposal assumes that some propositions make others true. The present discussion assumes that propositions are coarse-grained sets of possible worlds and asks what Yablos proposal looks like on that assumption. The conclusion is that the adequacy of the proposal turns on hard-to-settle questions about the truthmakers for propositions expressed by material conditionals.

Scanlon’s modal metaphysics

Abstract In Being Realistic About Reasons (Oxford University Press, 2014) T. M. Scanlon argues that particular fact about reasons are explained by contingent non-normative facts together with pure normative principles. A question then arises about the modal status of these pure principles. Scanlon maintains that they are necessary in a sense, and suggests that they are ‘metaphysically’ necessary. I argue that the best view for Scanlon to take, given his other commitments, is that these pure normative principles are metaphysically contingent in some cases and necessary only in a weaker sense.

Knowledge and Evidence.

Acknowedgments Introduction 1. Conditions for propositional knowledge 2. Minimal epistemic reasons 3. Justifying epistemic reasons 4. Foundationalism and some alternatives 5. Procedural epistemic rationality 6. Propositional knowledge References Index.