A widely held view in current philosophical theory says to be wary of conceptual analysis and its quest for analyticity. The major source of this suspicion traces back to reasons W. V. Quine gave 50 years ago in ‘Two Dogmas of Empiricism’ — namely concerns about reliance on notions of meaning and synonymy that are unclear. Since that time, there have been new sources of suspicion. In the philosophy of mind, for example, debates over consciousness have some philosophers doubting whether conceptual analysis can furnish as hefty a metaphysical conclusion as the denial of physicalism (Block and Stalnaker, 1999; Chalmers, 1996). And in epistemology, Stephen Stich and others worry that conceptual analysis of epistemic norms can only end up endorsing local intuitions about good thinking — intuitions that depend arbitrarily on the culture in which they were formed.

The Eleatic Visitor speaks forcefully when he insists, ‘Necessarily, whenever there is speech, it is speech of something; it is impossible for it not to be of something’ (Soph. 262e6-7). For ‘if it were not of anything, it would not be speech at all; for we showed that it is impossible for there to be speech that is speech of nothing’ (Soph. 263c9-11). Presumably, at 263c10, when he claims to have ‘shown’ that it is impossible for speech to be of nothing, the Visitor is referring back to the Parmenidean puzzles at Sophist 237ff.

In Religion within the Boundaries of Mere Reason Kant wrote that ‘freedom of the power of choice has the characteristic, entirely peculiar to it, that it cannot be determined to action through any incentive except insofar as the human being has incorporated it into his maxim.’ This is an obscure statement, in both meaning and provenance. Yet almost all recent interpreters of Kant's practical philosophy find it crucial for understanding his theories of freedom and motivation, since it seems to indicate what we are required to do in order to act by our own free choice. Here I refer to Kant's statement expressing the requirement that incentives be incorporated into maxims as his ‘incorporation requirement.’ How that requirement is best understood will be the leading question in what follows: a question I shall answer by showing why the incorporation requirement, and Kant's theories of freedom and motivation, should be understood differently from the way they are now usually understood.

In this paper I wish to defend a minimalist version of arithmetical Platonism — which I shall refer to as ‘minimal Platonism’ — from an objection which alleges that an advocate of this view is committed to an unduly capacious ontology. The objection, which I shall call the ‘Lightness of Being’ objection, runs as follows. The minimal Platonist is committed to the claim that arithmetical objects, such as numbers, exist provided that two conditions are met. The first is that terms for numerals are singular terms — where something's being a singular term is judged on the basis of purely syntactic criteria. The second is that some sentences in which these singular terms feature are non-trivially true. However, the names of fictional characters are also singular terms (when judged by the metaphysically lightweight criteria used by advocates of minimal Platonism).