Evading Truth Commitments: the Problem Reanalyzed

While evaluating a version of the Quine-Putnam indispensability argument that’s stronger than standard ones found in the literature, weak conditions for the dispensability of statements that quantify over mathematical entities — weaker than paraphrase — are argued for. These conditions are contoured to apply once a distinction between publicly held science and private belief is drawn. Dispensability projects face two problems: the representation problem and the deduction problem. The former is shown to be unsolvable. The deduction problem is no obstacle provided the representation problem can be solved. Because of the intractability of the latter problem, however, this is no comfort for nominalists committed to the dispensability of statements that quantify over mathematical entities. An important lesson is that “the Quine-Putnam indispensability argument” is concerned with practical dispensability not with in-principle dispensability. The assertoric use of a theory — by scientists — is a practical matter. 1. The family of Quine-Putnam indispensability arguments Here is an enthymemic blueprint for a family of arguments usually described in the literature as “the Quine-Putnam indispensability argument” (hereafter “the QP”): Premise: Certain statements that quantify over mathematical entities are indispensable to science. Conclusion: Those statements are true. This is an enthymemic blueprint of an argument, not merely because more is needed to justify the move from premise to conclusion, but also because philosophers have elaborated this purported argument in quite different and incompatible ways. One goal of this paper is to provide a reading of this “04azzouni” 2009/6/12