Al nominalista non manca proprio nulla? La dispensabilità dell'insieme vuoto in mereologia

Al nominalista non manca proprio nulla? La dispensabilità dell’insieme vuoto in mereologia - Quine’s commitment to nominalism has always required set theory to be replaced by an ontologically less dubious tool for the analysis of predication, one that is usually ABSTRACT Rivista di storia della filosofia, n. 1, 2009 mereological in nature, akin to the Calculus of Individuals he and Goodman developed in a seminal paper on nominalism. The problem Quine himself always acknowledged as central in any such replacement arises with the mereological "translation" of numbers. I show here that Quine’s proposed translation strategy, even when successful, raises even more serious issues since it requires mereology to supply a substitute for the empty set. After proving the indispensability, given Quine’s translation, of such an entity, I demonstrate that an exact mereological replica of the empty set (the "null object") cannot be admitted without engendering contradictions. I conclude by discussing some paraphrases of the usual mereological axioms that prima facie might seem to be compatible with the null object and assessing their implausibility.

Vincenzo Latronico, Al nominalista non manca proprio nulla? La dispensabilità dell'insieme vuoto in mereologia in "RIVISTA DI STORIA DELLA FILOSOFIA" 1/2009, pp 63-73, DOI: 10.3280/SF2009-001005