Abstract

TAJER, Diego. In Defence of the Finitist Argument. Rev. latinoam. filos. [online]. 2014, vol.40, n.2, pp.129-143. ISSN 1852-7353.

In this paper, I analyze the main replies that have been given to Etchemendy's (1990) finitist argument, and I show that none of them is successful. First, I describe and criticize the proposals that try to solve the problem by appealing to modal considerations. These solutions fail because they presuppose a very weak finitism, where the existence of infinitely many sets, or possible words with infinitely many objects, is accepted. But there are stronger versions of finitism that reintroduce the problem. Then I consider the solutions which appeal to semantical categories. One of them incorrectly categorizes the problem as a disagreement in the meaning of the quantifiers. The other fails because, if taken seriously, it would have harmful effects on logic in general. Finally I argue that the best solution is to bite the bullet and accept that logic shouldn't be strongly independent from some issues which were traditionally considered as 'extra-logical'.

Keywords : Logical consequence; Tarski; Etchemendy; Finitist argument.

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