La lógica y el dilema de Benacerraf

Abstract

In this paper I point out three consequences that apparently follow from adopting one horn of Benacerraf's dilemma (the one rejecting abstract entities as objects referred to by mathematical language). These consequences are:

1. The usual explanation of the successful application of logic to mathematics is lost.

2. Logic is incomplete.

3. Some "logical facts" cannot be described any more. In other words, giving up certain entities weakens the explanatory power of our theories to cope with sorne elementary logical facts.