Crítica, Revista Hispanoamericana de Filosofía, Volume 23, number 68, agosto 1991
La lógica y el dilema de Benacerraf
Raúl Orayen
Instituto de Investigaciones Filosóficas
Universidad Nacional Autónoma de México

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.

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