O problema de Júlio César em Frege

Abstract

The search for an adequate definition of numbers and for a criterion of identity for them are questions almost indissociable in Frege’s philosophy of mathematics. In the present work, the topic to be examined, the Julius Caesar problem, is a problem that concerns both a proposal for a definition of numbers and the establishment of a criterion of identity for them. The Julius Caesar problem takes place in three distinct situations in Frege’s writings. In the first two situations, it a ects, respectively, the first and the second definition of cardinal numbers that Frege gives in his second book The Foundations of Arithmetic. In the third situation, it a ects the criterion of identity for numbers that Frege gives in his third book Basic Laws of Arithmetic. All that being said, my main goals are two: (1) to determine whether the Julius Caesar problem that occurs in these three distinct situations is the very same problem or not; (2.1) if the problems in question are the same, to identify in general terms what the Julius Caesar problem is; (2.2) if this is not the case, to verify what is the Julius Caesar problem in each individual situation. Furthermore, I will criticize both Greimann’s logical approach and Heck’s semantical approach to the Julius Caesar problem in The Foundations of Arithmetic and in Basic Laws of Arithmetic. I conclude my dissertation by presenting and rejecting two alternative approaches to the problem in question, a metaphysical approach and an epistemological one; simultaneously, I argue in favor of my own formal approach to the Julius Caesar problem in both books just mentioned.