1
PhD student in philosophy at Tarbiat Modares University
2
Professor of the Research Institute of Iranian Wisdom and Philosophy
Abstract
Frege's main philosophical goal was to understand and determine both the ontological and epistemological status of mathematical truth. He proposed the doctrine of logicism for this goal. The doctrine of logicism explains that: 1. all the truths of arithmetic can be expressed using only logical notions. And 2.all arithmetical truths can be obtained from purely logical axioms using just logical laws and definitions. In order to defend this view, it would seem to be essential to provide a definition of the number of words in purely logical terms. But his definitions of the number of words, apart from other defects, were in conflict with the Caesar problem. The Caesar problem is the possibility of identity between mathematical objects and concrete objects; shown by the statement: 'is Caesar a number?' Frege's definitions and other contemporary solutions do not provide us with any answer to this question.
In this essay, we divide the Caesar problem into a variety of epistemological, metaphysical and semantically dimensions and we also show that a right solution must give us a sufficient answer to all these dimensions. Then we test Neo- logicism and show that this solution cannot solve this problem.
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