フレーゲの論理主義と数の存在論

Abstract

"In Grundlagen, Frege claims that (cardinal) numbers are objects existing on their own. But his realistic view about numbers faces an epistemological problem. For Frege, while numbers are objective entities, they can’t be given to us in standard ways (perception, intuition or representation). Numbers are abstract objects. It is natural then to ask: why would Frege adopt such a problematic ontology of numbers? And, how can we say for certain that there are indeed such abstract objects? This paper tackles these two questions. For the former, I give a characterization of his conception of numbers in terms of his logicist project and the insights underlying it, and show that for Frege numbers must be ‘logical objects’. To establish existence of numbers as logical objects, Frege in Grundlagen attempts to define them contextually by using so-called Hume’s Principle. I examine his argument, thereby attempting to provide an answer to the second question. Though a conclusive justification for his attempt can’t be given in this paper, a concept in Frege’s philosophy is proposed in order to better understand his argument. If developed, I am of the opinion that it might be possible for his ontology of numbers to be come less unproblematic and more substantial. Frege’s discussion on numbers contains compelling insights and arguments. It is my hope that some of these are revealed through this exposition."