What is a Number? On Frege’s Foundations of Arithmetic

Click here to read: On Frege

This paper explains Frege’s reasoning for why numbers are objects, as opposed to concepts or subjective ideas.  After explaining the gist of his reasoning, it raises two related, plausible objections to a construal of numbers as objects and shows why Frege dismisses them.  Toward the end, I raise a problem with his view, showing on his view that if numbers are objects then colors are also objects (a proposition Frege would like to avoid).  I then show one way that Frege might respond to this problem.

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