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Gottlob Frege
Referenced in
(Game) Formalism in the Philosophy of Mathematics
The premiere text on game formalism is not a defense made by an ardent supporter, but rather an attempt to refute it, written by
Frege
, where he lays into Heine and Thomae. Philosophers of mathematics claim that the position is still held by mathematicians, however, formalism in the sense that Frege set out to dispute, should be distinguished from what some argue is the more refined formalism of
Hilbert
, and
his program
.
Platonism in the Philosophy of Mathematics
The premier argument for mathematical structures having their own existence, is derived from
Frege
: The language of mathematics refers to and quantifies over these objects, and many theorems are true, but a sentence cannot be true unless its sub-sentences are true.
Gottlob Frege