Fourteen Arguments in Favour of a Formalist Philosophy of Real Mathematics


Authors
Karlis Podnieks
University of Latvia
Abstract
The formalist philosophy of mathematics (in its purest, most extreme version) is widely regarded as a “discredited position”. This pure and extreme version of formalism is called by some authors “game formalism”, because it is alleged to represent mathematics as a meaningless game with strings of symbols. Nevertheless, I would like to draw attention to some arguments in favour of game formalism as an appropriate philosophy of real mathematics. For the most part, these arguments have not yet been used or were neglected in past discussions.
Keywords foundations of mathematics  philosophy of real mathematics  formalism  platonism  consistency  inconsistency  incompleteness
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