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Philosophy of mathematics asks questions about mathematical theories and practices. It can include questions about the nature or reality of numbers, the ground and limits of formal systems and the nature of the different mathematical disciplines.

1 vote
0 answers
144 views

The nature of Nominalist Formalism

In this entry in the stanford encyclopedia of philosophy, it is stated that the theory of nominalist formalism deals with the metatheory problem of formalism as follows: Commendably, Goodman and Q …
J.M.W Turner's user avatar
6 votes
1 answer
683 views

Was Kant an Intuitionist about mathematical objects?

In regards to the ontology of mathematics, as far as I can understand, Kant believed that Mathematical objects existed only as features of our perception that influenced how we viewed things-in-themse …
J.M.W Turner's user avatar
3 votes
1 answer
370 views

Why is ZFC not as susceptible to Gödel's incompleteness as was the Principia Mathematica?

So, from what little I have read (such as this answer), it appears to be that one reason why the program of Logicism, as laid out in the Principia Mathematica, failed was that its goals (of finding a …
J.M.W Turner's user avatar
2 votes
1 answer
315 views

A Kantian Platonist view of mathematics

So my question, essentially, is this: is there any reasonable way in which one can say that mathematical Platonism is compatible with Kantian constructivism? For the sake of context, I was asked to e …
J.M.W Turner's user avatar