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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 explain this idea for a college interview, after saying that I found it to be preferable to Platonism in it's original form.

Essentially, I said that this sort of synthesis is the only way of solving the problem of how we can access the realm of forms. In particular, I suggested that the Kantian view of mathematics (unlike, say, formalism) allows still for forms to exist as objective entities, albeit of the perception rather than of objective reality. Additionally, I said that under Kantianism, the idea that the forms "project themselves" onto the world is still preserved - and that the only difference is that Kantianism suggests the projection is "in - out" (from the forms of perception to things in themselves) rather than "out - in" in the Platonic sense (from the "outer" world of forms to the world of appearances).

Does this sound stupid? Or is there a real sense in which "Kantian Platonism" can be a tennable position?

P.S. I am in high school, and I have never learned philosophy formally.

  • The projecting piece is a keen observation, but, so far as it goes, formalism also envisions such projection, from our symbolic devices. "Objective entities of the perception" are not objective in Plato's sense, as they are tied to our perception, and Hilbert's version of formalism also tied symbolic manipulation to "objective entities of the perception", see Was there a Kantian influence on Hilbert's formalist programme? The name "Kantian Platonism" would probably upset both Kantians and Platonists. – Conifold Dec 26 '19 at 5:16
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No it is not stupid. So far it goes, it is right about Kant. As to Platonism in philosophy of mathematics, people give widely different definitions, often explicit that they do not mean to describe Plato's own view. So anything you say about that is likely to be right according to someone's understanding of the term.

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    Thank you so much! You have no idea how much I have been tormenting myself, thinking I was just flat out wrong. – J.M.W Turner Dec 24 '19 at 19:28

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