>>12811665the thing is though that the real world, being a set of "objects" that are imperfect reflections of "ideal" objects, yield themselves to many "prisms" of understanding. You can understand the same thing in many ways.
For example, you can understand the political situation through prisms of many ideologies. Every ideology focuses on one aspect that might be true, but the whole ideology cannot explain the entirety of what's happening. Does that mean that ideologies are all false? Yes, in the sense that they are incomplete and no, in the sense that they are focused on one "correct" way of interpreting reality.
Similarly, conventional mathematics are a "prism" to look at "earthly reality". Is it the only and perfect prism? No. But that doens't mean that it doesn't reflect an "ideal reality". Somewhere, somehow, the ideal triangle exists, and all objects just share in the "triangleness" of that ideal triangle. Somewhere, there is an ideal "1" and all objects share in its "one-ness" to one degree or another.
Axioms are just starting points for these lines of though, just as the class theory is a starting point for Marxism. Just as one can't think with Marxist logic without acknowledging class theory, you can't do conventional mathematics without accepting the axioms.
So yes, Hilbert was right to an extent, and so was Kant. But they didn't discover anything new, but just added a clarifying footnote to Plato.
