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Tarskian

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Could you give me an example of two incompatible mathematical systems? There is a lot of research in inconsistent mathematics, but I am not sure that ...
May 07, 2024 at 14:05
Classical Euclidean geometry is arguable not "real" mathematics. As Kant pointed out, it is incredibly married to sensory input, to the point that it ...
May 07, 2024 at 13:46
Correct. Kurt Godel said yes. David Hilbert said no. They both have arguments that are equally convincing. I consider the problem to be undecidable.
May 07, 2024 at 10:36
Applied mathematics is actually not mathematics. As soon as it is about correspondence with the physical universe, it is about the use of mathematical...
May 07, 2024 at 07:05
In fact, I have also come to accept the alternative formalist view. Since N can also be described as a set-theoretical construct, it is just another s...
May 07, 2024 at 05:44
PA does not define N. N is defined as a set-theoretical construct while PA is an axiomatic theory constructed as such that all its theorems turn out t...
May 07, 2024 at 04:58
Actually, I have to agree to that. Formalism is a very consistent idea. Model theory can indeed be viewed as the correspondence between an axiomatic f...
May 07, 2024 at 04:29
I certainly do not believe that mathematics revolves around the correspondence with the physical universe. By "correspondentist", I actually mean: cor...
May 07, 2024 at 03:58
Look for example at the relationship between Peano Arithmetic theory (PA) and the natural numbers (N). PA does not create N. N exists independently fr...
May 07, 2024 at 03:39