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 ...
Classical Euclidean geometry is arguable not "real" mathematics. As Kant pointed out, it is incredibly married to sensory input, to the point that it ...
Applied mathematics is actually not mathematics. As soon as it is about correspondence with the physical universe, it is about the use of mathematical...
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...
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...
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...
I certainly do not believe that mathematics revolves around the correspondence with the physical universe. By "correspondentist", I actually mean: cor...
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...
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