>>11724764One of the axioms that constructs the naturals states that Successor{x} only equals Successor{y} if x=y.
1 and 2 have different successors (2 and 3), which implies 12.
So you have 1=2 and 12 at the same time. You might think this is ok, but consider the OR operator. It answers "TRUE" for two statements a,b if any of the following apply:
a is true AND b is not true
a is not true AND b is true
a is true AND b is true
If you have a AND not a both be true you do all kinds of crazy shit.
Consider the following statement:
Either 12 OR I am Based Tooker, blessed with the powers of flight, telepathy and solving Millenium prize problems.
12, therefore this statement is true.
But 1=2, and therefore the first part of this statement isn't true. But we've already proven that the statement is true, so therefore the second part must be true.
You can't resolve this without abandoning OR, XOR, XNOR and NAND as tools in your logic system, which leaves you with a logic system that can't define addition.
It's interesting to study paraconsistent logics like that but they are useless at modeling anything.
