Set Impossibility Theorem

Possible duplicate of my earlier work (circa July 14, 2017).

"If zero is a proof, coloring requires a standard, and coloring is always formal if we assume mathematics is formal and that zero is mathematical and the only foundation. If there are other foundations there may be multiple distinct proof theories. If zero is not proof, nature or infinity provide the solution [e.g. because real space must be empirical], no matter how simple [e.g. because without space we get zero], and/or proof lies outside mathematics [e.g. if there is an alternate to zero or space]."*

To summarize...

1. First option, not formal.
2. Second option, the matter is empirical, requiring infinity.
3. Option 3, rooted in zero.
4. Option 4, formal but different.


You see, there are always four alternatives.

(1) Accepting the formalism may require no matter.

(2) No formalism may mean no mathematics...

(3) A different formalism requires something like mathematics but of a different nature.

(4) And, if the matter is empirical it is not founded in mathematics.

...

Translating again:

If it is empirical or informal it is not mathematically grounded (2 and 4).

Now, if is empirical it cannot be mathematics (1 and 3).

...

*~ Source: The Ultimate Critique of Mathematics

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