This question of highest importance for everybody could not be answered in MO and will not be answered in Mathematics.SE. I can understand why the set-theorists there dive and attack it like vultures. I feel very sorry. Perhaps the prevailing understanding of logic and tolerance is here more suitable?

Background: Gödel proved the existence of God in a relatively complicated way using the positive and negative properties introduced by Leibniz and the axiomatic method ("the axiomatic method is very powerful", he said with a faint smile). To formalize the idea of a positive property, Gödel introduced a positivity operator. Just as a predicate or property provides a truth-functional assignment to individuals. We say that Pos(F) is true if F is a positive property. Please look it up if you have not yet heard of:

http://www.stats.uwaterloo.ca/~cgsmall/ontology.html
http://userpages.uni-koblenz.de/~beckert/Lehre/Seminar-LogikaufAbwegen/graf_folien.pdf

Couldn't the following simple way be more effective (and wouldn't it be appropriate to count it as belonging to mathematics)?

1. The set of real numbers is uncountable.
2. Humans can only identify countably many words.
3. Humans cannot distinguish what they cannot identify.
4. Humans cannot well-order what they cannot distinguish.
5. The real numbers can be well-ordered.
     QED

This question of highest importance for everybody could not be answered in MO and will not be answered in Mathematics.SE. I can understand why the set-theorists there dive and attack it like vultures. I feel very sorry. Perhaps the prevailing understanding of logic and tolerance is here more suitable?

Background: Gödel proved the existence of God in a relatively complicated way using the positive and negative properties introduced by Leibniz and the axiomatic method ("the axiomatic method is very powerful", he said with a faint smile). To formalize the idea of a positive property, Gödel introduced a positivity operator. Just as a predicate or property provides a truth-functional assignment to individuals. We say that Pos(F) is true if F is a positive property. Please look it up if you have not yet heard of:

http://www.stats.uwaterloo.ca/~cgsmall/ontology.html
http://userpages.uni-koblenz.de/~beckert/Lehre/Seminar-LogikaufAbwegen/graf_folien.pdf

Couldn't the following simple way be more effective (and wouldn't it be appropriate to count it as belonging to mathematics)?

1. The set of real numbers is uncountable.
2. Humans can only identify countably many words.
3. Humans cannot distinguish what they cannot identify.
4. Humans cannot well-order what they cannot distinguish.
5. The real numbers can be well-ordered. (This is a theorem of set-theory: E. Zermelo: "Beweis, daß jede Menge wohlgeordnet werden kann", Math. Ann. 59 (1904) 514-516)

6. If this is true, then there must be a being with higher capacities than any human. (It has been proved that humans cannot well-order the real numbers. No set-theoretically definable well-ordering of the continuum can be proved to exist from the Zermelo-Fraenkel axioms together with the axiom of choice and the generalized continuum hypothesis by S. Feferman: "Some applications of the notions of forcing and generic Sets", Talk at the International Symposium on the Theory of Models, Berkeley, 1963)

QED