First order logic, set theory and God

[I_am_not_mafia]

My point is though that first order logic is still nothing more than a way of describing reality.

Exactly, which makes it inherently linked to reality through its connection to truth. In that sense, one could just as confidently say that physical laws are descriptions of the dynamic behavior of matter in space-time.

I'm sorry, but what is your point again? 

My point is that first order logic doesn't describe reality very well.

There is an awful lot of fundamentally important stuff that it cannot describe at all. Making your so called proof worthless if you are trying to say something about the nature of reality. For example thermodynamics, complexity and chaos.

Exactly. True and False are abstractions. They do not exist in nature.

Mathematics is abstract, yet inherently grounded in reality. Guess what? Same goes for True and False. Consequently, this renders your argument completely false.

It is not grounded in reality any more than the English language.

Rubbish. It's extremely important.

What causes a hammer to exist for example?  When someone connects a handle to a head? When a wood is reshaped to create the handle? When metal is melted down and shaped into a head? When a tree is cut down? When ore is mined from the Earth? When a tree is grown? When a planet is formed? What is the single cause of a hammer? There isn't one. All we have is energy flowing through and reshaping matter in accordance of the laws of Thermodynamics. Your abstraction of True, False and causation miss all that because they are abstractions.

What you fail to grasp is that the law of causality is not descriptive but rather relational. A hammer's existence is not contingent upon whether or not the cause of its existence has to be known to us. Rather, the hammer's existence is already necessitated by an external cause preceding it, whatever that cause may be. Just as it is necessary for number 4, for instance, to occur between the numbers 3 and 5.

But just for argument's sake, the answer to your question would simply be - the causal link of all phenomenon that has brought the necessary and suffi­cient conditions for the realization of the hammer. That's it. Causality is merely established by the interdependence and relation between the cause and the effect.

Which completely misses the point I am making in that reality is continuous whereas your arguments of causality are discrete.

As I said, your description of reality is not sufficiently powerful enough to say anything worthwhile at all.