Proving 1).

Arithmetic is a kind of language formed by numbers and operations. Every number is also a truth, and we express them as a tautology: "1 = 1"; "2 = 2"; "3 = 3", etc.

We know that "1" links to "2", and the same for the remaining infinite figures, from the fact that they are all related to each other. For instance: "2" is "1 + 1"; "3" is "2 + 1" or "1 + 1 + 1", etc.

So, if we change the meaning of a single number (let's say, "1 = 2"

, all of them and their infinite possible operations would be affected. Thus, by limiting the enchainment of truths with a non-truth, no arithmetical operation would be true. And that happens in our natural language too, since every word gets its meaning by opposing the other ones.

Proving 2).

I.

In an infinite succession of eternal truths (since the nature of the truth as not contradiction is immutable), the last truth, that at the same time is the first one, guarantees the coherence between all of them.

If there were infinite truths and, nevertheless, we were lack of last truth, we could not affirm that 'the truth is the truth', since every truth links to another one, none that is not over all of them is capable of embrace them at the same level.

Any truth that one affirms presupposes, then, this deep truth: 'the truth is the truth'. And that, far from being a tautology, indicates us that the truth can exist by itself, that is to say, without real concern, or ideal.

NB: By "first and last truth" I mean a primordial truth that presupposes every single one, and that is itself presupposed by all of them. I'm not thinking in a circle, but in a common trunk with infinite ramifications.

II.

1. The set of true statements is finite or infinite.

1.1. If it is finite, it is limited by a truth or by a non-truth.

1.1.1. If it is limited by a truth, that truth is an unlimited one, that is, God.

1.1.2. If it is limited by a non-truth, we are speaking of pseudo-truths which cover an unavoidable contradiction. In that case, the proposition "An infinite set of true statements limited by a non-truth exists" is false too, being nonsensical to claim such a thing.

1.2. If it is infinite, it has or it has not a first Truth.

1.2.1. If it has a first Truth at the beginning of the whole succession, then this Truth is self-referent, it is its own cause and, therefore, it is God. Its truth value doesn't need neither logic demonstration nor empirical verification, as far as it is self-depending.

1.2.2. If it has not a frist Truth, then the proposition "the truth is the truth" is false, which would abolish every single truth, sending us back to point 1.1.2.

The reasoning in 3), 4) and 5) follows from 1) and 2) as indicated in the first message. It doesn't need a further explanation.

Greetings.

Daniel.