I don't think you are more rational than all those philosophers of the middle ages trying to demonstrate the existence of God by pure logic*. Logic, just like mathematics, is entirely inside the mind of the man. Whatever theory that is only demonstrated only "mathematically" or "logically" is just self-sustaining interesting reasoning but no science.

I'm still with Galileo. No empirical demonstration, no science. Thecimento(test, trial) gives the demonstration that the theory was good. Never the theory itself.

The idea, for instance, that before the big bang there was no space to be there is just a negation in words of the problem the mind has (and cannot solve). If the big bang is an explosion of matter, that matter will explode into some space which has to have been there to receive that matter. Besides, big-bang theories normally as far as I know talk about a pulsating universe, with infinitely repeated big-bang-expansion-contraction-big-bang cycles!

Saying that it is energy, or mass, (or energy-mass if you prefer) that creates space contravenes what our mind thinks when we think of mass, energy, or space. This negation is as far as I know performed either as pure imagined concept or, in the case of some other theories, with advanced mathematical "demonstrations". But yet again, nocimento, no science. Only theory with maybe a very intelligent and elegant layout.

According to the imperfect infinitesimal calculus of the ancient Greeks Achilles would "never" reach the turtle. The logic mistake in the reasoning is easily shown, first of all, by noticing in real life that Achilles does reach the turtle. If the reasoning could be performed by some creatures in a world where there is no Achilles and no turtle,so to say, to prove it wrong, the brilliant mathematical construction might go on being right in the mathematical mind of the mathematical theorizers. Mathematics is not empirical evidence. Human brain can fail. Mathematics is a creation of the mind. Pushing it to its boundaries might give incorrect results.

In the beautiful workLife of GalileoBertolt Brecht shows us Galileo while trying to convince two Dominican friars to look inside his telescope, to see the "Medicean planets". The Dominican friars, I go by memory, answer that they are not interested in looking inside the telescope until they don't have an acceptable theory first that may justify them looking into it. The instrument might have defects but the human mind when properly used cannot fail, that is. Such is the presumptuousness of the human mind.

* Failing miserably but often becoming "saints" in the process.

PS I still don't get which are the two notions that I go on mixing.