Postmodernism is therefore paradoxical ... Adhering to it is therefore irrational
All ideas are paradoxes, and yet we must adhere to some. The act of mapping reality to words necessarily creates lies. Imagining you have some ideas which aren't paradoxes is self delusion. And attempting to not have ideas is death. Therefore adhering to paradoxical ideas is rational.
I would say a hallmark of sanity is the ability to work within paradoxes.
To a hammer, everything looks like a nail.
The idea that there are an infinity of primes is not at all paradoxical, it's an uncontroversial factual assertion. Most of mathematics shows the same property.
> The act of mapping reality to words necessarily creates lies.
Not the words out of which scientific theories are constructed. Evolution. Biology. Physics. These are falsifiable (they must be to qualify as scientific theories), but they are not lies -- a word that means false claims made by a speaker who knows his claims are false. You're misusing the word "lies" to refer to something else.
> Imagining you have some ideas which aren't paradoxes is self delusion.
See above. Your claim that all ideas are lies is the essence of the postmodern position. A postmodernist first denies the existence of shared, objective truths, then tries to start a dialogue requiring what's just been denied.
> I would say a hallmark of sanity is the ability to work within paradoxes.
That's certainly true, but it doesn't follow that all is paradox, or that all statements are lies.
See my other response above about the materiality and contingency of linguistic utterances. Like all other physical phenomena, the scientific approach views language as an event, a behavior, a material process that is always context-dependent and, at the "lowest" levels, pervaded by uncertainty, even in our best attempts to model it.
Postmodernism is therefore paradoxical and logically invalid, in a broad and categorical sense. Adhering to it is therefore irrational and no different than any other non-falsifiable religion that must simply be accepted on faith, without any logical proof or reasoning.