In a post on Kant's Antinomies I said the truth of any language statement rests upon the inescapable foundation of language's truthfulness or meaningfulness, and this is why the antinomy is a false notion simply on principle. One knows this to be so without having to look at whatever particular antinomy may be in question, as this seeks to declare mutually incompatible language statements to be capable of co-existence, i.e. that they can contradict each other. A commenter sought to explain two plus two equals four being true not because it is a consistent statement of language but because it reflects the external world. However mathematics is an autonomous language that needs no reference to a world 'beyond itself'. The very thought of a world beyond itself has no place within the language of mathematics; it is a meaningless intervention within that mathematical language, the same as it would make no sense within the score for a piece of music. That the world or language of mathematics does reflect or correspond to the forms of the natural world, even at the most abstract, complex levels is because this intelligence imbues all of existence, the human mind included. Life and the intelligence intrinsic to life animates all within life. Life is not divided against itself. And so ordinary language that is self-contradictory is merely a false use of language that will be found to be simply erroneous.
However the language of ordinary discourse unlike that of mathematics is not entirely autonomous; that is, all that is referred to cannot all be contained on the page. However, many language statements cannot be said principally to point to some external reality, and are a matter of the correct working of language. An example below from an earlier post:
An idea extremely prevalent in the current era is that everything is equally valid. For instance you cannot, you will be told, say that one work of art is greater than another because of this equal validity of everything. So a quick look at the logic at play here.
Everything is equally valid. Therefore all statements are equally valid. And an example of one such statement within the totality of equally valid statements is that:
Everything is not equally valid.
And so if everything is not equally valid, then the first statement that everything is equally valid is false. So the statement of all being equally valid contains within itself its own disproof.
So the truthfulness of this was purely a matter of language and the equal validity of all was shown to be self-contradictory and so false. The idea of all being equally valid violates the necessary internal logic of language. Were there no such intrinsic order or intelligence to language, then no statements could be said to make any sense. However there are uses of language whose truth or falsehood rests also on their correctly referring to the world they allegedly point to. So, 'I am now standing on my head reciting a nursery rhyme' is a false statement as I am not doing those things. However as a matter of language it is fine. No such false statements can exist within mathematics.Statements within that field are purely autonomous. If it is true as a matter of mathematical language then it is true.
Someone might then think that statements of ordinary language are not primarily a matter of the internal logic or intelligence of that language, and so for one to say that 'I am wearing black shoes,' is true solely on the basis of whether it reflects that particular case. If he is wearing black shoes then it is true, and language has nothing to do with it. However any statement of language is existentially a statement of language, and if that person were to say instead, 'Black I wearing shoes am', then that would be not a reflection of anything but simply gibberish. It fails as a matter of language. So even the simple statement of wearing black shoes must first be a sensible matter of language. All language in the sense of a truth tool inescapably just so rests on the internal meaningfulness and logic of that language, which again can lead us back to the antinomy or paradox as simply a wrong use of language.