I'm going to have my first seminar mid-March and I thought it would be good to approach the conlanging community beforehand because I know all people here have very special experience with languages ‒ it's precisely the conlangers if anyone who should be able to answer the age-old question why all languages are so similar (i.e. syntactic structures; never mind phonology and orthography).

My second upload "The inevitable reason why all languages are similar"
is the first paper to give a formal proof that there simply isn't any other logical possibility. It's largely based on discussions on this list (thx's will be added in due time). Or actually it only proves that all possible grammars are axiomatic. It's written for an audience with a natlang perspective, so I should mention here that, additionally, when you define your conlang as one that is able to express "who did what to whom when where why how" etc. ‒ the usual stuff ‒ the semantics becomes likewise axiomatic.

In contrast to my hypothesis, Chomsky argues that these logical possibilities are endless, even so overwhelmingly that it would be impossible for a child to learn a language with the mere input and reasoning. People must be born with Universal Grammar, an innate syntactic awareness, and language learning is based on the gradual unfolding of UG. You can't directly prove Chomsky wrong because proving non-existence is generally considered impossible. That's why Chomsky has the burden of proof.

So the current situation is this: I've provided evidence that all possible languages must be based on the same logical structure, and this is why they are structurally similar. This means I won the argument. 

However, we should consider the possibility that I'm mistaken; and proving so might actually provide the evidence that Chomsky needs.
What I'm asking everyone to do is to think of a language which is not based on the same underlying structures as all other languages. I've heard people say that (syntactic!) languages could be "completely different" from natural languages, but I've never seen what it means. Can the conlanging community bring forward any actual example of this? Any single piece of evidence could be enough to falsify my argument and fortify Chomsky's claim.