everything that can be thought about, can be thought about as a set of numbers
Dick's gonna love you...
Any self-consistent language can be used to describe anything. That is where the power of math comes from: everything that can be thought about, can be thought about as a set of numbers. Absolutely everything.
By 'self-consistent language' I take it that you mean a self-consistent formal system. But, what exactly are you disagreeing to about in my post? Are you disagreeing that language is limited by conceptual scheme? Notice how conceptual schemes affect the kind of choice in axioms that are selected by formal systems. This is why formal systems have evolved over the years. The choice in axioms has changed and what is acceptable in one conceptual scheme, isn't acceptable in another one. Take the axiom of choice for example. In some schemes, the AC is not accepted. It is downright rejected. In other schemes, the AC is accepted.
Language has nothing to do with experience. Computer languages are almost as complex as human ones, but whether computers have experience or not is completely irrelevant to the fact that you can talk to them.
Language has everything to do with experience. It's our experiences that determine our language. Eskimo's I hear have more terms for snow than most other languages. The language evolves according to their experience, and in snow-laden cultures, it only makes sense to have more terms for snow given their heavy exposure to snow.
Computer languages has everything to do with human interest and human experience (since computers for the most part aren't making their own languages). Cobol meets a business need. The C++ language meets the needs of systems programmers, and so on. Experience dictates the kind of language that evolves.