[QUOTE]\nUsing your analogy, "identical to a square apart from translation,\nrotation, and scaling" is not a theorem. "Some particular entity is\nidentical ..." or "some set of entities are identical ..." might be a\ntheorem.\n\nYou're just misusing the word "theorem", that's all.\n[/QUOTE]\nNot really.\nA universal Turing machine can calculate any computable function, given\nenough memory space. That;s not obvious, it's not something I could\npersonally have derived from first principles.\nSo any Turing machine can emulate any other. That's not entirely\nobvious either, although most people could probably see that it\nfollows from theorem one.\nA computer plus a programming language is a Turing machine. Again,\nthat's not completely obvious, and it depends how we're using\nthe term "programming language". The core members of the set of\nprogramming languages do turn the computer into a Turing machine,\nbut there are marginal cases that don't. There are plenty of\nelectronic processing devices that don't ship with programming\nlanguages, though a programming language might have been used at\nsome stage of their manufacture. They're not core members of the\nset "computer", but they are often called "computers", so they\nare marginal members.\nSo it follows that any two programming languages are equivalent.\nThat's a theorem, it's not a conclusion that relies on observations\nof the external world. We know it must be correct, at least in\nso far as we can trust the internal processes of human reason.