—“Not quite, as Godel presented a mathematical model of this phenomenon. You cannot reduce this to mere positivistic linguistics. On which point, are you not assuming Chomsky’s universal grammar with your definition of grammar? If so, this has been shown to be unempirical.”—
I didn’t say anything like that. I’m saying that he’s correct.
I haven’t met anyone other than the author of the best book on the subject that understands the limit of Godel’s argument:
(a) we identify new constant relations (experiences)
(b) we invent new references
(c) we invent new paradigms
(d) we require grammars to talk about them
(e) we can make ungrammatical statements.
Godel said it. Turing said it. Kripke said it.
So there is no closure to logic without appeal to the operational, empirical, limits and completeness, and even then there is only closure on falsification not justification.
THE FUNDAMENTAL PROBLEM FOR PEOPLE IN PHILOSOPHY AND THEOLOGY:
There is nothing positivistic in P. It’s purely falsificationary. Either it survives adversarial competition by the terms stated in testimonialism or it doesn’t. If more than one does, then we just don’t know and nothing else can be said.
In general, i have found that the first and most significant hurdle that people have trouble with – at least those not educated in the sciences – is that all propositions are contingent and all truth propositions are achieved by falsification. And P articulates the METHOD for universal falsification.
Afterward: Chomsky was trying to bring Turing to language. His original paper is simply pulling Turing into language. Chomsky’s contribution – from my understanding – is correctly stating that:
(a) the brain produces experience by continuous recursive disambiguation.
(b) linguistic thought consists of rules of continuous recursive disambiguation.
(c) grammar regardless of language consists of rules of continuous recursive disambiguation.
(d) language serves as a system of measurement for thought – albeit we use many different paradigms (metaphysics) within each human language, and these paradigms vary according to the correspondent vs the three non-correspondent (fictionalisms).
(e) there appear to be higher demands on cognition for higher levels of thought. And we should expect aliens if there are any to use simpler or more complex grammatical structures given their abilities.