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Of course you can have infinitely many different semantics, but this is a question about available syntaxes. (Trivial proof: for each n, take the semantics S_n
by Smaug123 2y ago
Of course you can have infinitely many different semantics, but this is a question about available syntaxes. (Trivial proof: for each n, take the semantics S_n which assigns to the symbol "X" the meaning "integer n", just as English usually assigns to the symbol "3" the meaning "integer 3".)
- thriftwy 2y agoI'm not sure I follow. Natural languages usually have very simple syntax. The Greeks had great literature while still in "boustrophedon with no whitespace" phase. The number of possible symbol meanings may be unbound. And there may be symbol definition rules so that any effective symbol set used to write a text is still plausibly an alphabet. Chinese actually does fit the bill if you are allowed to define new valid characters according to best practices.
- Smaug123 2y agoYou're talking entirely about the meaning of symbols, right. That's not a question Turing addressed at all, and the answer is trivially "there are infinitely many possible semantics". Turing only addressed the question of how many physically distinct symbols there could be, and came up with the result "finitely many".
- thriftwy 2y ago[flagged]