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> However, even in the case of mathematics, this isn't true—there are a lot of non-standard models of arithmetic Believe it or not, there are people who use ac
by catnaroek 9y ago
> However, even in the case of mathematics, this isn't true—there are a lot of non-standard models of arithmetic
Believe it or not, there are people who use actual integers in computer programming. Not everyone is stuck with C and its ilk.
> However, even in the case of mathematics, this isn't true—there are a lot of non-standard models of arithmetic
Meaning is to be found in the axioms themselves, not in models.
- mcphage 9y ago> Meaning is to be found in the axioms themselves, not in models. Yep, and all of them are incomplete.
- catnaroek 9y agohttps://en.wikipedia.org/wiki/True_arithmetic https://en.wikipedia.org/wiki/True_arithmetic would like to have a word with you. (Of course, it's not recursively axiomatizable.)
- mcphage 9y ago> Of course, it's not recursively axiomatizable. Then again, who is these days?
- catnaroek 9y ago> Then again, who is these days? I have no idea what you mean by “who”. In any case, let's trace the conversation back to the original topic: (0) Integer arithmetic is well-defined. Nonstandard models of arithmetic are just that - models. The well-definedness of a theory doesn't depend on the existence of a unique model. (1) The fact you're programming a computer doesn't magically change the properties of the integers. It is even possible to have a data type for integers! (Not in C, though.)