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There is a way to look at mathematics as just a bunch of rewrite rules for things on paper. It might not be particularly inspiring, but it's a valid way to look
by IsTom 6mo ago
There is a way to look at mathematics as just a bunch of rewrite rules for things on paper. It might not be particularly inspiring, but it's a valid way to look at things.
- nextaccountic 6mo agoIndeed, there's a way to get a semantics for free, based on the syntax alone. For example, in the first order logic this is the Herbrand interpretation https://en.wikipedia.org/wiki/Herbrand_interpretation https://en.wikipedia.org/wiki/Herbrand_interpretation The point of mathematical semantics is that for any given theory, we can have other interpretations that don't just interpret symbols as themselves. So we could conceivably imagine an interpretation where ∞ doesn't just mean literally ∞ and nothing more.