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Regarding insults, you started by suggesting that philosophers of math were ignorant of the distinction between truth as either proof theoretic derivation from

Regarding insults, you started by suggesting that philosophers of math were ignorant of the distinction between truth as either proof theoretic derivation from axioms, or truth in a model and truth simpliciter, I don't think you have room to worry about who is being insulting. Philosophers typically would be introduced to these concepts in advanced undergraduate logic or early on in grad school. As for the rest of it, I'll leave with one final thought: as a meta-philosophical point, we should rarely attribute meaninglessness to statements unless we are forced to. And it's easy enough to show how to interpret existentials as meaningful even in the absence of a referent. You would have to have very compelling reasons for analyzing mathematical statements the way you want to, and I haven't heard any, only your conviction that it's right.

catnaroek 11y ago
> we should rarely attribute meaninglessness to statements unless we are forced to. You don't “attribute meaninglessness” to statements. Syntax is a priori meaningless, and the rules for manipulating it give it meaning. “Meaninglessness” is thus just the lack of a given meaning. > You would have to have very compelling reasons for analyzing mathematical statements the way you want to, and I haven't heard any, only your conviction that it's right. Here's a good reason: leveraging the power and reliability of computers for doing mathematics, which is only possible if syntax is mechanically interpretable. The kind of word tricks you suggest, like interpreting a sentence containing the phrase “the King of France” as implicitly asserting the existence (and uniqueness) of a King of France (in addition to whatever you explicitly say about him), are incompatible with a nice, compositional, crystal clear, reliable, mechanical interpretation of syntax.

catnaroek 11y ago

> we should rarely attribute meaninglessness to statements unless we are forced to. You don't “attribute meaninglessness” to statements. Syntax is a priori meaningless, and the rules for manipulating it give it meaning. “Meaninglessness” is thus just the lack of a given meaning. > You would have to have very compelling reasons for analyzing mathematical statements the way you want to, and I haven't heard any, only your conviction that it's right. Here's a good reason: leveraging the power and reliability of computers for doing mathematics, which is only possible if syntax is mechanically interpretable. The kind of word tricks you suggest, like interpreting a sentence containing the phrase “the King of France” as implicitly asserting the existence (and uniqueness) of a King of France (in addition to whatever you explicitly say about him), are incompatible with a nice, compositional, crystal clear, reliable, mechanical interpretation of syntax.