Looking back, it’s hard to say what gave me that impression. I think I was mostly just confused as to why you were spending quite so much time going over the syntax stuff ;) And
First of all, the dichotomy between “logic” and “mathematics” can be dissolved by referring to “formal systems” instead.
made me think that you though that all logical/mathematical talk was just talk of formal systems. That can’t be true if you’ve got some semantic story going on: then the syntax is important, but mainly as a way to reach semantic truths. And the semantics don’t have to mention formal systems at all. If you think that the semantics of logic/mathematics is really about syntax, then that’s what I’d think of as a “formalist” position.
Oh, I think I may understand your confusion, now. I don’t think of mathematics and logic as equals! I am more confident in first-order logic than I am in, say, ZFC set theory (though I am extremely confident in both). However, formal system-space is much larger than the few formal systems we use today; I wanted to emphasize that. Logic and set theory were selected for because they were useful, not because they are the only possible formal ways of thinking out there. In other words, I was trying to right the wrong question, why do mathematics and logic transcend the rest of reality?
Looking back, it’s hard to say what gave me that impression. I think I was mostly just confused as to why you were spending quite so much time going over the syntax stuff ;) And
made me think that you though that all logical/mathematical talk was just talk of formal systems. That can’t be true if you’ve got some semantic story going on: then the syntax is important, but mainly as a way to reach semantic truths. And the semantics don’t have to mention formal systems at all. If you think that the semantics of logic/mathematics is really about syntax, then that’s what I’d think of as a “formalist” position.
Oh, I think I may understand your confusion, now. I don’t think of mathematics and logic as equals! I am more confident in first-order logic than I am in, say, ZFC set theory (though I am extremely confident in both). However, formal system-space is much larger than the few formal systems we use today; I wanted to emphasize that. Logic and set theory were selected for because they were useful, not because they are the only possible formal ways of thinking out there. In other words, I was trying to right the wrong question, why do mathematics and logic transcend the rest of reality?