> While pithy, this reply just seems to ignore basically every point I raised and just reassert your original assertions without offering any reason to believe them.
I said that I didn’t understand your argument, so I asked some questions. And then I expanded my argument with reasoning, but apparently you feel that my reasoning is deficient, but lazily assert that I did not offer “any reason” to believe them. I honestly thought that I did offer reasons.
> In fact I’d say your whole series of comments here are rhetorical gimmick with some bravado like it’s a great philosophical insight while side-stepping the only interesting philosophical question here, which is how do we decide which concepts “actually” exist.
That’s an interesting philosophical question, but we’re having a discussion about programming languages and type systems, and I would say that the philosophical question of “what exists?” is side-stepping the interesting questions about type systems. In order to have a discussion about type systems we need to agree about what exists, and the best way to do that is to simply agree by convention that certain things (like type systems) exist.
Which is what I’d prefer. Same thing with mathematics… if we are talking about vector spaces, I don’t want to have a discussion about what “exist” means, I just want to use the word “exist” as a substitute for mathematical concepts, agree how we use the word in context, and then talk about math.
I said that I didn’t understand your argument, so I asked some questions. And then I expanded my argument with reasoning, but apparently you feel that my reasoning is deficient, but lazily assert that I did not offer “any reason” to believe them. I honestly thought that I did offer reasons.
> In fact I’d say your whole series of comments here are rhetorical gimmick with some bravado like it’s a great philosophical insight while side-stepping the only interesting philosophical question here, which is how do we decide which concepts “actually” exist.
That’s an interesting philosophical question, but we’re having a discussion about programming languages and type systems, and I would say that the philosophical question of “what exists?” is side-stepping the interesting questions about type systems. In order to have a discussion about type systems we need to agree about what exists, and the best way to do that is to simply agree by convention that certain things (like type systems) exist.
Which is what I’d prefer. Same thing with mathematics… if we are talking about vector spaces, I don’t want to have a discussion about what “exist” means, I just want to use the word “exist” as a substitute for mathematical concepts, agree how we use the word in context, and then talk about math.