Comment by auggierose
2 years ago
> That's like saying math is made up. Is it made up or is it discovered?
Personally, I think it is discovered, although the concrete incarnations are made up, of course. That's pretty much what it means to be a mathematical realist.
> You're just being pedantic.
I just know more about these things than you seem to do. People disagree on what the "right" logic is (personally, I think the right logic is Abstraction Logic), and the choice of your logic influences your axioms. First-order logic for example has no built-in functions as mathematical objects, so you need to come up with axioms for functions. Simply-typed higher-order logic, on the other hand, comes fully equipped with functions, so no need for additional function axioms. And also no need for additional axioms for other things, you can create numbers, trees, graphs etc. without introducing new axioms (except an axiom for an infinite type of individuals) for these things.
When I look at the book you cited, it's just full of really simple stuff made really complicated. Pointless, indeed. Personally, I am more interested in the opposite direction. But that's just my personal opinion.
>I just know more about these things than you seem to do.
No you're being pedantic. I don't think you know more.
Think about it. We both agree math is discovered. So why the hell are we diving into this tangent? It's because you decided to say that logic is made up and then subsequently agree it's not. The nuance of whether and what part of logic is made up is pedantic.
>When I look at the book you cited, it's just full of really simple stuff made really complicated. Pointless, indeed. Personally, I am more interested in the opposite direction. But that's just my personal opinion.
Sure tbh I never fully read the book. Skimmed. Seems to be a good resource for beginners. But I also don't think you're an expert.
Your interested in the opposite? You mean the philosophy of programming? Well good on you. You go study that then. Again I can't understand your genius.