This is a fine introduction to constructive logic. And, indeed, I suspect that constructive logic could be popular in this community, if it was better known.
Still, I don’t really understand what the purpose of this series is. Your first post made some bold claims regarding what mathematics is (and the title hints at something like that too), which I don’t think were sufficiently explained, and it’s strange to see none of that in part 2. Was that central to your goal or just a curiosity? Are we coming back to that in later parts?
My goal is mostly to collect my understanding of mathematics into some coherent collection that people can read. Mostly, I just want to expose people to an alternative way of thinking, as I’ve seen people from this community say things that rely on a narrow view of foundations. My plan for the series is not to be especially philosophical. The first post consists only of things which I think are obvious. As far as I can tell, the main reason people thought it might have been controversial is that they didn’t understand what I was getting at in the first place.
The content of this post is actually the meat of my series. I don’t think the philosophical discussion has much practical significance beyond settling one’s mind. I’m far more interested in doing mathematics than talking about the doing of mathematics.
I will eventually write a post pertaining to truth-maker semantics, and I’ll revisit some of the content from my first post then, but I wouldn’t consider the content of the first post central, or even all that necessary, for the series.
And does “mathematics” mean “constructive logic”? You criticise people’s narrow view of foundation, but aren’t you just replacing that with a different but equally narrow view? I think some philosophical discussion is required.
This is a fine introduction to constructive logic. And, indeed, I suspect that constructive logic could be popular in this community, if it was better known.
Still, I don’t really understand what the purpose of this series is. Your first post made some bold claims regarding what mathematics is (and the title hints at something like that too), which I don’t think were sufficiently explained, and it’s strange to see none of that in part 2. Was that central to your goal or just a curiosity? Are we coming back to that in later parts?
My goal is mostly to collect my understanding of mathematics into some coherent collection that people can read. Mostly, I just want to expose people to an alternative way of thinking, as I’ve seen people from this community say things that rely on a narrow view of foundations. My plan for the series is not to be especially philosophical. The first post consists only of things which I think are obvious. As far as I can tell, the main reason people thought it might have been controversial is that they didn’t understand what I was getting at in the first place.
The content of this post is actually the meat of my series. I don’t think the philosophical discussion has much practical significance beyond settling one’s mind. I’m far more interested in doing mathematics than talking about the doing of mathematics.
I will eventually write a post pertaining to truth-maker semantics, and I’ll revisit some of the content from my first post then, but I wouldn’t consider the content of the first post central, or even all that necessary, for the series.
And does “mathematics” mean “constructive logic”? You criticise people’s narrow view of foundation, but aren’t you just replacing that with a different but equally narrow view? I think some philosophical discussion is required.