Don’t think there is one single Less Wrongist philosophy of math, but the infinite set atheism tag might be of interest, it links to 2009!Yudkowsky’s guess that “I suspect that an AI does not have to reason about large infinities, or possibly any infinities at all, in order to deal with reality”.
Where does mathematics go? How is it that human mental mathematical abilities and the related “manipulations of symbols” can be used to achieve things in the world? Cf The Unreasonable Effectiveness of Mathematics.
Where does mathematics come from? On the surface, human mathematical activity seems quite different from what I imagine apes would be doing on the savanna.
It suffices for me if there is one philosophy of mathematics that exhibits Less Wrongist virtues 🙂
The Yud view seems not very complete from this. I’m saddened to see I can’t access the Q&A videos, but I found a transcript of #14 about infinite atheism here. Note that the most infinite thing in my example suspicious statement is quantification over natural numbers.
I like both your posts, thanks for summarizing these views. I think in combination it somewhat dissolved the philosophical mystery for me, but there is still some normal empirical mystery left. The Mac Lane stuff reminded me of something I read at Terence Tao’s, about how mathematicians use different intuitions like geometric, economic.
Don’t think there is one single Less Wrongist philosophy of math, but the infinite set atheism tag might be of interest, it links to 2009!Yudkowsky’s guess that “I suspect that an AI does not have to reason about large infinities, or possibly any infinities at all, in order to deal with reality”.
What do you think of Eric S. Raymond’s take?
Same question, what do you think of this take?
It suffices for me if there is one philosophy of mathematics that exhibits Less Wrongist virtues 🙂
The Yud view seems not very complete from this. I’m saddened to see I can’t access the Q&A videos, but I found a transcript of #14 about infinite atheism here. Note that the most infinite thing in my example suspicious statement is quantification over natural numbers.
I like both your posts, thanks for summarizing these views. I think in combination it somewhat dissolved the philosophical mystery for me, but there is still some normal empirical mystery left. The Mac Lane stuff reminded me of something I read at Terence Tao’s, about how mathematicians use different intuitions like geometric, economic.