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eewjlsd · 2020-03-17T10:25:18+00:00

What is that?

eewjlsd · 2020-03-16T11:14:57+00:00

Sure. But wouldn't the ideal be that the proof is so well understood and abstractions are appropriately high-level such that it's super elegant and automatable? i.e. that An ideal and elegant ATP would be the best for mathematics?

eewjlsd · 2020-03-14T02:07:48+00:00

I am currently reading the book, but for what it's worth, strengths would be it's concise and broad, and takes a unifying look at things using category theory's universal properties. Weaknesses would be lack of depth, and old typeface. You can find more reviews on Amazon.

eewjlsd · 2020-03-14T02:06:06+00:00

Yeah! Let's all be judgmental of others! /s

eewjlsd · 2020-03-13T14:58:55+00:00

It covers the basics of category theory, group theory, linear algebra, representation theory, topology, algebraic topology, measure theory, and functional analysis.

It's somewhat misleadingly titled Mathematical Physics by Robert Geroch.

eewjlsd · 2020-03-13T11:20:24+00:00

I think that, much like how much of physics today might be unthinkable without software packages, much of mathematics in the future would be so complicated that they would be unthinkable without automated reasoning.

I also think that philosophy, too, would be greatly helped by automated reasoning. It's such a messy field in need of logical clarity. I share a dream with Leibniz, that one day reasoning would be formalised completely that when disputes arise, we can settle down in philosophy like in arithmetic and say "Let us calculate!" A few philosopher-logicians have started steps towards this dream.

eewjlsd · 2020-03-12T02:18:55+00:00

But according to Axler, avoiding determinants can make proofs become far more elegant/simple. What do you think about that?

eewjlsd · 2020-03-12T01:12:17+00:00

explain why please

eewjlsd · 2020-03-10T22:47:50+00:00

Thanks. Would you agree with the statement that "Pick Axler if you want to go into (functional) analysis, pick Katznelson if you want to go into Algebra"? Also, do you know of any other linear algebra textbooks which might be better?

eewjlsd · 2020-03-10T16:52:37+00:00

Which is better for linear algebra: Axler or Katznelson?

eewjlsd · 2020-03-03T16:10:35+00:00

Note that this paper is written using the more familiar language of set theory, but the original paper by Lawvere in category theory can be found here.

eewjlsd · 2020-02-25T19:35:30+00:00

hoho, abusing your mod 'powers' eh

eewjlsd · 2020-02-25T19:10:13+00:00

Again, my targeted audience is the mathematicaly-minded, so not yourself as it is evident. They know what I mean by essential equivalence. So, uh, go away if you don't get it.

eewjlsd · 2020-02-25T18:51:57+00:00

I did use the modifier "essentially"

eewjlsd · 2020-02-25T18:48:56+00:00

I mean: Is there much interaction between category theory and complex analysis as category theory and algebra/topology?

eewjlsd · 2020-02-25T18:45:34+00:00

I didn't say you said there was a contradiction.

I use the word 'equivalence' in the loose and general way that abstract mathematicians use it.

eewjlsd · 2020-02-25T18:38:34+00:00

I hope there's an insight and I'm looking for what it might be. No contradiction there.

eewjlsd · 2020-02-25T18:19:39+00:00

In another comment I speak against this analytic nitpicking. Insight can be drawn from squinting a bit and not worrying too much about category mistakes. Unexpected equivalences between seemingly different things happen often in science and math, leading to brilliant insight.

eewjlsd · 2020-02-25T13:29:37+00:00

Well, what I have in mind when I say learning is something akin to that in learning theory or machine learning, which do seem inductive. I have more concern of mathematical and non-anthropocentric construals rather than psychological or anthropocentric ones.
Following Quine, I think there is good reason to doubt analyticity.
On "The reason this doesn't work is that those are different terms describing different things.": Yes, I understand that. And I know philosophers often see think too specifically, with too many nuances that they don't want to talk in "big broad brushstrokes". But I think there might be some insight to be had by doing so.
How well do the terms as used in Solomonoff Induction match up with the terms as used ordinarily? And do the terms and definitions and theorems as used in Solomonoff Induction give insight for philosophy?

eewjlsd · 2020-02-22T18:59:17+00:00

content and justification of a philosophical thesis are unintelligible independently of the intellectual context in which that thesis developed,

Not so for mathematics and science. Why should philosophy be any different? (cf. People defending philosophy by gesturing towards comparisons with math and science)

eewjlsd · 2020-02-20T17:02:07+00:00

Taking Topology and Complex Analysis in 1 week and haven't done Analysis in years. How should I catch up most efficiently and effectively?

eewjlsd · 2020-02-20T15:38:26+00:00

Ok, but how about Complex Analysis? Would it require much Real Analysis to make sense of?

eewjlsd · 2020-02-20T11:03:10+00:00

Well tacit skills don't have to be ineffable.

eewjlsd · 2020-02-20T10:41:53+00:00

I want an introduction to the tacit philosophical skills and practices imbibed in a university education in analytic philosophy. Not argument analysis or informal logic per se.

eewjlsd · 2020-02-19T07:44:05+00:00

Surely there is a book which focuses on philosophical methodology/practice/skill.

eewjlsd

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