Comments on: Lambda calculus for real analysis by Paul Taylor http://math.andrej.com/2008/02/02/lambda-calculus-for-real-analysis-by-paul-taylor/ Mathematics for computers Fri, 04 Jul 2008 17:33:28 +0000 http://wordpress.org/?v=2.3.3 By: Andrej Bauer http://math.andrej.com/2008/02/02/lambda-calculus-for-real-analysis-by-paul-taylor/#comment-6248 Andrej Bauer Sat, 23 Feb 2008 11:52:28 +0000 http://math.andrej.com/2008/02/02/lambda-calculus-for-real-analysis-by-paul-taylor/#comment-6248 I apologize for sounding so harsh. I did not meant to. Of course you did not offend me. I was just a bit annoyed that you were misinterpreting what I said. I should have waited a bit before replying. Thank you for showing interest in my blog, and I hope I did not scare you away! I apologize for sounding so harsh. I did not meant to. Of course you did not offend me. I was just a bit annoyed that you were misinterpreting what I said. I should have waited a bit before replying. Thank you for showing interest in my blog, and I hope I did not scare you away!

]]> By: Kevembuangga http://math.andrej.com/2008/02/02/lambda-calculus-for-real-analysis-by-paul-taylor/#comment-6167 Kevembuangga Mon, 18 Feb 2008 07:36:31 +0000 http://math.andrej.com/2008/02/02/lambda-calculus-for-real-analysis-by-paul-taylor/#comment-6167 I am sorry if I offended you... I am sorry if I offended you…

]]> By: Andrej Bauer http://math.andrej.com/2008/02/02/lambda-calculus-for-real-analysis-by-paul-taylor/#comment-6156 Andrej Bauer Sun, 17 Feb 2008 07:20:18 +0000 http://math.andrej.com/2008/02/02/lambda-calculus-for-real-analysis-by-paul-taylor/#comment-6156 You are a bit rash in concluding my philosophical stand on the nature of mathematics from the word "are", especially since this particular "are" appears in a sentence which does not express my opinion. It only explains that there are many other works, apart from the one you cited, which deal with the idea that spaces are more than just collections of point. Ooops, I said it again. I am doubly Platonistic now. Please read more carefully what I write. Even if I did say "spaces are more than just collections of points", how would that imply anything about my position about Platonism? In fact, I do say that spaces <b>are</b> more than just collections of points. But I am not a Platonist. I am just expressing my view as to what sort of mathematical objects geometry and topology are trying to (or should) capture. As far as translating cryptic mathematical notation goes: I did look at the paper you reference. True, nothing is hiding in it behind cryptic mathematical notation. Just some old regurgitated ideas, with relevant references missing. You are a bit rash in concluding my philosophical stand on the nature of mathematics from the word “are”, especially since this particular “are” appears in a sentence which does not express my opinion. It only explains that there are many other works, apart from the one you cited, which deal with the idea that spaces are more than just collections of point. Ooops, I said it again. I am doubly Platonistic now. Please read more carefully what I write.

Even if I did say “spaces are more than just collections of points”, how would that imply anything about my position about Platonism? In fact, I do say that spaces are more than just collections of points. But I am not a Platonist. I am just expressing my view as to what sort of mathematical objects geometry and topology are trying to (or should) capture.

As far as translating cryptic mathematical notation goes: I did look at the paper you reference. True, nothing is hiding in it behind cryptic mathematical notation. Just some old regurgitated ideas, with relevant references missing.

]]> By: Kevembuangga http://math.andrej.com/2008/02/02/lambda-calculus-for-real-analysis-by-paul-taylor/#comment-6145 Kevembuangga Sat, 16 Feb 2008 09:19:16 +0000 http://math.andrej.com/2008/02/02/lambda-calculus-for-real-analysis-by-paul-taylor/#comment-6145 "... does not seem to be written by a professional mathematician so it is hard to judge exactly what its mathematical contents is supposed to be." Well, Arntzenius is a philosopher: http://www.philosophy.ox.ac.uk/members/frank_arntzenius and of course, instead of having to "translate" cryptic mathematical notations into "ideas" the understanding has to go (for once...) the other way around, his proposals are on pp18-21 which may be you didn't reach. "... the idea that spaces *are* more than just collections of points." Don't you think that there is a strong and surreptitious platonistic slant in this very turn of phrase? (i.e. looking for the "essence" of spaces...) It's even more surprising since your work (as shown on this blog) appears to have a very pragmatic orientation, looking for "working solutions" rather than "grand metaphysical principles". “… does not seem to be written by a professional mathematician so it is hard to judge exactly what its mathematical contents is supposed to be.”

Well, Arntzenius is a philosopher:
http://www.philosophy.ox.ac.uk/members/frank_arntzenius
and of course, instead of having to “translate” cryptic mathematical notations into “ideas” the understanding has to go (for once…) the other way around, his proposals are on pp18-21 which may be you didn’t reach.

“… the idea that spaces *are* more than just collections of points.”

Don’t you think that there is a strong and surreptitious platonistic slant in this very turn of phrase?
(i.e. looking for the “essence” of spaces…)
It’s even more surprising since your work (as shown on this blog) appears to have a very pragmatic orientation, looking for “working solutions” rather than “grand metaphysical principles”.

]]> By: Andrej Bauer http://math.andrej.com/2008/02/02/lambda-calculus-for-real-analysis-by-paul-taylor/#comment-6139 Andrej Bauer Fri, 15 Feb 2008 22:01:33 +0000 http://math.andrej.com/2008/02/02/lambda-calculus-for-real-analysis-by-paul-taylor/#comment-6139 Well, the paper you reference does not seem to be written by a professional mathematician so it is hard to judge exactly what its mathematical contents is supposed to be. But yes, it is "somehow related", as are many, many other works dealing with the idea that spaces are more than just collections of points. This is a topic that was discussed by various philosophers and mathematicians throughout history. Well, the paper you reference does not seem to be written by a professional mathematician so it is hard to judge exactly what its mathematical contents is supposed to be. But yes, it is “somehow related”, as are many, many other works dealing with the idea that spaces are more than just collections of points. This is a topic that was discussed by various philosophers and mathematicians throughout history.

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