Re: [FRIAM] Why are there theorems?

2010-04-26 Thread glen e. p. ropella
Nicholas Thompson wrote circa 04/25/2010 01:50 PM: I was talking about plain old vanilla philosophical induction: The fallacy is that without deduction, induction can't get you anywhere, and that people who think they are getting somewhere through induction alone are so caught up in an

[FRIAM] Why theorems work. (was Why are there theorems?)

2010-04-26 Thread glen e. p. ropella
Russ Abbott wrote circa 04/25/2010 02:45 PM: Does knowledge generated by any so-called pure science promote species survival? Only by chance, it seems. Besides why should improved species survival be related to the possibility of interesting theorems? The importance to us of a domain is

Re: [FRIAM] Why are there theorems?

2010-04-26 Thread Owen Densmore
On Apr 26, 2010, at 7:48 AM, glen e. p. ropella g...@agent-based-modeling.com wrote: I think it is. (But as the thread develops, I'm less and less confident that it'll come to anything... Aaa! I can't believe I might agree with Doug on something. ;- The OP's Too many interesting

Re: [FRIAM] The Princeton Companion to Mathematics

2010-04-26 Thread joseph spinden
Please. It would certainly be nice to have a copy that did not give me a workout every time I picked it up. Joseph Spinden On 4/25/10 9:07 AM, Owen Densmore wrote: BTW: there is a digital pre-print version that has some of the publisher's marginal comments. Let me know if you'd like to

Re: [FRIAM] The Princeton Companion to Mathematics

2010-04-26 Thread joseph spinden
Apologies to the group for the spam. I thought I was just replying to Owen, JS On 4/26/10 10:06 AM, joseph spinden wrote: Please. It would certainly be nice to have a copy that did not give me a workout every time I picked it up. Joseph Spinden On 4/25/10 9:07 AM, Owen Densmore wrote:

Re: [FRIAM] Why are there theorems?

2010-04-26 Thread glen e. p. ropella
Owen Densmore wrote circa 10-04-26 08:59 AM: The OP's Too many interesting comments to follow up sorta sounds like I've lost interest! Heh, yeah; but words have consequences! ;-) No (good?) deed goes unpunished. -- glen e. p. ropella, 971-222-9095, http://agent-based-modeling.com

Re: [FRIAM] Why are there theorems?

2010-04-26 Thread Russ Abbott
I don't follow Glen's 'You can't generalize across all of math/logic to talk about why theorems? any more than you can generalize over all of natural language and ask why sentences? ' The original intent was to ask why there always seems to be hidden structure -- which is revealed by theorems.

Re: [FRIAM] Why are there theorems?

2010-04-26 Thread sarbajit roy
Actually I can follow Glen's line of reasoning (I think). For example, the way Maths works is that a theorem is proved by trying to prove a conjecture. When that approach fails you end up proving a special case of the conjecture - which in turn gets elevated to its own status as a theorem.

Re: [FRIAM] Why are there theorems?

2010-04-26 Thread Grant Holland
Sarbajit, My take is that contemporary abstract mathematicians have no interest (as mathematicians) in discerning truth. The truth about existence is the business of scientists, philosophers and theologians. Ever since Hilbert's program at the beginning of the twentieth century to

Re: [FRIAM] Why are there theorems?

2010-04-26 Thread glen e. p. ropella
sarbajit roy wrote circa 10-04-26 10:59 AM: Actually I can follow Glen's line of reasoning (I think). For example, the way Maths works is that a theorem is proved by trying to prove a conjecture. When that approach fails you end up proving a special case of the conjecture - which in turn

Re: [FRIAM] Why are there theorems?

2010-04-26 Thread Douglas Roberts
*SCREEENNNCKK* (The sound of Hell freezing over.) On Mon, Apr 26, 2010 at 7:48 AM, glen e. p. ropella g...@agent-based-modeling.com wrote: Nicholas Thompson wrote circa 04/25/2010 01:50 PM: Aaa! I can't believe I might agree with Doug on something. ;-)

Re: [FRIAM] Why are there theorems?

2010-04-26 Thread Nicholas Thompson
doug, Is THAT what it sounds like? A bit louder than the sound of one hand clapping. N Nicholas S. Thompson Emeritus Professor of Psychology and Ethology, Clark University (nthomp...@clarku.edu) http://home.earthlink.net/~nickthompson/naturaldesigns/ http://www.cusf.org [City University

Re: [FRIAM] Why are there theorems?

2010-04-26 Thread lrudolph
On 26 Apr 2010 at 23:29, sarbajit roy wrote: Actually I can follow Glen's line of reasoning (I think). For example, the way Maths works is that a theorem is proved by trying to prove a conjecture. When that approach fails you end up proving a special case of the conjecture - which in turn

[FRIAM] Schroedinger's What is Life?

2010-04-26 Thread Nicholas Thompson
All, I am working my way through this book, and, rather than write one huge email that nobody reads, I thought I would write some short ones that somebody might read. It's a splendid little book, very cleanly and economically written. S. is not beset with jargonophilia. The basic idea of

[FRIAM] PLEASE DON'T READ Nick's post: Schroedinger's What is Life?

2010-04-26 Thread Nicholas Thompson
Sorry, everybody: somehow I pressed the send button, when I meant to save it for further thought. The last sentence is just nuts. Nick Nicholas S. Thompson Emeritus Professor of Psychology and Ethology, Clark University (nthomp...@clarku.edu)

Re: [FRIAM] PLEASE DON'T READ Nick's post: Schroedinger's What is Life?

2010-04-26 Thread Steve Smith
Nick - I read it through before seeing your retraction. As you may recognize by now, your fallacy is probably not a consequence of your being an English (Psychology?) Major but actually just not reading the statement of the problem carefully enough. The 10^24 (molecules) vs the 10^21 glasses