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
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
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
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.
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.
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
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
*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. ;-)
of Santa Fe]
- Original Message -
From: Douglas Roberts
To: The Friday Morning Applied Complexity Coffee Group
Sent: 4/26/2010 1:57:31 PM
Subject: Re: [FRIAM] Why are there theorems?
SCREEENNNCKK
(The sound of Hell freezing over.)
On Mon, Apr 26, 2010 at 7:48 AM, glen e. p
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
Complexity Coffee Group
Sent: Saturday, April 24, 2010 10:47 PM
Subject: [FRIAM] Why are there theorems?
I have what probably seems like a strange question: why are there theorems?
A theorem is essentially a statement to the effect that some domain is
structured in a particular way
, April 25, 2010 6:47 AM
Subject: [FRIAM] Why are there theorems?
I have what probably seems like a strange question: why are there theorems?
A theorem is essentially a statement to the effect that some domain is
structured in a particular way. If the theorem is interesting, the structure
are not able to make an instant
in-depth analysis of a complex system.
-J.
- Original Message -
From: Russ Abbott
To: The Friday Morning Applied Complexity Coffee Group
Sent: Sunday, April 25, 2010 6:47 AM
Subject: [FRIAM] Why are there theorems?
[..] So the question is: why do so many
There are theorems because systems have relationships as well as
elements, from which arise emergent properties.
Grant
Russ Abbott wrote:
I have what probably seems like a strange question: why are there
theorems? A theorem is essentially a statement to the effect that
some domain is
Russ, I apologize for being so terse. Let me try again. Here is my take
on your question...
As we know, systems are more than just components, or elements. A system
must also have relationships among its elements before they it is worthy
being called a system.
But, when you take these
Russ -
Another great question.
While Doug and I have an awful lot in common, this is probably where we
most notably diverge. You ask "why", he asks "why ask why", I ask
"why ask why ask why". ("Who dat who say who dat?" might ring a bell
for some of the other old timers here).
I don't
Grant Holland wrote circa 04/25/2010 05:42 AM:
Thus the need for theorems arises due to a system having relationships
among its components. And we haven't even mentioned emergent properties yet!
But I think Nick's answer is relevant to this point, as well. Even in a
seemingly a priori
Steve Smith wrote:
You ask why, he asks why ask why, I ask why ask why ask why.
A recursive function definition requires a base case for escape. Doug
provides that case.
Marcus
FRIAM Applied Complexity Group listserv
Meets
string why()
{
while (!why())
{
why();
}
}
(string theory search)
On Sun, Apr 25, 2010 at 10:53 AM, Marcus G. Daniels mar...@snoutfarm.comwrote:
Steve Smith wrote:
You ask why, he asks why ask why, I ask why ask why ask why.
A recursive function definition requires a base
I agree that the key has to do with relations -- and that this is related to
emergence.
Individual carbon atoms are arguably fairly simple. But carbon atoms in
relationship either with each other or with other things form extraordinary
structures. In some sense those structures were hidden from
Russ,
Bypassing all the other replies, I find this question very interesting. When
faced with questions like this I usually give an answer, am told it is not
satisfactory, give another answer, am told it is not satisfactory, etc. Then at
some point I ask the questioner to give me examples of the
Sent: 4/25/2010 11:22:42 AM
Subject: Re: [FRIAM] Why are there theorems?
Russ,
Bypassing all the other replies, I find this question very interesting. When
faced with questions like this I usually give an answer, am told it is not
satisfactory, give another answer, am told it is not satisfactory
Individual carbon atoms are arguably fairly simple.
The word *arguably* being key, I believe.
To wit:
Carbon:
*Carbon* is the chemical
elementhttp://en.wikipedia.org/wiki/Chemical_elementwith
symbol http://en.wikipedia.org/wiki/Chemical_symbol *C* and atomic
glen e. p. ropella wrote:
But I think Nick's answer is relevant to this point, as well. Even in a
seemingly a priori discrete system like that of the natural numbers,
components are psychologically induced, not necessarily embedded in
the system.
There is (actually) only *one* (closed)
In answer to Eric and lrudolph, the answer I'm looking for is not related to
epistemology. It is related to the domains to which mathematical thinking is
successfully applied, where successfully means something like produces
interesting' theorems. (Please don't quibble with me about what
If I start from the Wikipedia definition of theorem -- *In
mathematics, a theorem is a statement which has been proved on the basis of
previously established statements, such as other theorems, and previously
accepted statements, such as axioms.* I end up looking at a house of cards
which will
On Apr 24, 2010, at 11:26 PM, Nicholas Thompson wrote:
Because of the fallacy of induction?
Do you mean this induction:
http://en.wikipedia.org/wiki/Mathematical_induction#Description
I.e. are you interested in proofs over the positive integers?
-- Owen
On 25 Apr 2010 at 10:51, Russ Abbott wrote:
In answer to Eric and lrudolph, the answer I'm looking for is not related to
epistemology. It is related to the domains to which mathematical thinking is
successfully applied, where successfully means something like produces
interesting' theorems.
So, the question is not about people, nor the way people do things. But it is
something about where people have been successful, with the recognition that
success in mathematics typically involves theorems.
Would it be fair to represent your question as:
What is it about the way mathematical
://home.earthlink.net/~nickthompson/naturaldesigns/
http://www.cusf.org [City University of Santa Fe]
- Original Message -
From: Owen Densmore
To: nickthomp...@earthlink.net;The Friday Morning Applied Complexity Coffee
Group
Sent: 4/25/2010 1:15:22 PM
Subject: Re: [FRIAM] Why are there theorems
: [FRIAM] Why are there theorems?
On 25 Apr 2010 at 10:51, Russ Abbott wrote:
In answer to Eric and lrudolph, the answer I'm looking for is not
related to
epistemology. It is related to the domains to which mathematical
thinking is
successfully applied, where successfully means something like
(expressions of ignorance to follow:)
I wonder in all this whether there is anything interesting to be said
by looking at the relation of syntax to semantics in mathematics,
perhaps not in the sense of applying language, but rather in the
sense of recognizing that mathematics shares syntactic
Too many interesting comments to follow up. But to Lee, Friam probably
doesn't forward attachments. I didn't get the article with your earlier
message either. There is an entry in the Stanford Encyclopedia of
Philosophy on Evolutionary
[russ.abb...@gmail.com]
Sent: Sunday, April 25, 2010 5:45 PM
To: The Friday Morning Applied Complexity Coffee Group
Subject: Re: [FRIAM] Why are there theorems?
Too many interesting comments to follow up. But to Lee, Friam probably doesn't
forward attachments. I didn't get the article with your
I have what probably seems like a strange question: why are there theorems?
A theorem is essentially a statement to the effect that some domain is
structured in a particular way. If the theorem is interesting, the structure
characterized by the theorem is hidden and perhaps surprising. So the
-
From: Russ Abbott
To: The Friday Morning Applied Complexity Coffee Group
Sent: 4/24/2010 10:48:21 PM
Subject: [FRIAM] Why are there theorems?
I have what probably seems like a strange question: why are there theorems? A
theorem is essentially a statement to the effect that some domain
Yes, to me a strange question, begging the follow-on question: why would
people want to think in such a way as to ask it? Such a
vague, immaterial-to-the-point-of-having-no-practical-application kind of a
question.
Abstract. Disconnected.
In other words: what's the point of such a question?
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