Posted by
John Kennison on
Apr 28, 2009; 2:14am
URL: http://friam.383.s1.nabble.com/The-Unreasonable-Effectiveness-of-Mathematics-in-the-Natural-Sciences-tp2714601p2729755.html
Robert:
As you say, logic can be viewed as a game, like chess. You also say that "More great technical innovations result from playing the game of logic than playing these other games." The question then is what is it about logic that leads to more great technical innovations than other games.
--John
________________________________________
From:
[hidden email] [
[hidden email]] On Behalf Of Robert Howard [
[hidden email]]
Sent: Monday, April 27, 2009 2:13 PM
To: 'The Friday Morning Applied Complexity Coffee Group'
Subject: Re: [FRIAM] The Unreasonable Effectiveness of Mathematics in theNatural Sciences
John: Why is logic valid?
For the same reason the rules of chess are valid: by definition. Its
validity is presupposed. If you don't like chess, don't play. If you do then
you have to play by the agreed rules. Else don't call it chess (or logic).
Make a new name for your game.
In logic, one begins with a rule that a proposition has exactly one of two
values: true or false. Other games, like fuzzy logic, have additional
"maybe" values, but we use the adjective "fuzzy" to distinguish these games
(or rule sets). Other rules are added to define ways to relate (or compose)
propositions in the form of conjunctions, disjunctions, etc; to build up
structures. All players agree to the rules and knowledge and science
progress. Some people don't like these games, so they don't play. Some
people play badly and aren't much fun. Some make mistakes (called fallacies)
that are hard to see by other players. Some prefer other rules, like "the
highest authority is always right" or "there is no truth; only love".
More great technical innovations result from playing the game of logic than
playing these other games.
John: Why is it useful to put together long strings of logical implications?
This is probably a result of trivial observation; nature puts together long
strings of related events of cause and effects; e.g. chemical reactions and
planetary motions. We are merely recording what we see in the formal
language of cause and effect, namely logic. In this case, logic is more of a
historian's tool.
--Rob Howard
-----Original Message-----
From:
[hidden email] [mailto:
[hidden email]] On Behalf
Of John Kennison
Sent: Monday, April 27, 2009 5:15 AM
To: ForwNThompson;
[hidden email]
Cc: Sean Moody
Subject: Re: [FRIAM] The Unreasonable Effectiveness of Mathematics in
theNatural Sciences
Nick et al,
This is a great question, with, I think, two parts. The first part is why
is logic valid. I am almost certainly a platonist or worse on this point
--it's validity simply seems to be obvious. Can the proposition that logic
is valid be supported by any argument that doesn't implicitly use logic?
(Okay, even "implicitly" assumes logic). The argument that we evolved to be
convinced by logical implications because it is useful for survival suggests
that logic is, at least, approximately valid, which is a lot less of a
conclusion than what I would want, and which doesn't explain why logic works
in modern physics.
The other part of the original question is, even if we grant that logic is
valid (or at least approximately valid) why is it useful to put together
long strings of logical implications? Believing that logical implications
are trivially true, I wonder how can long chains of such implications be
anything but trivial. (And if we believe that logic is at best approximately
true, wouldn't long chains of implications stop being good approximations if
each link in the chain is a little inaccurate.)
Perhaps Physics somehow restricts itself to a domain where logic works very
well. And maybe things like consciousness are simply outside that domain
(but I hope not).
I wonder if there is there a domain where logic is a useful approximation,
but long chains of implications are not useful? Perhaps social analysis?
Perhaps philosophy? Perhaps the humanities? Nick, and others,--I'd be
curious about what you think on this issue.
---John
________________________________________
From: Nicholas Thompson [
[hidden email]]
Sent: Sunday, April 26, 2009 1:40 PM
To:
[hidden email]
Cc: John Kennison; Sean Moody
Subject: Re: [FRIAM] The Unreasonable Effectiveness of Mathematics in
theNatural Sciences
Owen, et al,
Well, isn't this part of the broader mystery of why logic should get you
anywhere in the study of nature?
Isn't logic just a language trick?
Why should nature give a fig for the tricks we play with our words?
This is all reminding me, for some reason, of the "discovery" of the fact
that the differential of the integral is just the original function. There
seem to be two sorts of "discovery" in our discourse: One is the discovery
of something in nature that we did not already know. The other is the
discovery of a new implication in what we have already said that we did not
anticipate when we said it. I can see why mathematics can help with the
latter sort of "discovery", but have no idea why it should help with the
former.
In the emergence literature appears the endearing phrase "natural
reverence". The early philosophical emergentists believed that one had to
accept emergent properties with "natural reverence," since such properties
could not be reduced to the properties of their parts. I am deeply
ambivalent about natural reverence: one the one hand, I believe that there
is no point in being a scientist if you are not prepared to experience some
natural reverence. On the other hand, I also believe that natural reverence
is the enemy of discovery. Perhaps "natural reverence" is a fleeting
pleasure one gets before one gets down to the dirty business of figuring out
how things work: too little of it and one would never be inspired; too much
of it, and one would never be curious.
Nick
Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
Clark University (
[hidden email]<mailto:
[hidden email]>)
http://home.earthlink.net/~nickthompson/naturaldesigns/----- Original Message -----
From: Steve Smith<mailto:
[hidden email]>
To: The Friday Morning Applied Complexity Coffee
Group<mailto:
[hidden email]>
Sent: 4/26/2009 10:17:16 AM
Subject: Re: [FRIAM] The Unreasonable Effectiveness of Mathematics in
theNatural Sciences
Well said/observed David, I too am a Lakoff/Johnson/Nunez fan in this
matter.
While I am quite enamored of mathematics and it's fortuitous application to
all sorts of phenomenology, Physics being somehow the most "pure" in an
ideological sense, I've always been suspicious of the conclusion that "the
Universe *is* Mathematics".
This discussion also begs the age-old question of whether we are "inventing"
or "discovering" mathematics. Similarly, it revisits the question of whether
discoveries in mathematics portend discoveries in Physics (or other,
"messier" phenomenological observations).
- Steve
Prof David West wrote:
I'm completely of Tegmark's ilk:
I assume that means you would also adhere to the sentiment attributed to
Einstein:
"How can it be that mathematics, being after all a product of human
thought which is independent of experience, is so admirably
appropriate to the objects of reality?" Which contains the
fallacy, "independent of experience."
Thought - and mathematics! - is but a refined metaphor of experience.
(following Lakoff)
davew
A different response, advocated by Physicist Max Tegmark (2007), is
that physics is so successfully described by mathematics because the
physical world is completely mathematical, isomorphic to a
mathematical structure, and that we are simply uncovering this bit by
bit. In this interpretation, the various approximations that
constitute our current physics theories are successful because simple
mathematical structures can provide good approximations of certain
aspects of more complex mathematical structures. In other words, our
successful theories are not mathematics approximating physics, but
mathematics approximating mathematics.
-- Owen
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