Posted by
John Kennison on
Apr 27, 2009; 12:14pm
URL: http://friam.383.s1.nabble.com/The-Unreasonable-Effectiveness-of-Mathematics-in-the-Natural-Sciences-tp2714601p2725635.html
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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