Truth and Proof

PeterDF · Posted: Mon Oct 27, 2003 6:41 pm Post subject: Truth and Proof

Consider the following equation:

n x m = m x n

With every value of "n" and every value of "m" yet tried the equation has been found to be true.

BUT the equation cannot be said to have been proved, because for it to be proved one would have to show that the equation would hold for EVERY value of "m" and every value of "n". As there are an infinite number of possible "n"s and "m"s it cannot be proved that the equation holds in every combination of "n"s and "m"s.

This was the case made at a lecture at the LSE conference by the physicist Michael Redhead.

It was then that he - in his words - pulled a rabbit from his hat. One can simply know that n x m = m x n even if it can't be proved. Sometimes truth outruns proof.

At first I thought: Great! He is on our side. There are things in science that we can know, even if proof sometimes eludes us. But then it occurred to me that perhaps his argument would support the point of view of the theists - one might think of them saying that we can know God exists even if we can't prove it. I am still unsure what point he was trying to make.

But I thought it was a fascinating concept - the idea that one can KNOW something to be true without actually being able to prove it.

indianskeptic · Posted: Tue Oct 28, 2003 5:03 am Post subject: Re: Truth and Proof

Interesting.

There is actually a mathematical proof for the commutative rule, isn't there ?

Also, the moment anyone finds even a single value of m or n which does not follow the commutative law, the law ceases to be a law. Period.

Those are the important points, I would think.

seanf 2003 · Posted: Tue Nov 04, 2003 4:28 pm Post subject: Re: Truth and Proof

Hi guys. Sorry I dissapeared for so long - i've been pretty busy, and my opportunity to get on the net has been limited.

If m and n are matrices, then m x n doesn't equal n x m. However, if they aren't you would certainly expect the proposition to be true.

Jeremy1952 · Posted: Wed Nov 05, 2003 4:59 pm Post subject: Re: Truth and Proof

Important distinction in biology. Evolution is a process, not a theory. It is, in fact, how life has become diversified. The New Synthesis is a theory of evolution. It describes the real, physical process as well as we are currently able to describe it.

Lamark had a theory of evolution; So did Erasmus Darwin; and Charles Darwin came up with a pretty good one, given what he didn't know about the mechanics of heredity. None is a perfect description of what life herself does. The great ignoramuses of the world try to use this fact to challenge the reality of evolution, but it simply doesn't follow that an imperfect theory belies the truth of the underlying process it partially describes.

Science is neither a philosophy nor a belief system. It is a combination of mental operations that has become increasingly the habit of educated peoples, a culture of illuminations hit upon by a fortunate turn of history that yielded the most effective way of learning about the real world ever conceived. E.O.Wilson

Jeremy1952 · Posted: Wed Nov 05, 2003 5:00 pm Post subject: Re: Truth and Proof

BTW I just ran across a new proposition in string theory, that at string scale multiplication may not be commutative.

Science is neither a philosophy nor a belief system. It is a combination of mental operations that has become increasingly the habit of educated peoples, a culture of illuminations hit upon by a fortunate turn of history that yielded the most effective way of learning about the real world ever conceived. E.O.Wilson

Chris OConnor · Posted: Wed Nov 05, 2003 10:58 pm Post subject: Re: Truth and Proof

Jeremy

Hmmmm....at first I was in total agreement with your last post, but now that I have given it some thought I'm not so sure. It sounds like you are using theory and mechanism as synonyms. Isn't evolution the theory, and natural selection the mechanism?

Chris

"When once you have tasted flight, you will forever walk the earth with your eyes turned skyward,for there you have been, and there you will always want to be." -- Leonardo da Vinci

Jeremy1952 · Posted: Thu Nov 06, 2003 12:21 am Post subject: Re: Truth and Proof

No. Natural selection is part of the process of evolution. Variation, selection, amplification. . .

Theory is descriptive. A theory can be completely wrong; a mechanism is just how something works. The process of evolution was observed, one of the mechanisms is natural selection, and the theory of evolution codifies what we know about the process and its mechanisms.

Science is neither a philosophy nor a belief system. It is a combination of mental operations that has become increasingly the habit of educated peoples, a culture of illuminations hit upon by a fortunate turn of history that yielded the most effective way of learning about the real world ever conceived. E.O.Wilson


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