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Basically, The Notion Is Ridiculous

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Posted by Harvey on October 17, 2002 15:08:39 UTC

Hi Aurino,

Thanks for taking that bag of chips and giving me something healthy to digest.

***What I found interesting about that is, why would anyone need proofs for everything? For instance, if we know that physics is true, isn't experimental evidence all that is required as far as proof goes? Sure, our theories may be proved incomplete in the future, but the outcome of every single experiment can never, ever be questioned. Or can it?***

I'm not sure what you mean that "the outcome of every single experiment can never, ever be questioned", since this is common practice in science. I assume you mean something else.

***If I drop a stone and it falls to the ground, I may explain it as the result of a force called gravity. Later on I may choose to explain it as the effect of a curvature in spacetime. Other explanations might be thought of in the future, but no matter how you choose to explain it you can't possibly deny the fact that the stone fell to the ground.***

I agree. Of course, one could be philosophically nasty and say that there is no such thing as 'stones' just like there are no such thing as 'sound' in that reduction of those concepts lead to different concepts entirely (e.g., sound roughly reduces to air molecule vibrations, stones roughly reduce to a collection of atoms of carbon, silicon, etc). In that sense, nothing we say is 'true', it is merely a useful description for us to comprehend what's around us.

***Doing so is, in my opinion, the shortest route to a mental institution, unless you're doing it just for fun in which case anything you may come up with is of absolutely no relevance.***

Many philosophers are concerned about what are objects, I don't see it as a cause for mental illness unless you mean the kind of attention that Alan gives to such concepts.

***So do you believe that everything has to be proved, or do you find the notion ridiculous?***

Proof is one of those words which you must find out what that other person means when they use it. Commonly, proof is just sufficient evidence to come to a conclusion about an event, action, description, etc. Often, one means a scientific proof which is based on higher standards of evidence, theorizing, explanation, and prediction. However, and this is where Alan and Dick are confused, the proof is defined in terms of logical or mathematical terms. A logico-mathematical proof (theorem) is the ultimate means by which to know that you are right. You deduce from axioms, defined and undefined terms, and acceptable rules of inference to a conclusion. This is the proof of a formal system.

The problem, of course, is that the physical universe is not a formal system, or at least, we don't know enough about the universe to say that it is formal system. People who try to impose the rules of formal systems (esp. mathematics) on the universe are making significant miscalculations in their conclusions on what is true in the universe. You cannot provide mathematical proofs of the universe since one must assume certain axioms are true about the universe and one must interpret the results of the formal deductions in light of them being true for the universe.

I read an interesting article in a philosophy journal last night about how physicists attempt to do this by assigning isomorphisms between the mathematical structures and the physical (phenomenal) structures of the universe. The best we can hope for is that we are interpretations of the mathematical structures are genuinely isomorphic (or, partially homomorphic - don't worry about what that means) to the physical strutures of the universe. This is by no means a formal proof showing that mathematics results in physics. Rather, it only shows that we have justification in using these isomorphic results from mathematics in obtaining empirical success in science. Formal proof for the universe is not only impossible, it is rather ridiculous.

Warm regards, Harv

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