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Old 01-03-2012, 02:30 PM
Omphaloskeptic Omphaloskeptic is offline
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Quote:
Originally Posted by whc.03grady View Post
I appreciate the fact that physics isn't built atop logic in the sense that you describe (though I have other, unexpressed feelings about this that aren't germane to the topic at hand), and I likely slid into that way of thinking in an earlier post. But it still seems to me that if we're dealing with something like a miracle here.
I'm thinking of Hume's treatment of miracles, which in short says (taking his example), which is more believable? That someone rose from the dead after three days, or that everyone's evidence supporting that occurrence is mistaken? Which does reason compel you to bet on?

The same kind of reasoning seems to apply here: if you had to bet, would you bet that (a) there are cases where contradictions obtain; or (b) the descriptions/interpretations of those cases are in error? Now, it's clear where I place my money, but I'm curious as to why others might bet differently?
Well, I'm arguing that there is no logical contradiction, and that your interpretations are in error, so I guess that makes (b), but I think it's a different (b) than yours since I think you think it's somebody else's interpretations that are in error.

There's a big difference between quantum mechanics and miracles, which is repeatability. Miracles, at least of the sort you're talking about, are one-time events. This makes them very difficult to consider using the scientific method. With quantum mechanics, you can measure as many electrons as you want; when you always get the answers that quantum mechanics predicts, you may start to think there's something to it after all, weird or not.

Quote:
I wonder if you could elucidate on this a bit. First, I don't see how changing "not-alive" to "dead" makes a difference with respect to there not actually being a logical contradiction. Second, I don't get how the physicist "understand[s] that quantum mechanics allows superpositions of these two states." (If I could get a handle on this (and if it's true, of course!), it might be resolved for me and render the rest of what I'm saying irrelevant.)
I gave a little description of the treatment of superpositions later in my post, when I described measurements of an electron's spin. I should note that it is pretty easy to make measurements like this; this description is actually the description of (part of) a classic result called the Stern-Gerlach experiment. It's experiments like this that convince physicists of the need for superpositions.

Now the problem is, because strongly-quantum-mechanical effects primarily occur far outside of the range of everyday experience, human language is not very well-equipped to describe states like |alive>+|dead>. This I think is where your real problem is. You are trying to describe this state as "both alive and not-alive" and claiming a logical contradiction. But that description is intended to be very loose; it's not intended as a formal description of the state that you can directly translate into logic in the way you're trying to do. If you want you can tighten the language to make it clear that there's no immediate logical contradiction. One way to do this is to eliminate the definitions not-alive<=>dead and not-dead<=>alive, and say that "alive" describes precisely the quantum state |alive>, and "dead" describes precisely the quantum state |dead>. You could then describe the state as "not-alive" (i.e., not the state |alive>) and "not-dead" (i.e., not |dead>) without a logical contradiction. I don't find this particularly interesting, but I'm more in the shut-up-and-calculate school myself.

Quote:
What's more, I don't see how empirical results can trump principles of logic or reasoning. The whole process of science is built upon certain more or less formal principles of reasoning: "If a theory is confirmed so-and-so many times, we can regard it as true" would be an example. I wholeheartedly agree with this principle, but hopefully we all can see that no experiment has ever, will ever, or could ever be performed to show that it's a good principle. The scientific process relies quite heavily on the principles of mathematics for instance, principles which themselves are in no way proven by science.

What I'm trying to say in this post is there are certain meta-scientific principles by which science operates that are not themselves provable within science, yet are accepted (NB: I do not take this to mean scientific reasoning is in any way deficient). But why is it that when some results seem to run contrary to a certain principle (non-contradiction), that the impulse in this case is to pitch the principle, not the results?
A full response to these paragraphs would probably be an entire essay on the philosophy of the scientific method; that at least is what my fingers keep trying to type here.

- Why pitch the principle instead of the results? Because that's the scientific method, as I said earlier. If logic and empirical results disagree, it's the logic that eventually has to give. Obviously it's more complicated than this. What usually happens in the most exciting experiments is that a new result appears to contradict an existing *physical theory* (not "logic"--you still seem to be glossing over the necessary but fallible steps in translation between physical theories and logical statements, which is why you seem to be confused); this is usually because the new experiment takes place outside the parameter regime explored by the previous experiments which were used to "derive" (in an inductive sense, not the logical-proof sense) and confirm that theory. If the new experiment is repeatedly confirmed with enough confidence (something that can't be done with one-time miracles), then these experiments are used to derive a new theory, and the old theory is now discarded (or considered a special case usable only in restricted circumstances).

- The relation of mathematics and science is much more complicated than you seem to be describing. The Hamster King already did a good job discussing this, so I will stop here for now.