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ydoaPs

Quantum Aristotle

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I thought we just agreed that the laws are fine.

 

I thought we had agreed they are not relevant. :)

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Weird. We seem to be unable to understand each other.

 

They would always be relevant but they would only apply under certain conditions. If the conditions are not met in some case then they would not apply in that case. I suppose you could say they are irrelevant in such cases but really they remain relevant, just not applicable.

 

That is, the LEM may be 'irrelevant' to, say, the particle-wave duality, but this would not render it irrelevant to QM or imply the need for any modifictation. It would be just that there would be no contradiction, so we would have no reason to apply it in this case.

 

The contradictory for 'a wave' would be 'not-a-wave'. The contradictory partner for 'a wave' would NOT be 'a particle'. 'Wave-particle' is not a dialectic contradiction and thus the LEM would not apply. I don't feel it would be correct to say that the LEM becomes irrelevant because it could be a very misleading idea, but I suppose you could say this.

 

When we are deciding which of three pairs of socks to wear we can say that the LEM is irrelevant, but I'd rather say it doesn't apply. Otherwise there might be a misunderstanding about whether it applies, as it does, when there are only two pairs of socks.

 

The LEM would 'irrelevant' in your terminology in exactly the situations Aristotle tells us that it does not apply. I would prefer 'illegitimate'. or 'inapplicable' to 'irrelevant', and I suspect he would have preferred it also, but it's just a terminology thing. .

Edited by PeterJ

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The contradictory for 'a wave' would be 'not-a-wave'. The contradictory partner for 'a wave' would NOT be 'a particle'. 'Wave-particle' is not a dialectic contradiction and thus the LEM would not apply. I don't feel it would be correct to say that the LEM becomes irrelevant because it could be a very misleading idea, but I suppose you could say this.

no one in this thread objected with this example. whether or not it could actually be used to argue against LEM applicability in QM i can't say

 

perhaps you can explain why objections actually raised in this thread do no make LEM irrelevant or inapplicable instead of just repeating what your view is.

 

and maybe you can give a quick look over this http://arxiv.org/pdf/quant-ph/0101028v2.pdf - a difference they note between classical and quantum logic is LEM holds in classical

Edited by andrewcellini

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QM can be described using binary logic. Taking just the example of 1-D QM, it can be described as operators on the complex Hilbert space of wavefunctions on the line. Everything here can be described using binary logic: is the state this element of the Hilbert space? Is the sum of these two states proportional to this other state?

 

This doesn't contradict what ydoaPs has said; non-concretizable categories can be described using binary logic and sets. And that is what PeterJ seems to be trying to get at.

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This doesn't contradict what ydoaPs has said

this does contradict what he said as he explicitly says:

 

Boolean structure doesn't work.

QM can be described using binary logic.

how?

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this does contradict what he said as he explicitly says:

 

how?

Because when he says "Boolean structure doesn't work", he's making a very precise mathematical statement, which I'll try to replicate here: that if you think of a particle in a mixed state as being "partially in one eigenstate, partially in another", then Aristotelian logic and usual set theory doesn't work.

 

You can model that logic using Aristotelian logic, but you have to not think of a particle in a mixed state as being "partially in one eigenstate, partially in another"; instead, you have to think of it as being in a specific state that is a linear combination of other eigenstates.

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Yay - I think uncool may be on something like my wavelength.

 

 

Andrew - "no one in this thread objected with this example. whether or not it could actually be used to argue against LEM applicability in QM i can't say"

 

I don't think there's anything to add to this. The example seems applicable to QM as it is. For the LEM we have to establish a contradiction.

 

"perhaps you can explain why objections actually raised in this thread do no make LEM irrelevant or inapplicable instead of just repeating what your view is."

 

I have been explaining this all the way through, since it is my view.

 

"...and maybe you can give a quick look over this http://arxiv.org/pdf...h/0101028v2.pdf - a difference they note between classical and quantum logic is LEM holds in classical.

 

A quick look? Lol. Where exactly does it show that true contradictions exist? In philosophy there is extreme scepticism as to the possibility of true contradictions, so clearly none have yet been found, If contradicitons arise in the maths of QM for reasons given by uncool, viz. to do our underlying assumptions, then this would not count. I would happily concede that contradictions may arise in the maths, as result of a particular formalisation, but it's the phenomenon itself that must be shown to contradictory.

 

if there is a contradicton then there is no third option, and if there is a third option then there is no contradiction. How then, can there be a true contradiction?

 

Under these rules there is no possibility of true contradiction. This was Aristotle's genius, that he defined his rules so the the world could do what it likes but the rules would be unnafected. He was very aware that logic can prove nothing about reality and so set up the rules to allow reality to do what it likes without there ever being any need to abandon them.

 

But people very often define false contradictions and then wonder why the rules won't work. The classic and miost important example wiould be metaphysics, where it happens all the time, but it seems to also happen in physics.

 

Take the Mind-Matter problem. If we see this as a contradiction it is intractible, as history shows. So these decisions about what is a contradiction and what is not are vital.

 

But I've said my piece and as you point out, can only now repeat myself.

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A quick look? Lol.

yes, as in ctrl-f and search for excluded middle. i think it's the first one that's highlighted that's under the description of classical and quantum logical structure.

 

your invocation of true contradictions is completely irrelevant. i have to ask if you even know what a "true contradiction" in dialetheism is? you seem to be blending aristotelian logic and dialetheism (though aristotle did write about dealing with contradiction in a similar way he did not make a system of logic which followed similar rules).

You can model that logic using Aristotelian logic, but you have to not think of a particle in a mixed state as being "partially in one eigenstate, partially in another"; instead, you have to think of it as being in a specific state that is a linear combination of other eigenstates.

wouldn't that be something different than QM entirely?

Edited by andrewcellini

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wouldn't that be something different than QM entirely?

No. It's just a description of QM.

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I have no comment to make about eigenstates, but I'm hoping that uncool is correct about this.

 

Andrew. - I feel that dialethism is nonsense. I have been arguiing against Priest, Routley and Melhuish for years. My argument is that they are making exactly the same mistake that scientists often make in in relation to QM and that I am discussing here. So I'd agree that diaethism is directly relevant, but feel that you haven't quite grokked my point about logic yet. Dialethism claims true contradictions. I deny them.

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I have no comment to make about eigenstates, but I'm hoping that uncool is correct about this.

 

Andrew. - I feel that dialethism is nonsense. I have been arguiing against Priest, Routley and Melhuish for years. My argument is that they are making exactly the same mistake that scientists often make in in relation to QM and that I am discussing here. So I'd agree that diaethism is directly relevant, but feel that you haven't quite grokked my point about logic yet. Dialethism claims true contradictions. I deny them.

edit:

 

i've misread something you wrote earlier, my mistake. you referring to contradictions which satisfy LEM as "true contradictions" didn't help lol

Edited by andrewcellini

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Yes. I may well have made that mistake. If so pardon me. I should have said 'legitimate' or somesuch.

 

A contradiction would be a pair of assertions meeting Aristotle's rule for contradictory pairs, while a 'true' contradiction would be an assertion that is both true and false simultaneously.

 

Interesting that you brought up dialethism. Usually my argument is used to oppose dialethism and I believe it is successful, but since physicists sometimes see true contradictions in QM the same argument arises.

 

I see it a crucial topic with very important implications for philosophy and physics but often it gets bogged down in the details, as here, which are not really the interesting issue. .

Edited by PeterJ

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...

You can model that logic using Aristotelian logic, but you have to not think of a particle in a mixed state as being "partially in one eigenstate, partially in another"; instead, you have to think of it as being in a specific state that is a linear combination of other eigenstates.

...

wouldn't that be something different than QM entirely?

No. It's just a description of QM.

 

I would say that is a description of classical physics and the opposite of QM.

If you can factorize a state into a product of basis vectors then the state is not entangled. The important difference of quantum mechanics is that there exist superposition of entangled particles which can only be described by non-product states - for example the singlet state which I quoted above

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thank you for clarifying. that's essentially why i asked; it seemed as though uncool's interpretation could be used for something like a classical wave.

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I would say that is a description of classical physics and the opposite of QM.

If you can factorize a state into a product of basis vectors then the state is not entangled. The important difference of quantum mechanics is that there exist superposition of entangled particles which can only be described by non-product states - for example the singlet state which I quoted above

 

Which is why I said linear combinations of eigenstates. I'm not saying that the states are products of "basis vectors" (which I think you are using in a nonstandard way? do you mean vectors corresponding to configurations of individual particles?), but linear combinations of them.

 

And I don't think that's quite the important difference, because that's not the only way to see classical mechanics. You can see classical mechanics as dealing with the evolution of states in the same space as quantum mechanics - the major difference is that the different products don't "interact". Another way to see it is that the operators in classical mechanics all commute. This is a useful way to see classical mechanics as the limit of quantum mechanics

 

I could provide an example, but am short on time at the moment.

thank you for clarifying. that's essentially why i asked; it seemed as though uncool's interpretation could be used for something like a classical wave.

It can be used for classical mechanics, yes. This should be expected - after all, classical mechanics are a limiting case of quantum mechanics as hbar goes to 0.

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