Quantum Aristotle

[ydoaPs]

No need to look too hard, the task has been completed. It;s just that scientists and professional philosophers take no notice of Nagarjuna. He uses Aristiotle's logic and an axiom of unity, and all else follows.

 

No need to look too hard, the task has been completed. It;s just that scientists and professional philosophers take no notice of Nagarjuna. He uses Aristiotle's logic and an axiom of unity, and all else follows.

That's pretty bad metaphysics if it uses Aristotle's logic. The topoi which admit QM do not admit a Boolean structure, but rather a more general Heyting structure in which the law of excluded middle does not always hold.

 

Yes, but most scientists and philosophers do not apply the laws rigorously. You won't believe this, I predict, but it is the case. In fact for metaphysics the law of excluded middle is no problem, nor the LNC. I wouldn't be surprised if the same is true for QM, once Aristotle is read properly.

 

This may be one of those various occasions where philosophy has let physics down, in this case by muddling the logical issues.

It's entirely off-topic from the source thread, so I started a new one. I'm dying to know: how do you get QM from Aristotelian logic when QM can't coexist with a Boolean structure?

[PeterJ]

Hi ydoaPs

 

Okay, I'll bite.

 

I'd like to just send you to a couple of essays, but I'll summarise in case it works.

 

A legitimate dialectical contradiction depends on two things:

 

1. The contradiction is between A/not-A. (Ie. A/B is not a contradiction unless B stands for not-A)

 

2. It is a fact that one of A or not-A is true and the other is false.

 

If you examine the contradictions of metaphysics and physics they usually do not meet these conditions. Very often the second condition is ignored, and quite often both.

 

If an electron is a wave and a particle this would not be a contradiction.

 

If both Materialism and idealism are false this would not require any modification to A's rules.

 

Aristotle allows for all existential situations. The rules cannot be broken by Nature because where Nature seems to break them then there cannot have been a contradiction in the first place.

 

That's it in brief. I rely heavily on Whittaker's book on 'De Interpretatione' for my grasp of Aristotle and it is very clear. Unmissable I would say. It seems that people do not often read the small print for the laws of thought.

 

It might help if you could cite a specific contradiction that we could analyse.

Edited October 23, 2015 by PeterJ

[puppypower]

If you compare a continuous universe (contains all in the middle) with a quantum universe, the quantum universe has fewer states. What that means is quantum makes the universe less random than a continuous universe. Quantum loaded the dice of the universe so fewer sides can ever appear compared to continuous. For example, there would be an infinite number of energy levels for a continuous model of hydrogen energy levels. With a quantum universe there are only 5. The infinite sided dice of continuous become loaded so only five sides can appear in quantum.

 

The irony is, before the discovery of the quantum universe, science assumed continuous functions governed by logic; age of reason. After the discovery of quantum it assumed a random universe, even though quantum had loaded the dice compared to continuous and moved nature even more in the direction of rational determinism.

 

This irrationality may have been due to the atheist religion in science not wanting to concede anything to the deterministic approach of religion, even though quantum implied this even more so. It could also have also been due to a watering down of talent, since logic was harder to do than black box math. Or applied science and industry needed talent and could have more bodies with a black box approach; makes more money.

 

That aside, loading the dice also has the effect of saving time. If A and B need to happen, before C can happen, so the universe can evolve, then the fewer the options the faster this can happen. For example, in the case of the hydrogen spectra, instead of hydrogen fluctuating over a continuous spectrum with even slight changes of energy, quantum snaps the electrons into firm energy levels, ready for step 2. If we save time, more is left over allowing nature to progress even further before the universe ends.

 

Quantum moved the universe closer toward the ideal of the age of reason; logical determinism. However, the mind of science did not see this logical consequence, but history shows it became more irrational by assuming the universe had become more random. This may have been due to the stress of war and having to make the bombs. Random gives one better excuses for failure in front of hardline military types who have invested billions.

 

 

[ydoaPs]

Hi ydoaPs

 

Okay, I'll bite.

 

I'd like to just send you to a couple of essays, but I'll summarise in case it works.

 

A legitimate dialectical contradiction depends on two things:

 

1. The contradiction is between A/not-A. (Ie. A/B is not a contradiction unless B stands for not-A)

 

2. It is a fact that one of A or not-A is true and the other is false.

 

If you examine the contradictions of metaphysics and physics they usually do not meet these conditions. Very often the second condition is ignored, and quite often both.

 

If an electron is a wave and a particle this would not be a contradiction.

 

If both Materialism and idealism are false this would not require any modification to A's rules.

 

Aristotle allows for all existential situations. The rules cannot be broken by Nature because where Nature seems to break them then there cannot have been a contradiction in the first place.

 

That's it in brief. I rely heavily on Whittaker's book on 'De Interpretatione' for my grasp of Aristotle and it is very clear. Unmissable I would say. It seems that people do not often read the small print for the laws of thought.

 

It might help if you could cite a specific contradiction that we could analyse.

This isn't an empirical question. This is one of deep metaphysics. QM cannot be formulated on a cartesian closed topos. The typical choice of the category Sets isn't an option. QM has to be formulated on the category of presheaves on partially ordered sets (or something like it). But that's not cartesian closed, so it has a more general Heyting structure. Boolean structure doesn't work.

[PeterJ]

I see no problem with Aristotle's logic if applied properly. No need to complicate matters. There could never be a real life example of a failure in his logic since it does not make predictions for reality, The rules apply where the conditions apply, and if the conditions do not apply then his rules are irrelevant.

 

IF we have a contradiction THEN the laws of thought can be applied to them. First we have to establish the contradiction.

[ydoaPs]

I see no problem with Aristotle's logic if applied properly. No need to complicate matters. There could never be a real life example of a failure in his logic since it does not make predictions for reality, The rules apply where the conditions apply, and if the conditions do not apply then his rules are irrelevant.

 

IF we have a contradiction THEN the laws of thought can be applied to them. First we have to establish the contradiction.

They can't be applied if the structure of the universe doesn't permit them....as in a QM universe.

[PeterJ]

They can't be applied if the structure of the universe doesn't permit them....as in a QM universe.

 

Hmm. No good just stating this about QM. I'm disagreeing.

[ydoaPs]

Hmm. No good just stating this about QM. I'm disagreeing.

It's pretty easy to disagree when you're simply ignoring the argument and saying "nuh uh".

 

The most general structure shows that QM doesn't co-exist with Boolean structure. Classical physics is built on the category of Sets and the relations between sets. It should be obvious, since Aristotelian logic is just set theory in disguise that a subobject classifier can be defined that gives Boolean structure. Any Cartesian closed category will have a Boolean structure. Not only is it not possible to have QM on Sets, but it's also not possible on any Cartesian closed category.

 

QM has to be constructed on a topos that is the category of presheaves on partially ordered sets. This isn't Cartesian closed. The logical structure is more general. The law of excluded middle does not apply.

[PeterJ]

Oh, okay. Got it. This was my mistake. What I'm proposing is that QM would not require a modifcation to the LEM, so it seems that we need not disagree.

 

It's Heisenberg's view that I would oppose, since he concluded that QM showed that the universe broke Aristotle's rules for thinking.

[ydoaPs]

It's Heisenberg's view that I would oppose, since he concluded that QM showed that the universe broke Aristotle's rules for thinking.

It does, but it's not an empirical matter. Nor is it a matter of interpretation choice. On the deepest level of structure, QM and Aristotle are incompatible.

[PeterJ]

Not in my opinion.

 

It would be impossible for Aristotles rules to be incompatible with Reality. They're rules for logic - not for things. Things can do what they like. .

 

If you can find an example of a true contradiction, or an actual exception to the LEM you'll make a name for yourself. Philosophers are still arguing about the possibility and empirically the case is not settled.

[ydoaPs]

Not in my opinion.

Well, your opinion doesn't match fact.

 

It would be impossible for Aristotles rules to be incompatible with Reality. They're rules for logic - not for things. Things can do what they like.

Too bad they totally are. You cannot get QM on a topos that allows Boolean structure. The propositions (states) in QM cannot be related in a Boolean way. LEM doesn't hold for QM universes.

 

Philosophers are still arguing about the possibility and empirically the case is not settled.

The ones that actually know quantum mechanics aren't. This is pretty well known stuff over here in history and philosophy of science land. At a fundamental level, Aristotelian logic and Quantum Mechanics are incompatible. You can't have Quantum Mechanics and the Law of Excluded Middle; pick at most one.

[PeterJ]

I think you are abusing Aristotle in the same way as most people do, as well as being arrogant about how well philosophers understand QM.

 

But I'll wait for an example of a contravention of the LEM before going on, if you can find one.

 

It would be impossible for QM to break the LEM since Aristotle allowed for all possibilites. It's just that people don't read the small print. If you can prove that there is such a thing as a true contradiction you will become famous.

[imatfaal]

[latex] \vdash(p \vee \sim p)[/latex]

 

does not seem commensurable with

 

[latex]\frac{1}{\sqrt{2}} |\uparrow \downarrow \rangle - \frac{1}{\sqrt{2}} |\downarrow \uparrow \rangle[/latex]

[andrewcellini]

It would be impossible for QM to break the LEM since Aristotle allowed for all possibilites. It's just that people don't read the small print. If you can prove that there is such a thing as a true contradiction you will become famous.

the law of excluded middle isn't taken to be true in many valued logics, hence "many valued logic." LEM assumes that there are no other possibilities except a statement is true or false. there are no "in between" values or third possibilities.

i'm not sure of the "small print" you're referring to. care to share a reference?

Edited November 4, 2015 by andrewcellini

[PeterJ]

The LEM assumes there are no other possibilities where there is a contradiction. If there is no contradiction then the LEM is irrelevant to anything. So, to show a breach of the LEM one first has to first establish a contradiction. . .

 

If the LEM does not apply in some situation then that's no problem. This would not be a breach of the LEM. I'm suggesting that QM does not breach the LEM. To say it does not apply at all would be to say that no contradictions arise in QM that are subject to it, which cannot be true. But if parts of QM have no use for it that would not be surprising or have any philosophical consequences. .

 

To show that QM somehow invalidates the LEM we would have to identify a true contradition within the theory which does actually have a third option. If it simply does not apply in some situation this would be uninteresting. It only ever applies where there is a contradiction as specified by Aristotle.

 

Andrew - The best book I've found on the topic so far is CWA Whittaker, Aristotle's De Interpretatione - Contradiction and Dialectic. It's very good indeed. He disusses the small print for the 'laws of thought' at length, it being the topic of the book. John Corcoran is also very good and he has pointed out the mistake we regularly make with logic by overlooking the small print. On the whole this error goes unnoticed. It causes major problems in philsophy, but none in physics afaik just as long as we identify contradictions properly.

Edited November 5, 2015 by PeterJ

[Strange]

So are you just saying that in those situations where LEM applies (for example, binary logic) then LEM applies. And in the situations where it doesn't apply (quantum theory, multi-valued logic, etc) then it doesn't apply.

[PeterJ]

I'm proposing that there is no such thing as a true contradiction. Here 'true' would mean 'out there in the world'. If quantum theory departs from Aristotle that's fine, it's a theory.and can do what it likes. But there is as yet no evidence that reality itself departs from his rules. Some folks would see the particle-wave duality, superposition etc. as requiring a modification to the rules (Heisenberg et al), but this is not the case. Aristiotle covered all the bases.

 

My main point wouldbe that in order to legimately apply the LEM we must be sure that we are dealing with a contradiction. For a contradiction one member of the pair must be true and the other false. This is not something that the LEM decides, it is what we must decide before we know whether to apply the LEM. Aristotle makes this very clear and it is really just common-sense.

 

So, in order to show that QM requires abandoning the LEM we would have to show that it contains a contradiction for which there is a third option. But if there is a third option then there is no contradiction in the first place. For this reason Aristotle's rules cannot be broken by reality. They are rules for the dialectic, not for reality.

 

I suspect that there's a bit of a mismatch here between what I'm suggesting and the objections that are coming up, but we'll see.

 

Is that more clear? .

 

This problem is much more important in metaphysics, where Aristotle is regularly abused as a matter of course, but it comes up quite often in relation to QM.

Edited November 5, 2015 by PeterJ

[andrewcellini]

[latex] \vdash(p \vee \sim p)[/latex]

 

does not seem commensurable with

 

[latex]\frac{1}{\sqrt{2}} |\uparrow \downarrow \rangle - \frac{1}{\sqrt{2}} |\downarrow \uparrow \rangle[/latex]

peter, how can you reconcile what you've said with what imatfaal pointed out?

[PeterJ]

I'm afraid I have no idea what these sybols mean, Andrew, They could be ancient runes. Heisenberg uses the example, 'Here is a table' and 'Here is-not a table', I'd have to ask what the symbols claim about the universe, and in what way this claim would imply the failure of the LEM.

 

Any disagreement here, I hasten to say, is not about physics or its associated maths as far as I'm concerned. It is about how to interpret Aristotle and apply his rules, and how to relate them to QM and the data, which would be a given. . .

 

Keepimg the physics at my level here's what I'm proposing. The wave-particle duality is often seen as implying the breakdown of Aristotle's dialectical logic as a description of reality. But this duality is not a logical contradiction. If an electron is not a particle and not a wave then it is something else. If it is not here and not there then no it is nowhere. No logical problems arise. Conceptual problems arise but they are not the issue.

 

It would only be where we assume that an electron must be one thing or the other that logical problems would seem to arise, But if we make this assumption then we are breaking the rules. Aristotle tells us that whether this duality is a logical contradiction would be an empirical matter, not something we can just assume. If we assume it is a contradition and logical problems arise then this would indicate the falsity of our assumption.

 

It's a very simple issue but deceptively deep. The universe would transcend Aristotle's logic, but not contradict or entail any modfication to it,

 

This would be just as Kant proposes. Reality would transcend the categories of thought. But it would not break the laws of thought, even in physics. This would be impossible because Aristotle designed them to cover all the possibilities.

Edited November 6, 2015 by PeterJ

[ydoaPs]

being arrogant about how well philosophers understand QM.

followed by

I'm afraid I have no idea what these sybols mean

I'd have to ask what the symbols claim about the universe

The spin is clockwise and counterclockwise at the same time.

[PeterJ]

I don't know why you re-quoted those remarks. ydoaPs.. Do you have some sort of problem with them? Did I suggest that I was an expert in QM and the maths? Did you mean to suggest something helpful to the discussion? Why is this always such an unpleasant place to have a conversation? It sems to be unique among forums for its unpleasantness.

 

So, the spin is clockwise and anti-clockwise at the same time. Where is the logical problem? Obviously this is not a contradiction if both states can exist at once.

[Strange]

So, as Aristotelian logic only applies where Aristotelian logic applies, the question arises of how one can know when it applies. If one finds a case where there appears to be a contradiction, how does one know if this is a violation of LEM (or some other law of logic) or if it just a case where the logic doesn't apply?

Edited November 6, 2015 by Strange

[PeterJ]

I've been pondering the same question. This is why I'm not quite sure that YpoaDs and I have any real disagreement.

 

In logic the situation is easier since one can define or construct a contradiction and know that it is one. We can define a statement as being true or false and have to do this for our axioms. But in physics we are dealing with matters of fact so must establish contradictions empirically.

 

"So, as Aristotelian logic only applies where Aristotelian logic applies, the question arises of how one can know when it applies."

 

I would say it always applies in just the way that Aristotle specifies. But laws relating to contradictions will only apply where there is one.

 

Say the proposed contradiction is 'It is raining' and 'It is sunny'. The LEM would not apply since obviously this is not a legitmate contradiction (it could be foggy). This would not mean that the laws of logic do not apply to the weather. They just do not apply to this pair of statements.

 

"If one finds a case where there appears to be a contradiction, how does one know if this is a violation of LEM (or some other law of logic) or if it just a case where the logic doesn't apply?"

 

At this moment it seems to me that there cannot be a case of a violation of the LEM except where it is a mistake in a dialectic argument.

Whether the case you mention is in fact a contradiction would be an empirical matter. In philosophy often it would be a logical matter and so we can be certain of contradictions. We can construct statements that we can define as contradictory. In physics they can be defined for a theory but as Aristotle points out, whether our logic applies to reality in any particular case would not be something that logic can decide.

 

I would say that reality cannot violate the LEM. Ambiguous logical cases where the LEM would not apply are noted by Aristotle in De Interpretatione, where he clarifies the exact application of his system, but for him reality is not an issue. If an apparent contradiction turns out to have a third option then clearly it wasn't a contradiction in the first place.

 

The significance of this way of coming at logic is that it allows metaphysics to be solved in principle, by simply rejecting all those apparent antimonies as false contradictions. (As we do when we resolve the freewill/determinism contradiction with compatibilism). But the issue also seems relevant in QM since it seems to assumed sometimes that there is no third option even though the contradiction has not been empirically established. So Aristotle appears to fail, where in fact it would be just that we are not keeping to the rules.

 

All of this is based firmly on Aristotle's clear instructions for the use of his logic and is not some idiosyncratic opinion. I may be making the odd mistake, but I've written about this quite publicly and received no complaints. John Corcoran is excellent on these topics if you want to read someone with more clout. He also proposes that we usually overlook the details of Aristotle's rules and so reach incorrect results.

Edited November 6, 2015 by PeterJ

[Strange]

"If one finds a case where there appears to be a contradiction, how does one know if this is a violation of LEM (or some other law of logic) or if it just a case where the logic doesn't apply?"

 

At this moment it seems to me that there cannot be a case of a violation of the LEM except where it is a mistake in a dialectic argument.

Whether the case you mention is in fact a contradiction would be an empirical matter. In philosophy often it would be a logical matter and so we can be certain of contradictions. We can construct statements that we can define as contradictory. In physics they can be defined for a theory but as Aristotle points out, whether our logic applies to reality in any particular case would not be something that logic can decide.

 

My initial feeling was that reduces the value of logic, because we can't know when it applies or not. For example, some people reject the counter-intuitive results in QM and GR because they say they are "not logical". But actually, in both cases, the theory tells us what is expected and hence what is allowed by the specific form of logic that applies to that theory.

 

I suppose this is similar to the point that all the so-called paradoxes in relativity are not actually paradoxes, they only appear to be so if one doesn't understand the theory.