Law of non-contradiction (“LNC” to its friends)

On Uncommon Descent, Barry Arrington asks:

Let’s clear up this law of noncontradiction issue between StephenB and eigenstate once and for all. StephenB asks eigenstate: “Can the planet Jupiter exist and not exist at the same time in the same sense? That’s a “yes or no” question eigenstate. How do you answer it?

For some reason, Eigenstate’s response has gone astray, so here it is, as cross-posted elsewhere:

Eigenstate:

Theoretically, yes. In practice, the probabilities are so vanishingly small it’s indistinguishable from no.

Scale matters; superposition is fragile with respect to other elements in the system that force a classical resolution. Recent experiments have provided experimental verification that macroscale objects can be put in superposition (see here):

Quote

But although the rules of quantum mechanics seem to apply at small scales, nobody has seen evidence of them on a large scale, where outside influences can more easily destroy fragile quantum states. “No one has shown to date that if you take a big object, with trillions of atoms in it, that quantum mechanics applies to its motion,” Cleland says.

The “paddle” object in this experiment was just 30 micrometers long. But that’s freaking HUGE compared to the Planck length. Jupiter is just so many orders of magnitude bigger than that, that the prospects for superposition in that case become ONLY theoretical. Too many resolving influences make it statistically impossible.

The linked article describing the experimental evidence for QM weirdness “scaling up” includes this comment from a physicist at the U of Oregon:

Quote

“It’s wonderful,” says Hailin Wang, a physicist at the University of Oregon in Eugene who has been working on a rival technique for putting an oscillator into the ground state. The work shows that the laws of quantum mechanics hold up as expected on a large scale. “It’s good for physics for sure,” Wang says.

So if trillions of atoms can be put into a quantum state, why don’t we see double-decker buses simultaneously stopping and going? Cleland says he believes size does matter: the larger an object, the easier it is for outside forces to disrupt its quantum state.

(emphasis mine)

Those wacky physicists, I tell ya.

On an LNC-related note, this from the same article:

Quote

Next, the researchers put the quantum circuit into a superposition of ‘push’ and ‘don’t push’, and connected it to the paddle. Through a series of careful measurements, they were able to show that the paddle was both vibrating and not vibrating simultaneously.

(emphasis mine)

Sound familiar, StephenB (and Barry, if you’ve been reading our exchange)? I will note here that champignon’s comment on this being best viewed as a Law of the Excluded Middle issue is a point well taken. But that notwithstanding, you have QM weirdness in the real world ostensibly misbehaving against our propositional logic. “Vibrating” and “Not Vibrating” in the same sense, for the same object at the same time.

Here’s another example from a similar experiment (link), where Dr. Anthony Leggett of U of Illinois, Champaign, Urbana weighs in on a solar system body — not Jupiter but the moon (the moon was the example Einstein initiated these questions with: “does the moon exist if no one is looking at it?” :

Quote

For Dr. Leggett, quantum mechanics at the macroscopic level is still uncertain — and troubling. “It may bother me even more now,” Dr. Leggett said. “I’m interested in the possibility that quantum mechanics, at some stage, may be wrong.”

A few physicists have devised so-called macrorealistic theories to resolve the ambiguities of quantum mechanics. “What you get in quantum mechanics is not what you see,” said Dr. Philip Pearle, a professor of physics at Hamilton College in Clinton, N.Y. “Schrödinger felt this acutely. He himself felt something with quantum mechanics was wrong.”

Dr. Pearle and colleagues in Italy propose to add a term to Schrödinger’s equation that, in effect, constantly jiggles the fabric of the universe. Atomic-scale objects only jiggle a little and thus remain a blur, which preserves the predictions of quantum mechanics. Larger objects, like people or the Moon, jiggle more and quickly fall into a definite here and there, which corresponds to everyday experience.

(emphasis mine)

Barry, if you’ve read my earlier responses to StephenB on this, you will recognize the same ideas quoted here in my answers. Jupiter has a virtually zero statistical basis for avoiding decoherence, hence it will ALWAYS be there in the full, classical (non-superposition) sense.

Lastly, this, regarding the LNC-problematic nature of this second expirement:

Quote

The experiment combines two possibilities, known as a quantum superposition, for the direction of the flow of electric current: clockwise around the loop or counterclockwise.

The researchers measured an energy difference between the two states of the loop, a sign the current was a quantum superposition and not simply flipping directions.

Just as the cat is neither alive nor dead but a ghostly mix of the two possibilities, the current flows neither clockwise nor counterclockwise, but is a mix of the two possibilities.

(my emphasis)
Note that per superposition, this is not simply a matter of a “bi-directional current”. This is two otherwise exclusive one-way directions happening at the same time, exclusive states superimposed:

Quote

A measurement always gives one of the two possible answers, clockwise or counterclockwise, never a zero cancellation.

Glad to have the opportunity to settle this once and for all! Statistically, it will never happen for Jupiter, but it remains a theoretical possibility. It’s the same as wondering if I could fairly shuffle and deal a 52 card deck and deal the cards out, producing the same exact card order as the first shuffle a billion times in row. In theory, it cannot be eliminated as a possibility. As a practical matter, the odds are insdistinguishable from zero.

 

75 thoughts on “Law of non-contradiction (“LNC” to its friends)

  1. I am going to go on record and answer Barry’s ultimatum question.

    Short answer in the required format: No.

    Slightly longer answer: Unlikely.

    Now for the long answer.

    The moon, and other objects with which we deal on a daily basis do not exist and not exist at the same time and in the same formal relation. They just don’t. This property does not follow from anything. It’s an axiom based on long experience. As such, this axiom is subject to revision at any time. (Remember Euclid’s fifth postulate?)

    In the last 100 years we learned quite a few new things about the microscopic world. It’s very different. Microscopic objects can exist an not exist at the same time. Above we discussed one such example: the electromagnetic field inside a resonator cavity can be put in a state that is a superposition of no photons and one photon. By Barry’s own formulation, that photon does exist and not exist at the same time and in the same formal relation. This has been done experimentally.

    This is extremely hard to swallow. Physicists struggled with superposition and its particularly bizarre manifestations (e.g., entanglement) for a while. They invented hidden variables to try and harmonize quantum theory with our classical prejudices. That didn’t work, actually. Hidden variables lead to even bigger problems. Bohm’s theory was quite contorted, invented just to spite von Neumann, and couldn’t be extended beyond one-particle problems. Those of you who try to make excuses about different interpretation of quantum mechanics, take notice. There is just one working theory of quantum mechanics, the standard Copenhagen version. Everything else is half-assed attempts to get famous.

    So get used to it. Microscopic particles can exist an not exist at the same time an in the same formal relation. At this point, physicists have long accepted this and have other things to worry about. Such as these: Where is the boundary between microscopic an macroscopic? Is there a boundary? In the words of some famous physicist quoted by David Mermin, is the Moon really there when no one looks? (Hi nullasalus!)

    But that’s a story for another day.

  2. I’d like to second Elizabeth’s request and ask people to refrain from commenting on Barry’s policies at UD. There is another forum where this can be done. You know where to find it.

  3. William J Murray,

    “William J Murray: So? It’s still Mr. Arrington’s right to utilize whatever entrance exam he wishes, whether others consider it valid or not.”

    “So” means you believe the LNC is violated if an assertion is made, that is in fact, not TRUE.

    That means that your arguments that hinge on the belief in the existence of an “absolute good”, whether or not it really exists, are not valid logically, since only factual assertions are allowed in proper scientific debates, according to Barry.

    This also means that the existence of a designer must be physically true before it can be asserted.

  4. The existence of the designer is inferred via the existence of the design.

    Now if you can demonstrate that what we observe came about via blind and undirected processes, then we wouldn’t infer the existence of a designer.

  5. That means that your arguments that hinge on the belief in the existence of an “absolute good”, whether or not it really exists, are not valid logically, since only factual assertions are allowed in proper scientific debates, according to Barry.

    Arguments about any “absolute good” are not scientific in nature.

    This also means that the existence of a designer must be physically true before it can be asserted.

    Unless you are counting yourself and all humans out as physically true intelligent designers, then we can safely assert that intelligent designers exist.

  6. OK, guys, although I understand that there are strong views (including my own) around what is or is not happening to posters at UD, I’m going to move some posts (including my own) to guano, not because the views are invalid, or morally reprehensible or anything else, but because the whole point of this site is to attempt to stay rigorously on topic.

    Hold on to your hats…

  7. William J Murray,

    William J Murray: “Unless you are counting yourself and all humans out as physically true intelligent designers, then we can safely assert that intelligent designers exist.”

    Since humans are alive, I would count them out as designers of life.

    So, where is the evidence for, “The Intelligent Designer Of Life”?

    Implied by Barry, his existence can’t simply be asserted.

    No logical construct, concerning the assertions of the existence of the moon, Jupiter or the Intelligent Designer, should be allowed, that is not physically true and verifiable.

  8. William J Murray,

    William J Murray: Mr. Arrington’s entrance exam only asked a human-scale question about the LNC. ”

    It was not about the LNC, it was about the existence of the moon.

    He was “trying” to ask a question about the LNC and got it wrong just like you did.

    That rightly raised the hackles of people who do understand how to use logic.

  9. Treading a fuzzy line here…

    I’m trying to keep the subject to the LNC and Barry’s question itself, not the ethics of Barry’s posing it.

    But some things seem to me to be both within the rules and not within the rules simultaneously. Unfortunately pragmatics requires that I impose a dichotomy on a continuum, not to mention a superposition….

    If I’ve sliced in the wrong place with some posts, your indulgence is begged for, and bear in mind that your posts are not hidden, merely quarantined.

    And that I love you all. :)

  10. olegt:
    Sotto Voce,

    But then the L-NOT approach entirely misses the point. The question raised by StephenB was Can the planet Jupiter exist and not exist at the same time in the same sense?

    Here’s the thing: StephenB’s knowledge of logic seems to be limited to Aristotle. His conception of the LNC, as applying to the existence/non-existence of things as opposed to the truth/falsity of statements, is pure Aristotle. It is not how the LNC is treated in contemporary logic.

    In modern logic, the truth of the LNC just follows from the definitions of the operators & (AND) and ~ (NOT).

    Definition of NOT: The proposition ” ~A” is true if and only if the proposition “A” is false.

    Definition of AND: The proposition “A & B” is true if and only if the proposition “A” is true and the proposition “B” is true.

    Proof of LNC: A proposition can only be either true or false. Consider an arbitrary proposition “A”. If “A” is false, “A & ~A” must be false (from the definition of AND). If “A” is true, then “~A” must be false (from the definition of NOT), which means “A & ~A” must be false (from the definition of NOT). So “A & ~A” must be false.

    That’s the LNC. A completely trivial statement with a completely trivial proof. The only premise that might be contested is the claim that a proposition must be either true or false. But I don’t see quantum mechanics having any bearing on this claim. So quantum mechanics cannot conflict with the LNC.

    Now maybe quantum mechanics conflicts with StephenB and BarryA’s nonsense version of the LNC. Based on what I have read, I doubt their conception is even coherent enough to be refuted. But what matters is that this is not the LNC. Please let’s not cede a technical term in formal logic to them. We’ve already seen their cavalier misapplication of technically precise notions when it comes to information theory. Now they’re doing it with propositional logic.

  11. Sotto Voce,

    That’s fine, Sotto Voce. I am not going to argue the intricacies of LNC here. But you will not that StephenB and Barry have put the question differently, not even mentioning the LNC and cutting straight to the possibility of an object existing and not existing at the same time and in the same formal relation. My responses were directed at that from the get-go.

  12. Sotto Voce,

    Sotto Voce: Here’s the thing: StephenB’s knowledge of logic seems to be limited to Aristotle. His conception of the LNC, as applying to the existence/non-existence of things as opposed to the truth/falsity of statements, is pure Aristotle. It is not how the LNC is treated in contemporary logic.

    I don’t think that’s the problem, but it might be contributing to some overall confusion on their part. The problem, as I see it, is that logic is held in a rigid, simplistically classica, and universally applicable sense.

    champignon, over on UD, brought up an insightful point, which is that superposition is really problematic in terms of the Law of the Excluded Middle, rather than the LNC. I’m not sure it’s just a LEM problem and not also an LNC difficulty, as they are related by involution (double negation). It’s not an LNC problem per se, as you allow further down, but it’s a LEM problem that arises from many-valued logic.

    In fuzzy logic frameworks I’ve used in software development, the NOT operator is non-involutive, which means that we may have a truth value of “0.4” for Proposition X, while its complement — the result of the NOT operator — might be “0.52”, meaning the “not-not” of X (¬¬X) does yield X, and X + X[complement] does not add up to 1.0.

    That’s an intrinsic for fuzzy logic computing. And it’s just an overloading on the NOT operator – it has different dynamics from the classical (Boolean) operators.

    This is a problem for some folks (ahem!), because it’s problematic on some views to have “competing logics”, or to think of a logical framework as a framework rather than some metaphysical imperative of the cosmos.

    In modern logic, the truth of the LNC just follows from the definitions of the operators & (AND) and ~ (NOT).

    Yes, modern classical logic, or Boolean logic in geek speak. Fuzzy Logic is a superset of Boolean logic, and the operator overloading changes the predicate semantics. But it’s coherent, and extremely useful for some computing applications. The one time I used it on a commercial project, it got deployed on a financial modeling and investment analysis app, and it was highly effective.

    Definition of NOT: The proposition ” ~A” is true if and only if the proposition “A” is false.

    Definition of AND: The proposition “A & B” is true if and only if the proposition “A” is true and the proposition “B” is true.

    Yep, in a Boolean model. In a fuzzy model, that’s not the case, of course. And the parallels should be obvious here, which is why I brought up superposition and QM; reality is not “isotropic” in terms of applicability of LNC (or more broadly, classical logic). It’s not a good tool for modeling some parts of our observed reality. For what we experience at human scales and speeds, it’s rock solid. But we are at a point where we can scientifically measure, test and “see” at scales and speeds are are far removed from our natural human speeds and scales.

    Proof of LNC: A proposition can only be either true or false. Consider an arbitrary proposition “A”. If “A” is false, “A & ~A” must be false (from the definition of AND). If “A” is true, then “~A” must be false (from the definition of NOT), which means “A & ~A” must be false (from the definition of NOT). So “A & ~A” must be false.

    That’s the LNC. A completely trivial statement with a completely trivial proof. The only premise that might be contested is the claim that a proposition must be either true or false. But I don’t see quantum mechanics having any bearing on this claim. So quantum mechanics cannot conflict with the LNC.

    I agree, and it’s gratifying to see a good, clear synopsis like that. But the question from the DU geniuses was in regards to the universal and exhaustive applicability of the LNC, (or LEM, and more broadly, classical logic) in all contexts and enterprises.

    Now maybe quantum mechanics conflicts with StephenB and BarryA’s nonsense version of the LNC. Based on what I have read, I doubt their conception is even coherent enough to be refuted. But what matters is that this is not the LNC. Please let’s not cede a technical term in formal logic to them. We’ve already seen their cavalier misapplication of technically precise notions when it comes to information theory. Now they’re doing it with propositional logic.

    I don’t think they’ve misunderstood the LNC per se. They’d likely recount its proof in similar terms (not so concise, perhaps). They just get tripped up on what you process without a glitch — “A proposition can only be either true or false.”

    As you have it, it’s an axiom. But it’s just an axiom, and that’s key. StephenB also thinks it’s an axiom, but axiomata are magical for him, and… “authoritative”, I guess is the best word I can find. It’s not just that for propositional calculus, one must have a binary value pair {true|false} to make the operators and operands work. No, that’s how reality REALLY IS, “true or false”, fundamentally. Of course that’s incoherent, “fundamentally true or false”, and that’s why we understand an axiom to be just an axiom.

  13. Perhaps someone with greater insight can set me straight on Quantum Decoherence, especially in regards to Hugh Everett. It seems to me that, if a universal wave function is accepted as a possibly true model of reality, then all of existence is in a superposition, to say nothing of the moon.

    FWIW: I just discovered this site yesterday.

  14. I’m curious how the physicists here feel about E.T. Jaynes critique of quantum physics. Here’s an excerpt from his book Probability Theory, The Logic of Science:

    Those who cling to a belief in the existence of “physical probabilities” may react to the above arguments by pointing to quantum theory, in which physical probabilities appear to express the most fundamental laws of physics. Therefore let us explain why this is another case of circular reasoning. We need to understand that present quantum theory uses entirely diff erent standards
    of logic than does the rest of science.

    In biology or medicine, if we note that an e ffect E (for example, muscle contraction, phototropism, digestion of protein) does not occur unless a condition C (nerve impulse, light, pepsin) is present, it seems natural to infer that C is a necessary causative agent for E. Most of what is known in all fields of science has resulted from following up this kind of reasoning. But suppose that condition C does not always lead to e ffect E; what further inferences should a scientist draw? At this point the reasoning formats of biology and quantum theory diverge sharply.

    In the biological sciences one takes it for granted that in addition to C there must be some other causative factor F, not yet identifi ed. One searches for it, tracking down the assumed cause by a process of elimination of possibilities that is sometimes extremely tedious. But persistence pays off ; over and over again medically important and intellectually impressive success has been achieved, the conjectured unknown causative factor being fi nally identifi ed as a defi nite chemical compound. Most enzymes, vitamins, viruses, and other biologically active substances owe their discovery to this reasoning process.

    In quantum theory, one does not reason in this way. Consider, for example, the photoelectric effect (we shine light on a metal surface and find that electrons are ejected from it). The experimental fact is that the electrons do not appear unless light is present. So light must be a causative factor. But light does not always produce ejected electrons; even though the light from a unimode laser is present with absolutely steady amplitude, the electrons appear only at particular times that are not determined by any known parameters of the light. Why then do we not draw the obvious inference, that in addition to the light there must be a second causative factor, still unidentifi ed, and the physicist’s job is to search for it?

    What is done in quantum theory today is just the opposite; when no cause is apparent one simply postulates that no cause exists { ergo, the laws of physics are indeterministic and can be expressed only in probability form. The central dogma is that the light determines, not whether a photoelectron will appear, but only the probability that it will appear. The mathematical formalism of present quantum theory – incomplete in the same way that our present knowledge is incomplete – does not even provide the vocabulary in which one could ask a question about the real cause of an event.

  15. Ido: What is done in quantum theory today is just the opposite; when no cause is apparent one simply postulates that no cause exists { ergo, the laws of physics are indeterministic and can be expressed only in probability form. The central dogma is that the light determines, not whether a photoelectron will appear, but only the probability that it will appear. The mathematical formalism of present quantum theory – incomplete in the same way that our present knowledge is incomplete – does not even provide the vocabulary in which one could ask a question about the real cause of an event.

    That’s the way the cookie crumbles.

    Jaynes was being coy, methinks. There are plenty of examples in physics when a probabilistic result reflects our ignorance of the exact initial conditions. Statistical physics is a prime example of that. A physical system can have fully deterministic classical dynamics, yet even a slight uncertainty about its initial condition grows in time so that eventually we cannot predict where in the phase space it is. One can wax lyrical about the causative factors that determine the exact position of the system in the phase space, but it hardly matters because (a) they boil down to minutiae such as the 1000th digit in the system’s initial velocity and (b) we are usually not interested in the exact final state and a statistical description is entirely satisfactory. (Think of a volume of gas. Do you really want to know where exactly each molecule is at any given time? Probably not. The pressure they exert on the walls is of more interest.)

    And it’s not like physicists hadn’t tried to pin quantum uncertainty on incomplete knowledge. I’m sure most people have heard of hidden variables. Only this solution wound up being worse than the problem itself: hidden variables turned out to be quite unphysical. To conform to the results of quantum measurements with entangled particles, they would have to propagate faster than light. This would require sacrificing either causality or relativity.

    Physicists are rather fond of causality and relativity, so they decided to sacrifice certainty and make quantum mechanics indeterministic as far as the results of quantum measurements are concerned. The resulting logical structure, known as the standard (Copenhagen) formulation of quantum mechanics, is logically sound and fully compatible with experimental data. Alternative theories are not in high regard, primarily because they are specific to particular problems (e.g., Bohm’s applies to a single particle) and resist generalization.

  16. olegt,

    Thank you for your answer, olegt.

    I don’t know much about QM, but I have been impressed by Jaynes’ book, and I find it fascinating that an obviously clever guy and accomplished physicist like him, who must have been aware of Bell’s work, still had such disdain for QM. He was in good company of course.

  17. I also am new to this site, and am glad to see it. I retired from UD a year or so ago, but decided to get involved in the LNC discussion when I heard about the purge and Barry’s ultimatum question. I think it’s good to have a site to discuss the types of issues that arise at UD and elsewhere, but that moves off-issue comments to their own home.

    I am a reasonably well-educated layperson – not a scientist nor a philosopher, although I am a math teacher, and “aleta” is one of a number of internet names that I’ve posted under over the last ten years or so. My two main posts at UD on this subject are listed below, in case anyone here would be interested in commenting on them – any constructive criticism of, additions to, or affirmations of would be appreciated. FWIW, I have read over the comments in this thread, and it seems other here have made some similar points.

    Posts at UD:

    http://www.uncommondescent.com/intelligent-design/only-those-who-admit-the-foundation-of-argumentation-will-be-allowed-to-argue-at-ud/#comment-420703

    http://www.uncommondescent.com/philosophy/q-what-does-the-design-theory-debate-have-to-do-with-the-law-of-non-contradiction-lnc-a-a-lot/#comment-420906

    By the way, what is the syntax for url’s at this site? I couldn’t find anything in the intro posts that explains.

  18. aleta,

    I have been watching your LNC discussions there and commend you on your patience.

    It seems that the ID side doesn’t understand the borders between reality and the things we describe them with.

    In the case of logic, they seem to miss point that logic works with assertions, not reality.

    Whatever we assert, logic has to deal with it, real or imaginary.

    If that wasn’t the case, we could never use logic to build a what-if scenario.

  19. Pingback: Uncommon Descent | Marking up ES’s attempted rebuttal of the Law of Non-Contradiction on perceived implications of Quantum effects

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