Aristotle On Non-Contradiction: Why UN Chief Ban Ki Moon’s Views On Free Speech Are Invalid

The simplest version The Philosopher gave is this:

It is impossible to hold the same thing to be and not to be.

If something is a “Quantum Superposition” it cannot also simultaneously be “Not a Quantum Superposition”. If something is a “House” it cannot also simultaneously be “Not a House.” That is to say, somebody cannot think that a thing is a “Quantum Superposition” or “House” and also think simultaneously that is it “Not a Quantum Superposition” or “Not a House.” Somebody may certainly claim to hold both beliefs simultaneously, but they are either confused about the word simultaneously, or they are lying or switching between beliefs temporally. It is plausible, or at least intelligible, to say that at this instant I think “House” and at the next instant I think “Not a House“, and that I may oscillate between these views, but I may not hold both at the same time.

Another example: UN chief Ban Ki Moon said yesterday, “Freedoms of expression should be and must be guaranteed and protected,” but then he also said, “When some people use this freedom of expression to provoke or humiliate some others’ values and beliefs, then this cannot be protected in such a way.” So he is either deluded (or thinks his audience is), or he is lying or he changed his mind and settled on the position that speech should be regulated by the UN. Time will tell.

Dispute this? Then forget all of mathematics for a start, which depends fundamentally on this principle. Aristotle goes on to say (Metaphysics Book 4, Article 4):

There are some people who, as we have said, both maintain that the same thing can be and not be and say that it is possible to hold this view. This is the view of many who study nature. We have assumed here that it is impossible for the same thing to be and not to be at the same time, and on the basis of this we have shown that of all principles this is the least open to question.

But this principle is one which is not provable: it is one that just is true, or we believe is true, based on no evidence except our introspection.

Some people, through their lack of education, expect this principle, too, to be proved; for it does show a lack of education not to know of what things we ought to seek proof and of what we ought not.

Note to moderns: this is not an ad hominem, but an observation. Here is the kicker:

For it is altogether impossible for there to be proofs of everything; if there were, one would go on to infinity, so that even so one would end up without a proof; and if there are some things of which one should not seek proof, these people cannot name any first principle which has that characteristic more than this.

If you don’t have a ground, then down you must go and forever, as each turtle supports the weight of those above it. You will never have anything to say that anybody should ever believe, and this by your own admission. Every valid argument, on the other hand, is a chain, anchored to a immovable base of truth.

Now, if you are one of the Moons of the world and believe (based on what principle?) the law of non-contradiction false, but do not wish to defend this view, then Aristotle says you are “no better than a vegetable” and shame on you. But if you do try a defense, then Aristotle asks you to “say something that has meaning both for [yourself] and for someone else. For this [you] must do if [you are] to say anything at all.” But in doing this while you are “trying to do away with reason, [you are] also accepting it.” And obviously, if you say Non-contradiction is false, you have “conceded that something is true quite independently of the process of proof.”

Aristotle then goes on to destroy the not-non-contradiction position, adding in the end that

if all contradictory assertions made about the same thing are true [a necessary implication is non-contradiction is false], all things will clearly be one. A trireme, a wall, and a man will all be the same thing, if it is possible to assert or to deny anything of everything…For if anyone thinks that man is not a trireme, according to their theory he clearly is not one; but in this case he also will be a trireme, if the contradictory statement is true.

There is of course more, much more. Best to go to the original.

44 Comments

  1. Either there is Freedom or there is not Freedom.
    Your quotation commences, “Freedoms of expression…:” The [definite article] freedom of expression is unitary, inclusive, and ‘not to be abridged,’ not qualified. Moon’s first word invalidates his assertion.

  2. Sure, a good follow-up to the comments back there. Again, these kinds of jabs are not exactly on the target, they only seemingly seem so because if one appears to be denying the absoluteness of such idea of “non-contradiction”, apparently one is mistaken for someone who believes that everything may and should be “contradicted”.

    I have yet to see that one being defended around here.

  3. Dr. Briggs (or anyone who might know):

    (1) God is not man.

    (2) Man is not God.

    (3) Yet Jesus Christ is both God and man.

    Please explain, given (1) and (2), why (3) does not violate the impossibility of “both to be and not to be”.

    Thanks in advance!

    V/r.

  4. Moon is simply saying that the type of speech that is protected (in his view) by the concept “freedom of expression” is not the type of speech described by his phrase “to provoke or humiliate some others’ values and beliefs.” To analyze his statement in the way that you have is being overly pedantic.

    I would submit that most of your readers (including me) support “freedom of expression” but would not support the right to scream “fire” in a crowded theater (which is certainly expression). Logical purity could be gained, I suppose, by saying “freedom of expression must be supported conditionally and here are my views on those conditions….” but would communication be enhanced?

  5. (1) God is not man.
    (2) Man is not God.
    (3) Yet Jesus Christ is both God and man.
    Please explain, given (1) and (2), why (3) does not violate the impossibility of “both to be and not to be”.

    I can, although slightly trollishly I admit, answer that question very well.

    The thing is, that whenever some contradiction is “spotted”, the law still “stands”. What happens is, because we care about that law, we just decide from the moment we see the contradiction that there is no contradiction, therefore the premises were wrong in the first place.

    That is, “God is not man” should be replaced with “God is not man except Jesus” and the same exception should be given to the second premise. Or some other variant.

    The beauty of this way of doing things is that you can proclaim that the law of non-contradiction stands unbeaten no matter how preposterous the examples might be, thus turning the so-much-important law of the “universe” of non-contradiction become merely an all-too-human stand against ambiguity in speech.

    Which makes us go back to the original post. Of course the guy called “Moon” is not metaphysically incorrect. He just used the words “Freedom of Speech” in a qualified way that isn’t as simplistic as the meaning mr. Briggs alluded to. For Moon, freedom of speech apparently ends when someone makes fun of some religion. I couldn’t disagree more with him, but that does not make him metaphysically wrong.

  6. Again, these kinds of jabs are not exactly on the target, they only seemingly seem so because if one appears to be denying the absoluteness of such idea of “non-contradiction”, apparently one is mistaken for someone who believes that everything may and should be “contradicted”.

    Hello Luis! My my, it seems like only yesterday.

    If something is absolute, then it holds for everything everywhere. If relative, then it is possible for it not to hold, even if it always is held.

    If committed to the relative nature of the LNC, then you must ipso facto be committed to the possibility that something can both be and not be at the same time and in the same respect.

    If one acknowledges this, then it admits the conclusion that no reasoning is adequate for any conclusion. Indeed, even saying “it works” carries with it the implicit possibility that it “doesn’t work” at the same time and the same respect. Thus even pragmatism is defeated.

  7. If one acknowledges this, then it admits the conclusion that no reasoning is adequate for any conclusion.

    I was following your reasoning and nodding all the way until this sentence, which does not follow.

    Notice the key word here: “does not follow necessarily“.

    The problem here is that you think I demand an absolute conclusion. Thing is, I’m fine with an imperfect conclusion. A conclusion whereby I state to myself, “taken into account non-contradiction, such and such follows, however, we should hedge this a little bit for fat tail events”. My, you made me talk like Nassim Taleb.

    If one acknowledges this, then it admits the conclusion that no reasoning is adequate for any conclusion.

    Exactly, if you are commited to only look for absolute conclusions. Thing is, I am not. I am perfectly fine with a fuzzy yet practical “good enough” conclusion.

  8. @Luis:

    To prove my point, I’m going to amend your reply to me to better reflect your philosophy:

    I was/was not following your reasoning and nodding/not nodding all the way until this sentence, which does not/does follow.

    Notice/Don’t notice the key word here: “does not/does follow necessarily“.

    The problem here is/is not that you think I demand an absolute conclusion. Thing is/is not, I’m/I am not fine with an imperfect/perfect conclusion. A conclusion whereby I state/don’t state to myself, “taken into account non-contradiction, such and such follows/does not follow, however, we should/should not hedge this a little bit for fat tail events”. My, you made me/didn’t make me talk like Nassim Taleb.

    Exactly, if you are/are not commited to only look for absolute conclusions. Thing is, I am not/I am. I am/am not perfectly fine with a fuzzy/definite yet practical/impractical “good/not good enough” conclusion.

    That’s better; I’m not thoroughly informed/un-informed.

  9. Josh, you are having a problem detecting the difference between the possibility of something against the omnipresence of that same something. And it’s starting to tire me, since this is the tenth time I try to convey this difference to you.

  10. @Rob

    “I would submit that most of your readers (including me) support “freedom of expression” but would not support the right to scream “fire” in a crowded theater (which is certainly expression).”

    Well, either there is fire or there is not. If there is, then why would the speech be in any way restricted. Even if there is no fire, then I can determine this for myself, chose an appropriate exit strategy, decide on not panicking and getting trampled.

    Unfortunately, the entire premise of the “can’t shout fire in a crowded theater” is based on the assumption that humans are mindless irrational beings that cannot think for themselves and need to be controlled and restrained constantly. It’s a viewpoint that leads to increasingly fewer liberties and freedoms. If actual crimes are committed and people directly harmed by these actions then there are mechanisms in place to address the injuries. But hurt feelings can occur in a variety of ways and due to a variety of causes (including mental illness). Who will decide how widely the net should be cast to find the “cause” of said hurt feeling (producer, director, actors, editors,costume makers, prop maker, translator, not to mention investors).

    No, I don’t think most readers of this column would agree with your restrictions on free speech (but I could be wrong).

  11. Josh, you are having a problem detecting the difference between the possibility of something against the omnipresence of that same something.

    Oh I get that: something that is potential need not be actual. Problem is, every time you say words in the form of a proposition to me, you make it actual necessarily. You make it present.

  12. That is to say, if committed to the possibility of the LNC being turned over, then you must contain in each truth claim qualifications of the sort which I put in bold in the post above. And this will be implicit in every truth claim you make to me or anyone else. I’m sorry you’re tiring, but I’m duty bound to defend truth, so I can’t just let fallacies go, especially when it’s germane to the OP!

  13. Again, our subject said, “Freedoms…”
    If there are two of something, there must be a difference. Moon claimed existence of more than one; we can decide to accept and then differentiate between his “Freedoms:” e.g., ‘fire/theater’ may be actual [Truth/Beauty], may be false [?!?!] – consequence resolved, later. We merely confuse the issue and waste breath.
    Freedom of speech cannot be abridged, as God cannot be Man.
    False premises > return to ‘Go.’

  14. What Moon should have done is defined “to provoke or humiliate some others’ values and beliefs” as not an act of free expression, as opposed to classing that act under it. By that he would have avoided the contradiction, however illegitimately.

  15. That is to say, if committed to the possibility of the LNC being turned over, then you must contain in each truth claim qualifications of the sort which I put in bold in the post above.

    And the use of which would exactly be what, apart from satisfying your own obsessive atention to a perfect rigor? Of course, if your goal is to create the “perfect language”, we can discuss these things to incredible detail, but I think we are doing mostly fine with the language we have.

  16. @Charlie Martin:

    “What about an undecidable proposition?”

    What about it? An undecidable proposition P is always undecidable relative to a formal theory T, meaning T can neither prove P true nor P false. So what?

  17. @ Rob,

    The shouting fire in a crowded theater thing is a qote from Supreme Court Justice Oliver Wendell Holmes Jr in a 1919 decision that upheld the conviction of a man under the espionage act for doing nothing more than criticizing the conscription act. This decision stood for the proposition that the Federal Government has the authority to censor and or punish any speach contrary to official govenrment positions. It adds nothing to any debate on free speach.

    See:
    http://www.popehat.com/2012/09/19/three-generations-of-a-hackneyed-apologia-for-censorship-are-enough/?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+Popehat+%28Popehat%29

  18. This is a very provocative post! Better not tell Ban Ki about it.

    Poor Ban Ki. He thinks speech (specifically a YouTube video) provoked Muslims into insane and violent mob behavior. Whereas the slaughter of thousands of Muslims by a cruel dictator (in Syria) did not provoke. Therefore, the video is the problem, whereas the slaughter of innocents is not.

    But it appears that the violence in Libya was orchestrated by Al Qaeda. Let us recall that Al Qaeda is (proudly) guilty of mass murder, but apparently not of provocative phraseology, according to Ban Ki.

    So which is the crime, mass murder or provocative words? Which one results in abundant bloodshed and death, and which one cannot actually hurt you?

    PS for extra credit: which is worse, shouting “fire” in a crowded theater or slaughtering theater goers with bullets?

  19. @Luis:

    Of course, if your goal is to create the “perfect language”, we can discuss these things to incredible detail, but I think we are doing mostly fine with the language we have.

    Case in point of my own use of imperfect language: I have no clue what you are talking about or why my words would have elicited this response. That is not my goal. I said propositions, not sentences.

    As for “perfect rigor,” something else I think is impossible in this state of existence:

    Compare the humility of a man who says “we know very little for certain” to one who says “we know nothing for certain.” It is actually the second man who comes out as dogmatic and arrogant by that statement, putting his absolutist stamp down on the human race. You never really got around that objection, btw, in your guest post. But I’ve exhausted this ground. I’ll leave you be on this topic.

    Parting shots from Chesterton:

    “We are on the road to producing a race of men too mentally modest to believe in the multiplication table. We are in danger of seeing philosophers who doubt the law of gravity as being a mere fancy of their own. Scoffers of old time were too proud to be convinced; but these are too humble to be convinced. The meek do inherit the earth; but the modern sceptics are too meek even to claim their inheritance.”

    “Just as one generation could prevent the very existence of the next generation, by all entering a monastery or jumping into the sea, so one set of thinkers can in some degree prevent further thinking by teaching the next generation that there is no validity in any human thought.”

    “The pragmatist tells a man to think what he must think and never mind the Absolute. But precisely one of the things that he must think is the Absolute. This philosophy, indeed, is a kind of verbal paradox. Pragmatism is a matter of human needs; and one of the first of human needs is to be something more than a pragmatist. Extreme pragmatism is just as inhuman as the determinism it so powerfully attacks. The determinist (who, to do him justice, does not pretend to be a human being) makes nonsense of the human sense of actual choice. The pragmatist, who professes to be specially human, makes nonsense of the human sense of actual fact.”

    -Bows out; vaya con Dios, Luis Dias

  20. Would it have been more clear if Ban Ki Moon had said: “Freedoms of expression should be and must be guaranteed and protected, except where harm or insult is the intent”?

    He didn’t say this, but I think this would be the common interpretation.

  21. @ad:

    “Doesn’t physics claim that certain particles are their own anti-particles?”

    Yes some particles are their own anti-particles (photons, pi zero, etc.). What exactly do you think this implies?

  22. Compare the humility of a man who says “we know very little for certain” to one who says “we know nothing for certain.” It is actually the second man who comes out as dogmatic and arrogant by that statement, putting his absolutist stamp down on the human race. You never really got around that objection, btw, in your guest post. But I’ve exhausted this ground. I’ll leave you be on this topic.

    Arrogance is a perceived attitude, a very subjective judgement. I left it as an open question in my original post for you to answer for yourself. Clearly you disagree, but in no way that qualifies as an “unanswered objection”. I also find it disingenuous that you qualify my own position as “absolutist”, when it is your position that is so. This is not a “judgement” or anything like that. It is a very technical word that characterizes all sorts of philosophies that share certain fundamental absolute truths.

    Chesterton was witty, but what can I say but “I don’t agree”? So he thinks that all of us who aren’t christian absolutists like him are dimwits. Well then, whatever rocks your boat old silly man.

    And for the sake of goodness, stop addressing me as if I’m spanish.

  23. Matt,

    If you’re going to start commenting on third world idiocy in the UN, you’re going to be very busy and even more boring.

  24. I should add.

    Dr. Briggs (or anyone who might know):

    (1) God is not man.

    (2) Man is not God.

    (3) Yet Jesus Christ is both God and man.

    The Christology behind this is highly complex, and it is probably impossible to reconcile the two without appealing to the metaphysics of the ancient world. Suffice it to say, though, that there is no “both-and” contradiction here.

  25. John R T, same as it is today. The person who think he/she has been insulted or has suffered injury as a result. In a court of law. It’s reflexive and dependent on a plaintif. The law simply identifies what is or is not an accountable action, but is not proactive in preventing it.

  26. Dr. Briggs (or anyone who might know):

    (1) God is not man.

    (2) Man is not God.

    (3) Yet Jesus Christ is both God and man.

    As alluded to by Rank Sophist, Post-apostolic Christian scholars sought to expand upon and develop logically the clear, but not fully explicated teachings of the apostolic writers that posited Jesus as God “manifest in the flesh”.

    These later thinkers were well-versed in Greek philosophy and certainly understood and accepted the Law of Non Contradiction. To be faithful to the apostolic witness and to accord with sound principles of philosophical reasoning (eg law of NC)they developed over a long period of time, and through extensive debate and discussion, complex and sophisticated doctrines to reconcile the apparent contradictions at the heart of the Christian faith.

    Thus we have profoundly philosophical/theological notions of the triune nature of the Godhead, and of the Son, the second person of the trinity, emptying himself(kenosis in Greek)and becoming a human being. Most particulary, in reference to the “dilemma” proposed above, they posited the concept of the two natures of Christ, one divine and one human co-existing seamlessly but dinstinctly in one person(hypostasis).

    I undoubtedly am guilty of shamelessly simplifying these profound and sophisticated concepts but I merely wish to point out that a serious amount of philosophic effort went into making theological arguments that accorded with logic and reason. One may have one’s opinions on the success or otherwise of these efforts but to dismiss the early Church thinkers as ignorant and irrational “faith-heads”, as is often done, is way off the mark. They knew their Aristotle!

  27. I guess, according to Aristotle, we now know which posters here are no better than vegetables.

    You gotta appreciate the christian love displayed here…

    The Christology behind this is highly complex, and it is probably impossible to reconcile the two without appealing to the metaphysics of the ancient world. Suffice it to say, though, that there is no “both-and” contradiction here.

    Of course not. It’s almost a tautology, in the sense that whenever a contradiction is spotted, immediately is denied by the “rationalist” who will come up with contrived schemes and exceptions (making up new metaphysical rules) to end the contradictions. In the new schematics, the contradictions stop existing.

    It’s like when certain fictions are caught contradicting previous canon and so on. People make up for the plot holes and contradictions with convoluted excuses and then at the end it’s all okay. But in that case everyone knows it’s fiction, and that what happened there was the author kinda messed up the canon.

    Not the christian theology though. That one is perfect by definition, so any convoluted idea that can explain away any possible “contradiction” will be accepted as dogma, and anyone who points the finger laughing at the exercise will be name-called as vegetables.

    That’s christian logic for you.

  28. I think one cannot argue consistently for the freedom of expression, that is misguided. You can however (and should) argue for the freedom of thought. If there is respect for the freedom of thought, we have the right orientation towards human beings (as rational animals). Yet freedom of expression is more like favoring the animal (over the rational) and ultimately to our detriment. If we are granted freedom of expression without freedom of thought we are no longer human beings (let’s hear it for modern education). If we have freedom of thought there will also be freedom of expression to the right extend. I cannot imagine otherwise.

  29. I think one cannot argue consistently for the freedom of expression, that is misguided

    Why not?

    If we have freedom of thought there will also be freedom of expression to the right extend. I cannot imagine otherwise.

    I can. It’s fairly easy when you consider that everyone has had freedom of thought (no single state has ever managed to force your thoughts), and freedom of expression is something rare to find in history.

  30. RE Aristotle: “It is impossible to hold the same thing to be and not to be.”

    THAT IS FALSE (though, outside of quantum phenomena, it is true one thing cannot be a different thing at the same time). People hold & cherish contradictory views & values & behaviors all the time–especially with religion. Psycology/psychiatry call it “cognitive dissonance.”

    EXAMPLE: An episode of “Cops” (or similar show) presented a scene in which a brutal drug trafficker’s house was raided. Therein they found a shrine to the Madonna (the bad guy was a Roman Catholic, like much of his Central/S. American peers). Only this shrine incorporated handcuff & other such items. The cop/fed involved explained that this shrine was an attempt to solicit the Madonna’s intervention for the bad guy’s welfare–so he wouldn’t be arrested for drug trafficking or killed while killing his rivals, etc.

    No interpretation of R. Catholic doctrine can accommodate such killing & activity…but this bad guy managed to comingle such mutually exclusive doctrines.

    But, chances are, such extreme examples are unnecessary–most people can spot this sort of thing among their peers on numerous & much more mundane matters. And most people will notice that for those with such contradictory views/values/behaviors (usually observed by behaviors that are consistently at odds with asserted values) those holding such contradictions are totally blind to them…and they often develop sophisticated rationalizations/explanations as well. Such is the realm & appeal of philosophy, especially that unmoored from quantitative reality.

  31. @Ken:

    “THAT IS FALSE (though, outside of quantum phenomena, it is true one thing cannot be a different thing at the same time).”

    Are you saying that quantum phenomena are examples of things that are and are not at the same time? If that is what you are saying then could you explain why?

  32. @luis

    – Why not?

    Well, you might, but more likely you will act like Moon and exclude some expressions you deem highly undesirable: obscenities, incitements and the like.

    – I can. It’s fairly easy when you consider that everyone has had freedom of thought.

    That is arguable, basically we did not have freedom of thought. The fact that the conversations you are having with yourself (if that is what you mean by thinking) are hidden does not mean they are free. The heretics of the past were not burned at the stake because they expressed themselves, but because they cherished forbidden thoughts.

    Do you know the history of the knight-Templar? Surely they were not executed because they expressed unwelcome views. They were tortured for other reasons and confessed to being devotees to idols (I am simplifying things here) That is what sentenced them to the stake. The point is, your statement is just wrong.

    Freedom of thought means freedom to be a human being. Freedom of expression means freedom to act like an idiot.

  33. It is a contradiction to defend freedom of expression and simultaneously condemn and try to suppress it when it irritates people. Freedom of expression then means nothing. It can be persuasively argued as truth that Mohammed was a religious plagiarizer, pedophile, mass murderer, and false prophet. If someone turned this argument into a best selling book with a subsequent popular American released film, are we responsible for the rioting and murder of a mob half-way around the world? Should we ban this expression? Should we become slaves to their anger and ignorance? Is this what some people are proposing? Really? Then maybe we should riot in response to such utter foolishness. Oh yes, we don’t do that because – get this now – we live in a society that respects free expression and that would be against our own precious ideal of free expression. To compare this to shouting “Fire!” in a crowded theater – when there is no fire — is just silly and embarrasing. If you are in a theater where there is a fire, then not yelling “Fire!” would not only be suppressing the truth, but harmful to people who would die from the smoke if they found out too late. I do not like mocking other people’s religion; I have manners. But it is dangerous to the very nature of our culture to have someone decide which expressions are acceptable or not.

  34. G. Rodrigues

    A particle can be or not, here or there. A particle has a spin about ALL axes. Plus the mind boggling entanglement. There is more. It led Feynman to humorously say that quantum electrodynamics (interactions of light and matter), which is taught at graduate level, can not be understood by the general public. But not to worry, he added, because his students did not understand it either. Neither did he. Nature can be seen as experimentally proven absurd.
    So it seems that on the very small scale Aristotle is wrong. But it does not invalidate his statement(s) when applied on human scale.

  35. @Sextus:

    “A particle can be or not, here or there. A particle has a spin about ALL axes. Plus the mind boggling entanglement.”

    The first statement is, technically speaking, incorrect. For the second I am not completely sure what you mean by it, but the way I am reading it, you are correct but there is no contradiction with the law of non-contradiction. Likewise with the third statement, that is, whether mind-boggling or not, there is no contradiction between entanglement and the law of non-contradiction.

    Look, there can be *NO* contradiction between QM and the law of non-contradiction. In fact, there can be *NO* contradiction between physics as we know it and practice it and the law of non-contradiction and anyone who says otherwise, does not know what he is talking about.

    I can explain all this in painstaking detail, but first, you will have to be *explicit* about where *exactly* you think the contradiction between QM and the law of non-contradiction is.

  36. The principle of superposition states that a particle like an electron exists in all theoretically possible configurations simultaneously. So it is A and non-A at the same time. Wasn’t it one of the aspects of the dispute between Einstein, Podolsky and Rosen on one side and Copenhagen “gang” on the other? They (EPR), standing on the firm ground of the law of non-contradiction, claimed that a particle like photon has to have a definite spin. It was later experimentally verified that EPR were wrong.

  37. @Sextus:

    “The principle of superposition states that a particle like an electron exists in all theoretically possible configurations simultaneously. So it is A and non-A at the same time.”

    Wrong, that is not what the principle of superposition states. Consider some particle (e.g. an electron) that can be in a state A, where A means that the particle is localized in region A; consider a state B, where likewise B means that the particle is localized in region B. For the purposes of this example, assume A and B are disjoint regions of space, and sufficiently apart that our measuring devices can distinguish between them (e.g. A = earth, B = Andromeda galaxy). Since the state space of a quantum system (e.g. an electron) is a complex Hilbert space, any “linear superposition” with complex coefficients is also a state of the particle — this is the principle of (linear) superposition.

    Why did I put “linear superposition” between quotes? Because this is physics terminology and it is misleading. The mathematical terminology of *linear combination* is much better in this respect. A linear combination of states is *NOT* some weird state where the system (e.g. an electron) exists, somehow, in both states at the same time, rather it is *itself* a state. Going back to my example, you can ask if the particle is in A or in B. If you measure the position with sufficient precision, you will get that it is either in A or in B, not some weird combination of both. And what about before the measurement? The answer here depends on the interpretation of QM you buy into; suffice it to say that none entails any denial of the law of contradiction.

    And you are confused about the EPR paradox, in more than one way, but I will stop with the explanations of QM. If you want to learn about it, you know the drill: hit the books.

    For the last time, there can be no contradiction between *any* physical theory and the law of non-contradiction. For suppose there were. Formalize the physics necessary in a first order theory. The fact that there is a contradiction with the law of non-contradiction means that the theory is inconsistent. By the principle of explosion the corresponding formal theory proves *everything*, every single statement in the language of the theory and its denial: it proves that 1 = 0 and 1 is not equal to zero. It proves that electrons exist and electrons do not exist, etc. It would be a *useless* theory.

    So please, stop with this foolish ignorant talk about QM contradicting the law of non-contradiction.

  38. @Sextus:

    Bibliographic reference for what specifically? What I said about QM can be found in any decent book on QM. I have with me Merzbacher, “Quantum Mechanics” 2nd edition, Landau-Lifschitz “Quantum Mechanics” (the two volumes, but in Portuguese translation) and Isham’s “Lectures on Quantum Theory”. Any decent university’s library will yield other texts, including the volumes of Jauch and Piron on the foundations of quantum mechanics. So what exactly do you want to know?

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