What Is the Law of Non-Contradiction? – #3 Post of 2011

Post Author: Bill Pratt

I am constantly amazed that there are people who try to deny the law of non-contradiction, which is the most basic principle of rational thought.  What is the law of non-contradiction?  There are at least three ways to state it:

  1. A thing cannot both be A and not-A at the same time and in the same sense.
  2. A thing cannot both exist and not exist at the same time and in the same sense.
  3. A statement cannot both be true and not true at the same time and in the same sense.

It is impossible to deny this law without invoking it in your denial, yet time and again I have heard people try do just that!

Why would I spend a blog post writing about this?  Because a person who thinks that this law is not true will become a thoroughly confused individual whose thought life is a complete mess, full of contradictions and inconsistencies.  I have met a few of these people, and they both sadden and scare me.

All of our beliefs, thoughts, and knowledge are built on top of the law of non-contradiction, so when a person tries to deny this foundation, they are bound to go way off track in their pursuit of understanding reality as it really is.

If you have any doubts about this fundamental law of rationality, try and deny it, but then write out your denial in a sentence – “The law of non-contradiction is false” – and ask whether your statement is both true and false at the same time and in the same sense.

If the law of non-contradiction is false, then your statement of denial must be both true and false.  But if your denial is false, then the law of non-contradiction is true!  By denying the law of non-contradiction, you have just affirmed it.  The more you try to deny the law, the more you will affirm it.

Trust me.  You cannot win.

38 thoughts on “What Is the Law of Non-Contradiction? – #3 Post of 2011”

  1. What about John ch 1?

    In the beginning was the Word

    And the Word was with God

    And the Word was God

    This is a contradiction yet it is true.

    One cannot be with someone and also be tht person

    It say the Word was With God but also God.


  2. Steve,

    John 1:1 is not contradictory if you understand the trinity. Jesus (referred here as “The Word”) is one of the persons in the God head. There is also God the father and the Holy Spirit. All 3 are equally God and share the same attributes but each has different functions. I’m sure if you search this site you will find a great explanation of the trinity.


  3. The key there is “at the same time, and in *the same way*”
    But ultimately, I agree with Greg. The point being made in St. John’s construction is Trinitarian.

  4. The last two paragraphs don’t really follow from the preceding ones. If the statement “A statement cannot both be true and not true at the same time and in the same sense” is false that would mean that “a statement can both be true and false…” etc, not that “all statements have to be both true and false…” etc.

  5. Out of interest, who exactly is denying it, and what form does this denial take? I’m presuming this relates to apologetics in some way.

  6. I have specifically heard Christians, pantheists, and skeptics deny this law on multiple occasions. This isn’t an “apologetics” thing per se; it’s just a critical thinking issue that I wish to see corrected. Consider it a public service to everyone who wishes to think clearly.

  7. debunk, but the problem is that for any statement, there remains no recourse for why that statement should be viewed as only true or false, rather than both. Any such rule is a variant on the law of noncontradiction or is logically incoherent. Therefore, every statement is either both true and false or is true or false. This is just analytically true.

  8. Giving that everyone seems agreed that the LNC could not possibly be any other way, what is the opinion on Matt Slick’s argument that a God is required for the law to be true?

  9. Andrew, that is a great question! I was not aware of Matt’s argument, but I am familiar with a so-called “transcendental” argument for God which posits that a God must be the source or ground of logic. While I think it is both valid and sound (although I here again stress I am unfamiliar with Slick’s version, just in case it differs from Van Til’s, Clark’s, or Bahnsen’s), I think it is ultimately unconvincing (and stands virtually no chance of being convincing to anyone who is not already a theist). The reason I take it as sound is because I reason from a God to logic: I think God, as a metaphysically necessary being, therefore grounds necessary truth. Logic is necessary truth. Therefore, God grounds logic. Therefore, without God, logic does not exist. But this is unlikely to convince any agnostic or atheist. Just goes to show valid and sound arguments aren’t enough to make a good argument! 🙂

  10. I think there is “theistic” potency of the Transcendence argument, and that it lies in the equivalence drawn between that view, God is everywhere, so His ethical/rational nature is everywhere, and the view that axiomatic truths are self-proving, they simply are as they are. Either way places the root of reason, logic, morality both outside humanity (the evolution argument) and outside every particular human (me). I am subject to *something.*

    The rest of the story is establishing who or what that *something* is. I don’t think this line of argument, the common nature of ethics, or the common truth of reason and logic, will get us very much further down the road.

  11. Randy, a good debate between Slick and Matt Dilahunty on this argument (TAG) is available on YouTube. Google the following terms together: YouTube matt slick atheist experience.

    To me, one cannot that something is both axiomatic and dependent on a deity. That applies to logic and morality. If they require creation then they aren’t axiomatic, and are on the way to being subjective.

  12. Not familiar with the Slick/Dilahunty debate, but I think you are misunderstanding theistic claims. We are not saying that God created logic and morality. We are saying that logic and morality are part of God’s nature, so they have always existed just as God has always existed. There was never a time when God existed and logic and morality did not exist. God never woke up one day and decided to create logic and morality.

  13. “Not familiar with the Slick/Dilahunty debate, but I think you are misunderstanding theistic claims.”

    Well you can’t really assess whether I’m creating a strawman until you are aware of the claims Slick is making. He seems to be saying without God the LNC could not exist. To me, that makes no sense. Try to envisage a universe without the LNC. You’ve explained eloquently yourself why such an idea is self-defeating. At any rate, I’d recommend the debate.

  14. Hi Bill,

    Your argument seems only to prove it is self-defeating, and so necessarily false, that for any proposition P, P is compatible with ~P. However, as you undoubtedly know, advocates of paraconsistent logic hold there is some proposition(s) P that is compatible with ~P, even if most propositions are not compatible with their negations. So if asked if that very statement, or proposition, is true or false, they would say it is true, that in the case of this statement, it is a proposition that is not compatible with its negation. How would you reply to the advocate of paraconsistent logic? How would you show it is necessarily false?


  15. If a person says that there are some propositions for which the law of non-contradiction does not apply, I would say that he does not understand what the law of non-contradiction says. How can something be true and false at the same time? I would like to see an example of such a proposition.

  16. I imagine an advocate of paraconsistent logic (to play devil’s advocate) would reply that your question, “How can something be true and false at the same time,” assumes that the law of non-contradiction is true, that is, that no proposition P is compatible with ~P. But that begs the question, since the question is whether the classical law of non-contradiction is true or if paraconsistent logic is true. As far as examples, the advocate of paraconsistent logic would not have to provide an example of a proposition that is compatible with its negation. It is enough to say that there may be such a proposition, even if we have not come across it yet. At any rate, it seems that we have still not shown that the contention “there is some proposition(s) P that is compatible with ~P, even if most propositions are not compatible with their negations” is self-defeating and so necessarily false. Is there any way to show this? If not, then how can we say the classic law of non-contradiction is undeniable, as there appears to be an affirmable position, namely paraconsistent logic, that denies the classic law of non-contradiction?

  17. Hi Bill, I am struggling to see how we can show that all reality must be rational, that it, that it is not even possible that there is some irrational reality. How can we refute the idea that there may be contradictory realities, even if most reality is not contradictory? I can see that with respect to anything I know (e.g. my own present existence), I must think that thing is what it is (law of identity) and not its negation (law of non-contradiction), but what about the many things that I do not know. What shows that there cannot be something, even one thing, that violates the laws of logic, and so is non-rational and unknowable? In other words, it seems we must show that to know anything one must presuppose not simply that that thing is what it is and not its negation, but that all things must be what they are and not their negation. But it only seems the former, and not the latter, stronger law must be presupposed to know something. So, again, I don’t see how to prove that all reality is rational. Your expert advice on this would be very appreciated. Once again, can you specifically show that to know something we must presuppose that all things are /must be identical to their respective selves and not identical to their respective negations? Thanks, Bill!

  18. You cannot prove the law of non-contradiction – it is a first principle. It is self-evident. You cannot present an argument to prove that the law is true because you are assuming it is true all the while you’re making your argument.

    To say that it is possible that there are propositions that violate the law of non-contradiction is like saying that it is possible that there exists a square circle or that somewhere in the universe 2+2=7. The moment a person points to a statement and says that its opposite is also true, that person has uttered a self-contradictory statement. This will happen every single time the person attempts to do this because the law is undeniable.

  19. Hi Bill, thanks for your response. I agree that self-evident things cannot be directly proven, but you seem to be saying we can indirectly “prove” the self-evident law of non-contradiction by showing that it is undeniable, that is, that any attempt to deny it affirms it in the process, specifically, as you argue, by using the law of non-contradiction in the process of making the denial. What I am hoping is that you can show this. Would you be so kind?

  20. No when he said ” then your statement of denial must be both true and false.” he meant that for the principle to be false when you say it is false then your statement about it being false can’t follow the laws of the principle so you must in fact have a statement that is both true and false at the same time, if not then your wrong and the principle is then re-affirmed to be true.

  21. This is something I wrote a while back that address the LNC for quantum mechanics which might be of use to some:

    A friend of mine was using his apologetics know-how with an atheist and using principles that are self evident in nature, such as the law of non-contradiction, to argue for the existence of God. The atheist claimed that quantum superposition violates the law of non-contradiction and thus my friend’s whole argument was null and void. Knowing that I have knowledge in quantum theory and apologetics, my friend asked whether quantum superposition does violate the law of non-contradiction. (Of course some of you are wondering what in the world the law of non-contradiction has to do with the existence of God, or even what the law is? That’s a good question, but one to be answered another day. As to what it is, the law of noncontradiction says that a true statement and its opposite cannot both be true at the same time in the same sense. In logic it is stated as A ≠ not A.)

    Since this comes up so often with skeptics and atheists who try to use arguments from quantum mechanics against the classical apologetic argument for the existence, or at least the certainty of the existence, of God, I thought I would post my reply to my friend here for all of my Christian friends to use who might come across a person who tries to use the ill-fated quantum approach against God. (Of course God created the quantum world, so it isn’t so likely that such arguments can be used against His existence. Such attempts show either a misunderstanding of the nature of God, or a misunderstanding of nature itself.)

    Before I present the reply, I need to give some background on how the argument the atheist is using arises in quantum mechanics. There is a classic experiment used to demonstrate the non-intuitive nature of the quantum world. It is called the two-slit experiment. Light is made up of discrete packets of energy called “quanta.” You can never have a half, or any fraction of, a quanta. In one sense, it is like having a gum ball from a gum ball machine. You get a whole gum ball. You can smash it, chew it, or whatever, but you still have the same about of gum and it only comes in whole gum balls. So, light is generated from atoms and absorbed by other atoms as quanta packets of energy (called a photon). (The light we see in a room with a typical incandescent light bulb is many millions of quanta, so one quanta of photon energy is very very small.) In the experiment, a single quanta of light is shot towards the double slit. There is a piece of film on the other side. When both slits are open, the light appears to go through one of the two slits and be absorbed by the film at one point at a random position (see figures at end of this write-up). But when this is done over millions of shots, the image on the film is an interference pattern as if the photons went through both slits at the same time (the image on the film is the classical wave interference pattern of light). (An interference pattern is the crossing pattern you see when you drop two pebbles in a pond as the same time and the waves interfere – high crests and low crests – with light it is bright and dark areas.) But since only one photon is shot at a time, it is odd that the film shows an interference pattern when intuition would say a particle of light, the photon, would only go through one slit or the other, but couldn’t go through both. To test that, one can put a detector at the slits to try and see if the photon goes through one slit or the other, or both. When that is done, the photons are detected at only one slit or the other, randomly, and the interference pattern on the film disappears (it is what you would expect if the photons did go through only one slit or the other). So, knowing which slit the photon goes through destroys the interference that appears on the film that would appear when you don’t know which slit the photon goes through. Quantum mechanics is a mathematical formulation of this behavior for predicting the outcome of experiments called observations. Each detection on the film would be an observation. As such, what is called an observation does not require a human observer, but does require some sort of detector, whether it be a
    film, a photo-detector, or anything that could absorb the photon. Now knowing the weird behavior of the quantum world, I give the reply to the question. The friend also wanted to know the definition of quantum superposition.

    The quick answer is: if a particle could actually be observed as A and not A at the same time, that would violate the law of non-contradiction. Since that cannot be done, even in the quantum world, there is no violation!

    Quantum superposition is the mathematical addition of probability densities of all of the possible states of a quantum system. The result of the superposition of the densities is used to calculate the probability of observing the system in one of the states. In a binary
    probability space there is a chance that a quantum event can be observed as A or as not A. In the two slit experiment, it is the probability of a photon going through slit A or slit B. Slit B would be not A. When you don’t observe the slits to know which slit the particle went through, you find that it goes through both. So, this guy is saying that both A and not A exist simultaneously and the law of non-contradiction is violated. But that is not exactly the case! When the quantum system is observed, it is observed in the context of a particle with specific location and it can only be A or not A, it can’t be both. But when the system is not being observed, it is not in the form of a point like particle, it is in a wave form where the quanta of energy is spread across the possible states as a wave. It is in the wave form until it is observed. The observation collapses the wave to a point like particle where the law of non-contradiction is also observed (like popping a whole balloon by a pin at only one point on the surface of the balloon). One could say the law of non-contradiction is only valid in the world of observables (the world in which we interact). But it can also be said that since the energy is in a wave form when it is not being observed, that it is not true that it is A and not A at the same time, but that it is something else, a wave, that only has the potential to be either A or not A once it is observed. In other words, it is a whole other form that makes no sense in terms of A and non-A. It is like saying a potato is mashed potatoes, French fries, and a baked potato all at the same time, when it is not any of them when it is a potato in the garden. The potato has the potential to be any of those forms of potato, but isn’t any of them until one takes the potato and does something with it. The same thing applies in the quantum world. A wave has the potential to be observed at slit A or slit B (since a quanta of energy must be observed at one point), but while it is still a wave, it cannot be observed at both slits at the same time because an observation would cause it to no longer be a wave, but a particle. Bottom line is that having the potential to be one thing or another does not violate the law of non-contradiction. If the particle could actually be observed as A and not A at the same time, then there would be a violation of the law of non-contradiction!

  22. Walt,
    This is an outstanding explanation of quantum mechanics and why it does not violate the law of non-contradiction. Like your friend, I have had several skeptics throw this objection my way over the years. Would you mind putting this in the form of a blog post for my site? I’ll send you an email to discuss.

    Many thanks,

  23. Good answer! Similar to my answer when someone says that the LNC is a proof of God, because God is its only explanation. If God created it, it follows that he could have decided not to. Then it would follow that he could exist and not exist at the same time. In which case no apologist could argue against atheism!

  24. Believe me, I’ve heard ’em Bill. Your mate (!) Geisler’s co-author Frank Turek used that very argument on me. If he started losing an argument with you, his last resort was to say that the very fact that you were using logic in an argument with him was a tacit admission that God exists!

    See also Matt Slick’s version of TAG, saying that the logical absolutes are proof of Hod’s existence. That’s two apologists for you right there.

  25. To be fair too, I’ve never heard a counter apologist arguing against the existence of the LNC, so I guess we’ll just have to trust each other! You can google Matt Slick TAG, and find his argument. To me it makes mo sense that without God, the LNC wouldn’t exist, but I have heard LONG debates where that claim is made. And isn’t Walt above saying that his friend made the same claim, saying the LNC is part of his ‘evidence for God’? Perhaps I misunderstood (I can just about see an alternative interpretation, I’m not being disingenuous).

  26. Andrew,
    You are confusing two different things. There are lots of Christians who will argue that the very existence of logic and rationality requires the existence of God. I agree with them.

    But what they do NOT say is that God CREATED the laws of logic. Most Christian theologians understand the laws of logic as being part of God’s nature. They are built into God, so to speak, and have therefore always existed.

  27. I’d guess to you this distinction is essential; to me it appears hair splitting. Creating it, or it being an intrinsic part of his nature – it makes no difference to my point. Either way you’re suggesting that without God we’d have a universe where LNC does not apply – and you’ve made the point well yourself why such a notion is nonsensical.

    And saying it’s an intrinsic property of God seems little different to saying it’s an intrinsic property of reality – and simply could be no other way, God or no God.

  28. 🙂

    Clearly most philosophers affirm the LNC (in some form). I was just pointing out that there are some that are skeptical about it. In general Priest’s objections center around particular systems of logic or particular cases (where the LNC either does not obtain, or is a general case rather than a universal law). It isn’t good practice to convince someone that something (like the LNC) is universally true by showing them that a particular case backfires on them. You have to demonstrate that any conceivable case backfires, etc (without being too formal about it).

  29. I’ve just come upon your blog. In your final paragraph you state that “If the law of non-contradiction is false, then your statement of denial must be both true and false.” Should that not be “your statement of denial could be true, false or true and false” and would therefore not prove anything? Or am I just being naive?

  30. This post is severely confused on multiple fronts. Firstly, your definitions of the so-called “laws of thought” are incorrect. Those are logical laws, they don’t refer to “things” at all. They regard thr validity of arguments, not the world; logic, not metaphysics.
    The Law of Identity refers to a number of different laws, but most crucially the law that “For all X, X=X”. The Law of Non-contradiction doesn’t regard existence, it regards the so-called exclusivity of truth & untruth: “It’s not the case that P & Not-P is true”. The Law of the Excluded Middle says that truth & untruth are exhaustive: “Either P or Not-P are true” (there’s nothing besides truth and untruth).

    Now, these are not indisputable and to claim that they are demonstrates that you know nothing about formal logic. Logic’s which restrict each of these laws exist & are used in all sorts of areas. Logics that restrict the Law of Identity are called Non-reflexive logics, and have been used in Newton da Costa’s research on the understanding of quantum mechanics, as well as in the SQL database language in Computer Science.
    Logic’s which restrict or violate the Law of Non-contradiction are called Dialetheic Logics, a subset of Paraconsistent Logics. These systems have applications in resolving certain paradoxes, the most famous of which is the Liar’s Paradox:

    “This sentence is false.”

    If that sentence is false, then it also true because it says (of itself) that it is false. Therefore, it’s true & false simultaneously. If you say the sentence is true, then the sentence is false because it asserts (of itself) that what it says is true. Therefore it’s true and false simultaneously. If you say the sentence is neither true nor false, you’re rejecting the Law of the Excluded Middle which you said was impossible.If you say the sentence is nonsense, you’d need evidence for that besides begging the question in favor of consistency. And besides which, neither of those suggestions get around the paradox. Here’s are 2 Revenge Paradoxes to show why:

    “This sentence is neither true nor false.” If it’s true, it’s both true & neither true/false. If it’s false, it’s both false & neither. If it’s neither, then it’s true & neither again.

    “This sentence is nonsense.”
    If the original paradox was nonsense, so is this one. But the paradox agrees, it says (of itself) that it’s nonsense. Ergo, it’s both true & nonsense. If you say it’s false, then surely it’s either false or nonsense. Which means it’s true again.

    So on the face of it, we have a violation of the Law of Non-contradiction. And it was a perfectly rational explanation, it was not “crazy”. It’s not a parlor trick, it’s a bona fide, arguable example of a contradiction that is also true. This paradox also showed up in hehe foundations of mathematics in hehe he form of Russell’s Paradox.

    Excluded Middle (EM) is a more common case where people have argued for violations. Aristotle believed that contingent statements about the future violated EM. Propositions containing terms without referents have been argued to violate EM (such as “The present king of France is bald”). Intuitionistic Logic allows for exceptions to EM when discussing infinite domains and is a well-studied Non-classical logic, and has interesting consequences & discoveries in mathematics (such as the Theory of Smooth Infinitesimals).

    The analysis presuppositional apologists & trascendalists give makes no sense, and is at odds with how professional logicians & mathematicians actually argue. That’s not to say that Non-classical Logics are obviously true. But the argument you guys give is ridiculous, irrational and logically invalid. It simply begs the question, and you can beg the question in favor of any position or claim.

  31. It’s easy to subvert the “law” if you start from the open whole rather than from separation which reason and thought start with as their foundation. EVERYTHING known or sensed starts from “open unknown” which is open to limited stuff appearing within “it”. “It” “itself” is Non. Nondifference. Nonseparation but wholly openly able to shine it’s light on and with and within all that can appear within “it”. Reason is an ability that is able to appear within you. You are not limited to reason. Neither is God nor you nor is openness it’s nonself. Reason is just like any sense ability. Sense abilities enable us to share openly or “so called” closedly. but no closings/knowns ever really can last without the open source which is no thing per se known objectively. ALL “knowns” and experiences will be and are forgotten and replaced within openness/now. This is why it is so hard to make an object of “now”. It is open sharing that really can’t be escaped. All seemingly separate for a time (and they seem separate due to our ability to temporarily sense and reason with memory ability which is open too) bodies and sensed “things” and desires also, share being limited on earth but are always returning to the open whole source now. When we feel according to “the law” we feel that it is what we know that is real and our open sense is forgotten. It’s inevitable that we feel separate even though we are obviously really here now only together wholly. When we see and feel as if to really be parts and partial according to some “law’ that we assume is real and that everything falls within the limited law we feel limited. We become open to all manner of fear and closing oriented feelings. It’s belief in this “law” and all “closings”/”knowns” that we should fear. They make us able to feel separate and at odds with open NOW. NOW does not fit within the “law” but the “law” fits within open NOW. All “knowns” are limits but not all of limits are known. We don’t have to know limits in order to be open. Openness and the whole and the source is an order of “being” not limited to relative based sense. But it’s easy to sense being wholly open if you allow your reason to loosen. There can be reason starting from open wholeness sense and there can be reason starting from single separations sense. I always feel better when I’m open. No thing is “only”. All things are open and sharing now. Study nonduality and never settle for any conclusion based on relative sense and you will gradually loosen and feel free of this hold that, sense of differences being the only reality, has had on us. “You” will feel and “be” open. It’s an absolutely natural high and open sense as opposed to our usual seemingly natural sense of closings and separations. Sense of “own” will lose it’s meaning.

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