Quantum Mechanics and the Laws of Logic, Part 1


Having worked at science-faith apologetics organization Reasons to Believe for more than 20 years, I’ve observed that scientists and philosophers often think differently about the world. With the types of specialized training in their academic backgrounds, scientists and philosophers tend to ask different kinds of questions about reality and truth. Unfortunately, they also have a tendency to talk past one other. Recently, I had a social media interaction with a scientist about whether the findings of quantum mechanics invalidate the logical law of noncontradiction.

Here, in part 1 of 3 in this series, I’ll provide a little background on the laws of logic and the theory of physics known as quantum mechanics. Then I’ll share some of my interaction with the scientist about the relationship between the two topics.

Three Foundational Laws of Logic

The study of logic recognizes three laws of thought as bedrock principles: the law of noncontradiction, the law of excluded middle, and the law of identity. Their importance to human thought and discourse cannot be overstated. These logical anchors, so to speak, can be stated to reflect a metaphysical perspective (what is or is not—being) or an epistemological perspective (what can be true or not true—truth).1

Here are the three logical laws stated and explained:

1. The law of noncontradiction: A thing, A, cannot at once be and not be (A cannot equal A and equal non-A at the same time and in the same way); they are mutually exclusive (not both). A dog cannot be a dog and be a non-dog.

2. The law of excluded middle: A thing, Ais or it is not, but not both or neither (either A or non-A), they are jointly exhaustive—one of them must be true. There is no middle ground between a dog and a non-dog.

3. The law of identity: A thing, Ais what it is (A is A). A dog is a dog.

Law of Noncontradiction (LNC)

To help explain further, here is an example of a logical contradiction from the claims of two world religions:

A. Jesus Christ is God incarnate (Christianity).

B. Jesus Christ is not God incarnate (Islam).

According to the LNC, these two statements (represented as A and B) negate or deny one another. In other words, if statement A is true, then statement B is false, and conversely. Thus, logically, both of these statements cannot be true. So contradictory relationships reflect a “not both true” status.

Quantum Mechanics (QM)

For a basic understanding of quantum mechanics, Live Science defines it this way:

Quantum mechanics is the branch of physics relating to the very small.

It results in what may appear to be some very strange conclusions about the physical world. At the scale of atoms and electrons, many of the equations of classical mechanics, which describe how things move at everyday sizes and speeds, cease to be useful. In classical mechanics, objects exist in a specific place at a specific time. However, in quantum mechanics, objects instead exist in a haze of probability; they have a certain chance of being at point A, another chance of being at point B and so on.2

The challenge of QM in the context of the LNC is that light (a subatomic object) seems to be both a wave and a particle simultaneously, thus A and non-A.

Logical Interaction

Here is what a scientist said to me on social media:

The law of noncontradiction is violated by solid empirical science. At the quantum level, a subatomic particle can be in multiple locations at the same time. A particle can be both a wave and a particle. At the quantum level, cause may occur after effect. If this is true at the molecular base of our reality, how strongly can we hold on to the law of noncontradiction?

I responded by thanking the scientist and saying that philosophers and scientists need to dialogue with each other more on these kinds of topics. I then offered my brief take on the issue.

The LNC cast metaphysically (in terms of being) states the following: “Nothing can both be and not be at the same time and in the same respect.” I don’t think quantum mechanics actually denies the law of noncontradiction. What we can say is that under certain experimental conditions, light (a subatomic object) appears as a wave. But under other experimental conditions, light appears as a particle. So subatomic objects are not particles that are also nonparticles or waves that are also nonwaves; they are objects that behave sometimes like particles and sometimes like waves. Light behaves as a wave and a particle in different experimental conditions and, thus, in different logical respects. Hence, the experimental results of QM do not invalidate the LNC (A cannot equal A and equal non-A at the same time and in the same relationship).

The fundamental problem with any denial of the LNC is that the laws of logic make rational thought possible. In this very case, both a scientist and a philosopher exchanged ideas under the assumption of existing laws of logic. Thus, philosophers need input from scientists just as scientists need input from philosophers. And Christians would do well to populate both critical disciplines.


If I were to summarize the issue so you can use it on social media, I would say that quantum mechanics is counterintuitive to our ordinary notion of how larger objects react, but it is not a genuine violation of the law of noncontradiction. The laws of logic are considered necessary and inescapable because all thought, correspondence, and action presuppose their truth and application.

Reflections: Your Turn 

Can you concisely state and explain the three laws of logic? Have you used them in your interactions? Visit Reflections on WordPress to comment with your response.


For studies in logic in the context of the Christian worldview, see Kenneth Richard Samples, A World of Difference: Putting Christian Truth-Claims to the Worldview Test (Grand Rapids: Baker, 2007), chapters 3 and 4.


    1. Kenneth Richard Samples, A World of Difference: Putting Christian Truth-Claims to the Worldview Test (Grand Rapids: Baker, 2007), 42–44.
    2. Robert Coolman, “What Is Quantum Mechanics?” Live Science, September 26, 2014, https://www.livescience.com/33816-quantum-mechanics-explanation.html.

  One thought on “Quantum Mechanics and the Laws of Logic, Part 1

  1. June 11, 2019 at 5:24 am

    Certainly, instead of saying A and B about light and then finding it is scientifically self-contradictory, we should see that it proves that our definitions of A and B (particle and wave) are not exclusive or opposites.

    In some ways, this is the same as the Christological debate on the dual-nature of Christ. People lost sleep and peace and position over explaining or thinking too much over the contradiction that seems to be in the definition that says all things are “exclusively” EITHER one or the OTHER.

    Since there is one exception, with light (or in theology, with Christ) that means that it is a generalization not a proof that the law of self-contradiction is not a law. It’s proof that the definitions include a third but rare category.

    • June 11, 2019 at 9:33 am



      If the law of non-contradiction is not a law, then all rationality is undermined.

      Under certain experimental conditions light behaves like a particle. Under different experimental conditions it behaves like a wave. Those are in different respects. The traditional understanding of quantum mechanics affirms this truth.

      There is mystery in how Christ can be one person with two distinct natures, but if it is truly contradictory then the incarnation is false. But again logically we can say that Christ is human in a different way than he is divine.

      Best regards.

      Ken Samples

  2. Eleder Iruzkin
    June 11, 2019 at 10:22 am

    Let me please qualify all three laws the same way you do with the first one:

    1. The law of noncontradiction: it is not both A and not A, at the same time and in the same way.

    2. The law of excluded middle: it is exclusively A or not A, at the same time and in the same way.

    3. The law of identity: A is A at the same time in the same way.

    Thanks to the “at the same time and in the same way” proviso, I think that Quantum Mechanics doesn’t violate the law of noncontradiction. As you very well pointed out, “what we can say is that under certain experimental conditions”, there appears the corpuscular or the undulatory behavior of an observable. Now, that behavior is experiment-dependent, that is to say, observables neither are corpuscular nor undulatory in themselves but only in relation to the conditions of the process of observation. Here the crucial point is that observables, by definition, are not in themselves, but relating to an observer. So, when the law of identity states “A is A”, its crucial that we don’t forget the clause “at the same time in the same way”, which involves the conditions relating A, the observer or logician included. BTW, this notion is what Buddhism calls it “emptiness”, the relational character of all things.

    Another question is the definition of Quantum Mechanics as “the branch of physics relating to the very small”. Again, observables are not “small” or “big” in themselves, but regarding something else. So, we can try and define again Quantum Mechanics as “the branch of physics relating to two different orders of magnitud” or, so to say, more figuratively, two different “powers of ten”: that of the observable and that of the observer, respectively. Thus Quantum Mechanics is the observation and description of a world of a certain order of magnitude from the perspective of another world of another order of magnitud.

    As for the law of noncontradiction and religion, according to what we have said above, it seems perfectly possible that “Jesus Christ is God incarnate” from a Christian worldview (set of conditions #1) whereas “Jesus Christ is not God incarnate” from an Islamic worldview (set of conditions #2). It all depend’s of each one’s soteriological needs.

    If we take the Christian notion of original sin, vicarious sacrifice and substitutionary atonement, there follows, theologically, Jesus Christ as God incarnate. Now, if we take the Islamic notion of “fitrah” or “original disposition” (towards good/God) that denies the notion of original sin (not of sin), plus the statement “Every soul earns only to its own account; no soul laden bears the load of another” (Qur’an 6:164, 17:15, 29:7, 35:18, 39:7, 53:38, Arberry), there is no need for a redeemer, hence “Jesus Christ is not God incarnate”. Now, this doesn’t obviously solve out the, for instance, identity or historical implications of each statement…

    What I mean is: If we try to impose Christian theology to Islamic soteriology, Islam collapses, and viceversa. And if we try to impose Islamic soteriology to Christian theology, Christianity collapses, and viceversa. In other words, granted every genuine religion is a complete and consistent system in itself, we cannot fairly reduce one religion’s logical premises to another one’s without a serious danger of distortion.

    Hence, in order for the interfaith dialogue to be fruitful, Raimon Panikkar proposed seeing the relationship between two faiths as an “homomorphism” (= a structure-preserving map between two algebraic structures of the same type, such as two groups, two rings, or two vector spaces -Wikipedia; see also the topological concept of “homeomorphism”), where each system has its own inner consistency by its own right, and the same time there is some room for some kind of corresponde between them, without completely and distortingly reducing one to the other. Therefore, this view entails a systemic approach to religions, that is trying to figure it out a system of believe of systems of believe.

    Than you very much for your very thought provoking post. I look forward to reading Parts 2 and 3. Best.

  3. June 11, 2019 at 10:40 am


    Thanks for your comments.

    In reality or in truth (regardless of Christian or Muslim perspective), Jesus is either God incarnate or he isn’t. Not both and one or the other. Thus homomorphism violates the law of non-contradiction.

    Best regards.

    Ken Samples

    • Eleder Iruzkin
      June 11, 2019 at 1:27 pm

      Ken: Differences aside, the statement “Jesus is either God incarnate or he isn’t” pretty much resembles that of physics, “the photon is either a wave or is not”. And for that, you nicely provided the answer: depends on the type of observation.

      For instance, according to certain Christian view (as you know, there are many), Jesus is God all the time, that is to say, before, during and after incarnation. Therefore, there is a time in which Jesus is God incarnated and other times in which he isn’t (incarnated).

      So both alternatives of the sentence “Jesus is either God incarnate or he isn’t” are plausible although not at the same time and in the same way, as we say. It depends on settled conditions in each case. So, instead of speaking in terms of “reality or truth” (which I don’t mean to deny), I think it may be helpful to take any statement this other way, that is, asking ourselves: “under which observing conditions Jesus is God incarnate?” and “under which observing conditions Jesus is not God incarnate?”

      Now, given the very same certain observing conditions, I agree, “Jesus is either God incarnate or he isn’t”. The difficulty, I think, is to precisely specify all the conditions implicitly involved in any statement. I would also add that as far as the disagreement persists, that means that there are still “hidden variables” in play for both parts, waiting for being discovered and brought to consciousness.

      As for the algebraical notion of homomorphism, I think of it as two parts in dialogue: the first one composed by a soccer team under the soccer rules and mindset, and the second one composed by a basket team under basketball rules and mindset. (Or even a relay theme running 400 metres!) There are so many things they share together: the ball, the concept of score, of rival, of duration of the match, of win/lose, of referees, etc. And there are also so many things they differ from one another: playing with the feet or with the hands, the number of players, goal and basket, etc. We know that reducing one to the other is not entirely possible, not fair. And yet, there is still some chance for both parts in dialogue to reach a consensus about both soccer and basketball being sports in their own right…

      Best regards.

      • June 11, 2019 at 2:01 pm


        Four points:

        1. According to historic Christianity, the truth of Jesus Christ being God incarnate is not dependent upon mere human observation but upon God who is truth and reality actually revealing the truth of the incarnation that is then confirmed to humans by prophecy and miracle.

        2. Historic Christianity and historic Islam both reject the idea that Jesus being God incarnate is merely a matter of human observable perspective. So both religions reject homomorphism.

        3. The proclaimed divine revelations of the Bible and the Qur’an make contradictory claims concerning the true identity of Jesus Christ. So one or both are logically false.

        4. For Homomorphism to be true then both historic Christianity and historic Islam would be false.

        Ken Samples

  4. Eleder Iruzkin
    June 11, 2019 at 4:49 pm


    1. For sure an event is absolutely dependent on God. For sure an event is not dependent upon mere human observation (which would be a purely idealistic standpoint) but you cannot either dismiss human observation from the equation if that human being is going to communicate something about that event. For example, human confirmation depends on a proper understanding of the event to properly confirm it in the first place. Probably God has revealed more, much more, than a particular person has been able to realize and communicate at some point.

    2. “Jesus being God incarnate” is at least a statement –a piece of text– in need of a meaningful context; and, in the interfaith dialogue, a meaningful shared context at that. Subjectively, one can legitimately stand for whatever but in the intersubjective arena, according a common ground of meaning is essential for the mutual understanding. Which, I think, heavily depends on both interlocutors’ wills and skills at “homomorphizing”.

    3. I would say that maybe we are too prone to read both texts, the Bible and the Qur’an from an unilateral non-homomorphic context: that of the Bible only or that of the Qur’an only. I think a more ambitious task here would be to figure it how them both could be logically true. Again, I believe a common context is in need (hopefully, in the way!). I like a lot quantum physicist Niels Böhr’s quote: “Profound truths recognized by the fact that the opposite is also a profound truth, in contrast to trivialities where opposites are obviously absurd.”

    4. Paraphrasing the line above, “It is the hallmark of any deep truth that its negation is also a deep truth” (Wikiquote).


    • June 11, 2019 at 5:10 pm


      This will have to be my last response. I’ve generously allowed you to post very long comments on my blog page.

      Traditional Islam denies the very essence of historic Christianity:

      * Islam dies the Trinity (affirming unitarianism)

      * Islam denies the Deity of Christ (affirming Jesus is a mere human being)

      * Islam denies the imago Dei (asserting that human beings are not made in Allah’s image)

      * Islam denies Original Sin (affirming people are born good)

      * Islam denies the Crucifixion (affirming someone other than Jesus died on the cross)

      * Islam denies salvation by Grace (believing personal submission is required to earn paradise)

      If Islam is true, then Christianity is false and vice versa. The laws of logic are stubborn things.

      Historic Christianity and traditional Islam both reject homomorphism.

      The findings of quantum mechanics do not support homomorphism which is itself a denial of the laws of logic.

      Homomorphism, like religious pluralism, doesn’t make all religions true but rather makes all religions doctrinally false.

      See my book God among Sages: Why Jesus Is Not Just Another Religious Leader (Baker, 2017).

      Respectfully yours,

      Ken Samples

  5. June 11, 2019 at 6:50 pm

    If I am awake then I am not asleep. If I am asleep then I am not awake. But sometimes I am asleep and sometimes I am awake. I don’t see any problem with the law of non contradiction. Now if my wife’s observations are correct then first thing in the morning before I have had a coffee I exist in a state that is neither asleep or awake! Do I break the law of noncontradiction? Or have I found that there is a continuum of levels of consciousness, and the problem resides in my initially defining asleep and awake as mutually exclusive?

    • June 11, 2019 at 7:16 pm


      Your description of “neither asleep nor awake” state sounds like you are basically awake but sluggish.

      I think your example lacks necessary precision. Cast the law of non-contradiction either metaphysically or epistemologically concerning levels of consciousness and tell me what you get (A and non-A).

      Nothing can be conscious and non-conscious at the same time and in the same way.

      Your neither awake nor asleep state is basically a limited awareness consciousness but clearly not non-A (non-conscious). You are conscious in a different respect than you are less conscious (sleepy).

      Levels of consciousness don’t rule out the law of non-contradiction. If it did, then levels of consciousness would have no logical meaning.

      Ken Samples

      • June 11, 2019 at 8:47 pm

        Thanks, I think I understand. So if I rated my alertness on a scale of 0 (deep sleep) to 10 (fully awake) then I could say that when I am at eg level 7 then I cannot at the same time be at not7?

      • June 11, 2019 at 9:14 pm


        Not in my view. You’re clearly awake. Awake and alert are not the same thing.

        What is the opposite of 7? If A is 7 define non-7?

        Defying the laws of logic would bring a halt to all thought, speech, and action. If awake can mean everything that isn’t awake then awake and sleep have no meaning.

        The laws of logic are stubborn things.

        For more on logic, see my book A World of Difference (chapters 3-4).

        Ken Samples

    • June 24, 2019 at 7:40 am

      Thanks for the link.

      Ken Samples

  6. Rita
    June 25, 2019 at 3:52 pm

    Fascinating interchanges! Thank you, Kenneth, for your responses and unraveling different positions.

    • June 25, 2019 at 4:13 pm

      Thanks, Rita.

      Ken Samples

  7. June 27, 2019 at 10:50 am

    As a Christian who majored in physics in college, I enjoyed all three articles of this series. In the first article, you wrote, “The challenge of QM in the context of the LNC is that light (a subatomic object) seems to be both a wave and a particle simultaneously, thus A and non-A.” I think an additional defense of the LNC can be mounted on the basis of the fact that, according to QM, a particle is actually a collapsed wave function (think of a “wave packet” that is tightly shrink-wrapped around the particle). Thus, “particle” does not equal “non-wave,” but rather a particular configuration of waves.

    • June 27, 2019 at 11:52 am

      Thanks, John.

      Ken Samples

    July 9, 2019 at 7:33 am

    You say: ” What we can say is that under certain experimental conditions, light (a subatomic object) appears as a wave. But under other experimental conditions, light appears as a particle. So subatomic objects are not particles that are also nonparticles or waves that are also nonwaves; they are objects that behave sometimes like particles and sometimes like waves. Light behaves as a wave and a particle in different experimental conditions and, thus, in different logical respects. Hence, the experimental results of QM do not invalidate the LNC (A cannot equal A and equal non-A at the same time and in the same relationship).”
    “They say: “Since the days of Einstein, scientists have been trying to directly observe both of these aspects of light at the same time. Now, scientists at EPFL have succeeded in capturing the first-ever snapshot of this dual behavior.” https://m.phys.org/news/2015-03-particle.html HMM?

    • July 9, 2019 at 9:20 am


      If QM denies LNC then it reduces to absurdity.

      The laws of logic anchor intelligible reality.

      Ken Samples

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