Quantum Mechanics and the Laws of Logic, Part 1

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, A, is 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, A, is 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.