Can quantum science, the laws of logic, and the Christian faith coexist? Yes, they can. In fact, Christian thinkers have historically made many significant contributions to the study and development of both science and logic.^{1}

In the first two parts of this series, I briefly examined whether the experimental results of quantum mechanics (QM) invalidate the law of noncontradiction (LNC) and whether the laws of logic rule out a place for religious mystery (faith).

Here’s a summary of how I addressed these issues:

- In part 1 I explained in a social media dialogue with a scientist why the results of QM need not be interpreted to invalidate the LNC.
- In part 2 I explained that while the laws of logic don’t rule out mysteries of faith, the laws of logic are still considered necessary and inescapable because all thought, correspondence, and action presuppose their truth and application.

In this article I continue my social media dialogue with the scientist. This time we discuss the issue of whether there are *other* forms of logic besides Aristotelian logic. Sometimes the results of QM are interpreted along the lines of Eastern mystical religion, which has its own proposed logic.

Here’s my scientist friend’s comment:

I took a course in college logic. However, it is derived from the Greeks and Western thinking which is ingrained in our culture and society. However, in recent years, I have encountered Eastern views of reality and logic as well as modern efforts toward integrating Eastern and Western schools of thought.

**Three Foundational Laws of Logic**

Before we unpack my response to my scientist friend, let’s refresh our memory of the three foundational laws of logic (explained in more detail in part 1 of this series).^{2}

1. The law of noncontradiction (LNC): 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 (LEM): 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 (LI): A thing, *A*, *is* what it *is* (A is A). A dog is a dog.

**My Response**

I responded by saying that I think it is fair to say that the consensus of historic Christianity (philosophers and theologians) considers the three laws of thought (LNC, LEM, LI) as not just one version of logic but rather as the nature of reality. While these laws are sometimes referred to as “Aristotelian” or “Western” logic, in actuality Aristotle didn’t invent these laws. Rather, he discovered and formulated them. Yes, there are other forms of logic, especially Eastern, but these Eastern forms of logic usually reject the law of noncontradiction. (Western logic accepts an either-or differentiation, whereas Eastern logic affirms a both-and synthesis.)

The problem, however, is that the laws of logic are necessary for all rational people and must be universal to all cultures and worldviews. A person cannot significantly think, speak, or act without relying on the laws of logic (LNC, LEM, LI).3

Therefore, I recommended that my scientist friend approach Eastern logic with great discernment and critical analysis.

**A Takeaway**

Here’s a way for you to summarize and use this lesson. While there are other approaches to logic than the three laws that Aristotle discovered and articulated (Western logic), Eastern approaches to logic usually deny the laws that make reality rational and intelligible.

**Reflections: Your Turn**

What happens to our thinking, speaking, and acting if the laws of logic are denied?

**Resources**

- 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*, chapters 3 and 4.

**Endnotes**

- For more on how Christian thinkers have historically contributed to the disciplines of science and logic, see Kenneth Samples, “Five Ways Christianity Is Reasonable,”
*Reflections*(blog), August 30, 2017, https://reflectionsbyken.wordpress.com/2017/08/30/five-ways-christianity-is-reasonable/. - Kenneth Richard Samples,
*A World of Difference: Putting Christian Truth-Claims to the Worldview Test*(Grand Rapids: Baker, 2007), 42–44. - See Ronald H. Nash,
*Life’s Ultimate Questions: An Introduction to Philosophy*(Grand Rapids, MI: Zondervan, 1999), chapter 8.

Thanks for the link.

Ken Samples

There is the classic retort from Ravi Zacharias (quoting from memory)

“Even in India they look both ways before crossing the street. It’s EITHER you OR the bus, but not both.”

Thanks, Steven.

Ken Samples

Great “lessons.” Can the Law of Noncontradiction be applied to transgendarism or non-binary personhood,or fluid genderism, which is such a huge issue in our society at this time? If so, would you be willing to tackle it?

Rita:

Very interesting and provocative topic.

The reliable definition and justification of terms would be critical. For example, transgenderism allows for a person to distinguish their sex (biology) from their gender (psychology). If this is accepted then the person may be a man in one way and a woman in a different way.

The critical issues it seems to me are whether one can reasonably distinguish between sex and gender and, as you noted, whether gender is non-binary.

Because of my traditional apologetics focus, I don’t think this is a topic I would write a blog article about. But others do albeit not necessarily from a laws of logic perspective.

Thanks for asking the tough questions.

Ken Samples

Rita, I think the truth claims of the gender activists would be like nailing jello to the wall. Principles of logic would be of little use.

Sjwilling, had to laugh at the picture of the jello on the wall – I tend to agree, unfortunately. Fortunately there’s God and prayer!

Interesting question – can one reasonably distinguish between sex (biology)

and gender (psychology) – in those terms – or whether gender is non-binary? Hadn’t thought of them as separate (I’m inclined to think them not). Thank you for your response.

Hello Kenneth!

In my transition from atheism to Christianity, QM was very important. In particular, once I left the world of pop-sci and started reading textbooks and papers, I found that the physical world was not only compatible with God’s existence, but almost seemed ideally designed for it.

Whatever the weird behavior, QM uses classical logic as its foundation: QM uses linear algebra (for “wave mechanics”, it is essentially an infinite dimensional space, with functions used in lieu of finite-dimensional vectors, but it’s still linear algebra). Linear algebra in turn is axiomatized in terms of classical logic (optionally via set theory).

I read von Neumann’s work on a “quantum logic” (an alternative logic based on QM) many years ago, which was interesting as a way of making some aspects concrete, but nevertheless is not a useful way of doing QM, and thus not used in practice.

The wave particle simultaneity is only in infinite dimensional spaces, e.g. position/momentum and time/energy. Without going into details, the momentum operator is -iħ∂Ψ/∂x, whose eigenvectors (eigenvectors are the pure/definite states in QM) look like e^ikx, which is a periodic (repeating) function and thus wavelike. Therefore it is common in the field to view particles as primarily point particles with wave-like aspects to their behavior.

I think it is better to first understand QM in terms of the finite dimensional situations, and without canonical conjugates (i.e. position or momentum but not both). This way we can deal with finite vectors and without complex numbers. If there are two possible outcomes of a measurement, say spin up and spin down, then one would think of a mixed state not as “both spin up and spin down” but as say 30% spin up and 70% spin down: State = √(30%)|Up> + √(70%)|Down> (where “|Up>” represents the state being purely definitely spin up, and “|Down>” represents the state being purely definitely spin down). It’s not until a measurement is made that the state will drop down into either √100%|Up> or √100%|Down>. It’s misleading to think of the state as “being a 30% chance the state is really spin up and a 70% chance it is spin down”. Its true state really is the mixture. There are differences between the kind of “probability” used in QM and probabilities we ascribe to things due to our ignorance – in fact you cannot mix them in QM and if you wish to use the classical “ignorance” probabilities in your calculations, you need to use a formalism called “density matrices” to make sure they don’t get mixed together.

I sometimes wish RTB dealt more with some of the ways that QM is relevant to God’s existence, so my thanks to you for talking about it some 🙂

Thanks, Dustin. I appreciate your comments.

Encouraged to hear of your journey from atheism to Christianity.

Best regards in Christ.

Ken Samples

Can I send you something I personally wrote l to office email because it is long. But it addresses this very question. I am not sure I want to make it public until I’ve had critical review first because some of my conclusions are – scientifically unorthodox.

17 pages mostly non-technical.

Don: You can send it to the reasons office to my attention. I can’t promise a response, however.

Ken Samples