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Gödel’s Incompleteness Theorems: The Cause—and Cure—of Wokeness?

Why do so many people today think there are only arguments, not facts?

In modern “woke” ideology, there are no facts, only arguments which express cultural power— based on the acceptance of those arguments by current society. In such ideologies, it is not important whether or not the arguments are logically consistent or if they are true in any real sense. What is important is whether or not they achieve the desired results in politics and society.

This is not a criticism. It is a description of their methodology (for a review of the academic literature on the subject, see the book Cynical Theories by Helen Pluckrose and James Lindsay.

Many people wonder how we got here. Why do so many scholars actively reject logic as a method of finding the truth, and reject truth-finding altogether as a valid enterprise? Here, I am going to present a speculative history of postmodernism, which is the precursor to modern “wokeness.” I’m calling it a “speculative history” because I think there is an important factor at play which is almost never documented. I think that it performed a causal role in the development and pervasive acceptance of postmodern thought.

The Struggles Between the Sophists and the Logicians

Every age has had its share of postmodernists—people who think that “what is real” is so distant as to be unknowable. Therefore, in absence of the ability to know truth, the purpose of argument is to assert power and dominance, not find truth.

In the pre-Socratic period in ancient Greece, these people were known as “Sophists,” which is where we get the term “sophistry.” The sophists were orators who, like the postmoderns of today, used words for power rather than truth. Socrates criticized them for confusing flattery for art, persuasion for truth, and pleasantness for goodness. In that day, the methods of the sophists were readily countered by the logicians of the day. So, although the sophists were present, they were readily countered by the logicians.

In fact, you see this struggle between logic and sophistry in many ages and eras. In the time of Descartes, there was a question of whether or not knowledge is possible, or if we might be deceived about everything. What if the world as we see it is really just an illusion? Descartes, a logician, worked through the skeptical thoughts which were active in his own day and showed that skepticism is not warranted. Even taking into consideration the greatest of our fears about the ability to know the world, skepticism is not warranted.

As you can see, the sophists have always been present, but, in most ages, they have been countered by logicians. The response of the logicians to the sophists has kept skepticism and sophistry confined to intellectual sideshows instead of the main event.

Kurt Gödel’s Bombshell

The war against skepticism was doing well in the late 1800s and early 1900s. The period known as the late modern period (approximately 1850–1950) included huge advances in knowledge in numerous areas, especially mathematics and physics. In fact, this exuberance for the progress of mathematics led many people to believe that mathematics could be “completed”—that we could develop a set of axioms which could be used to mechanically determine the truth of any theorem of mathematics.

To that end, Alfred North Whitehead and Bertrand Russell published Principia Mathematica in 1910, aimed at fulfilling this program. The logicians believed that their method was so reliable in producing knowledge that it didn’t ever need to rely on external considerations.

However, in 1931, Kurt Gödel (1906–1978) proved his incompleteness theorems. These theorems showed that the task that the logicians assigned themselves was impossible. There was no single axiomatic system that could be used to mechanically prove every true theorem. From this followed a series of similar findings on the limitations of formal systems.

In short, what Gödel effectively did was to shatter the dominance of logic over skepticism. Gödel
showed that, even in logic, one couldn’t be sure of the truth.

I believe that the rise in the general acceptance of postmodern thought in the generation following Gödel is based on this result. It is not that there were people who were arguing along the lines of “because of Gödel’s incompleteness theorems, we are now skeptical.” But rather, the presence of Gödel’s incompleteness theorems caused logicians to lack the moral courage to counter the claims of the modern sophists.

For the centuries, when the sophists attack truth itself, the logicians responded, “yes, indeed we can know truth.” However, following Gödel, logicians no longer believed this to be the case, and so kept silent as the postmodern movement gained steam.

Regaining Ground

So, how does one respond to the claims of the modern sophists in light of Gödel? The fact is, Gödel himself had the answer, but the modern period was not ready to accept it.

Gödel’s theorems are about the ability to mechanically find truth, not about the ability to find truth at all. The error that crept in was the mechanical philosophy that was also present at the time. Mechanical philosophy (known by many different names—naturalism is its current incarnation) is the belief that everything in nature is simply matter in motion. That is, there are no spirits, souls, or any non-physical component to reality, including human beings. You are merely a machine made of mud.

Because Gödel’s theorems say that you cannot mechanically find truth, if it is true that you are merely a mud machine, then, by extension, you can’t find truth either. However, for Gödel, the human mind was more than mere machine. The human mind was a spiritual entity. As such, it was capable of going beyond the mechanical, and connecting with the infinite.

What Gödel’s incompleteness really showed is not that skepticism and sophistry should win the day, but, rather, our theory of reality will affect our ability to believe in the truths that we find. If we believe that nature is just a machine, then we are left in the same predicament as a machine.

Our machines can’t tell if we are typing brilliance or nonsense in them. Likewise, if we are machines, than neither can we. However, if we are more than machines, then we can indeed look into the beyond and discover truth. In fact, the ability to discover truths such as Gödel’s indicates that we are indeed more powerful than machines.

We can indeed find truth, and we can use our abilities to discover truth about the world rather than merely assert power over one another.

You may also enjoy: Is technology really progress? Let’s talk about that
Tradition itself is a type of technology. Tradition tells us the set of decisions that will likely bring us the most happiness in our present culture as compared to all we are likely to encounter.

Jonathan Bartlett

Senior Fellow, Walter Bradley Center for Natural & Artificial Intelligence
Jonathan Bartlett is a senior software R&D engineer at Specialized Bicycle Components, where he focuses on solving problems that span multiple software teams. Previously he was a senior developer at ITX, where he developed applications for companies across the US. He also offers his time as the Director of The Blyth Institute, focusing on the interplay between mathematics, philosophy, engineering, and science. Jonathan is the author of several textbooks and edited volumes which have been used by universities as diverse as Princeton and DeVry.

Gödel’s Incompleteness Theorems: The Cause—and Cure—of Wokeness?