#BTColumn – The dilemma of mind and matter

Disclaimer: The views and opinions expressed by this author are their own and do not represent the official position of the Barbados Today Inc.

by Adrian Sobers

“Mathematicians think in symbols, physicists in objects, philosophers in concepts, […] and idiots in words.” – (Nassim Taleb, The Bed of Procrustes)

“There are other approaches to the foundations of mathematics, but set theory is the one that came up with this rigorous way of defining infinity.” – Eugenia Cheng

Urban Dictionary defines meta as “seeing the thing from a higher perspective instead of from within the thing, like being self-aware.” If you get your meta wrong, everything else is suspect. This is especially the case for physics, the discipline that Nassim Taleb calls “confident and convincing”.

This became even more evident in reading Frank Wilczek’s (mostly) excellent book, Fundamentals: Ten Keys to Reality.

I say mostly because Wilczek’s metaphysics left a lot to be desired. Wilczek presents Fundamentals as “an alternative to traditional religious fundamentalism.”

He continues, “It takes up some of the same basic questions, but addresses them by consulting physical reality, rather than texts or traditions. The spirit of their enterprise, and mine here, transcends specific dogmas, whether religious or antireligious.”

“In studying how the world works, we are studying how God works, and thereby learning what God is. In that spirit, we can interpret the search for knowledge as a form of worship, and our discoveries as revelations.”

However, after discussing the fascinating fundamental physical realities of our universe, we are left with an inadequate grounding for “the style of thought” that enables us to grasp said fundamentals.

To account for the fact that physical fundamentals cannot adequately account for the mind that grasps these fundamentals, Wilczek introduces the concept of complementarity. Briefly, when we consider something from different perspectives, it can “seem to have very different or even contradictory properties.” Humans are a good example: “We are tiny and enormous, ephemeral and long-lasting, knowledgeable and ignorant.”

Wilczek identifies “ideologies or religions that claim an exclusive right to dictate uniquely ‘correct’ views” as “contrary to the spirit of complementarity.” (No word if that statement itself is to be taken as a “correct” view and therefore contrary to “the spirit of complementarity”.)

At some point, even the most charitable writer has to declare their hand as it relates to meta. In this context, what are we to make of the mind that not only grasps, but acts on the physical fundamentals of our universe.

Here Wilczek leans more on the poetic than physics: “Matter, deeply understood, has ample room for minds. And so, also, it can be home to the internal worlds that minds house.

“There is both majestic simplicity and strange beauty in this unified view of the world. Within it, we must consider ourselves not as unique objects (“souls”), outside of the physical world, but rather as coherent, dynamic patterns in matter.”

“Were it not so strongly supported by the fundamentals of science,” he ends, “it would seem far-fetched. But it has the virtue of truth.” Far-fetched? Definitely. Having “the virtue of truth”? Hardly. I’m a sucker for pairing and Fundamentals goes well with The Story of the Cosmos by Daniel Ray; specifically, the second essay by Melissa Travis, A Glorious Resonance.

Travis cites agnostic physicist Paul Davies who frames the dilemma of mind and matter with a passing mention of mathematics: “One of the oddities of human intelligence is that its level of advancement seems like a case of overkill. While a modicum of intelligence does have a good survival value, it is far from clear how such qualities as the ability to do advanced mathematics . . . ever evolved by natural selection.”

His reference to mathematics is not insignificant. Travis writes: “The observation that there is a special relationship between mathematics, matter, and mind is rooted in some of the earliest philosophical thought of the Western tradition.”

Travis notes that “Planck, a theist, and Einstein, who rejected the idea of a personal God, both recognised that naturalism falls far short of explaining the resonance between mathematics, nature, and mind.”

Naturalism not only falls short, but flat on its face. In Journey to the Edge of Reason, Stephen Budiansky introduces us to Kurt Gödel, one of the few people who conversed with Einstein as intellectual equal. They often conversed on politics, philosophy, and physics. Einstein called Gödel “the greatest logician since Aristotle” and the two men shared one fundamental quality, “both went directly and wholeheartedly to the questions at the very center of things.”

And it is in Gödel’s contribution to the foundation of mathematics that we find a convincing case as to whythe materialistic meta just doesn’t add up.

As Gödel argued, “the mind was based on far fewer physical foundations, and far more spiritual influences, than the twentieth century wanted to believe. Eventually the truth will be discovered—even though science is headed in a materialistic direction for the foreseeable future.”

Ms. Cheng addresses the practicality question early on in her book Beyond Infinity, “You can get by perfectly well in life without understanding anything more about infinity than you did when you were five years old. But for me the usefulness of mathematics isn’t about whether you need it to “get by” in
life or not. It’s about how mathematical thinking and mathematical investigation sheds light on our thought processes.”

Similarly, we can “get by” fine without ever thinking about matter, mind, and metaphysics or the foundation of mathematics. But a lot of our problems are grounded in bad metaphysics (and anthropology); and one of the most practical things we can do is work on correcting them. (Failing that we will have to be content with the usual patchwork here and there.)Gödel’s contribution to the foundation of mathematics is a good reason to question the narrative that tries to keep God (especially of a personal variety) out of the equation.

Gödel’s fascinating story is a reminder that any attempt to reduce the mind to matter (brain itself) doesn’t square with reality. Adventurous readers can read the entire article, but a phrase from the abstract should suffice here.

In Theism, Explanation, and mathematical Platonism, C. P. Ruloff alludes to the correlation between “our mathematical beliefs and mind-independent mathematical truths”.

Briefly, are there objective mathematical truths “out there” awaiting discovery, or, are mathematical truths merely human constructs (with the obvious implication, as is the case with objective moral truths,that they can be de- and re-constructed to suit every passing whim and fancy).

Dutch mathematician L. E. J. Brouwer is one of many who argued that mathematics is entirely a human construct. Mathematics, according toBrouwerand company, was not related to any “objective” truth and opposed the Platonic concept of mathematics as a body of objective, preexisting truths that are independent of our minds. However, this idea, like its counterpart in the area of morality (true for you, not true for me), is utter nonsense.

Gödel’s first public lecture, delivered at a meeting of the American Mathematical Society and the Mathematical Association of America, was aptly titled The Present Situation in the Foundation of Mathematics. However, it was when he delivered the Gibbs Lecture later in his career that he laid out what Budiansky (Journey to the Edge of Reason) calls “several powerful arguments against the notion that mathematics is nothing but a creature of man’s own invention.”

Gödel argued that the act of mathematical creation itself “shows very little of the freedom a creator should enjoy”, as the creature (mathematics) immediately begins to make demands on its supposed creator (mathematician).

Therefore, even if we created basic principles about integers, Gödel argued that our creative powers would go no further as the mathematician is not in a position to also create the validity of the theorems.

This, along with other arguments he developed in the lecture led him to two choices, and a conclusion “decidedly opposed to materialistic philosophy.”

Gödel rejected the idea that the mind could be reduced to the mechanistic operation of the brain and therefore this, as he put it, “seems to imply that mathematical objects and facts (or at least something in them) exist objectively and independently of our mental acts and decisions”.

An omniscient being can instantly perceive that “12 × 31” and “372” aretwo different ways of expressing the same thing. However, this is an equivalency that humans have to work out (even mental math champions). If we reduce our thoughts to mechanistic operations of the brain, then (pray tell), how do we account for the obvious goal-directed mental agency required when little Johnny sits down to do his sums?

When little Johnny attempts to solve 43 + 4, he must be able to make free choices along the pathway of reasoning. (If he can’t then why grade his paper?) As it turns out, even the most basic of mathematical reasoning requires us to reason according to, and this is the important part, immaterial and external mathematical rules (truths, call it what you wish) that cannot be grounded in human beings.

In other words, we would have to be the biggest of little Johnny’s namesake to think that his mind can be reduced to matter (and still expect to be taken seriously). Plato once said, “God is always doing geometry”, to which Gödel’s thesis advisor quipped, “God never does mathematics. An omniscient being needs no logic and no mathematics.” But we do. Which is sufficient reason for us to not only wonder, but worship.

Adrian Sobers is a prolific letter writer and commentator on social issues. This column was offered as a Letter to the Editor.