Bertrand Russell

It is hard to imagine anyone who contributed more or detracted more from 20^th century Intellectual History than the indefatigable Bertrand Russell (BR). 

Co-authored with Alfred North Whitehead, Russell’s Principia Mathematica brought Issac Newton into the 20^th century. Plus, BR was the first major thinker to throw a flag on ‘the calculus’. Discovered simultaneously by Newton and Leibniz c. 1700, calculus was assumed to provide the ‘final answer’ to Zeno’s pesky paradoxes. It doesn’t! 

Russell pointed out that calculus is a computational method useful for making calculations about real phenomena but not for modeling those phenomena per se. The idea that ‘calculus’ describes something real about the world is an example of what Whitehead called, the fallacy of misplaced concreteness. Bottom line: Zeno lives on…and we have BR to thank.

Finally, Russell’s tireless activism in pursuit of World Peace, while often misdirected (“Better Red than Dead”), cannot go unmentioned.

On the other hand, Russell fell back on the tired ‘Problem of Evil’ as his rationale for atheism (Why I am not a Christian) and his reformulation of set theory, while insightful, cost us a half century. It is these last two aspects of his legacy that concern us today and we will attempt to show that, surprisingly, the two are really one. 

Russell noticed that self-referential propositions can be inherently self-contradictory. Consider, for example, the proposition: ‘All propositions are false’. There is an inherent contradiction here. If ‘all propositions are false’, then the proposition, ‘all propositions are false’ must itself be false; and if ‘all propositions are false’ is false then it is true and if it is true then at least one proposition must be true, which violates the premise; ergo contradiction.

So, Russell MacGyvers it! He adds an axiom now known as the Axiom of Foundation to Set Theory; it states that sets cannot be elements of themselves. Now if a set cannot be an element of itself, then what appears to be a self-referential proposition turns out to be a meaningless word salad. Inconveniently however, reality does not step aside, not even for Bertrand Russell. 

Consider, for example, the set of all mathematical objects; such a set would itself appear to be a mathematical object in which case it would be an element of itself and no contradiction would result. How brazen! Does reality dare contradict philosophy? When the ideas of an intellectual clash with reality, reality is supposed to step aside. 

But Russell is unphased. If ‘Set A’ contains itself as an element, then ‘Set A’ cannot be a set after all. It may walk like a set and it talk like a set, but it cannot be a set. ‘Why? Because BR says so!’ 

In his best imitation of a 1950’s parent, Russell stifles all dissent. Surprisingly, we, like cowed children fearing a smack, sheepishly comply. But if Set A is not a set, what is it? It’s a ‘class’, obviously…do keep up! (If you have the feeling that you’re caught in an ‘Alice story’, you’re not wrong.)

Just as a simple ‘abracadabra’ in the mouth of a certified magician can turn lead into gold, so Russell, a certified logician, was able to turn absurdity into truth. How 21^st century of him! 

But ‘you cannot fool all of the people all of the time’ – A. Lincoln. From the get-go a few brave souls, living like Obi Whan Kabobi on the edge of civilization, dared to raise doubts. “I don’t see any clothes here, do you?” But it was not until the 1980s that Peter Aczel (PA) led a no holds barred assault on Russell…and vanquished him.

Thanks to PA, we now understand that the Axiom of Foundation is not a necessary part of Set Theory, that we can get along just as well without it and open a huge new universe of possibility in the process. Aczel reformulated Set Theory to include self-referential sets without generating any contradiction. 

I would argue that a Universe without self-reference could not exist at all or, if it did, it would be a lifeless wasteland (because what is ‘life’ but self-reference?). A single cell curates its contents, sustains its identity, and modifies its environment. It’s a recursive engine.

Genesis:  “…the earth was without form or shape, with darkness over the abyss and a mighty wind sweeping over the waters.” Were it up to Russell and the Axiom of Foundation, we’d be there still. 

In 1908 Russell stated the rule that held logic in thrall for nearly a century: “Whatever involves all of a collection must not be one of the collection.” 

Turns out, the huge intellectual edifice known as ‘Christianity’ has its own Fundamental Axiom, and it’s the exact opposite of Russell’s: “There is at least one collection that is one of the collection.” In other words, there is at least one set that is a member of itself.  

I call this the Axiom of Incarnation. This is the non-negotiable bedrock of Christianity: God, Being per se (Exodus 3: 14, John 1: 1-5, 14), containing everything that is, is also a person, a quantum of being (Jesus, the Christ). God is an element of God! Being at its most fundamental level is self-referential. 

Examples of recursive process abound in the stories and doctrines of Christianity. To cite just a few:

• “Love your neighbor as yourself.” (Mt. 22: 40)

• “Whoever eats my flesh and drinks my blood remains in me and I in them.” (Jn: 6: 56)

• “Blessed are the merciful for they will obtain mercy.” (Mt. 5: 7)

• “Forgive us our trespasses as we forgive those who trespass against us.” (Mt. 6: 12)

• “I am in my father, and you are in me, and I am in you.” (John 14: 20)  

Cosmologists claim to be able to account for the emergence of a Universe without resorting to the God Hypothesis; maybe so! But can there be a Universe without the Axiom of Incarnation? Because of Incarnation, the Universe acts on each of its members, each member acts on every other member, and every member acts on Universe. That’s recursion! That’s solidarity! That’s life! 

Recursion is a fundamental feature of Christian doctrine and, as it turns out, of the Cosmos itself. So a Universe is possible! And so of course, BR could not possibly be a Christian because his philosophy cannot tolerate the Axiom of Incarnation… the Problem of Evil has nothing to do with it. Sorry, Bertrand! Next time around, “Know thyself!”

Buckminster Fuller famously said, “I seem to be a verb;” and we now know that he was right. In fact, the fundamental unit of Being is a recursive loop, a process, a Rondeau Time Crystal, a verb. Turns out, the Universe spends more energy maintaining inertia than it takes to fuel a simple loop process in space and time. So, 1 < 0 in celestial mechanics? I don’t suppose BR would agree with that either.

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M.C. Escher’s Drawing Hands (1948) depicts two hands sketching each other into existence, visually capturing the self-referential loop at the heart of logical paradox and the Incarnation.¹

¹Scanned from The Magic of M. C. Escher Artist: M. C. Escher Year: 1948 Medium: Lithograph Dimensions: 28.2 cm × 33.2 cm (11.1 in × 13.1 in) Preceded by: Up and Down (1947) Followed by: Dewdrop (1948)

https://www.aletheiatoday.com/thoughtswhileshaving/time-crystals-and-pepperland