Suppose a scholar presented themselves to us, declaring themselves to be an expert on Plato and Aristotle, yet they also casually and explicitly dismiss the idea of ever learning any of that Greek language stuff as being gratuitous, unnecessary, otiose, boring, and let’s face it, just too hard. Persons who do not have a background in scholarly investigation may not appreciate how truly shocking such a declaration would be. This would be like someone proclaiming themselves an expert auto mechanic, but they’d never bothered to own their own tool kit, much less get all nasty and greasy working on an actual engine.

Now as someone with an earned Ph.D. in philosophy, I can comfortably teach Plato &/or Aristotle at a 100 or 200 level in college; in a pinch, with time I could prep myself to do a 300 level course. But a 4^th year (400 level) undergraduate course, never mind a graduate level course? Not a chance. No amount of enthusiasm on my part could overcome the indisputable fact that my minimal and altogether fragmentary grasp of the Greek language thoroughly disqualifies me from doing anything like research level work on such thinkers.

Well, the same thing is true about Whitehead, only the language now is not Greek, it is abstract algebra. Things are so bad in Whitehead scholarship, that it is likely most persons who’ve established their name in that field not only have no facility with the topic, they do not even know THAT there is a difference between their painful encounters with high-school algebra and ABSTRACT algebra, much less have any idea WHAT the differences are.

And yet, without some minimal facility in the subject, it is impossible to really understand how Whitehead thought, since it was precisely within abstract algebra that Whitehead spent 40 years of his professional life cultivating his habits of thought. Abstract algebra may be legitimately described as the logic of pure relational thinking. Given that Whitehead was a pure relational thinker, having a minimal handle on this ought to be considered a sine qua non of Whitehead scholarship.

And it doesn’t matter that it is “hard”; in point of fact (paraphrasing Tom Hank’s character from the film A League of Their Own) it is supposed to be hard … it’s the hard that makes it great. Yet despite the ready availability of tools to help bootstrap one’s grasp of the subject,ⁱⁱ most scholars dismiss out of hand any thought of even considering gaining a basic handle on abstract algebra, the only handle that will actually provide them with an entry into Whitehead’s thought.

And then there is #2 …ⁱⁱⁱ

To be filed under the heading, “words is hard,” it is essential to understand that Whitehead never used “foreign” words, and he invented new terms even less frequently. Notoriously technical notions like “prehension” and “concretion” from Whitehead’s corpus are, in fact, English words that had simply fallen out of use. Even the word “atomic” – which comes from the Greek a-tomos, meaning “uncut” or “undivided” – was, by the time Whitehead centered it within his philosophy, respectably anglicized so as to no longer count as foreign. But he generally used these terms in a way that contemporary readers entirely fail to realize is alien to their accepted understanding. In my notes I mentioned that I’d say more about “group theory,” the “mathematical theory of groups,” and now is the time to fulfill that promise with an e.g. of just how crazy making Whitehead’s choice of terms can be.

By the time Whitehead wrote and published his Universal Algebra in 1898, group theory was a well established branch of mathematics, with a well established name. In the above mentioned 1898 UA, Whitehead generously cites those mathematicians who had completed much of that establishment 20+ years prior to his own UA. But in UA, Whitehead defines and discusses an abstract structure that he calls a “group.” My right hand to any god you do or do not believe in, I was literally reduced to tears trying to make sense of this structure, because it bears absolutely no relation to the well known and well established concept of group that is the basis of the mathematical theory of groups. But I simply could not bring myself to believe that he would be this obstinate and arbitrary. He could have called his structures “collectives,” or “constellations,” or “system X,” or anything. But no; he called them “groups,” even though, by all that is wholly holy, he D0g Bamned^iv knew better.

Another example to show just how deep his English obstinacy ran. Isaac Newton and Gottfried Leibniz both invented the calculus at about the same time (certainly independent of one another.) But Newton’s symbolism was catastrophically bad, while Leibniz’s was so clear and intuitive that it is still used to this day, 300+ years later. But Newton was English, and the English refused to adopt that damned German’s symbolism, even though it crippled the development of mathematics in England for some 200 years. Whitehead is the perfect exemplar of this stubbornness. In his 1922 Principle of Relativity he not only uses the archaic and uninterpretable Newtonian symbolism, he occasionally switches over to the readable Leibnizian symbolism, demonstrating that he actually knew better.

Tears, I tell you. Reduced to tears.

Whitehead uses words you are not familiar with (prehension, concretion) even though they are perfectly respectable English words. Other words are one’s you “just know you know”, such as “God” or “atomic.” Per “God,” Whitehead could have more profitably taken up the perfectly decent Greek term “arché,” which means both “source” and “beginning,” and this would have readily captured what he meant by “God” (the font of creativity, and the basis of rationality in the universe.) Whitehead’s “God” is less personal than Aristotle’s “unmoved mover.” But “arché” was and is Greek, so that just wasn’t going to happen, making “God” the only term that came close. And like the starting gun at the wrong-way race, people ran with it to the point that they weren’t even on the same track as Whitehead.

“Atomic” is another one. Everybody “just knows” what the means, so they never trouble to find out what Whitehead was actually saying. Whitehead meant the original sense (which is how the term got incorporated into English) as an undivided whole. Indeed, Whitehead’s holism is such an overwhelming and omnipresent aspect of his work from at least 1920, that it is a tad stunning how anyone could miss it. Yet miss it they do^v, and read into it some kind of libertarian isolationist individualism which could not be more absolutely antithetical to everything Whitehead said.

Whitehead was what we now call a “relational realist,” someone who takes relations as fundamentally real in themselves, and not a mere façon de parler, a short form of speech where only the substantive “things” related, the “relata,” are real in any sense. Whitehead stands within an almost vanishingly small minority in this respect, as far as the sweep of Western philosophy is concerned. But no one in this tiny circle could even possibly prioritize the libertarian notion of the absolute individual as anything other than an indefensible fallacy, that is false at every level, from the metaphysical on up.

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i “Absolutely bananas” is a technical, philosophical term …

ii Tom Judson’s Abstract Algebra: Theory and Applications is both eminently readable and free for the download; so it is not as though the expense was prohibitive. Hermann Weyl’s classic Symmetry, while it does require a purchase, is hardly in the same class as university text books price wise, and is an illustrated (for crying out loud!) introduction to the nature of the mathematical theory of groups. I’ll have more to say about group theory in just a moment.

iii I did that on purpose.

iv That’s another technical, philosophical term.

v Confession: when I first read Process and Reality, I missed it as well.