Definition (and Proof)

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I was recently in a conversation on social media that – rather magically, I thought – did not instantly zig into infantile spew. It did, however, take the predicted zag into a stream of superficial (if rather more maturely presented) fatuous nonsense that gave me enough pause to suggest this post.

There is, especially among persons of an especially right-wing political leaning, an inclination to demand simple, clear, and absolute definitions with regard to all terms in general, but especially those with even a patina of political significance. Thus, with the histrionic attacks on that vanishingly small minority of persons who identify as “trans” (a group that comprises <0.5% the last time I looked it up) the demand by persons of a neo-fascist inclination (and TERF’s; politics makes for strange bedfellows) the self-righteous demand to “define” “woman.”

(Funny how they never demand a definition of “man.” But then, it is only women whose rights they wish to strip away, after all.)

Back in Aristotle’s day there was yet some hope of justifying a faith in definitions as being foundational to rationality. That said, Diogenes going about Athens with a plucked chicken (a ‘featherles biped’) mocking Plato by shouting, “Behold! A man!” might have inspired a measure of humility. But these days, any such sophomoric dependence upon definitions is patently childish, if not downright infantile. Let us call such juvenile insistence the “Dictionary Game.”

YAAFI

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What does “YAAFI” mean? Well, we’ll get to that in a moment.

First, let me say that this little editorial addition to my blog is not going to be explicitly or obviously “Whiteheadian,” although everything I write is to some considerable degree informed by those studies. That said, this will be more in the way of a personal screed mostly (if not entirely) lacking in scholarly &/or academic virtues. In other words, I intend to not only go full snark, but to occasionally employ “adult language.” Now, said “adult language” will certainly not exceed anything you’d hear with profligate abandon among a bunch of teenagers. Indeed, I consider “profligate abandon” far more adult language than the “fucks” I’m about to liberally dish out. I mean, seriously: when was the last time you saw “profligate abandon” used in a YA novel? When was the last time you saw a YA novel that didn’t have at least one “fuck”? (I don’t actually know; I read fucking adult literature.)

I needed a picture, and I thought “Storming the Bastille” was either subtle and clever, or irrelevant and funny.

Oh yeah, perhaps I should add that my tongue will, on at least an occasion or two, be squarely planted in my cheek. I will trust to the context to make those occasions obvious.

Panpsychi… Wut?

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There is a philosophical position known as “panpsychism.” While it is not an overwhelmingly popular position, it has been getting some attention of late. And as Whitehead himself is frequently characterized as a panpsychist, it seems worthwhile to cast an eye on this notion and say something about it. And of course, the first thing one should say should be an answer to Gollum’s question (“What is it, Precious?”)

The basic idea of panpsychism is that mental activity (the “psych” in “psychism”) is everywhere (the “pan” part. And by everywhere, it is meant to be at all levels of reality, large or small. Mental activity is, in this view, a fundamental element of all that is real, an ontological “primitive” (if you will) that is not constructed from other elements but rather is itself something that is always already “there.” The advantage of this notion is that it goes a long way to resolving the “mind/body” problem by basically arguing that there was never a real problem, only a problematic and erroneous characterization of the real.

Topoi? Gud Boi!

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I am rereading rereading Robert Goldblatt’s book, Topoi, though in many respects it seems like I’m reading it for the first time. When there is enough time and space between myself and some volume or other, that experience of ‘(re)reading it for the first time’ is not all that uncommon. It occurred not too long ago with E.P. Thompson’s The Making of The English Working Class, and Durrell’s Alexandria Quartet. Those works both had in the neighborhood of forty years between the first and the second readings, so I feel less guilty at the sense of surprise and pleasure. With Topoi, my excuses are somewhat more thin, though I can still assert with considerable truth and honesty that there’s been considerable intellectual development on my part since the first time I tackled the book. I mention this not just to make what amounts to little more than a peculiar Facebook post (some people share pictures of their meal, after all), but to set up a discussion of why a Whiteheadian should pay special attention to that area of abstract algebraic thinking known as Category Theory. I’ll first spend a few words talking about the book itself.

The word “topoi” is the plural form of “topos,” which seems rather more elegant than saying “toposes.” A topos is a category theoretic structure that is rich in a variety of “nice” formal characteristics, the details of which I’ll spare you (as that would require an entire book on category theory to explain.) Now, a category (such as might take on the structural features that would further specify it to be a topos) is a mathematical constructions that turns away from “objects” so-called to devote particular attention to functions, transformations, and operations without any special concern for the supposed “what” that is being transformed or operated on. As such, category theory is arguably the purest form of algebraic thinking around. It is scarcely an accident that Leo Corry’s magnificent history of the development of abstract algebra, Modern Algebra and the Rise of Mathematical Structures, ends with the emergence of category theory.

A Cosmology Group

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It occurred to me the other day that more can and ought to be said about contemporary issues with gravitational (physical) cosmology, especially as this is the source of so much dubious triumphalism from so many physicists. As usual, I want to preface my comments with some explicit remarks about terminology. The word “cosmology” covers a number of topics, not all of them entirely overlapping. So in specifying gravitational cosmology, I am specifically pointing out that branch of astrophysics that deals with the large scale structures of the physical universe. There are also those areas of inquiry that can be qualified as philosophical cosmology and theological cosmology. An example of the former would be Whitehead’s work in Process and Reality (PR) dealing with what he called “cosmic epochs” as these are informed by his work in natural philosophy as found in his triptych (Enquiry into the Principled of Natural Knowledge (PNK), The Concept of Nature (CN), and The Principle of Relativity (R).) As one might well expect, theological cosmology deals with cosmological principles with a focus on god(s) and creation. (Examples here would include medieval arguments for the existence of god(s) from design, etc.)

From JWST

The philosophical and theological approaches can and often do overlap. There is less room for such overlap with gravitational cosmology, because the latter is focused upon scientific – and hence, in some respect or other – broadly constructive and falsifiable principles. Philosophical cosmology can overlap with gravitational when (as is the case with Whitehead’s work) there is a fundamental challenge to the theory of nature that is being employed on the physical side. In such a case, questions arise as to the very nature of the above two qualifiers, “constructive” and “falsifiable.” I am less inclined to see any real overlap with the theological approach, however. When that appears to occur (almost, if not simply, exclusively at the insistence of the theologians), what is really happening (I would argue) is that the theologians are folding physical ideas into their theological arguments, and offering nothing in return to the physicists.

What a math …

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So I did a thing …

Get your mind out of the gutter, it was nothing like that. I did a presentation at the Personalist Forum conference, which happened to take place fairly close to where I live. (Normally it is at Western Carolina University, but due to scheduling conflicts had to be moved.) This year’s venue was at the American Institute of Philosophical and Cultural Thought, here in Southern Illinois. The topic is about learning the basic tools needed to genuinely follow Whitehead’s thought. The title is Learning the “Language,” where ‘language’ is very deliberately scare quoted.

This talk came hard on the heels (as opposed to “heals,” though that too is relevant in an ironic way) of a major surgery I’d just been through. While complicated enough under the best of circumstances, my procedure proved to be especially difficult. By all estimates, I came through it with flying colors, but I was still quite punchy at the time I made my presentation. I mention this in the talk.

I do word stuff with my mouth.

That being said, it came off quite well. The subject is “close to my heart,” as it were, and even working from nothing more than an outline I was able to present my case. As I say in the talk, my hope is and remains that the failings of the presentation and the presenter do not mask the fact that there is a legitimate issue and complaint involved in much of existing Whitehead scholarship. Below is the suggested reading list I handed out at the talk, which I’ve expanded a little for this blog post.

As a rule, I despise pictures of myself, and find videos simply unwatchable. I did finally watch this one, and it is less execrable than one might otherwise suppose.

Suggested Readings

Habit of thought:

Alfred North Whitehead, Principles of Mathematics (New York: Henry Holt, 1911.) Free for the download from Project Gutenberg, https://www.gutenberg.org/ebooks/41568

Philip J. Davis and Reuben Hersh, The Mathematical Experience (New York: Harper Paperbacks, 1999.) This book really cannot be praised enough, a book that everyone should read regardless of their interest in Whitehead.

Morris Kline, Mathematics for the Nonmathematician (Mineola: Dover Books, 1985.)

George Polya, Mathematics and Plausible Reasoning, vol. 1 & 2 (Princeton: Princeton University Press, 1990.)

Thomas Tymoczko (Editor), New Directions in the Philosophy of Mathematics (Princeton: Princeton University Press, 1998.) Part of the effort to understand mathematics as inquiry, rather than set theory done badly.

Hermann Weyl, Symmetry (Princeton: Princeton University Press, 1981.) One of those books that earns the label “classic,” this introduces some of the essential characteristics of group theory without getting into a lot of mathematics.

History:

Edna Kramer, Nature and Growth of Modern Mathematics (Princeton: Princeton University Press, 1981.) For my money, hands down the best general history out there. So of course it is out of print, impossible to find, and insanely expensive.

Morris Kline, Mathematical Thought From Ancient to Modern Times, volumes 1 – 3 (Oxford: Oxford University Press, 1990.) Pretty good, and at least it can be had without mortgaging your first born child.

Leo Corry, Modern Algebra and the Rise of Mathematical Structures (Basel: Birkhäuser, 2003.) This is an outstanding book, delving into the origins and problems that led to the emergence of abstract algebra, from the 1820’s to the 1940’s. Whitehead is discussed, but not very closely. Still, the nature of abstract algebra is developed in its historical context to a degree not available anywhere else. By my standards, the book is on the pricey side, but still well worth the investment

Abstract Algebra:

There are plenty of good books out there. The trouble is that it is quite difficult to get your head wrapped around the topic w/o some kind of mentor (i.e., math professor) there to help you out. Keep in mind that math books are the hardest to copy edit, because the editor must be as good at math as the author (which never happens.) So you’ll find yourself up against a wall where you’re wondering if you simply don’t understand what’s being said, or if there’s a typographical error in the text. I solved the problem by getting an MA at DePaul.

But if you want to give it a go on your own, most any intro book from Dover will do:

https://doverpublications.ecomm-search.com/search?keywords=abstract+algebra

Special mention for:

Nathan Jacobson, Basic Algebra, vol. I & II (Mineola: Dover Publishing, 2009.) These two volumes are exceptional for their comprehensiveness. I originally acquired these books as first edition hard covers, back when a hard cover cost a little less than a new car. I liked them well enough that when I discovered that Dover had them as eBooks I purchased them again so that I’d have a copy on my kindle. Be warned, though: the “basic” in the title is a tad misleading. These are the books that convinced me I needed to return to graduate school to learn abstract algebra.

Happy-Fluffy-Touchy-Feely-God-Talk

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Or

How a Vine can Kill a Tree

There is a certain group of scholars – I’ll name no names – which has taken on such a dominant position in Whitehead scholarship (at least, within the US), that one could arguably characterize their position as “hegemonic.” I have personally met a number of individuals associated with this group, whom I’ll simply call “The Group,” and freely admit that they are, as individuals, fine, generous, and altogether excellent folks. My complaint here – and I will be complaining rather sharply – is not with any of them as particular persons, but rather with the hegemonic direction in which The Group has taken Whitehead scholarship. That direction is what I am calling “Happy-Fluffy-Touchy-Feely-God-Talk” (HFTFGT from now on.)

Now, there is no question that Whitehead spoke of “God” extensively in his writings. Many people have the devil’s own time with such talk, those whom I’ll often characterize as “Ouchie Atheists,” for whom any such discussion drives them either into a fury or else into something like a cognitive anaphylactic shock. (Sometimes both.) This is one of the lesser pities of our day and age, a consequence of neo-fascist Christian Dominionist fundamentalists having hijacked the word and all discussions thereof. It is additionally unfortunate with regard to Whitehead scholarship because his use of the “G-word” could easily be replaced throughout his text with the Greek word “arché,” which would eliminate at a stroke the difficulties the Ouchie Atheists have and (arguably, at least) make it possible for them to dive more deeply into Whitehead’s texts and arguments. But Whitehead was intransigent in his refusal to employ non-English words. “Atom” was an exception. Though it originated with the Greeks, it had by his time – both by convention and courtesy – been thoroughly adopted as “English.” This is a little ironic, since contrary to most physicists of his day, Whitehead continued to use it in the original Greek sense of “a-tomos,” meaning “uncut.” So an atom for Whitehead was not a microscopic corpuscle, but an undivided whole which could be of any size.

I like the word “arché” because it can be translated as “foundation/font,” and this is what Whitehead meant by “God”: the rational foundation of reality, and the font of creativity. (This latter is one of the things that distinguishes process philosophies from static, substance based ones: the universe is a process of creative advance.) Notice that I do not suggest the Greek word for “god,” “theos” (or possibly “theou,” my Greek is not very good.) This is a deliberate choice, readily justifiable by even a moderately close reading of what Whitehead actually says, particularly within the pages of his masterwork of metaphysics, Process and Reality (PR).

With, however, the exception of one sentence.

This sentence appears in the last few pages of PR, which are separated from the rest of the volume as Part V. The language and argument of this final, very short “part” is fundamentally different from the preceding hundreds-plus pages of text, and this radical difference has led some to wonder just how genuinely integral an element of the rest of the discussion it truly is. In these final, very few pages, Whitehead allows himself to slip into more poetic language, most particularly with the above mentioned one sentence – which I’ll not quote. (If you know, you know, and if you don’t you’ll recognize it instantly should you ever read PR to the end.) But members of The Group, and others sympathetic to their program, latched onto that one sentence and ran with it. They ran fast, long, and hard, and are still running. From this we get the HFTFGT of process theology.

And it has swallowed the scholarship whole. So much so that Whitehead’s triptych of 1919 – 1922 (Enquiry into The Principles of Natural Knowledge, The Concept of Nature, and The Principle of Relativity with Applications), a revolutionary re-evaluation of the entire philosophy of nature, have largely vanished from the canon of Whitehead’s works that are studied. (Let me reiterate that this is within the US. Chinese scholars, for example, recently celebrated the centennial of those works with no fewer than three separate conferences, one for each book.)

Even those works of Whitehead’s that do receive some attention receive it only selectively. Thus part IV of PR, for example, is often skipped over and ignored with students sometimes being told to ignore it because it is “irrelevant.” One might, alternatively, point out that part IV is the beating heart of Whitehead’s entire relational system, where he presents his mature mereotopology, his non-metrical theory of curvature (“flat loci”), his subtle theory of physical connectedness and causality (“strains”), his completed theory on the internalization of relatedness as the flipside to the theory of the externalization of relatedness found in part III, etc. But part IV also involves a lot of logical and mathematical thinking “stuff,” and so one can just skip over that because it doesn’t feed into HFTFGT. A more cautious reader might suspect that what this rather demonstrates is that it is HFTFGT that is flopping around looking for relevance. But such cautious readers are not being invited into the club, and their professors are not encouraging their students to adopt such cautious approaches.

It is partly as a result of this narrow and eminently disputable presentation of Whitehead’s philosophy that many outside the field who might otherwise profit from engaging with Whitehead’s ideas (especially persons in the sciences), explicitly reject the notion out of hand. Because, after all, Whitehead is “nothing more than” a lot of HFTFGT. And people “just know this to be the case” because they are constantly and loudly reminded of this “fact” by those experts who are only interested in HFTFGT.

(Of course, persons in the physical sciences tend to reject any suggestion of engaging in philosophy because it is, after all, philosophy. They often do this as they explicitly engage in philosophical discourse; and do so badly.)

Such a reductionist caricature of Whitehead’s thought is, of course, the worst sort grotesquely fatuous twaddle imaginable. Let me repeat, Whitehead wholly re-imagines Nature in a relationally robust and holistic framework that is original, insightful, and logically rigorous. But consider in comparison what your grasp of Christianity might be were it the case that all you ever heard about it came from the neo-fascist Christian Dominionist fundamentalists. Your idea of Christ would look more like Adolf Hitler. (By the bye, in contrast to the neo-fascists, the advocates of HFTFGT promote a vastly more Christ-inspired vision of God and the gospels that is genuinely loving and caring for ALL of creation.) And so it becomes increasingly difficult to even suggest to people who are not already heavily, even exclusively, invested in HFTFGT to cast even a casual eye on Whitehead’s work.

Which brings us to the matter of how a vine can kill a tree.

There is a method of killing a tree called “girdling.” A tree grows out as well as up. But if something is tightly bound around the outside of the trunk (it is “girdled”) the tree can no longer grow outwards. And it is these outer portions that carry the nutrients up the trunk to the rest of the tree. So the effect is like a garrote.

A vine is capable of girdling a tree. There is no malevolence involved, no ill or predatory intent; but the effect is the same. This is what ‘The Group’ is doing, I would argue, to the larger tree of Whitehead scholarship. (One of the ironies here is that they themselves are being girdled by the neo-fascist Christian Dominionist fundamentalists, who deny that liberal – never mind process – theology even qualifies as Christianity, or as anything other than the work of the Devil, even though this form of “devilry” is demonstrably truer to the Gospels. But just try to find someone who is not already an expert in the field who is even aware of the existence of process theology.)

I don’t want the HFTHGT people to go away, but I would like to see a serious effort on their part to acknowledge that their project emerges from a vanishingly small corner of Whitehead’s work. I don’t want to chop down the vine, but I would like the vine to stop strangling the tree. This would include exercising some genuine circumspection about what they attribute to Whitehead, as opposed to what they themselves rather freely speculate about, far beyond anything he – in his meticulous, mathematically rigorous and disciplined way – ever pretended to entertain.

Limits of Reason, 1.X … rev Ϡ

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Yes, I have been away from this blog for a long time. No, I am not going to talk about that.

I’ve been thinking a great deal about the connections (possible and otherwise) between various aspects of theoretical computer science, and reasoning in general and empirical science in particular. When I talk about “theoretical computer science”, I definitely do not mean applied problems such as the rendered graphics in an FPSRPG (and that shot most assuredly DID hit, you cheating bastards!) No, I mean the mathematical and logical puzzles associated with what it is possible to compute, in the absolute limit of possibility, and what (among that collection of puzzles) can be reasonably computed given the physical and temporal constraints of the universe.

Computability: What can or cannot be computed, period. For example, can you write a program that will test all other programs to see if they run. Absolutely not! Take the program itself, flip a few relations, and then feed that to itself and you will force it into an infinite loop that it cannot solve. Due to the logician Alonzo Church, this is known as the “Halting Problem.” One of the favorite ways of demonstrating a problem is unsolvable is by proving its solution would also solve the Halting Problem.

Say Goodbye, It’s Independence Day.*

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*(A line from a Springsteen song, in case you didn’t know.)

With the “Supreme” Court and it’s viciously ideological rightwing members now stampeding the United States full-tilt to all-out fascism, there is little to celebrate this July 4th. Even if Trump does not run or does not win (for whatever reason, including federal indictments), even if, by some incomprehensible miracle, the moves the court will make in its next session do not entirely erase the majority of voters voices from our political enterprise, matters remain dire.

It is clear that the overwhelming majority of the Republican party has abandoned any pretense of decency, of reason, and most certainly of democracy. Absent a series of what appears, as of this writing, to be highly unlikely events, the experiment that was the United States is done for. So, on this holiday, I leave you with these “postcards.”

(I add this last one for those who think there’s no difference between the two.)

So this evening while you’re testing your luck at whether or not you blow your hand(s) off, and terrorizing the dogs, cats, birds, veterans with PTSD, etc, in your neighborhood with explosive devices, perhaps cast a thought to little things like the Declaration of Independence and the Constitution of the United States, and whether these things actually matter to you, or if all you care about is feeling good about white supremacism and other fascist instruments of hegemonic domination.

This Is Not a Person Either

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This has been hard for me, getting to this place.

Getting to this place where I can write.

Getting to this place where I can write what is obvious.

It is not an accident that within a matter of a couple of days, this “Supreme” court has viciously curtailed human rights while indefensibly expanding gun rights. But take a look at the picture below. Look at it carefully. This is not a person.

This is a variant on the AR-15 assault rifle. Infantile purists will delaminate if you say “AR” stands for “assault rifle.”

But if you are a woman, if you are non-binary, LGBTQIA+, it basically has more rights before this court than you do. In other words, before this court, you are not a person. Add BIPOC to the previous list, because unless you are white and male, if you go parading around with an assault weapon you are unlikely to be allowed to survive, never mind pass unharrassed, by our massively militarized Law Enforcement.