Western Academic Logic Has Broken Through! (Maybe?)

"An increasing number of logicians are coming to think that Aristotelian logic is inadequate." - Graham Priest, in a 2014 article I link to below.

Albert Einstein was asked to contribute an essay on Bertrand Russell for a compendium on Lord R, and  it eventually appeared in Volume V of The Library of Living Philosophers, edited by P.A. Schilpp, 1944. In "Remarks On Bertrand Russell's Theory of Knowledge," Einstein said he immediately said yes when asked to write on Bertie, because, though he didn't enjoy a lot of contemporary scientific writers, he'd spent "innumerable happy hours" reading Russell, and the only writer he enjoyed more was Thorstein Veblen (who, incidentally, forecasted the obvious state of academia today, but in 1899!). Then Einstein realized he had a lot of cramming to do: he'd limited himself to physics, and had embarked on Russell's turf, which Einstein found "slippery." It seems clear from the outset that Einstein is dubious about Russell's field - logic - and how it undergirds mathematics and (maybe?) all knowledge.

The key questions for Einstein are: "What knowledge is pure thought able to supply independent of sense perception? Is there any such knowledge? If not, what precisely is the relation between our knowledge and the raw materials furnished by sense impressions?" Einstein's essay was published in 1944.

My experience with reading on various logics is sketchy. I'm not of a logical bent temperamentally - I tend to think Rhetoric has more dramatic and personal effects, socially -  and yet I find any forays into Boolean thought, logic trees, Aristotle, informal fallacies, logical paradoxes, and how number theory fuses with logic? It's all delightful: I always cop an intellectual buzz if I get deep enough to "get lost"in it. Reading logic books feels a lot like reading linguistic books: I get to the point where all I can see in my mind's eye is absurdities, Cheshire Cats smiles floating before my eyes, the worm ouroburos eating its own tail, the seemingly surrealistic glint of reading a book about how words work, which uses words itself. A world filled with Dali-esque melting watches. For starters.

On a certain level, I think logic is bunk, or tends to the buncombe. And yet, it underpins all our advanced technology, including this thing I'm using right now to get my points across, so we must take It seriously. I think logic works fantastically well at very small levels, like logic gates in circuitry. I'm not sure it works all that well when describing society or as an approximation of the language of everyday living in the Cosmic Goof. Ahhh...but maybe I'm not reading the right type of logic? Or: how am I defining logic?

Every thought, even unconscious thought, can and has been modeled as the logic of neurons firing in a massive parallelism, involving ion channels, action potentials, axons and dendritic spines, all-or-nothing events, and, occurring in the synaptic clefts: the constant release and re-uptaking of neurotransmitting chemical messengers. I'm fascinated by the neuro-logic that does all this and creates circuits of perceptual frames commonly called metaphors, but I (logically) digress...

A pretty cool article in one of my favorite online magazines, Aeon, recently ran an essay by a philosopher named Graham Priest, and it's called "Beyond True and False,"and in it Priest argues that Western logicians, who have long dismissed Buddhist logic as mumbo-jumbo and "mysticism" have come around to an appreciation of it. The 2nd CE Mahayana Buddhist thinker Nagarjuna had insisted that "things derive their nature by mutual independence and are nothing in themselves." Any "thing" is empty, and yet it exists. We can only talk about a thing's "nature" when we include it in a field of other things. If you grok this immediately, you're the sort of person I love to party with.

Priest was one of the developers of something called plurivalent logic in the 1980s, and he asserts that neither he nor his colleagues knew anything about Mahayana Buddhist logic at the time...but their thinking had arrived at a very similar place. It's a breezy essay and delivered the reading-about-logic goods enough for me to get "high" off it. Try it, if you haven't already. It combines Buddhism and databases; what's not to like?

So, for Aristotle, there was only True or False, although I think Aristotle is more complicated than Priest lays him out here. The weird thing about Aristotle, as I continue to read him: his uber-famous book on Logic seems less nuanced about "reality" than his long, compendious and damned amazing book on Metaphysics. In his Logic, there is the Principle of Non-Contradiction (PNC) and the Principle of the Excluded Middle (PEM), which never made sense to me, irregardless the many modes I used to wrap my neurons around it. Methinks THC and CBD tend to dissolve PEM, PDQ.

Nagarjuna was working with the 600-plus year Buddhistic system of the catuskoti, or the logic of "four corners." Some statements are True, some False, just like Aristotle (it's highly unlikely Nagarjuna read Aristotle). But: Buddhistic logic had two more values: some statements are Both True and False; the fourth value was: some statements are Neither True nor False. Aristotle had actually briefly addressed the idea that a statement could be Both True and False, as if it were relatively trivial: these had to do with statements about future events. These statements violated his Principle of Non-Contradiction, so he seems to have wanted it to seem trivial.

Bertrand Russell, along with Alfred North Whitehead, had tried to use logical set theory to firmly put mathematics on a solid foundation. Indeed, the set of all sets is a member of itself; the set of all cats is not a cat, so it's not a member of the set of cats. (By the way: I find set theory a sure buzz, not unlike one small toke of very potent weed; your mileage may vary.) The problem of statements that were self-referential proved Russell's and Whitehead's undoing. Remember the Barber Paradox? Or simply the hilariously vexing problem of this sentence?:

                                            This statement is false.

So yea: let's apply Aristotle's PNC to the set of all the sets that are not members of themselves.

Well, okay, after awhile my head explodes; my consciousness becomes pixillated and then spontaneously rearranges into a collage of shards of paisleys and encaustic purples and pinks. I like it.

Back to Priest's essay: I didn't know about Relevant Logic from the 1960s, which presaged Priest's and his colleagues' Plurivalent Logic. I hadn't known about the 1905 logical proof about ordinal numbers and the limit of noun phrases in a language with a finite vocabulary, from the Hungarian Julius Konig (worth a buzz all by itself). What a cool article.

When Priest tells us that Nagarjuna said that language frames our conventional "reality" but "beneath" this is ultimate reality that we can experience only in special states - such as meditation - but we can't say anything about this "ultimate reality" because it's ineffable and that saying anything about it puts us back into conventional "reality" (<-----I have made it a practice to put quotes around the word "reality" to draw attention to the fierce contentiousness of the term)...Dude! This guy was saying this in the 2nd century of the Common Era.

So the high point (and I do mean "high") of Priest's essay was the discussion about two different ineffable "realities": 1.) the "real" one
                                2.) the "nominal" one; the one where we use language to talk about how wild and transcendent our experience was of the ineffable.

Let us apply good ol' Aristotle's PNC to the above? If it's "ineffable" we can't say anything, period, right? It contradicts itself.

Or maybe: I say all we can say is what we can say, along with lots of hand waving and gestures and hopping up and down, dancing. Jumping outside these particular logic systems (or "Jootsing" as Douglas Hofstadter coined it: jumping outside of the system) into another logical system, let us say that, under the "game rules" of Nagarjuna and Aristotle, we can speak of anything, even the "ineffable." The problem is, we might find ourselves in a straightjacket on the way to the Funny Farm. Either that or find we've obtained disciples, so may as well go for the big bucks with a New Religion.

It turns out that when you convert a logical function (which only relates to ONE other thing, such as your biological father) to relational ones (which can derive any number of outputs), you can arrive at a Six-Value Relational Logic - Priest and Co's Plurivalent Logic. In this system, statements can be:

1. True
2. False
3. True and False (EX: "Both crows and horses can fly." Or better: "This is a sentence that has twenty-three words in it.")
4. Neither True nor False
5. Ineffable
6. Both True and Ineffable (Konig's thing, as shown in the article.)

Furthermore, with relations, these values become fuzzified. Indeed, my Generalist's approach to understandings of logical systems sees Plurivalent Logic as almost the same as Fuzzy Logic, developed by Lofti Zadeh around the same time Priest and Co were doing their thang.

By the way: has anyone found a value that is Both False and Ineffable? If so, I implore urgently: send it to me via Angels and/or quantum encryption, or a secret, coded message in tomorrow's crossword puzzle. Muchas gracias.

Western Counterculture Intellects Were Ahead of the Academics? Maybe?
Jeez! I like Priest for his wowee-gee presentation of developments in academic logic in the 20th century, but fer crissakes Priest!: read Gregory Bateson's work from the 1960s and 70s: he was pushing for a logic of relations then. And Robert Anton Wilson was telling his dope-smoking intellectual readers about multivalent logics in the 1960s: Von Neumann's quantum logic of "maybe" as a third value beyond Aristotle's True and False. RAW also turned the present writer (OG) onto Anatole Rapoport's four valued logic of True, False, Indeterminate, and Meaningless. RAW also showed how Korzybski, by 1933, had developed an Infinite-Valued Logic in which we must use our wits to assign probabilities to the veridicality of statements. RAW even promulgated the logic of "Sri Syadasti," in the serious-joke religion of Discordianism, which was developed in the 1960s. Note the many-valued stoner logic there! It seems to anticipate Priest and Co's 1980s Plurivalent Logic by at least a decade. (Could it have secretly influenced the academics?) Timothy Leary developed, in the early 1970s, a type of neuro-logic that was embedded in a system of phenomenological "circuits" in human minds that developed according to genes, accidents, habits, learning, the culture a person was born into, the language they used, their education, and their openness to novelty. These counterculture thinkers noted and cited a plethora of examples on non- and anti-Aristotelian thinking that had run through world cultures, running back to Taoism and the I Ching.

So: I've seen this many times before. The longtime academic seems to either not know, or knows but pretends to not know, that things are muddied once they survey the vast historical mindscape outside their Ivory Towers. I've seen it so often I expect it. Or hell: maybe Priest is at best oblivious. Or worse: dismissive. At least Priest admits Aristotle's bivalent logic has major problems and that 1800 years ago a non-Westerner was prefiguring the thought systems that he and his friends thought they were inventing. And also, Priest is right: seemingly "pure" thought-systems in logic and math later on prove to be surprisingly useful in the workaday world in the sensual, sensory, existential, phenomenological space-time continuum.

Works Consulted:
- "The Logic of Buddhist Philosophy," by Graham Priest, Aeon.
- cool interview of Graham Priest by Richard Marshall. Priest seems pretty cool for an academic.
-The Fringes of Reason: A Whole Earth Catalog: "Beyond True and False: A Sneaky Quiz With Subversive Commentary," by Robert Anton Wilson, pp.170-173. For Generalists interested in multivalent logics, this piece complements Graham Priest's piece on Buddhist philosophy, above.
-Ideas and Opinions, Albert Einstein. "Remarks On Bertrand Russell's Theory of Knowledge," pp.18-24
-The Chinese Written Character As A Medium For Poetry, by Ernest Fenollosa and Ezra Pound (1936)
-Steps To An Ecology of Mind, by Gregory Bateson
-Godel, Escher, Bach, by Douglas Hofstadter
-Laws of Form, by G. Spencer Brown
-Fuzzy Thinking: The New Science of Fuzzy Logic, by Bart Kosko
-Prometheus Rising, By Robert Anton Wilson, esp. pp.217-252