Overweening Generalist

Friday, May 23, 2014

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

12 comments:

Roman Tsivkin said...

Lovely stuff, Michael. I'm a big fan of the philosopher/logician/mathematician/musician/magician Raymond Smullyan, who's penned quite a few very entertaining books on Godelian logic puzzles...his non-logic books are excellent too (e.g. The Tao Is Silent). I found this list of self-annihilating statements through Smullyan: https://www.ling.upenn.edu/~rclark/gorn.html
Btw, Ray's birthday is coming up -- he is going to be 95 on May 25th, and he is still writing & having fun.
Cheers,
Roman

Eric Wagner said...

Terrific piece. Some passage in post-1945 Cantos by Pound might seem false and ineffable.

I find it interesting that you use the word "grok." Have you read Stranger in a Strange Land? I loved that book so much in high school. I read it in German a few years ago. I don't know German very well, but I remembered the novel so well that I enjoyed the experience.

michael said...

@Roman-

I had a favorite Smullyan quote from my logic notes ready to go for this piece, but it didn't make it; I should've shoehorned it in:

"Of all the lies people tell about me, half of them are true."

Smullyan delivers the logic-buzz goods every time for me, and Happy 95th trip around the sun, Ray!

The intersection of logic and humor seems endlessly fascinating to me. Which reminds me of George Carlin's news that "Medical researchers have discovered a new disease that has no symptoms. It is impossible to detect, and there is no known cure. Fortunately, no cases have been reported thus far."

Anonymous said...

A rich and meaty stew of ideations.

I was quite impressed while young
that Booles logics were a mathematic
parlour game with no external use,
then some wag tried to build a few
switches and realized that logic of
the boolean variety described it.

In the 70s the electronic gadgetry
had evolved beyond Aristotles odd
binary either or but nothing else.
Boolean logics were extended by a
device called tri-stating so you
had on/off (binary) disconnection
(tri-stating)elctronically.

This gives you a four valued truth
table for each individual input
or output. Most comp logic is
taught as on/off binary because
it's easier to understand.

The true horror is only seen if
you use an analog scope to look
at the real wires, there all you
have is a noisy mess which has a
probability of being interpreted
as a one or a zero by what it is
connected to. This is what happens
when the pristine math concepts
are dragged from their platonic
perch into messy utility. We now
cover this up by using digital
scopes which display nice neat
ons and offs, masking from the
eyes of youth the ugliness about
the real world.

Electronics isn't dumb, it uses
what it can grab from academe as
useful fictions to avoid startling
the young. Priest is just doing
what everybody does, modelling a
world with the building blocks he
has access to. Narrative always
gets pruned and the knowledge gap
between human and omniscient is
Lovecraftian.

I consider the desire to not find
out an unforgiveable sin against
the self. This hasn't made me too
popular but it's a small price to
pay considering the alternative
I see portrayed around me.

The sheer nuttiness of epistemological cartoons as a basis
for thinking about "reality",
whatever reality means is amazing
to watch. As in those who agree
are good, those who disagree are
evil. And since Aristotle said
there is no middle possibility
you have a neatly packaged on/off
infallible logic which cannot in
any way match the world.

You see this in strict materialism
hilariously, the idea that there
are real bits buried way down in
the microscopic is as dead as a
Dodo bird, but most of thinking
is done with the fiction of a
solid matter world.

Then you get to the neural epic
of today, when you measure the
actions against volition you find
the body already acting before
the mind has decided to. At this
point all the fuses blow (WTF!!)
because the part people think of
as themselves is supposed to be
in charge. We like explanations
to fit our neatly constructed
fictions about ourselves. As
Freud demolished some we are about
to see a lot more fade under the
glare of science. It's all about
the struggle for meaning which
is the only interesting game in
town. IMHO the need for a better
E Cartoon isn't going to cut it.
We are either going to understand
the world or become extinct.
See how convenient a binary choice
is for incentivising...GRIN

michael said...

@Eric-

Thanks!

I've used "grok" many times and of course I've read SIASL.

I've made a note to re-read post-1945 Cantos with the idea of some statements being both False and Ineffable, but the only logical way I understand to do this is via Konig's use of a Cantor-like infinity, with numbers mapped along noun phrases in a known language in order to be able to "say" something that's both True and Ineffable. I'll take the challenge though.

Cleveland Okie (Tom Jackson) said...

Michael,

When I was in college, my roommate took a logic course and would entertain me with stories about it. The professor delighted in attacking illogical statements made by Spock.

"It combines Buddhism and databases; what's not to like?" Although I didn't really get into it in my review of Ramez Naam's "Nexus" on my blog, there's a lot of Buddhism in the novel. I'm sure you'd find the book interesting.

michael said...

@Anon-

Thanks for the choice comment, as always.

Korzybski and Bohr said there probably was no deep "reality" and we could only make maps of whatever we're trying to describe, and no matter how finely detailed we make the maps, they will never match the territory. Or this is my thumbnail map of what I think both of those guys were saying...

What about RAW's "maybe logic" as a usable-for-John Q Public-walking-around-epistemology?

In RAW's long introduction to Rodolfo Scarfolotto's book _The Alchemy of Opposites_, RAW cites the Jains:

"The Jains, a little-known Hindic religio-philosophical movement, managed to combine Von Neumann's maybe-logic (2500 years before he invented it) with Buddhist detachment and produced a 7-valued logic:

"Maybe it is.
Maybe it is not.
Maybe it is and is not.
Maybe it is indeterminate.
Maybe it is and and it is indeterminate.
Maybe it is not and it is indeterminate.
Maybe it is and it is not and it is indeterminate."
-p.16, op cit

michael said...

@Tom-

I read your review of Ramez Naam's _Nexus_ and it sounded really cool; how will I fit it in with all my other reading projects though?

The preceding is a cool problem to have.

George Carlin put a brilliant comic spin on Zeno's arrow paradox, the one the proved movement was impossible. He notes that "it is said" that we see our lives flash before our eyes during sudden death. So imagine you're swimming in the ocean, get caught in a riptide and it pulls you out to sea, your muscles tire, you begin to swallow water, and you know suddenly you're a goner. "The flashback movie begins to roll."

"It seems to me that if it's a flashback of your entire life, you'd have to watch the whole thing, and that would include the ending. Which means seeing yourself arrive at the beach, walk into the surf, start to drown, and have the whole movie start over again. Therefore you'd have to watch it a second time, which would include you arriving at the beach, walking into the surf, and...you get what I mean? Thanks to the flashback, you can never die. The movie runs forever."
-Napalm and Silly Putty, p.193

Once I read this bit, I never heard "my life flashed before my eyes" the same way I used to.

Woody Allen wrote - I can't remember where - that he had his life flash before his eyes, and recounted a series of vivid images he saw, like goin' down to the country store to buy some gingham for Betty-Lou; goin' down to the swimmin' hole to catch a mess o' catfish...then realized the "life" that he was experiencing was someone else's.

That would seem like such a rip-off! But as you'll be dead in a moment, what does it matter?

Thorfinn Axelson said...

Nice post. All Life is process, all business is service. These things that the specialized experts have concentrated on for so long are real enough, to them, to affirm 'the world of things', to them. I don't believe the mind is brain-local, just because the hardware resonates on MRI...I can't find Howard Stern inside my transistor radio either. Doesn't mean he is not "in there", for someone else.
My great Aunt believed my friend could see her, when he appeared in her living room on TV during our first rural news broadcasts, and would make an effort to tidy up before he 'arrived'. Compound the ungoing confusion with that of the nature of time, another thing-abstract, clock signal has usurped the flow of process and has begged Stanford Fleming's, and Musssolini's to make the train run around IT. The train, the engine, would be timed quite fine, without the clock. Time is fake, things are fake, but the believe in them, not intellectually, as Micheal is so engaging in explicating, but functionally, is real. When the burning bush, or the broadcast box speaks, what is the process, and what is the business? We are one. Mind your Business. Someday our grandchildren will scoff at the word libertarian as another cult of intellectuallys trying to secure the best things in life, a product of product ontology, not service. This is when RAW states "not that kind of libertarian" in reference to the things we label 'poor people'. He didn't believe in poor people, only poor process, and poor service, likely. This quality of service Is why I read your blog, and if someone hated rich people, I believe RAW would just as likely leave them to the sum of their parts as well. I have read All Tom Robbins' novels, but I can't say if they stand up. Like the post on smell reminded me of Jitterbug Perfume, this puts me in mind of Still Life with Woodpecker. Tom Jackson, along with Michael, should both be rewarded for their service to the RAW process, maybe? Too bad there is not a thing in the world to give them. Keep up the good process! Ax

Anonymous said...

Now I'm off on another tangent as
Ax triggered the thoughtchain.

When do you become "poor" ?
Is it birth into a family of poor
people, is it when you finally get
a low-paying job, or is it after
you graduate with crushing student
debt, or when you are forced into
Bankruptcy, how do rain forest
tribal folk fit into the chosen
definition ?

My favorite part of Stranger was
the opportunity to see it enacted
as a real life drama in Waco with
Khoresh (the roasted Lamb of God)
playing the part of the Martian
whose thoughts deviated from what
Janet Reno thought was "good".
The best part was the commercials
interspersed with the dramatic
events. This is how great religions are born, from States
over-reach to create martyrs out
of relatively innocous loons.

You can use this to riff on more
uses of poor.

What does a school system which
can not teach reading and spelling
have to do with poor ?

Thorfinn Axelson said...

What about poor self esteem. The six pillars of self esteem, by Rand's boyfriend, Nathanial Branden. Poor is in your head, RAW would have said, without a doubt, was he ever poor, on welfare. sure. But not without selfreflectionately inducing himself into a richer mindset. Poor is an affirmation. To have nothing is not poverty. It is something else. Even in selling my Jack Lalane Juicer to make rent, I was never poor. The kids in the East Congo, or the milkweeds of the UN; who is poor? The poorest man in the united states (he stands for all the debt) is Obama. As John Prine sang, "Don't you tell me that the white house is my home." Who made Who made who poor? Who?

Drew Zi said...

"Money is a sign of poverty"

-Iain Banks.