Very nice Kant-antinomy piece. Some people actually read Kant only for the ethics.
Hard to imagine.
Inspired by your paper, I boldly advocate accepting that we live in an antinomic universe. Antinomies are everywhere and increasing rapidly --- sort like tribbles . . . if tribbles had fangs . . . and an injectable neurotoxin.
Two quick cases.
(1) The Quantum Physics notion of superposition. A particle may have, say, spin up and spin down. This is NOT a contradiction, say the physicists, since the two spins are in superposition, they are not occurring at the same time and place. But this is just Quantum physicist trepidation: A single particle can have 2 opposing spins at the same time and place. How? Shrug: The spins are antinomies — contradictory. This happens throughout physics.
(2) Consider the set of even numbers (E). It has the same cardinality as the set of natural numbers (N), aleph-null. Proof: E can be put into one-to-one correspondence with N. So, E and N are the same “size.” But clearly E is “smaller” than N: E lacks all the odd numbers but the odds are completely in attendance in N, along with everything else. So E is both smaller than and the same size as N. Mathematicians hate this, by and large. But some embrace it. And of course, math is crawling with antinomies.
We philosophers should embrace that we live in an Antinomic Universe. Contradiction is that rough beast, it’s hour come round at last . . . after logical empiricism and all similar big-tent philosophies since Parmenides have failed . . . slouching towards Athens to be born.
Or, to end on a more upbeat note: There is grandeur in this view of our universe with its contradictory powers breathed into all. And whilst this planet has gone cycling on according to the more-or-less fixed law of gravity, endless forms most beautiful and most wonderful have been and still are being . . . contradictory.
Yeah, I’d go even further. Our universe doesn’t just happen to be antinomic. All creation is just division in nothing: 0 and 1, P and not-P, matter and anti-matter. Binary code is the clearest case: its zeros and ones are pure divisions in nothing. And you can’t write a program without both ones and zeros. So basically you get “something” — P and not P — when you divide nothing. And so, when you discover the true antinomies, you’re discovering the basic building blocks of reality.
such great writing! lax ethics rules and safe spaces for antinomies. a wishbone breaking at reason. a house divided must stand. and i especially appreciated the "erstwhile".
Excellent, excellent post. I better understand now where you were going with diagonalization.
From my perspective, the dialectics "come in fours" (less a claim of reality and more a claim on recursively productive negotiation with a hint of perhaps also real). Antinomies arise, according to my telling (please let me know if I ever say something that has been said before, i am more well-dabbled than well-read) as a result of trivializing OR idealizing two of the four, the result of which limits insights to moving from "false dichotomies" to continua or to boiling down "false continua" to binaries.
A reframing of the whole as including a social element whereby we must always negotiate the difference and propriety of "coherence" vs "adherence" is akin to a "little bang," a spontaneous negotiation of specificity vs sensitivity and cohesion vs comprehensiveness. Rather than effectively reifying the "bottom-up construction" metaphor most common to analytics, this negotiation is more middle-out and outside-in. The more coherent a concept, the more beneficial adherence becomes. The more adherent someone is, the more is to be gained from decoherence.
This creates a kind binocular vision where even confirmation bias (what is coherent with individual experience, often reduced to what one "wants" to see) "opposes" "conformation bias (conformity and adherence to narratives that signal that confirmity, or what one "must" see in the social sense). At the same time, there is another negotiation of what to do with the decoherence of the two: a bias toward agency within whatever context (defy the group in the name of [idealized] autonomy, deny the self in the name of [idealized] unity,) or a bias toward fluidity (trivialize the social pressures in the name of self-esteem, defer to the group ["go with the flow"] in the name of well-being).
The best achievable is, in essence, an "equivalence principle" where coherence, adherence and decoherence are indifferentiable within a reference frame. But the question remains what we might find once we step out of the elevator and how it would change our treatment of the next elevator we find ourselves stuck in.
Yeah, I think we’re on the same page. What I call positive and negative diagonalization might just map onto what you call trivializing and idealizing or middle-out/outside-in. But there may be some differences too. Alas I’m not sure I understand our respective methodologies well enough to know what they might be :)
Have you done any thinking along the lines of specialized archetypes? The ones I have been using are scientist v artist, which you have echoed here with mathematician v poet, and pragmatist v Philosopher. Framed as diagonalization, I would say the diagonals of two opposing would approximate to the specializations of the other two. However, there is also a mirrored version of each specialization. For example, "pseudoscience" I see as a natural opposition for those who "structure" their perspective according to the very real over-adherence/conformity of the sciences. They are attempting to "decohere." To fight "conformation bias," they overengage "confirmation bias," errors of commission afforded on the perceived magnitude of errors of omission.
"Trivialization" likewise has two forms. One is necessary relative to capacity limitation and the attempt to "trivialize noise," a tradeoff in attempting coherence. The other is the "near-enemy" (in the Buddhist sense) of conflating sufficiency with "absolute sufficiency." This can be done by rationalizing or false-dichotomizing sufficiency/triviality according to and within the paradigm to which one is adhering. Sufficient, else trivial. Necessary, else arbitrary. Elegant, else mundane. Symmetrical, else biased.
In my typical fashion, I call this "Bae's Ifforelse" which is a very elaborate means of proving something is Bae by proving that it is not not Bae. 🫠
Here’s my simplified version. Mathematician (clarity/triviality) meets poet (profundity/obscurity) and synthesizes into clarity plus profundity or triviality plus obscurity. Typically the positive synthesis prevails in the beginning but over time degrades into the negative. That’s why you hate your favorite band’s new album :)
I like it! Yours better captures the real personalities of people. Mine is meant to be generalizable to "everything human," but therefore misses on some of the richness in "being a real human."
For example, where you have mathematical clarity/triviality, I have an "archetypical scientist" specializing in "specificity" and struggling with its near enemy "insensitivity." Thus, when a scientist declares something exact [idealized specificity], you can expect that he is "rounding" via insensitive means, but you shouldn't expect know exactly where, for what purpose or the magnitude of the error. The "artist" specializes in sensitivity, but struggles with the near enemy of "inspecificity" (equivocation). To claim that something is "perfect" or "ideal" is essentially "idealism squared" (declaring something ideal explicitly/redundantly rather than implicitly). Hence why "imperfection is the ideal" is a thing we can both understand and find examples that more or less match.
"Trivialization" and other reductive attributions are not so much a function of what is being strategically ignored or abstracted away, but rather the purpose of the strategy invoked... which is hard to always know as the individual doing the trivializing, and perhaps unknowable without outside and opposing perspectives.
So yes, much overlap.
Oh, I should also note that an important implication (if I am right) is that abstraction is rightly seen as opposed to generalization, and maths is a special case that itself cannot be generalized, and to do so is to either reify the quant or to equivocate the Qual.
Also, in response to: "Structure is just parts in opposition. And parts in opposition are the real hopeless romantics because they truly need each other."
Structure/process/influence, in my conception of them, USE the search for (sensitivity to) equivalence principles to communicate a reference frame. For example, try to picture what I mean by "the process of erosion" and it is essentially without an anchor. If, however, I specify a structure (a coastline, a riverbed, a landmass), then you are able to triangulate what counts as "influence" or "confluence" between/among the structures and processes. I refer to these as "chimeraphoric sets." There are other such sets, but if we focus on your treatment of "structure" here, notice how "opposition" could also be process or influence. In the typical definition of structure, the "arrangment" of parts implies a process of arrangement and influences for doing so. "Influence" is based on "inflow," which intuitively matches the idea that to "influence" a river's flow (the process), it is best to instead act against the riverbed (the structure). Boiled down, structure is "that which is most stable within a frame of reference," process is "that change which is most stable" within a frame of reference, and influence is "that relation between or among stabilities within a frame of reference."
Much more to be said, of course, but this seemed like a unique example of how you are communicating your reference frame. That you see structure as defined by its "internal oppositions" meand, to me, that you see this opposition as the least changing element of the reference frame you are proposing. A kind of "generative opposition," which I much appreciate.
Notice also how in the bottom-up constructionist metaphor, the structure is a single (idealization/sterilization via abstraction) "distributive" element where the resistance to change is defined by its weakest point relative to any given "applied force" (generalization of influence and conflation/trivialization of processes). One of my overall points to the scientist archetype is that the concept of "structure" is an equivalence principle in which one cannot declare that it is more abstract than general, nor that it was abstracted before it was generalized. That is true of "mathematical structures" as much as "the structure of poetry." We cannot tell whether we are reducing to "simplest" or "fewest" parts, projecting it as syntactical, or what combination thereof. We also have no means of establishing its sufficiency or necessity. What we can say is that something seemed "sufficiently coherent" such that we stopped looking elsewhere and began to adhere instead, or we can say that something adhered sufficiently to the expectation or prediction of it so as to seem coherent. However, the modern Adherence paradigm most commonly conflates their local (individual or group) sense of "sufficiently exact" (the product of a process) with "exactly sufficient" (the structure of structure, ad infinitum, amen) the latter being provably incoherent for beings of non-infinite affordances.
This piece is great in many ways. I think it is especially great that the antinomy of antinomy, as I understand it, is that we can't think with antinomies and can't think without them.
You say that the analytic-continental divide consists at least partly in differing attitudes toward contradiction--but is that really so? Analytics don't use exactness solely to show that neither side can be correct, after all. Some of us take a more ecumenical approach to antinomies: trying to show what is right about both sides by reconciling their main ideas in the shape of a hybrid view.
That’s a nice way to put it. I was thinking: we must take antinomies seriously; we can’t take antinomies seriously. But I really like your version.
The analytic approach typically involves taking sides. But different analytic philosophers will take different sides. And when neither can convince the other, they’ll look to hybrid views wherein further conditions —epicycles — are offered as a kind of tribute to the opposition. But they rarely ask the Kantian question of why both sides strike us as compelling in the first place. It’s like they want to resolve the antinomy before they’ve understood its source.
Very nice Kant-antinomy piece. Some people actually read Kant only for the ethics.
Hard to imagine.
Inspired by your paper, I boldly advocate accepting that we live in an antinomic universe. Antinomies are everywhere and increasing rapidly --- sort like tribbles . . . if tribbles had fangs . . . and an injectable neurotoxin.
Two quick cases.
(1) The Quantum Physics notion of superposition. A particle may have, say, spin up and spin down. This is NOT a contradiction, say the physicists, since the two spins are in superposition, they are not occurring at the same time and place. But this is just Quantum physicist trepidation: A single particle can have 2 opposing spins at the same time and place. How? Shrug: The spins are antinomies — contradictory. This happens throughout physics.
(2) Consider the set of even numbers (E). It has the same cardinality as the set of natural numbers (N), aleph-null. Proof: E can be put into one-to-one correspondence with N. So, E and N are the same “size.” But clearly E is “smaller” than N: E lacks all the odd numbers but the odds are completely in attendance in N, along with everything else. So E is both smaller than and the same size as N. Mathematicians hate this, by and large. But some embrace it. And of course, math is crawling with antinomies.
We philosophers should embrace that we live in an Antinomic Universe. Contradiction is that rough beast, it’s hour come round at last . . . after logical empiricism and all similar big-tent philosophies since Parmenides have failed . . . slouching towards Athens to be born.
Or, to end on a more upbeat note: There is grandeur in this view of our universe with its contradictory powers breathed into all. And whilst this planet has gone cycling on according to the more-or-less fixed law of gravity, endless forms most beautiful and most wonderful have been and still are being . . . contradictory.
Yeah, I’d go even further. Our universe doesn’t just happen to be antinomic. All creation is just division in nothing: 0 and 1, P and not-P, matter and anti-matter. Binary code is the clearest case: its zeros and ones are pure divisions in nothing. And you can’t write a program without both ones and zeros. So basically you get “something” — P and not P — when you divide nothing. And so, when you discover the true antinomies, you’re discovering the basic building blocks of reality.
Of course (slapping head). This is a good insight. Antinomies are the foundation of it all.
such great writing! lax ethics rules and safe spaces for antinomies. a wishbone breaking at reason. a house divided must stand. and i especially appreciated the "erstwhile".
Excellent, excellent post. I better understand now where you were going with diagonalization.
From my perspective, the dialectics "come in fours" (less a claim of reality and more a claim on recursively productive negotiation with a hint of perhaps also real). Antinomies arise, according to my telling (please let me know if I ever say something that has been said before, i am more well-dabbled than well-read) as a result of trivializing OR idealizing two of the four, the result of which limits insights to moving from "false dichotomies" to continua or to boiling down "false continua" to binaries.
A reframing of the whole as including a social element whereby we must always negotiate the difference and propriety of "coherence" vs "adherence" is akin to a "little bang," a spontaneous negotiation of specificity vs sensitivity and cohesion vs comprehensiveness. Rather than effectively reifying the "bottom-up construction" metaphor most common to analytics, this negotiation is more middle-out and outside-in. The more coherent a concept, the more beneficial adherence becomes. The more adherent someone is, the more is to be gained from decoherence.
This creates a kind binocular vision where even confirmation bias (what is coherent with individual experience, often reduced to what one "wants" to see) "opposes" "conformation bias (conformity and adherence to narratives that signal that confirmity, or what one "must" see in the social sense). At the same time, there is another negotiation of what to do with the decoherence of the two: a bias toward agency within whatever context (defy the group in the name of [idealized] autonomy, deny the self in the name of [idealized] unity,) or a bias toward fluidity (trivialize the social pressures in the name of self-esteem, defer to the group ["go with the flow"] in the name of well-being).
The best achievable is, in essence, an "equivalence principle" where coherence, adherence and decoherence are indifferentiable within a reference frame. But the question remains what we might find once we step out of the elevator and how it would change our treatment of the next elevator we find ourselves stuck in.
Yeah, I think we’re on the same page. What I call positive and negative diagonalization might just map onto what you call trivializing and idealizing or middle-out/outside-in. But there may be some differences too. Alas I’m not sure I understand our respective methodologies well enough to know what they might be :)
I agree and also suspect a great deal of overlap.
Have you done any thinking along the lines of specialized archetypes? The ones I have been using are scientist v artist, which you have echoed here with mathematician v poet, and pragmatist v Philosopher. Framed as diagonalization, I would say the diagonals of two opposing would approximate to the specializations of the other two. However, there is also a mirrored version of each specialization. For example, "pseudoscience" I see as a natural opposition for those who "structure" their perspective according to the very real over-adherence/conformity of the sciences. They are attempting to "decohere." To fight "conformation bias," they overengage "confirmation bias," errors of commission afforded on the perceived magnitude of errors of omission.
"Trivialization" likewise has two forms. One is necessary relative to capacity limitation and the attempt to "trivialize noise," a tradeoff in attempting coherence. The other is the "near-enemy" (in the Buddhist sense) of conflating sufficiency with "absolute sufficiency." This can be done by rationalizing or false-dichotomizing sufficiency/triviality according to and within the paradigm to which one is adhering. Sufficient, else trivial. Necessary, else arbitrary. Elegant, else mundane. Symmetrical, else biased.
In my typical fashion, I call this "Bae's Ifforelse" which is a very elaborate means of proving something is Bae by proving that it is not not Bae. 🫠
Here’s my simplified version. Mathematician (clarity/triviality) meets poet (profundity/obscurity) and synthesizes into clarity plus profundity or triviality plus obscurity. Typically the positive synthesis prevails in the beginning but over time degrades into the negative. That’s why you hate your favorite band’s new album :)
I like it! Yours better captures the real personalities of people. Mine is meant to be generalizable to "everything human," but therefore misses on some of the richness in "being a real human."
For example, where you have mathematical clarity/triviality, I have an "archetypical scientist" specializing in "specificity" and struggling with its near enemy "insensitivity." Thus, when a scientist declares something exact [idealized specificity], you can expect that he is "rounding" via insensitive means, but you shouldn't expect know exactly where, for what purpose or the magnitude of the error. The "artist" specializes in sensitivity, but struggles with the near enemy of "inspecificity" (equivocation). To claim that something is "perfect" or "ideal" is essentially "idealism squared" (declaring something ideal explicitly/redundantly rather than implicitly). Hence why "imperfection is the ideal" is a thing we can both understand and find examples that more or less match.
"Trivialization" and other reductive attributions are not so much a function of what is being strategically ignored or abstracted away, but rather the purpose of the strategy invoked... which is hard to always know as the individual doing the trivializing, and perhaps unknowable without outside and opposing perspectives.
So yes, much overlap.
Oh, I should also note that an important implication (if I am right) is that abstraction is rightly seen as opposed to generalization, and maths is a special case that itself cannot be generalized, and to do so is to either reify the quant or to equivocate the Qual.
Also, in response to: "Structure is just parts in opposition. And parts in opposition are the real hopeless romantics because they truly need each other."
Structure/process/influence, in my conception of them, USE the search for (sensitivity to) equivalence principles to communicate a reference frame. For example, try to picture what I mean by "the process of erosion" and it is essentially without an anchor. If, however, I specify a structure (a coastline, a riverbed, a landmass), then you are able to triangulate what counts as "influence" or "confluence" between/among the structures and processes. I refer to these as "chimeraphoric sets." There are other such sets, but if we focus on your treatment of "structure" here, notice how "opposition" could also be process or influence. In the typical definition of structure, the "arrangment" of parts implies a process of arrangement and influences for doing so. "Influence" is based on "inflow," which intuitively matches the idea that to "influence" a river's flow (the process), it is best to instead act against the riverbed (the structure). Boiled down, structure is "that which is most stable within a frame of reference," process is "that change which is most stable" within a frame of reference, and influence is "that relation between or among stabilities within a frame of reference."
Much more to be said, of course, but this seemed like a unique example of how you are communicating your reference frame. That you see structure as defined by its "internal oppositions" meand, to me, that you see this opposition as the least changing element of the reference frame you are proposing. A kind of "generative opposition," which I much appreciate.
Notice also how in the bottom-up constructionist metaphor, the structure is a single (idealization/sterilization via abstraction) "distributive" element where the resistance to change is defined by its weakest point relative to any given "applied force" (generalization of influence and conflation/trivialization of processes). One of my overall points to the scientist archetype is that the concept of "structure" is an equivalence principle in which one cannot declare that it is more abstract than general, nor that it was abstracted before it was generalized. That is true of "mathematical structures" as much as "the structure of poetry." We cannot tell whether we are reducing to "simplest" or "fewest" parts, projecting it as syntactical, or what combination thereof. We also have no means of establishing its sufficiency or necessity. What we can say is that something seemed "sufficiently coherent" such that we stopped looking elsewhere and began to adhere instead, or we can say that something adhered sufficiently to the expectation or prediction of it so as to seem coherent. However, the modern Adherence paradigm most commonly conflates their local (individual or group) sense of "sufficiently exact" (the product of a process) with "exactly sufficient" (the structure of structure, ad infinitum, amen) the latter being provably incoherent for beings of non-infinite affordances.
So is this very essay poetry or is it math? 🤔
Both and neither. It’s the “diagonalization” of poetry and math.
This piece is great in many ways. I think it is especially great that the antinomy of antinomy, as I understand it, is that we can't think with antinomies and can't think without them.
You say that the analytic-continental divide consists at least partly in differing attitudes toward contradiction--but is that really so? Analytics don't use exactness solely to show that neither side can be correct, after all. Some of us take a more ecumenical approach to antinomies: trying to show what is right about both sides by reconciling their main ideas in the shape of a hybrid view.
That’s a nice way to put it. I was thinking: we must take antinomies seriously; we can’t take antinomies seriously. But I really like your version.
The analytic approach typically involves taking sides. But different analytic philosophers will take different sides. And when neither can convince the other, they’ll look to hybrid views wherein further conditions —epicycles — are offered as a kind of tribute to the opposition. But they rarely ask the Kantian question of why both sides strike us as compelling in the first place. It’s like they want to resolve the antinomy before they’ve understood its source.