Hegelian contradiction and the prime numbers (part 2)
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Both TFA and the linked article referenced by TFA seem to me to be the ramblings of somebody trying really, really, hard to pull a rabbit out of a hat. By linking together abstract concepts you can prove that philosophy and mathematics are one and the same!
>So it’s very remarkable that Hegel’s mystical starting point, which is purely conceptual and abstract – and makes no reference to physical reality or empirical knowledge whatsoever – nonetheless implies a structure of ‘becoming’ that is equivalent to the fundamental structure found everywhere in physical science.
Well, you can read Hegel this way... I guess. Figure it makes for some really warm and fuzzy insightful feelings, regardless of whether they are meaningful.
If you're interested, Shapiro's "Thinking about Mathematics: The Philosophy of Mathematics" gives a nice introduction into that topic, discussing several schools of philosophy and their thinkers (without forcing the authors pov on the reader). We had a seminar discussing that book, and while most philosophy students seemed happy to skip that seminar (too much math/logic), those of us with a MINT background (CS major here) found it quite amazing.
Now step back 30 feet...oh, it’s water lilies or a bridge or a willow tree.
The brain is very plastic indeed both in constructing things or interpreting them.
(This is a question I'm struggling with for real right now so if I could get some kind of answer to this it would ease a lot of my brain pressure. I never used to have this problem before I learned how to 'generate' new perspectives by 'thinking with words'. It always used to be just one perspective, just one identity.)
All of them are "true" and "correct", but which one is relevant? That's when you need to start to place things into context, and it wildly varies depending if you're an ant, a human being or a rock.
Like Monet: splotches of paint resolve into water lilies but we're not seeing water lilies we're seeing various RGB luminance values from our optic nerves and our brain resolves them to a scene which we again break down into constituent parts, water stems, flowers... and rebuild into water lilies... which we again dissect looking for meaning.
The point then is to look at a perspective as just a point in a greater flux. The flux is the correct 'one' that's where the meaning is.
I'm sure Hegel would slap the taste out of my mouth for that analogy but he's dead and no one else seems to know what he meant either, so I feel safe.
Which one has predictive power?
...
"I think it’s worth emphasising that when Hegel talks about pure being he isn’t talking about an abstract concept. He’s actually talking about a real phenomenon, an actually existing thing, which he claims we all have immediate access to, if we’re prepared to perform the mental exercise."
I cannot help but read the claim of the second paragraph as being a presupposition of the sort disavowed in the first.
> Jacques Bouveresse is interested in the incompleteness theorems of Kurt Gödel and their philosophical consequences. On this account, he has attacked, in a popular work Prodiges et vertiges de l'analogie, the use made of these theorems by Régis Debray. Bouveresse denounces the literary distortion of a scientific concept for the purpose of a thesis. This distortion, according to him, has no other purpose than to overwhelm a readership which lacks the training necessary to comprehend such complex theorems. Bouveresse's reproach to Debray is not that he uses a scientific concept for the purpose of an analogy, but that he uses such a difficult to understand theorem in the attempt to provide an absolute justification in the form of the classic sophism of the argument from authority. According to Bouveresse, the incompleteness of a formal system which applies to certain mathematical systems in no way implies the incompleteness of sociology, which is not a formal system.
[0] https://en.wikipedia.org/wiki/Jacques_Bouveresse#Incompleten...
The only real connection to Hegel is that Hegel talks about "being" and "nothing" kinda-sorta turning into one another, which the author riffs on in terms of differential equations and takes as corresponding to the differential equation for a harmonic oscillator.
The rest -- the idea that you can see the Riemann zeta function as something a bit like a Fourier transform of the integers -- is old hat. (As Terry Tao put it at one point: "the Riemann zeta function is essentially the Mellin transform of the Dirac comb on the natural numbers". See also du Sautoy's popular book about RH, "The music of the primes".)
The idea that sometimes you have two things turning into one another is not exactly startling, nor is it original to Hegel. The idea that this yields harmonic-oscillator-like dynamics is also not exactly startling, and in any case it's not something Hegel had any idea about. The thing that's distinctly Hegelian here, so far as I can tell (note: I am very far indeed from being a Hegel expert) is the idea that it's being and nothing that are in this relationship, and that specific aspect has nothing to do with the author's calculations. (He just writes them as x and y. They could equally have been "ham" and "eggs" or "Vishnu" and "Shiva" or "Linux" and "Windows" instead of "being" and "nothing".)
First of all: If that's your idea of "strong evidence" then there are a bunch of other things that seem preposterous to me but have "strong evidence" for them. For instance: Mathematicians have found it very useful to build mathematics on top of set theory; that is, to think of numbers (and everything else) in terms of structures of things belonging to other things. This is "strong evidence" that the notion of belonging-to is fundamental, and therefore that capitalism is the One True Economic System. (This absolutely honestly seems to me no more far-fetched than your argument here.)
Second: so far as I can see, even if we take the argument of the OP seriously, there is absolutely no reason to say that the things in these "dynamic and independent structures" are being and nothing. As I said above, they could just as well be any two things. Horizontal and vertical. Penn and Teller. Red and blue. But taking them to be "being and nothing" is the only thing that really connects this to Hegel at all.
Of course anyone's welcome to see parallels to anything anywhere. If the Riemann zeta function makes you think of Hegel, fair enough. It might make someone else think of Beethoven, or civil engineering. The only thing I take any exception to here is the idea that this somehow indicates that there's something specially insightful in Hegel rather than that human brains are good at spotting patterns, including patterns that aren't really there.
It takes some suspension of disbelief (but then, the scientific psychologies that took over clinical practices are skating on thin ice and only successful in certain serious mental illnesses ) but it's well worth reading at least Malcolm Bowie's intellectual biography of him and maybe Zizek's "Less than nothing" to have some access to Lacan. (Lacan, of course, is a long self-winding reiteration of Hegelian theory on a pseudoclinical domain)
> But, in addition, the Zeta function represents the whole numbers as a sublated unity, where the entities internally relate via the exchange of a conserved substance. And this whole moves and changes with time. This is quite unlike the vision offered by set theory.
The way modelling normally works is you have a certain phenomenon (falling rocks, fish populations, market booms-and-busts) that you attempt to describe numerically, and then create a mathematical model to make conclusions about the phenomenon. Here we have the opposite: the author takes the phenomenon (the Hegelian contradiction) and uses the model to make conclusions about mathematics!
Ok, so after his navel-gazing was tested against observation, how accurate was it at describing life, the universe, and everything?
The problem with linking small pieces of science to large works of metaphysics is like finding shapes in the clouds or "Five ways TV shows predicted the future!" If you have enough material to sift through you can draw a circle in it and decide this particular piece of the morass is significant while ignoring the rest of the meaningless unfalsifiable piffle.
There's a lot more to it than "meaningless unfalsifiable piffle".
Judging by its adoption, quite a lot.
> Maurice Merleau-Ponty wrote that "all the great philosophical ideas of the past century—the philosophies of Marx and Nietzsche, phenomenology, German existentialism, and psychoanalysis—had their beginnings in Hegel."(wikipedia)
Psychoanalysis is a different beast, but there has been some interesting recent (post-Popper, which I must mention since people seem to end psychoanalysis with Popper which seems premature) work on it, even from outsiders and psychologists.
This is a lot more philosophically fraught. If you believe that mathematical entities exist in some acausal, nonphysical realm separate from the activity of beings doing math, you need to explain how those beings can access them. If you take Brouwer’s position that mathematics is the free languageless creation of the mind, then it’s no longer true that prime numbers would be irreducible if not for mathematicians.
Which highlights Hegel's central flaw in derivation - possibilities are infinite without any grounding assumptions. At best you would get a smaller but still infinite subset compared to literally everything (all valis equations vs all equations even 2 = 1).
There is no need to "access" what may simply be rederived. It isn't a physical place. The only constraints are on what configurations are possible within the system attempting to describe it. You can't describe 0 to 1024 with only a single bit.
In a "world of silence" with no "life" capable of describing primes it would still hold that the smallest non-1 divisions of 6 particles would be 2 and 3 and for 7 it would be 7 - even though there is nobody around to understand this.
>This counterfactual independence (as we may call it) is accepted by most analytic philosophers. To see why, consider the role that mathematics plays in our reasoning. We often reason about scenarios that aren’t actual. Were we to build a bridge across this canyon, say, how strong would it have to be to withstand the powerful gusts of wind? Sadly, the previous bridge collapsed. Would it have done so had the steel girders been twice as thick? This form of reasoning about counterfactual scenarios is indispensable both to our everyday deliberations and to science. The permissibility of such reasoning has an important consequence. Since the truths of pure mathematics can freely be appealed to throughout our counterfactual reasoning, it follows that these truths are counterfactually independent of us humans, and all other intelligent life for that matter. That is, had been there been no intelligent life, these truths would still have remained the same.
[0] https://plato.stanford.edu/entries/platonism-mathematics/
But if you wanna take a shot at dismissing anything that Nietzsche or Heidegger wrote, without resorting to cultural bias points, be my guest. There's a PhD in it for you.
It does sound anti-intellectual to dismiss all those thinkers as iffy, but I'd much rather retain the option of treating their views with skepticism than enrol in a PhD programme where it's implicit that all one can do is write footnotes on the work of these great men. (You seem to imply that — unless, that is, the student is a rare and impertinent genius who has the temerity to take them on.)
"there are to kinds of philosophies: the ones people kill each other over and the ones nobody uses"
Marx was humanist, so time already told I guess.
From https://en.m.wikipedia.org/wiki/Falsifiability
"Sir Karl Popper is not really a participant in the contemporary professional philosophical dialogue; quite the contrary, he has ruined that dialogue. If he is on the right track, then the majority of professional philosophers the world over have wasted or are wasting their intellectual careers. The gulf between Popper's way of doing philosophy and that of the bulk of contemporary professional philosophers is as great as that between astronomy and astrology."
And back to first principles here. We're not talking about whether Marx is bad; we're talking about whether Hegel is bad, because Hegel's dialectic was fundamental to the thinking of Marx and pretty much everyone who was anyone for the past two centuries of critical thought. And it wasn't just targeted at Marx, either. The broad brush also painted Nietzsche, Heidegger, "existentialism", even Wittgenstein (who was sort of a critical reaction to Hegel) as somehow wrong.
In my shallow, lazy, uncritical mind, this smells a great deal like a political bias masquerading as an idea.
Is there a philosopher whose significant ideas were not steps into the unknown, moving beyond accepted thought? No philosophical idea worth considering is incontestable.
PhDs and research in political economy, critical theory and sociology - the three most "Marxist" disciplines one can name at universities - are awash with criticisms of Marx, either major or minor. In fact, there seems to be more people criticising (or at least amending) his work than there are still people defending it. This is especially true in the analytic side of political economy, in which many researchers believe (rightly or wrongly) that the last vestiges of Marx have been finally cut off by Sraffa, and the most we can hope for is Ricardian socialism or social-democratic reform. The very author of the piece we are commenting on has published amendments to Marx's consideration of the theory of value in an attempt to dissolve the transformation problem. Even Marxists (considered as those with an affinity to Marx who reject a few or some of his theses) themselves disavow Marx to various degrees - either in his theory of value (Sraffa, Yoshihara, Roemer, perhaps Okishio) or his construction of historical materialism (Elster), the transformation problem (Laibman, Mohun, Veneziani). In fact, the number of people who hold that Marx was absolutely correct and that interpretation can save him from criticisms since the 60s is vanishingly small, though it does wield some influence - Kliman, McGlone, Carchedi, Freeman, Moseley, Patrick Murray. But all of the figures I have mentioned engage in critique and counter-critique of each other, sometimes even stretching to the mean-spirited. They are not isolated or refusing to engage on dogmatic principles. Even the most ardent defenders of Marx to the letter are accomplished academics, often professors of philosophy or economics, with PhDs and tenure.
On the matter of Freud I'm not so familiar other than to point out that psychoanalysis is not psychology and it is not taken as part of psychology. The question of whether it qualifies as science or not, or whether it can become scientific (in its post-Freud incarnations) is still debated. But criticisms of Freud are everywhere, not least from actual philosophers in psychoanalysis - Feminist philosophy has been very critical of Freud, for example. Extremely influential philosophers in the continental tradition have been critical of Freud - Deleuze and Guattari, for example.
It's not at all fair to say that Freud and Marx, at the least, are not treated with skepticism, even in the disciplines they are most popular in. Outside of those disciplines they are dismissed, and in my opinion, dismissed out of hand. They do not hold some great sway that makes them unquestionable today. There may have been a time at which that was true (perhaps when Das Kapital was being used as a textbook at some Japanese universities in the 20s and 30s) but it is certainly not true today, at lesat if we consider published research rather than the (sometimes misguided) opinions of students who may cling dogmatically to Marx and Freud or to anti-Marxists Karl Popper.
An attempt to entirely refute Marx or Freud would not be taken seriously in academia — there's always some kind of affirmative stance in relation to the old theorists. Unless you are some kind of genius or enfant terrible.
I don't think that's true either; while it's more likely to be true inside the three disciplines I named, it's not true outside them. Samuelson's and Steedman's criticisms of Marx are held to be pretty much the end of Marx in economics, for example - and economics is far larger of a science in academia than political economy is. There are theories of Marx which are held by many to be simply wrong, or perhaps with some insight that he offered but his theories don't live up to, even what Marx called the theories he was most proud of. Obviously nobody can refute Marx entirely in one fell swoop - since Marx's project was multi-disciplinary and very few people nowadays have knowledge in all the requisite fields to a sufficient level - but as I said, Marx and Freud are questioned both sympathetically (thinking with) and unsympathetically (questioning their bedrock philosophies and most proud achievements). I really think they are only held to the esteem that other greats are held - and possibly less. Keynes, Weber and Aristotle in my judgement enjoy far more support than Marx and Freud do today the entire academy considered as a whole.
Samuelson was a genius and a once-in-a-generation thinker. I specifically avoided excluding the existence of such people who can take on the incumbents of the theoretical pantheon.
You at least concede that great thinkers are all more or less held in a certain level of esteem. It's precisely this pious, respectful attitude that makes unsympathetic critiques rare. I'm not saying that an academic world in which such critiques were commonplace would be better, or even possible. The conservatism and conventionality of the framework in which academic work takes place may well be intrinsic to the social function of the activity. The fact is that a vast amount of work is done which rehearses, builds on, applies, or seeks to recover value from the work of the 'masters'. Skepticism is not the word I would use to describe the way the literature is typically approached. Criticality is circumscribed by a sense of decorum — one must not be too critical of a thinker whose work so many others have engaged with. To be too critical would be arrogant, or at the very least it would indicate that one was in the wrong intellectual milieu.
I really am not aware of highly respected "unsympathetic" engagements in today's academia. Yes, there were high-profile disputes in the past between contemporaries — Einstein and Bergson, for example. But today refutations and dismissals don't seem to be considered appropriate. The overwhelming mood is one of appreciation of classic texts within small specialized interest groups. Rigorous refutations (as in Samuelson's work on Marx) really don't seem to happen very often at all. They almost seem like something rude.
Even to the extent that Marx was wrong in the particulars, he got a lot of essentials right in new and unique ways. More importantly, it's impossible to have a serious conversation about labor that excludes Marx entirely (unserious conversations are another thing). And we've now had over a century of refutations of various types and degrees, from both right and left. Contributing something actually new and significant to the literature would be even more difficult than developing a thorough and academically rigorous "refutation".
Hence, the nitpicking about details from the left, and the unrigorous blanket rejection from the right. Both are far safer ground than trying to introduce breadth on the left or rigor on the right.
>The "fascist" Nietzsche was above all considered to be a heroic opponent of necrotic Enlightenment "rationality" and a kind of spiritual vitalist, who had glorified war and violence in an age of herd-lemming shopkeepers, inspiring the anti-Marxist revolutions of the interwar period.
I'm a fan of rationality and object to the violence enthusiasts he inspired gassing my relatives but each to their own.