Postmodernism and Mathematics
I am interested in what postmodernism has to say about mathematics.
I recognize that postmodernism is a broad category and that there will be a range of views. I don't have time to immerse myself in the literature, but citations and quotes are encouraged.
What I am interested in is the notion that mathematical knowledge is not inherently objective but is shaped by cultural, historical, and social factors.
This to me seems a much richer discussion that the same argument put up against morality, certainty or any act of cultural valuation.
For the average person, perhaps, maths has an almost preternatural capacity to work and deliver and is therefore objective - a foundational truth in our world. (Also Wigner's "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" )
Some postmodernists might argue that attempts to ground mathematics in a set of foundational axioms or principles are inherently problematic and may reflect particular cultural or ideological biases. They may question whether mathematical concepts truly represent universal truths or if they are constructed within specific cultural contexts.
How far can this be taken?
I personally have no strong commitments in this space and am not a mathematician. So I come with disabilities. I am however a reluctant anti-foundationalist and my intuition and experience suggests that human knowledge is contingent and tentative - an ongoing conversation which evolves over time.
I recognize that postmodernism is a broad category and that there will be a range of views. I don't have time to immerse myself in the literature, but citations and quotes are encouraged.
What I am interested in is the notion that mathematical knowledge is not inherently objective but is shaped by cultural, historical, and social factors.
This to me seems a much richer discussion that the same argument put up against morality, certainty or any act of cultural valuation.
For the average person, perhaps, maths has an almost preternatural capacity to work and deliver and is therefore objective - a foundational truth in our world. (Also Wigner's "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" )
Some postmodernists might argue that attempts to ground mathematics in a set of foundational axioms or principles are inherently problematic and may reflect particular cultural or ideological biases. They may question whether mathematical concepts truly represent universal truths or if they are constructed within specific cultural contexts.
How far can this be taken?
I personally have no strong commitments in this space and am not a mathematician. So I come with disabilities. I am however a reluctant anti-foundationalist and my intuition and experience suggests that human knowledge is contingent and tentative - an ongoing conversation which evolves over time.
Comments (167)
Likewise, but this:
Quoting Tom Storm
struck me as inherently plausible as a PM position, but inherently implausible as a serious position per se. Im not sure how it could be argued that natural numbers, for instance, are culture-bound as a concept.
https://thephilosophyforum.com/discussion/comment/692175 ^^
While Im no math wiz either, I think (else presume) I know enough about maths to express the following (may I be corrected where appropriate):
Some maths are universal in their semantics (however these semantics might be expressed symbolically, if at all so expressed).
From these universal maths then can and often do get constructed derivations which, as such, often enough dont consists of the same universality of semantics in that which is derived, but are to some extent constructed.
For instance, the mathematical semantic here expressed by the symbol 1 can only be universal. The symbol one here holding the semantic of a unity (which can get rather metaphysical when getting into the metaphysics of identity theory). It is a universal not only to all humans but also to all lesser animals that can in any way engage in any form of mathematical cognition.
So something like the semantics to 1 + 1 = 2 can only be universal relative to all sentience that is in any way capable of any mathematical cognition regarding addition.
On the other hand, mathematics which are very advanced derivations of this and similarly universal mathssuch as surreal numbers or the mathematics to qubitswill be in part contingent on mathematical factors whose semantics are not universal to all those who can engage in mathematical cognition. Such complex mathematics can then be argued to be in some way constructivist (if in no way speculative) and, thereby, to some extent culture-relative.
For example, the Principia Mathematica (written in 1910) is commonly known to take about a thousand pages to in part formally prove that 1 and 1 is in fact equivalent to 2. No such formal proof occurred previously in human history (obviously, this didnt prevent humans from successfully applying the mathematics of 1 + 1 = 2). Yet, while everyone has always universally agreed that 1 + 1 = 2, the formal mathematical proof of the book by which this is established is not universally agreed upon without criticism. As one example of this, at least one of the axioms the book uses, its introduced axiom of reducibility, has a significant number of criticismthereby not being universally apparent in the same way that 1 + 1 = 2 is but, instead, being a best reasoned supposition which was set down as axiomatic.
So, 1 + 1 = 2 is universal and hence not culture relative or in any way socially constructed. The formal proof that 1 + 1 = 2 is however not fully comprised of that which is universal and thereby in no way culture relative or socially constructedbut, instead, can be deemed to be in part constructivist in ways which imply the relativity of some of its mathematical semantics (however these are expressed symbolically).
More directly to the quoted question: The mathematical semantics of 1 + 1 = 2 is in no way arbitrary. But its formal mathematical proof in some ways is (albeit yet constrained to reasoned best inferences).
The proper answer to the quoted question should then be relative to those specific mathematical notions implicitly addressed. Overall, the answer is "no and yes," this at the same time but in different respects.
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P.s. In large part posting this in a want to see if any more formally mathematical intellect would find anything to disagree with in what was here expressed.
Quoting AmadeusD
The phenomenologist Edmund Husserl analyzed the historical origin of numeration in terms of the construction of the concept of the unit. Number doesnt just appear to humans ready-made as a product of nature. It requires a process of abstraction. First one has to recognize a multiplicity, and then ignore everything about the elements that belong to the collectivity except its role as an empty unit. Enumeration, as an empty ' how much', abstracts away all considerations that pertain to the nature of the substrate of the counting. Enumeration represents what Husserl calls a free ideality, the manipulation of symbols without animating them, in an active and actual manner, with the attention and intention of signification.
So rather than a perception of things in the world, counting requires turning away from the meaningful content of things in the world. The world is not made of numbers, the way we construct our perceptual interaction with the world produces the concept of number, and this construction emerged out of cultural needs and purposes , such as the desire to keep track objects of value.
Not sure what you mean by this. Chess has a long history and has had changes over time in different cultures. For example:
Quoting https://en.wikipedia.org/wiki/Chess#1200%E2%80%931700:_Origins_of_the_modern_game
Quoting javra
Im not a mathematician either, but I know that there are multiple interpretations of the status and role of the number one (and zero) , including whether it is a basis for all other numbers or whether it is derived. Some argue that the concept of 2 is more fundamental than 1. Theses disputes suggest in a subtle way the cultural basis of concepts of number.
What defines modern chess is its rules. What defines mathematics is also its rules. You can make up any sort of game, but not all games will be chess. You can make up all sorts of mathematical systems, each with its own rules. A different culture may come up with a different kind of mathematics, but its usefulness and applicability will be different from our mathematics and if it wants the same applications as our mathematics, it must be our mathematics.
Quoting Joshs
I am not aware of any mathematical system in which 0 is derived from other numbers instead of other way around. ChatGPT told me "Another example is in certain number systems, such as the surreal numbers or the hyperreal numbers. In these systems, 0 may be defined in terms of certain sequences or sets of other numbers, providing an alternative perspective on its construction.", but I don't think that is true.
So that "one unity and another unity will be equivalent to two unities" is then a universal staple of all mathematical cognition: in all humans as well as in lesser animals.
Hence, my question was intended to be specific to whether you find the semantic of "a unity"/"1" to be arbitrary and thereby not ubiquitously universal?
That's the issue right there isn't it. If there are variations in how maths is done, this does not appear to undermine its capacity to produce consistent results every time.
Quoting Joshs
That's what I'm looking for. It's not an easy thing to fully understand.
Quoting Joshs
Any thoughts on the unreasonable predictability of maths? Does maths allow us to make any assessment of realism?
Quoting javra
Great and thoughtful response: I'll mull over it.
I found a link to an old article about a postmodern way of doing math.
"Thus, by calculating that signification according to the algebraic method used here, namely:
Followed by a conclusion that the erectile organ "..is equivalent to the
Attributed to the french psychoanalyst Lacan..
That said, there are lots of post-modernist critiques of how mathematics is taught. This makes sense as "mathematical foundations," is simply not something most people care or even know about, and so it's not a good place to "challenge power dynamics," at least not for any sort of social effect. Math classes, however, are an entirely different story.
Post-modern critiques of pedagogy on mathematics run the gambit from the readily apparent ("we should get kids interested in the philosophically and theoretically interesting areas of math and not teach it as 'arbitrary calculations that must be performed to pass tests'"), to the plausible ("math would be more interesting if it applied to real world questions, particularly questions of epistemology and statistics, or probability") to the dubious ("allowing some public school kids to take advanced mathematics perpetuates oppression and hurts society because Asian and European-decended kids currently make up a disproportionate number of students in these classes and colleges and employers like to see math credentials,") to the batshit insane ("we should push the limits of student's creativity by introducing elementary school students to category theory and grounding equality relations in that versus set theory so that they realize the many layered meanings of even the most seemingly self-evident of relations.")
Does your language here suggest that you take post modernism to be a posturing deceit?
Quoting Count Timothy von Icarus
I'm not aware of a maths specific critique. Just taking as the starting point anti foundationalism and the notion that all human knowledge is radically contingent. What does this mean for maths and how do post modernist theorists assess it's reliability and, presumably, its lack of grounding?
This is also how I see it. We can of course debate on what exactly are these rules based on, be it a concept of unity, negation etc. but it looks to me that the absolutely minimal set of concepts is not culturally defined, but something like Kantian, universal categories. When we establish the rules, for example Peano axioms, it is not debatable if those rules won't work (unless of course there's a flaw in the rules). It's another thing if some culture refuses to use a set of rules.
This seems counter to common sense (other than the first half-line). "enumeration" is an act and you're obviously correct here (just think of roman vs arabic numerals), but "number" is merely the observation of more than one thing at a time. The function of 'maths' is unchanged across any iteration.
The concept of number really isn't different anywhere.
By no means. It's just that a lot of people into POMO are very open and vocal about wanting their work to achieve some sort of positive "social change." If this is your goal, the very small and isolated world of mathematical foundations is probably not the place to focus.
Challenging mathematics lack of grounding is already a major issue in mathematics. It was the defining historical trend in the field over the 20th century. The deflationary theories of truth that came out of undecidablity, incompleteness, and undefinablity seem in the same wheelhouse (more an inspiration for POMO, or ammunition for it, than possible targets). So, attacking the grounding would be nothing new, whereas attacking the reliability seems extremely difficult if we're not talking about applied mathematics (and if we're talking application then we're generally talking about something else outside mathematics). I mean, is any one going to argue that "given we assume Euclid's axioms, parallel lines never meet," is unreliable? That sort of statement is all about what else is true if the axioms are true (not that the axioms are actually "true"). How could a tautology be unreliable?
Certainly there are lots of critiques about how mathematics is used or appealed to in the sciences, social discourse, and philosophy, but that seems less directly related to mathematics itself.
The way in which mathematics would seem to be most open to attack for being unreliable would be in terms of foundations or application. Application is dealt with vis-á-vis other fields, and foundations is already an open question.
But the postmodernists would argue that it is empirically derived. This is how you can argue in favor of a postmodern view. Mathematics has an empirical origin -- not from a universal truth. They are not there to question the veracity of the math methods -- they are there to argue against the objective truth -- (referring to a priori or universal truth).
And there's the bumper sticker
Quoting Tom Storm
Cuts right to the core of something that we all assume has to be a core, namely math.
On the one hand:
Quoting javra
Quoting 180 Proof
But on the other hand, maybe:
Quoting Joshs
Quoting Joshs
First of all, it is too important of a question to answer quickly and easily. And then boom:
Quoting Count Timothy von Icarus
This recognizes the issues at the foundations of math but also fixes "math as math" in itself, as a long-form tautology. From within the tautology of math, there is no room for cultural or historical influence. Or maybe the culture is that of universe, and its history is all time, and the society is the society of minds. Only such influences will produce a math, and because these influences are so simple (universe, mind, all time) that math is so simple and need never change - we've fixed it that way in its own axioms.
And I've just built a POMO language around the same math.
We can drop right back into the question and ask, even with new axioms, would we really have a new math?
I don't think we ever can or will. Math is sort of how we think, not what we think. Math turns whatever we think, objective. It makes objectivity by being math. It is therefore, non-cultural. It is just human.
If you are not understanding '1+1=2' then you are not doing math. If you were to prove '1+1=7' you would be using new words, but needing the same logic and math to demonstrate how this still works. Working itself is the math of it.
It is possible to live a whole human life without any math (the animals do it, probably early man did it). Or you could be raised to think all of math is simply addition and subtraction, and never understand cultures and society's that use multiplication or division. But those worlds where a new conception of math, a postmodern sense, might be said to grow don't address the question head-on. Once there is any math, it will always need a logic, and once there is a logic, it will have a math, and once there is math, it will have words and representations for the same things (representations relative to representations), and once there are words, there will be syntax and logic, and math.
And it's not that we are simply a "rational animal" - minds do other things besides math. But we are an an animal that can do math, and when we do math, we are generating the simple, logical, axiom following, universal. So math ends up objective, as objectivity is its default method.
But a mathematician talking about post modernism... that might be interesting.
Could be. But no one is claiming PM is entirely original in this.
Quoting Count Timothy von Icarus
I'm sure, but no one is saying it is.
Quoting Count Timothy von Icarus
If this is what they do. But I don't think it is the reliability as such they would unpack, perhaps more the context of that reliability - the world we assume maths seeks to map and explain. But that is my question - what do they argue in this space?
From Joshs earlier response, it seems that Husserl's phenomenology has a framework for exploring the nature of mathematical objects and structures. It examines ways in which mathematical objects are given to consciousness - an investigation of the ontology of mathematical entities. The old quesion: are mathematical objects mind-independent entities, or are they dependent on human consciousness?
And I suspect some postmodernists coming after this might find that the role of consciousness or, perhaps, the human point of view is what gives maths its power. It isn't that maths is discovered but invented. I'm curious how that this might be laid out. I suspect it will be too technical for a layperson.
A conversation between both would be interesting (and perhaps incomprehensible).
Quoting Fire Ologist
Nice.
Quoting Fire Ologist
Ok. I'd like to hear what @joshs might say in response to this. It simultaneously suggests that maths is an intersubjective phenomenon but what is the relationship of the reality we map maths too (or visa versa)?
Unless what youre really interested in is postmodern philosophy itself, youre probably better off looking at the foundations of mathematics and the regular philosophy of mathematics that isnt usually labelled postmodern(ist).
When I was learning logic I had a look at Frege, Russell, Hilbert, etc., and found that, as @Count Timothy von Icarus has pointed out, doubts about the basis of mathematics are independent of (and preceded by half a century) what I think you mean by postmodernism in philosophy. One way of putting that is to say that some philosophers of mathematics and foundationally inclined mathematicians were becoming postmodern even before postmodernity. (Alternatively, perhaps these concerns are not postmodern at all but are quintessentially modernist)
So in the philosophy of mathematics you got formalism, intuitionism, and so on, alongside Platonism. Social constructivism too. Heres an open access paper:
Social constructivism in mathematics? The promise and shortcomings of Julian Coles institutional account
This leads me to think that social constructivism/constructionism is not necessarily postmodern in the philosophical sense, even if these distinct approaches are lumped together in the popular imagination.
EDIT: And note that the theory discussed in that paper is based on the social construction theory of John Searle, not usually regarded as a postmodernist.
Quoting Jamal
That is definitely an interesting strand which you and the Count have raised.
I'll mull over what's come in so far and see if I need to refine my OP quesion somewhat.
Thanks for the article. Looks interesting. Possibly too technical for me, but I like the thrust of the enquiry.
The idea of 'truth-value realism, which is the view that mathematical statements have objective, non-vacuous truth values independently of the conventions or knowledge of the mathematicians' is I guess what I am am exploring too.
Quoting Count Timothy von Icarus
Not necessarily. After all, Gödel, the originator of the incompleteness theorems, was guided by his self-declared mathematical Platonism, the belief that humanly-created formal systems are undecidable' only in being incomplete approximations of absolute mathematical truths. Husserls phenomenology questions the philosophical naivety on which Godel's theory of the object rests.
Yes I see. First, distinguish between the truth and the realism issues, because they are, or can be, independent. Regarding truth, have a look at Fictionalism in the Philosophy of Mathematics.
I know, and nobody can blame the postmodernists for that.
PS - That was a dumb thing of me to write. I was in a tram packed with very loud Swifties. Big concert tonight. I was a bit overwhelmed
No worries. I assumed youd assumed I was replying to your comment in the Shoutbox about Nietzsche.
I guess I don't see math as separate from the mapping process in the equation 'math properly mapped=reality.' My equation would be 'a mind mapping=the reality of math.' So the math is more closely tied to the mind's activity, than it is to a reality separate from the mind.
The objectivity of math comes in the picture where two people can't seem make 2 plus 2 equal anything but 4. Everyone (objectivity) sits in the place of Reality (objectivity). And everyone sees the same thing when 2 is added to 2. So I call my subjective experience when 2 is added to 2, objective, because no other subject is really even trying (let alone able) to show me something other than 4. This tells us something about the minds. The mind is a part of reality, so it tells us something about reality. But minds map to other minds, and the mapping is actual communication when they map through something objective. My mind can map to your mind, when we use math, for instance. But my math won't necessarily map to anything other than another mind.
Same goes for logic. Same goes for language. But the objects of language are much more complex than mere numbers. With numbers and math, we can quickly and easily connect minds. With language it is harder, because the objects of language keep the minds apart further; but every now and then someone says "I see what you are saying" and repeats it in their own words so the first person says "yep, you got it." At that point the minds are mapped to each other through the words. Like they do with math. And now we might call something objective, as in, something that the mind will have to see if the mind is looking the same way as another mind.
Interesting. I once posited here somewhere (perhaps unwisely Kantian) that maybe maths may be part of our cognitive apparatus - like space, perhaps a preconscious organising feature of the human mind, a frame upon which were able to understand the physical world.
Quoting Fire Ologist
Many postmodernists seem to challenge the idea that language represents reality. So if language seems to be metaphor - maths appears to be more than this and I come back to it's 'unreasonable effectiveness'. I'm not sure we can really say that language is as effective as a maths equation.
It's not this, my comment was just about the context in which math is consistent within assumed axioms. Saying "if these are the rules of the game, these are the legal moves," doesn't need to suppose that the rules aren't influenced by culture, history, language, etc., that there might not be different or better rules, or that the rules themselves are tautologically true. It's to say something more like "here are Jim's rules for Chess and if you play Chess according to Jim's rules x follows." So, it's more like a sample space of possible tautologies. Saying "here is how Jim plays Chess," isn't to say anything about the cultural or historical influences on why Jim plays Chess that way.
Maybe there is a post-modern argument to be made that these social or historical factors shouldn't be ignored as much as they are (that said, historical analysis of mathematical concepts seems quite common in mathematics books I've read). But we aren't fixing anything with its own axioms, we are studying what happens, given we provisionally accept some axioms. This to me seems like a distinct difference.
This hinging on the bifurcation I initially mentioned in my original post, heres a simple argument for (some) mathematical statements having such "truth-value realism":
Regardless of ontological approach (materialism, idealism, dualism, pluralism, and so forth), that quantity occurs in the world is a fact. Secondly, the cognition of quantities can only occur via mathematical semantics (this irrespective of their symbolic representation, if any). Therefore, some mathematical statement (namely, those which can be mapped onto the empirically know world) have "objective, non-vacuous truth values independently of the conventions or knowledge of the mathematicians".
This conclusion, however, will directly ground mathematical thinking in the metaphysics of identity as foundation, for quantity can only occur with the occurrence of individuated identities (i.e., units, aka unities of that being addressed), and these are not always as intuitive as they might at first appear (the Sorites paradox as one easily expressed example of this).
At any rate, the only way I see of disparaging this stated conclusion is by disparaging the reality of quantity in the world.
Quoting Jamal
One could examine social constructionisms along a realist-relativist dimension, with Searle being a realist and writers like Ken Gergen identifying themselves as postmodernist relativists.
Quoting Banno
As if we havent already heard plenty from the likes of Sokal. Reactionary anti-postmodernist chatter from mathematicians , scientists and politicians is no less common than pomo investigations of mathematics.
And if you are interested, fictionalism is just one of the schools of thought surrounding the foundations of mathematics within nominalism, there are many more. And you should also read up on the Grundlagenkrise (which I plan on making a thread on). This article is also a good cursory view on the ontological view of platonism. But I think that this article is even more general and talks not only about numbers but also about universals in general.
Speaking of Fictionalism, it battles with Quine-Putnam's indispensability argument, which was mentioned on the "Infinity" thread (a mess of a thread admittedly)
Good points on the grounds of mathematics. Now perhaps we could have a thread on postmodernism and science, differently from postmodernism and mathematics, there is looots of content around that :razz:
A bitterly ironic area to consider considering that most POMO thinkers tended to be far to the left side of the political spectrum. For decades they sharpened and refined their critiques of the sciences, and no one really paid attention to them. Then, finally, a huge swath of the public did start taking their critiques seriously, but it tended to largely be the far-right of the political spectrum who did this. "Who funds this research? Who stands to gain financially? What are the power relations in the field? What are the socio-historical factors influencing theory?"
These finally became areas of core focus, but ironically the goal of the critiques became things like denying climate change and denying that vaccines were beneficial.
Quoting Count Timothy von Icarus
The only thing the far right took seriously from pomo critiques of science was the fact that they were questioning science. They never had the slightest understanding of exactly what pomo was questioning about science, and so didnt realize that pomo was not so much interested in rejecting the value or legitimacy of established scientific assertions, but instead wanted to bring to light its unexamined presuppositions so that it could be dethroned from its authoritarian pedestal. The far right, by contrast , maintains science on a pedestal of extreme authority, and specifically rejects scientific conclusions when they are derived using methods that are too relativistic for the right, such as climate science.
Many have gotten the idea that the far right in the U.S. believes truth is something made up, and they blame pomo for this. But it is one thing to claim that they ignore or distort facts , it is quite another to assert that they have taken radical relativists to heart and think that there are no correct facts. I've heard it said the right is living in a post-truth world. My response is that one could not fond a find a group of people more wedded to a doctrinaire and almost fundamentalist concept of truth.Talk about facts of the matter. The Trumpian right fetishizes and reifies facts with a religious zeal. Unfortunately they reduce scientific facts to simple causal relations. They tend to be metaphysical, or naive, realists about both ethical and objective truth.
It is this Ayn Randian mentality toward rationality that makes them unable to appreciate ambiguities and complexities of the sort that crop up in climate change and covid science. The continual on-the -fly adjustments in medical recommendations in response to new study results over the course of the pandemic do not fit the simplistic image many Trump conservatives have of how science was supposed to operate. Their thinking about science has on the whole not progressed beyond a Baconian hypothetico-inductive methodology. As a result, they lost faith faith in the veracity of what they were being told.
Quoting Count Timothy von Icarus
Its not just a matter of avoiding fixing our axioms.
Axiomization itself, and the propositional logic it is grounded in, are deconstructed by writers like Wittgenstein, Husserl, Heidegger and Deleuze.
Quoting Joshs
How is that not blatantly incongruous (this in non-dialetheistic systems, if it needs to be said)?
Where truth is understood as conformity that which is actual/real/factual, that the truth that there is no truth is itself and affirmed truth is not true on account of having no truth-valueand that one must be learned in many an authority figure to comprehend thiscertainly seems post-modernistic to me. And, here, truth is whatever one wants to be true just in case one has the leverage, or power, to force the belief of its reality upon not only oneself but upon as many others as possible. Truth here can only be created in radically relativistic manners, rather than ever being the ontically uncreated waters in which we swim and breathe as psyches (this metaphorically speaking) and, on occasion, being that which can be discovered. In which case, this metaphysical/naive realism regarding ethical and objective truths wherein facts can be and are ignored and distorted is in perfect keeping with the radical relativism wherein there is no objective truths to speak of. This, again, granting a non-dialetheist reality.
Yeah, what would mathematicians know about maths?
The article I shared was about as sympathetic as you might expect, and more than I expected. It takes an example from the literature,
...and points out that
But no doubt you have a different opinion?
Horseshoe theory in full display. Not that it is impressive, being extreme is a big thing to have in common.
Quoting Count Timothy von Icarus
You really can't expect that to be in the modern far-left's script because the people who write the script are exactly the people who funded that research.
Very much so. One problem is that PoMo has spiritual objections to truth, but mathematics takes a far more pragmatic approach. So mathematicians will insist that certain statements are true. PoMo, not so much.
There are whole worlds between platonic realism and post modern relativism.
That is, if we drop the notion of truth as a valid assessment of our utterances in favour of the will to power or some such, we are endorsing the powerful, reinforcing their hegemony.
Post modernism cannot speak truth, therefore it cannot speak truth to power.
Quoting Banno
What would philosophers such as Descartes, Leibnitz or Avicenna know about maths? Dont be fooled by the fact that recent philosophers like Derrida, Heidegger and Husserl didnt contribute innovations that would be considered mathematical within a conventional criterion of maths. Their work was intimately engaged with and reflected a profound understanding of the deepest foundations of mathematics and logic, every bit as much as predecessors like Leibnitz.
Quoting Banno
This article is as ignorant of and unengaged with the actual arguments of key pomo figures like Deleuze and Derrida as is Sokals. None of the philosophers I follow claim that 2+2 can equal anything other than 4. They recognize that it is precisely the nature of numeric calculation that it abstracts away all meaningful contexts associated with what is counted, leaving only the repetition of same thing, different time. Derrida writes:
The contentlessness of numeration leads to the fascinating fact that its components originate at different times and in different parts of the world as a human construction designed for certain purposes . And yet, even though these constructions emerged as contingent historical skills, their empty core of the identical again and again allows them to be universally understood.
But the later Wittgenstein complicates matters here. Maths may have at its core empty repetition of the same, but its evolution plugs this into operations, rules and procedures that dont guarantee in advance the persisting identity of their sense. As Lee Braver interprets him,
Quoting javra
I didnt mean that I believe , or postmodernists believe, that
the far right ignores or distorts facts. I meant that those more moderate than the far right who share with the right a rejection of pomo relativism believe that the right is ignoring or distorting facts. In other words, both the non-pomo left and the far right believe in the non-relativist objectivity of scientific truth. They just disagree on what constitutes the proper scientific method for attaining objective truth. Postmodernists, on the other hand , disagree with both of these groups on the coherence of their various ideas of objective truth.
I'm having a hard time understanding this. To not be presumptuous, can you clarify the following:
According to radical relativism, is the "scientific method" which produces the claim that dinosaurs walked the earth along humans on a par to rather distinct, also termed "scientific method" that produces the claim that humans did not exist when dinosaurs roamed the earth?
Secondly, are both just mentioned claims of objective truth of equal value in their being socially constructed truths that nevertheless compete for dominance within society?
Lastly, if postmodernists do not believe in there being correct facts - else expressed, do not believe in objective (rather than fabricated/created) truths - how do postmodernist resolve the contradictory nature of the two just stipulated claims?
That certainly describes part of the "far-right". And it would be fair to say that POMO is often used selectively. Arguments against the institutions of science can be pulled out of their original context and still employed effectively.
However, I wouldn't characterize the entire Far-Right as hewing to realism or an "objective" view of truth or morality. The intellectual base of the "Alt-Right," is almost the opposite. You could consider Nick Land, Gavin Yarvin, the whole "Dark Enlightenment Movement," the Hestia Society, etc. These figures are often anti-realist re history, and quite relativist vis-á-vis morality. For BAP's brand of Nietzscheanism, it seems morality is quite relative, defined by the heroic individual.
History doesn't exist as a truth to be discovered but is all narrative, a battlefield. Aesthetics (for them, those of the Dark Age or Middle Ages) not truth should ground political judgements. Virtually everything is a "psyop" because what is important about events is the way people use them to shape the "perceived truth" of the world and the Zeitgeist, not the "objective truth" of events.
Consider Nick Lands "core" influences: Gilles Deleuze, Curtis Yarvin, Georges Bataille, Karl Marx, Friedrich Nietzsche, Immanuel Kant, etc. or his focus on cybernetics, hyper-reality (and his hyper-racism), nihilism. His biggest impact can be seen in the widespread cries for "accelerationism" (originally Lenin's idea) you see in Right Wing spaces online, and which now even seem to be bleeding into Republican policy in the House ("make it worse, fix nothing, so as to accelerate the collapse.")These people are on the Right because they are anti-egalitatian, reactionary, often pro-eugenics, etc., but they also seem born of POMO in many key respects. They grew up reading and in some cases teaching Deleuze and Derrida, but then remained/became reactionary neo-fascists.
This sort of seems inevitable to me. What kept POMO on the left in the first place? The relativism it allows for allows it to be reformulated in right wing terms quite easily.
Core ideas in POMO show up in the pre-Socratics but never really take hold as a significant factor in philosophy. Why is this?
One big reason might be ancient philosophy's focus on techne over gnosis as a paradigmatic form of knowledge, e.g. "knowing how to repair a boat," versus "knowing why boats float." Techne is demonstrative in a very apparent way. If you claim you know how to fix a car and then can't get it to start, it is clear that you don't know how to fix that particular car. Success is definable in a prephilosophical way.
Modern philosophy is much more concerned with how we know the truth values of propositions. However, it seems like Plato or Aristotle fairly often consider "knowing," in terms of "knowing how to do something."
I would not say that math is demonstrative in the way that patching a flat tire is, but it certainly has many demonstrative elements. We generally talk about "learning biology," but it would be a bit uncommon to say "I know how to do biology," or "I am doing political science." We'd be much more likely to say "I am learning about political science," than "I am learning to do political science." But with mathematics, "doing" seems to have a much more central role. "I know how to do mathematics," rolls out a lot more often than "I know how to do linguistics." We "calculate" and "compute" as verbs distinct from "knowing about."
There is, of course, still "knowing about mathematics" as well. But part of mathematics seems very much to be performative. "I know how to do long division," isn't as much a claim about knowledge of the properties of division with larger numbers as it is a claim to be able to carry out a certain sort of activity.
Someone can be said to be "good at math," in the way we say someone is "good at gymnastics," or "good at painting." That is, in general, to be "good at biology," means to be highly knowledgeable about it, but being "good at math," is often a statement about performance of tasks as much as, or even more than, being knowledgeable about mathematics.
And maybe this is why so many people who stop at high school level math tend to think of it in such objective terms. It seems like higher level mathematics moves more into "knowing about," while introductory math focuses heavily on "knowing how to."
I think it would be better to ask what postmodernism has to say about the sciences in general, not narrowing down to math. What does postmodernism say about logic? What does postmodernism say about philosophy?
I would argue hardly anything itself.
Postmodernism is more concentrated on society and how society works, human behaviour and those reflect on things like mathematics etc. And this very common also to for example the history of science and how social sciences look at the sciences. They aren't interest in the subject matter itself, they are interested more on the community that makes up the scientific community and how it behaves.
Hence for example the findings of Thomas Kuhn and "Kuhnian paradigm shifts" only show how this community works and doesn't tell us of the actual science matter itself. And mathematics is in this same category.
Yet on many occasions the mathematicians or scientist don't understand this. They think for instance Kuhn, from all people, is somehow degragading their actual field of study as if it would say about something about the science or math itself. It doesn't.
This is something that people should understand here. It's about just how much people are Platonist and how much constructivists and what has happened for this to change. Not exactly on what post-modernism says about Platonism and Constructivism philosophically. Then you end up with nonsense.
Unbeknownst to the publishers it was satire, exposing the lack of scientific rigor of the postmodernist.
Not sure they've fully recovered from that.
https://en.m.wikipedia.org/wiki/Sokal_affair
It doesn't help that it happened again in 2018 with significantly more ridiculous articles:
https://en.m.wikipedia.org/wiki/Grievance_studies_affair
Pomo was never in high regard among the general population , so there was nothing to recover from. Those who have a rigorous , scholarly understanding of the best works in this area of philosophy know that Sokal never bothered to do his homework, having failed to show an adequate comprehension of the arguments involved.
Quoting Count Timothy von Icarus
Nick Land is not a relativist in the pomo sense of the term; he is not simply reformulating but missing the essential features of ideas by Deleuze , Derrida and others. If someone produces a set of ideas and they are grotesquely misread, should we blame them for that, or should we blame the one who completely misses their point? I agree with you it is inevitable that any complex, difficult to understand new ideas will be misread in ways diametrically opposed to the intent of the author, but I sense that , given the fact that your own thinking differs from the ideas of figures like Kuhn, Derrida and Deleuze, you see unproductive elements in what you call pomo relativism and therefore you dont think theyre being entirely misread by people like Nick Land.
Well, to my best understanding, post-modernists can speak fabricated truth to powers that likewise fabricate truths - without there being any right or wrong to it. It's one interpretation of the "Will to Power".
I personally view fabricated truths as deception - be it self-deception or otherwise - if not outright lies. But that's just me.
Can there be a notion of progress in ethical or scientific understanding that doesnt need to rely on a true-false binary? You wrote earlier that we all consciously or unconsciously cling to some form of what Mircea Eliade termed an axis mundi. Can we make progress in understanding and navigating the world by continually revising this scheme, without having to declare the earlier versions false?
Tricky question in so far as I too am a construcitivst in many a sense, though by no means a radical relativist.
I'll use the notion of scientific progress as an example: to me, there can be no such thing - to include no Kuhnian paradigm shifts that in any way improve anything of our understanding - without there being an objective reality to be progressed toward via scientific investigations - one that is in and of itself true. (Granted, this to me requires a different metaphysical approach than either that of physicalism or of any notion entailing an Abrahamic deity as ultimate reality, to list just two.)
So appraised, while the Newtonian understanding of the physical world was and remains quite pragmatic for everyday purposes, it is nevertheless a false understanding of the physical world. This just as much as declaring the the sun revolves around the Earth is pragmatic for everyday purposes (such as is implied in sunrises and sunsets) but nevertheless false.
In the absence of a functional theory of everything regarding physicality, the same too can be hypothesized of the theory of relativity as it currently stands (nevertheless granting many a variation in its interpretation).
To me, then, if progress is in fact made from understanding A to understanding B, this then entails the (non-fabricated) truth that B is a better understanding than is A. That, though, does not then entail that understanding B is the (objectively) true understanding (if this notion is in any way intelligible). But it does entail that understanding A was then in some way faulty - and, in so being, it can then in this sense be declared false. This will however extend beyond a strictly bivalent notion of truth-value (for me, one that however still makes no use of dialetheism; one that nevertheless acknowledges partial truths, along with different vantages of reality to which these pertain).
Complex topic, but I think that summarizes my view. In short, if progress is in fact made, one's formerly held but now discarded understandings will be far more false - falser - that will be one's currently maintained understanding.
I don't see where "blaming" comes into it, just the sense in which one is influenced by/comes out of the other. I do also find it worthwhile to distinguish between "misreadings," i.e., "this is obviously not what x passage says," and "readings the author would disagree with." Sometimes, author's premises and reasoning seem to lead directly to conclusions they would like to avoid. For example, it seems like there is plenty of evidence to suggest that Kant was aware that his work could be taken as promoting a sort of subjective idealism, and that he sought to rectify this. But I don't think people who read Kant as a subjective idealist are necessarily "misreading" him so much as pointing out ways in which is work supports conclusions he may have disliked.
Reading Kant as saying something like "ethics should be determined on a case by case basis, based on pragmatic concerns and utilitarian calculus," would be an obvious misreading. Differences between these two are not always very clear cut.
Then we also have "selective readings." I would place "deflationary" versions of Hegel, Marxist readings, etc. in here. They don't misread so much as pick and choose, but they do sometimes misrepresent to the extent that they claim that the original author's reading is their own (e.g., Marxists turning Hegel into a boring libertarian Marxist.)
Where does Land fit in here? IDK, it seems pretty hard to argue he wasn't rooted in to core of continental and post-modern philosophy early in his career. He got his PhD and then taught at an English-language hub of the general movement and published extensively drawing on Deleuze, Guattari, Bataille, Lyotard, and Lacan, was a PhD advisor in this setting, and led a cybernetic/cyberfeminist collective. The younger Land who gets described "Deleuzo-Marxist," and was able to have a successful career in this setting at a prestigious university totally misreading his peers seems like a hard claim to make. He was certainly able to keep up with the discourse, and had he never made his swing over to the right, I don't think anyone would question his falling in squarely into the POMO label.
Which is funny since it's hard to see what could be more "challenging the foundations of power and dogma," in these settings than being right wing. I recall reading an article recently that back in the 80s academics skewed 2:1 in favor of the left. Now it's closer to 10:1, and in the Harvard Crimson's review of that university's faculty it was 26:1. In Land's setting, it would probably be closer to 100%. He's living into transvaluation and norm challenging birthing the "demon child" if you will of course that means overthrowing core assumptions in your culture!
Costin Alamariu, or Bronze Age Pervert, is a more obvious example since he is largely drawing on a single source, Nietzsche. Certainly, his work is abhorrent, and I think it gets framed as a "misreading," because of this. There is a definite tendencies towards "No True Nietzschean," arguments when someone transvalues values the wrong way, towards the wrong politics. I couldn't make my way through more than a small amount of his stupid book, but nothing I saw screamed "misreading," to me, and apparently his advisors at Yale agreed.
I am not super familiar with Land, but what I've seen from him wouldn't place him outside the scope of post-modernism, but for the political slant.
Funny enough, the Anti-Defamation League has a whole article on "accelerationism," and claims the term, largely through Land, has lost all connection with its original use in leftist circles. This just seems like a hollow claim. Gilles Deleuze and Félix Guattaris pitch about "accelerating the process," by which capitalism undermines itself is still the core concept when the term is employed by neo-fascists, they just see a different sort of future as resulting from this.
Quoting Joshs
More that this, people seem to resent pomo without taking much trouble to understand it. The subject seems to bring out antipathies the way Communism used to. Notice how Jordan Peterson uses the term 'postmodern Marxists' to rally his troupes and disparage the current era of alleged meaninglessness.
Quoting ssu
It's maths I'm interested in precisely because maths seems to offer a type of perfection and certainty that science and certainly philosophy do not. My question is niche not general. If postmodernism has a tendency to devalue or critique foundational thinking, how this applies to maths seems more interesting to me than how it applies to science (which is tentative and subject to revision) or philosophy (which might be seen as a swirling chaos of theories and positions).
It's interesting to note that while some believe pomo can come to a conclusion that 2 + 2 = 5, those with knowledge of the subject here suggest this is a straw-man and a fit up.
Quoting Count Timothy von Icarus
That's an amusing line. :up:
Nice manipulation of context.
In the case of scientific understanding, a spectrum from naive to well informed to me seems more relevant than a true false binary.
Quoting Joshs
Along the same lines, declaring the earlier versions naive seems more descriptive of the situation than false.
Here's the context:
Quoting Arthur T. White
There are no true sentences except when there are?
Equals, not merely equivalent to.
Was it approximately 1000 pages or closer to about 360?
Also, the proof is mentioned near the end of the book, but that doesn't mean that that many pages are required to complete the proof, since there is a lot of other material between the axioms and that particular proof. It may be that it would take a lot less pages to simply get to the theorem from the axioms.
Quoting javra
No proof had been given with constraints such those of PM, but the theorem is easy to prove in Peano's system that was a couple of decades prior to PM.
Quoting Tom Storm
Whats amusing about this is Peterson doesnt realize that thinkers he mentions as card-carrying postmodernists like Derrida and Foucault offer ideas directly counter to marxist dialectics. Postmodernism arose in opposition to, not as an elaboration of Marxism.
Quoting Tom Storm
Youre right to see maths as a central concern of pomo thinkers. They recognize that the essence of modern science is the marriage of the pure mathematical idealizations invented by Greek and pre-Greek cultures and observation of the empirical world. The peculiar notion of exactitude which is the goal of scientific description has its origin in this pairing.
Was the axiom of reducibility used in the proof?
If I recall correctly from my readings about this, Godel did not arrive at realism until long after he proved the incompleteness theorem. In any case, the proof of the incompleteness theorem does not depend on any particular philosophy.
Is that a rhetorical question meant to convey that Descartes and Leibniz knew little about mathematics? Or is it meant ironically to say that indeed they knew a lot about mathematics? In any case, of course it is famous that Descartes and Leibniz are among the most important mathematicians in history.
Thanks for the corrections.
Quoting TonesInDeepFreeze
Bad online reference apparently. Yes it now seems to be the latter.
Quoting TonesInDeepFreeze
A best inference on my part, The axiom was indeed introduced in PM according to this reference. Haven't been able to verify if it was used to prove 1 + 1 = 2.
Let me know if you find these well received corrections make a change in what I uphold in that post: to paraphrase, that some more basic aspects of mathematics give all indications of being universal while other more developed maths do not.
Quoting Count Timothy von Icarus
One problem here is the impossibility of coming up with a one-size-fits-all definition of what it means to be left or right wing. So much depends on the issue. I have my own peculiar way of thinking about the conservative-liberal binary, which is easy to poke holes in, but at least it gives some basis for discussion. It resembles in some respects the attempts by Jonathan Haidt and George Lakoff to provide a profile of a personality type which gravitates to one pole or another of this binary. But whereas their analysis was based on psychological disposition, I view this binary as a developmental spectrum paralleling the history of philosophical eras. For me conservatism is equivalent to traditionalism, and philosophical traditionalism, from the vantage of writers like Deleuze, supports hard categorical distinctions that lead to the placement of particular genders , ethnicities, races, within rigid, opposed boxes, and organized hierarchically. This is of course a gross simplification , but hopefully you get the idea. Deleuzes approach, by contrast, abandons hierarchical , categorical thinking for endless differences upon differences both within and between, that blur and entangle the boundaries between distinctions that place individuals and groups either exclusively inside or outside.
Nick Land is an unusual personality, to say the least, so it may be impossible to place his thinking within any familiar political category, but to the extent that he embraces any significant features of Deleuzes thinking, I would have to say that he doesnt see the world the way that traditionalists do, based on the way I have characterized philosophical conservatism.
Quoting Count Timothy von Icarus
This is true if left and right stand for nothing besides mindless reactions against whatever the other side does.
But if you entertain my view of the binary as correlated with stages of a historical intellectual development, it matters what one is challenging the foundations of power and dogma in favor of. If Land subverts the establishments norms because he truly believes in rigid boundaries of gender, racial, class or whatever, and their strict hierarchization , then this places him by my reckoning on the philosophical right. If , on the other hand, his aim is to anarchically tear down all extant hierarchies and stratifications , with no desire to replace them with new ones,( Im reminded of Zizek endorsing Trump in order to blow up the whole political order in preparation for his Marxist utopia), then Id place him on the philosophical left regardless of how violent and disruptive the results.
Thanks, interesting article.
I didn't find in that, or in any posts in this thread, anything mathematically interesting PM critique of mathematics. I suppose the reason is that there's none.
If I read correctly from that article, it is more about power and politics. According to him, according to some PM writers, science and mathematics are oppressive systems etc. So it appears to be more critique about how amazingly correct and effective mathematics is, not that mathematics is not objective. (I'm thinking about Adorno and Horkheimer here).
I don't opine on those. Though, of course, certain concepts that are basic to certain areas of mathematics are not even universally known, let alone universally accepted. But, coincidentally, in another thread someone else mentioned stick counting. I don't necessarily say that it is universal, but I do think that if anything is objective, then finitistic reasoning, whether abstract or concretized by algorithmic manipulation of discrete tokens, is objective. Yet, objectivity and universality are not necessarily the same.
Quoting TonesInDeepFreeze
Doesnt this depend on how one interprets the significance of performing a mathematical proof? Are you familiar with what Wittgenstein had to say about what it is we are doing when we construct a mathematical proof?
Quoting TonesInDeepFreeze
Indeed they are. I was suggesting that even though pomo philosophers have not contributed specifically mathematical innovations, the best of them have as deep an understanding of the underpinnings of math as did Descartes and Leibnitz.
How one regards the significance of formal proof and formal theories may be philosophical, but the incompleteness proof itself about formal theories does not require any particular philosophy.
Got it. Thanks.
I say that without prejudice to the question of whether the mentioned postmodernist philosophers do or do not understand mathematics as well as Descartes and Leibnitz did (even recognizing that Leibnitz's calculus needed to be rectified by late 19th century concepts and then 20th century axiomatizations (which also include non-standard analysis that does formalize infinitesimals)).
But do you think those postmodernist philosophers understand 20th century foundational mathematics as well as mathematicians and certain others in the philosophy of mathematics do?
Quoting Olento
I think youll find that the most interesting pomo analyses of mathematics are neither strictly about power or politics, although these are never absent . Rather, they reveal the historical and philosophical origins and significance of the concepts of objectivity, correctness , exactitude and effectiveness that is peculiar to mathematical logic. That is to say, they dont deny that mathematics contributes these qualities, what they are interested in showing is that such qualities are secondaryto and derived from more primordial and fundamental ways of thinking that are precise in a different but more powerful way.
Doesnt it require interpretation? It may seem as though it is in the nature of proof that it be absolutely transparent to anyone who understands mathematical proof, but hasnt there been a lot written over the past 70 years or so (I believe Ian Hacking had some interesting things to say about proof) relativizing its very nature?
One may discuss its philosophical implications, but the proof itself doesn't require a philosophical interpretation.
I am not familiar with the notion of 'relativizing its very nature', so I can't opine on it.
Any one else read that as "porno"? May just be the font, or my glasses....
Quoting Joshs
Can you explain this further? What is this "more primordial and fundamental" way of thinking from which mathematical 'qualities' derive? And how does the derivation work? And are "objectivity, correctness , exactitude and effectiveness" "peculiar to mathematical logic"? Why?
I did read have a cursory read of Izmirli's piece which you provided. Aside from the historical survey I wasn't quite sure what the piece was saying. I was just pointing out that people's take on postmodernism varies. In this case, White versus @joshs. It seems to me that joshs was making the point that White has it wrong.
Yes, I'm interested in this too.
Exactly, do not make the mistake that people engaged with the "culture war" make here.
As I was saying, the objectives of social sciences when approaching math is different from math. Postmodernism is similar: if it's focus is how the past modernist agenda is over and how it's about "an acute sensitivity to the role of ideology in asserting and maintaining political and economic power", it's nonsense then to talk about 2 + 2 = 5, because any postmodernist that is against 'naive realism' isn't trying to debunk arithmetic with natural numbers. He or she may be interested in what questions we want to use arithmetic and where not, especially when it comes to applications and modelling the real world. Just look at the role we give the indicator GDP or GDP per capita. Yes, calculating the GDP you do use math, mainly arithmetic actually, but obviously the calculation has a lot of implications to political and economic power. And counting the GDP is really in the field of economics and other social sciences.
This kind of answer (that pomo makes 2+2=5 OK) is simply from someone who doesn't know and doesn't care to know what the pomo/sociel science gobbledygook is about. It's just nonsense, period. Hence it's a danger! And that seems to be what for example mr White above is saying that you quoted.
And of course there is postmodernist nonsense. The laxness of rigor was shown very well by Alan Sokal and he does have a genuine reason for being critical where "leftist" academics is going. Yet I can assure that similar nonsense can be find also in the 'hard sciences': it's just usually hidden in such complicated math and jargon, that nobody can clearly understand what kind of nonsense it is. If you would put the end conclusions in plain English, which is totally forbidden, then only the layman would notice the crap the 'academic' study is. Especially the use of math is a culprit here as if you don't understand the math, you don't understand what the whole thing is about.
A previous similar attitude between the 'hard' (true) sciences and social sciences was by C.P. Snow and his book two cultures from 1959. There Snow paints this picture of one scientific culture, the hard sciences, still upholding the true foundations of science and then there being this soft underbelly, the social sciences and those academics who study them and their utter ignorance of nearly everything.
Now some might argue that Snow only attacked the ignorance of social science people about science (and thus the issue simply would be that academic people have too narrow and specific areas of study), but that's actually not the case. Snow's hubris and arrogance can be seen actually from the end of the book. There he purposes that since the "other culture" has so badly lost itself, the 'true' science ought to tackle the most difficult problems of the current era, namely the Cold War and nuclear weapons armament! Well, science didn't solve the Cold War, MAD kept the politicians from not starting the war and economic realities made the Soviet Union to collapse. Something that C.P. Snow was clueless about among others.
Yet many even now purpose that since postmodernism (or whatever leftism it supposed to be) has so badly crippled the social sciences, then natural science should take their role too!
Maybe those people are not real post-modernists, but they do exist:
Quoting WSJ
We all remember the 2+2=5 nonsense of 2021-2022 (that a prized mathematician even went to Twitter to defend), whatever label we apply to the people that pushed it. It was brought up in this thread exactly because it is a deconstructing of mathematics as culturally relative.
A lot of confusion around the word postmodernism. In the field of philosophy it tends to lumped in with trends that are quite tangential to it and in many cases opposed to it (Marxism). Pomo authors like Foucault, Deleuze and Derrida often get blamed for the excesses of wokism and cancel culture, when in fact the repressive moralism coming from these movements is attributable to such doctrines as Critical Race Theory, and figures like Franz Fanon and Antonio Gramsci. These approaches are heavily influenced by Marx and psychoanalysis, which are put into question by pomo writers like Foucault and Derrida.
You surely can get a clueless person that has only been taught something what you would call 'post-modernist' to say something incredibly stupid.
That's the way how the "culture war" works: find the most stupid, most fringe remark from the social media (very easy to do) and then declare: "Look at these idiots!" You aren't engaging in discussion, trying to understand the others point of view or to get the most sensible argument. Nope. You are there to win the argument and warn how dangerous the other side is.
And there's a lot of ignorant views there. The basic problem is simply when you teach the critique of something, but not the actual school of thought or philosophical view being criticized, the person is simply clueless.
But let's take for instance one of these "pomo" attempts that was declared to be the threat for mathematics (I forgot by whom). So I listened to the lecture. She didn't say 2+2=5. The basic reasoning was to find examples closer to the lives of the pupils and understand when the lack basic skills and how to operate then.
I did have a thread of Decolonizing Science which was basically the same subject matter, not "pomo", but still.
I think I've just become a bit cautious of those that warn about this pomo-leftism in science or math. In the end they aren't interested in the actual math, so one shouldn't be so angry about it. It's just the present way of virtue-signalling.
:ok: Very well put. Actors such as JBP and Shapiro are doing a disservice to their own cause when they bring up Derrida and Foucault, all the while the people they want to fight are seldom named some might say they are poisoning the swamp, but realistically they are just ignorant. But then, what about Lacan?
I don't understand what you are getting at. I provided plain proof that there are indeed people who deny mathematics for political (leftist) reasons. Maybe they are not post-modernists, perhaps some are and others aren't, or maybe none of them are. What place is there for post-modernism to be productive in mathematics after all? As Count said:
Quoting ssu
Maybe she (whoever) didn't, but many did.
Mathematical logic and its use in geometry produces pure, but empty idealities. They introduce the pure idea of precision, exactitude, accuracy that then becomes the basis for the aim of exactitude of correctness in the empirical
sciences.
The catch is that applying the pure idealizations of geometry to the natural world is describing a world that is no longer empty, no longer protected from contextual change in meaning. There are no pure forms , shapes in nature, and no self-identically persisting objects. For the purposes of convenience, scientists, beginning with figures like Galileo, fabricated a geometricized idea of the empirical object. As Husserl writes of this invented object:
What Husserl means when he says only ideals have a rigorous identity is that in order to adopt the notion of a self-identical empirical object, or the concept of a logical subject and predicate , we have to conceal the subjectively changing processes of actual experience, to freeze them into temporarily unchanging identities so we can compare and manipulate them. The world doesnt come to us packaged as self-identical objects.
Heidegger writes:
He's a radical libertarian in key respects, so it's much more the latter. However, I would still place him squarely on the far, reactionary right.
Land is concerned with freedom and sees democracy and liberalism as incompatible with it. We can consider the Alt-Right racist who asks: "how can the leftist claim to be concerned with freedom? Why can't like minded individuals like me live in our own 'whites-only' communities? Why are we not 'free' to do this? They say they are for freedom, but then they want to enforce a hegemonic value system on us. Sure, they might allow the Amish their own small communities (although even there they interfer with gender politics), but they won't let us do as we please."
Perhaps a bit more sympathetically, the Silicon Valley start up captain asks: "why am I not free to hire and promote people based solely on my own judgement? Why must my actions be forced or prodded into conforming to the goals of the leftists re "diversity?" Why must diversity be defined how they define it and why must I be coerced into acting according to their standards?"
For Land, the ideal is something of a cross between the ancient city-state polis and the Silicon Valley start up. The CEO is the philosopher king and no outside moralizing agent has the right to tell him or her what the good is. If people don't like living in an Alt-Right City State they can flee. But the merit and the greatness of the CEO philosopher king will make some city states better than others, and so people will be free to also subject themselves to the "great men" (or women) who produce the most vibrant polis.
Is this not more free than the leftist vision where an overarching moralizing set of norms is applied universally, using state coercion whenever it is necessary? And isn't saying "thou shalt not have hierarchies," itself an absolutist decree being made from on high? Why aren't we free to generate the neo-facist, neo-feudal aesthetic we find interesting? Isn't this more true to the goal of exploring "the infinite plurality of creative spaces?" How committed to this infinite creativity are you really if your response to some forms of it are "no, you cannot be creative like that!"
"But you have to be creative while allowing creativity for all, without dominating them," can be met with, "why? Why must I subscribe to your dogmatic declaration of the appropriate scale for considering the actualization of freedom? Why must it be for the individual and not the fascist collective?"
IDK, reading Land, it's hard to deny that his style, verbage, analysis, and influences are deeply rooted in Continental Philosophy (the overlap with POMO is of course strong, but hardly absolute). His right wing turn certainly seems more like an internal type of critique rather than a rejection of the system he started in.
And I think Land's critique is particularly difficult for his former school to deal with (which might explain why the rebuttal attempts tend to involve a lot of moralizing and ad hominems). The Thomist or Platonist has no problem dismissing Land as a man child with a defective sense of freedom as largely limited to negative freedom from restraint, and a deficient understanding of the virtues. Rule in accordance with the Logos is not equivalent with rule in accordance with desire. When a parent sends their child down for a nap despite their tears they are not engaged in the arbitrary elevation of their will over their child's or acting "dogmatically," but in an way informed by what is truly good for the other.
I am not sure what a good POMO rebuttal to Land would be. I've certainly yet to see one.
I might be wrong. I find your style quite obtuse. To be candid, it seems intended to be clever rather than clear.
So for instance that second quote from Husserl looks to want to say that an individual is determined by the predicates that apply to it, but of course Kripke's modal logic tells us otherwise. No fault to Husserl, since possible world semantics post dates him. But why the language?
If I am right you have not explained a "more primordial and fundamental" way of thinking from which mathematical "qualities" derive.
I find the following laughable, so I must be misunderstanding it:
This seems to be saying that maths is only about maths; the "existential foundations" of maths are applicable in applied maths, or physics, or engineering.
Maths has a far, far greater reach and explanatory power than 'historiography'.
Mathematical logic at least explicates symbolic logic, and symbolic logic is useful. We are all typing on computers whose invention and development are based on concepts in symbolic logic, mathematical logic and the theory of computability that really took off with mathematical logic (though, I woudn't necessarily be unsympathetic to the idea that we might all be a lot better off without these blasted, annoying, buggy, and intentionally mal-designed digit boxes).
Deleuze is not commanding anybody to discard hierarchies, hes showing how we can understand them as deconstructing themselves. Either you see this or you dont. If you dont, then Deleuzes opinion is that your idea of freedom is a compromised freedom because it is unable to see beyond stratified categories that restrict as much as they liberate you. Its your loss, not Deleuzes. Hes just offering what he sees as options. Its up to you whether you recognize them as useful alternatives or not.
Land isn't responding to only Deleuze, although it seems likely given some of his lines that he would say he is doing to Deleuze what Deleuze claims to do to other thinkers: "buggering" them to produce demon offspring. That the demon offspring is recognizably related to the author but a sort of heretical corruption is sort of the point. I don't know how someone who conceives of their philosophy in such a way can be "misread," as it would seem that "misreading," shows proper application of the method that is recommended.
Quoting Count Timothy von Icarus
Youre not resolved of the responsibility to read Deleuze carefully. You dont get off the hook that easily. Deleuzes work is rigorous in what it is trying to say. It can be placed in just as precise a region as any of the other philosophers of our era. Deleuze lets us know the difference between buggery, where he uses authors like Leibnitz and Spinoza for his own purposes, and where he rejects what he doesnt like in their work. Readers of Anti-Oedipus have no doubt he was influenced by Freud and Lacan but leaves them decidedly behind at a certain point.Readers also know where he stands in relation to Derrida , Husserl and Hegel. Deleuze work tells us where to situate him with respect to the history of philosophy, praising Foucault and Heidegger but also letting us known where they fall short , venerating Nietzsche as his most important influence, resurrecting Bergson for his notion of lived duration but critiquing his subjectivism.
Despite his differences with Derrida, I believe Deleuze would endorse the latters thoughts about truth and relativism:
Right, but the question was: "did elements of the Nu/Alt-Right grow out of/use ideas from post-modernism?" not "does Nick Land understand Deleuze in particular?"
The attacks on science and the concept of accelerationism in particular don't change much in content when employed by their new users.
By way of example, we might allow that Karl Marx seems to have misread Hegel in some core respects, but he certainly didn't misread or fail to understand [I]everything[/I] Hegel was laying down. Nor would it be unfair to say Marxism clearly grows out of Left-Hegelianism.
However, like I said, it seems unreasonable to assume that someone who had a successful career as an academic publishing on Deleuze and wasn't subject to particular criticism until after he adopted controversial political opinions completely misread his sources. I don't even know if these sorts of questions are answerable. You get no clear summary of Plato in Aristotle, and lots of contravening opinion, but whether Plato's star pupil failed to understand him seems unlikely, even if no clear answer lies in the text.
As for the quote, the debates about Derrida are interminable. The claim of his critics is not that he didn't ever voice positions akin to that quote; this is easy to verify. The question is if other parts of his work contradict that sentiment, or claims that it becomes "truth for me, but not for thee," in practice. I'm not really interested enough to care who was actually right here, and it's irrelevant to the point about the modern right being influenced by post modernism.
Quoting Count Timothy von Icarus
If we agree that there are in fact substantive ideas offered by particular authors labeled as postmodern , then in order to determine whether someones ideas grow out of/ use ideas from pomo, we first have to establish what exactly were talking about, and I think that requires picking a specific writer, whether it be Deleuze, Foucault or Lyotard. and determining a connection with Lands work.
Quoting Count Timothy von Icarus
A lot of scholar glom onto and base their careers on parsing each word of a major figure. They hew so close to the original texts that it is difficult to see where their thinking departs from the master until they write something controversial.
Youd be surprised by how wildly students of particular philosophers can misread them. For example , Graham Harman, who founded object oriented ontology, a branch of speculative realism, offers a reading of Heidegger about as far removed from pomo as I can imagine. I recently read a piece which claimed, somewhat convincingly in my opinion, that Land settled on a libertarian Kantianism, which it seems to me is impossible to characterize as growing out of Deleuze or pomo. Your thinking doesnt grow out of an approach that is built out of a direct critique of what youre growing into.
I think its the case that Land was always a traditionalist, but also a cultural hipster who joined the latest intellectual fad (which happened to be Deleuze) without absorbing more than superficial elements of him. As he became older and learned to read philosophy more carefully he discovered his true mentors were not pomo at all but transcendental idealism.
Quoting Joshs
Has pretty much been the way I've been thinking about the question. At a certain point "postmodernism" isn't a useful frame for thinking -- you have to dig into a particular author because they don't necessarily agree with one another. "Postmodern" is a generalization about history (in various disciplines -- the periods differ depending upon which discipline you look at), but that generalization doesn't have a general perspective on all science, or mathematics specifically -- which shouldn't be surprising given the themes.
This is true, and it's worth noting that many of the "big names" associated with the movement rejected the label. It's seems like only younger scholars ever came around to embracing it.
Well, to my broader point, it certainly seems like elements of the right have taken Baudrillards thesis in The Gulf War Did Not Take Place, to heart. If you look at narratives on the war and Ukraine, what can be said to have "actually happened," invocations hyperreality, or the ubiquitous claims of wartime events as "psyops," it seems at least something has seeped in.
Perhaps we can't rightly call anti-realism vis-á-vis history, (or even contemporary events) post-modern, but it certainly gets lumped in with the term, and it's a cornerstone of Alt-Right thought.
I generally find myself agreeing with Freinacht (who does seem to embrace the pomo label) on the ways in which the movement is itself post-modern. At the very least, it is emblematic of the problems many post modern thinkers were striving to identify re globalization and late stage capitalism. I think "blame" narratives miss the mark, because in many cases theorists were diagnosing problems, and this is unfairly conflated with them advocating for those same problems.
https://metamoderna.org/4-things-that-make-the-alt-right-postmodern/
If we allow that critical theory and identity movements fit under the umbrella of post modernism then the relationship is even more obvious because the Alt-Right is both a self-conscious reaction to these movements, while also itself being a similar sort of identity movement employing similar methods of critique.
Yes, I am aware of this - it's generally one of the first things people say when you use the term postmodernism. I chose to keep it broad to see what would come in since I am no expert. I'm not really interested in any particular writer and I wanted to see what people would select and highlight. We've done ok with 4 pages so far.
Quoting Count Timothy von Icarus
Could you cite some examples of anti-realism as an explicit doctrine of the far right? I cant help but think your own realist-based thinking is leading you to inappropriately lump together as anti-realist everyone who doesnt accept the scientific consensus of what has been objectively proven to be true, and ignoring their reasons for rejecting it. There are a wide variety of realisms, and I view the far right , to the extent that generalizations can be made here, as embracing a more traditionalist form of realism than the one you endorse. I think this is the source of your difference with the far right, and pomos alleged influence here is largely a popular scapegoating for cultural trends they have almost nothing to do with, based on an inability to read them effectively.
Gotcha. And surely I don't mean to denigrate the attempt -- I've been scratching my head about how to respond and that's still the closest thing I had in my mind.
A riskier response, in generalities: I'm always open to philosophical broaches of sciences by scientists or laypersons with knowledge of the particulars. As such I don't mind a few silly vaunts into the territory of 2+2=5 -- we can all think through it and feel our way to a conclusion so there's no need to think this sacrosanct or silly if a person with knowledge is exploring, though we certainly don't need to believe it's true either. It could just be interesting and that's enough, though I know I can't make five eggs out of a double of two eggs.
But I've come around to denying Quine and thinking philosophy is different from science -- so I'd say postmodernism is philosophy, and mathematics is science, so the relationship is a bit open to explore and depends upon particulars.
In crude terms, the various strands of thinking often loosely described as postmodern seem to be a form of skepticism and a disavowal of metanarratives and foundationalism. They are also known for relativism and perspectivism. From conceptual frames like this, I wonder how math and its underlying assumptions are understood. Particularly given maths status as a universal language, with exceptional effectiveness.
Joshs said something interesting here:
Quoting Joshs
This notion of 'mathematical idealizations' which are essentially empty seems a promising direction as per below -Derrida followed by Joshs
Quoting Joshs
Derrida, writing in Margins of Philosophy, says:
I guess I've been curious how this approach applies to maths. What does it say about the certainty and universal reliability of equations?
All topics are connected by finitely many degrees of separation.
Golly this was 7 years ago: https://thephilosophyforum.com/discussion/512/reading-group-derridas-voice-and-phenomenon/p1
That's where I'd start because @Joshs mentioned Husserl's understanding of mathematics and Derrida is critiquing Husserl's interpretation of the sign from the deconstructive perspective -- at least if we want to generate thoughts from a text roughly in line with the ideas of the thinkers, though we'd have to apply some interpretive leaps from Derrida to Husserl in conversation.
At least as a thought.
After that -- I think the certainties of mathematics can easily be accommodated to the uncertainties of a given post-modern philosophy. The interesting bit is how you do it, and I agree it's interesting but you're asking a question that's hard without more textual fidelity, imo. Though a historicist would say that.... :D
Not too surprising, I think. At least if I'm right that science and philosophy are different, and math is science.
Quoting Moliere
Heidegger argued that modern philosophy from Descartes to Nietzsche is grounded in a particular notion of the mathematical which founds the modern conception of science. With Descartes is born the contemporary philosophical metaphysics of the subject-object binary. The subject posits the object via an axiomatic method that defines in advance what it means to be an object, and in this way the modern notion of the mathematical becomes the basis of what subject and object are.
Eugene Gendlins analysis helps to clarify Heideggers comments:
What's odd is that the article, which @Joshs pilloried, makes much the same point as he makes.
It specifically provides an example of where a re-situated 2x5=1 is true.
It also presents a sympathetic account of PoMo pedagogy in maths.
No pleasing some folk.
The irony...
It's Critical Theory, not 'Critical Race Theory'. You should read it.
Both exist and one is derived from the other. The post I replied to specifically said the latter. I have much better stuff in my reading list, that is especially clear to me when I see that "reading Critical Theory" has not taught you how to use an ellipsis.
The whole point of the "9/11 didn't happen," meme popular on places like 4chan isn't that people actually think that the government falsified the construction of the Twin Towers in some objective sense, and then faked an attack on non-existent buildings. That would be too ridiculous even for those circles. The point is that history is whatever people in power say it is (and that Alt-Right activists possess this same power to change history). Objective history is inaccessible, a myth. The history we live with is malleable. It's a joke, but a joke aimed at an in-crowd who has come to see the past as socially constructed.
This is what is normally refered to as anti-realism in philosophy of history at least.
Are there people who really believe that Taylor Swift's entire career was a "psyop" to build up a media figure who could be leveraged for political gains? I'm sure there are, but the whole wave of attacks on her has an air unreality. The audience isn't supposed to see it as objective truth, the point is precisely that it is ridiculous, as this gets it into the mainstream media which in turn makes it real in a way, because once something is in mass media then people need to take a side based on their identity allegiances. It's trolling, which is at the heart of the Alt-Right. And at the heart of that sort of political trolling is the same sort of "performative transgression," you see in third wave feminist actions like the "Slut Walk."
This is a movement that happily rejoiced in the term "alternative facts."
Another main route for anti-realism to enter the far-right has been through esoterica, particularly Julius Evola and Rene Guenon. On places like 4chan it is not rare to have people talking about tulpas, creating realities through concentrated thought thinking something is true makes it so although this generally partially ironic (like everything in the Alt-Right). Hence, their God who was created from memetic energy or whatever. Everything is ironic and unreal, a sort of trolling of the "real" to show its total groundlessness. The Christchurch shooter covered his weapons in meme jokes because even terror attacks are covered in a level of irony and unreality, DFW's sincere post-irony in the flesh.
The subtext behind declaring every mass shooting a "hoax" is that "you can never be sure what is happening in current events." In a world where consensus reality has collapsed, identity has primacy and determines the world narrative. Daniel Friberg doesn't urge "rebutting" or "debunking" leftist "lies" but "deconstructing their narratives" in "metapolitical warfare." When Mark Brahmin lays out his plan for a new religion based on worship of Apollo he is not claiming the Greco-Roman gods are "real," but that they were real and can be again. (And we can consider all the neopagans and the ubiquitous references to "LARPing" here too.)
This certainly looks a look like the campus projects that grew out of continental philosophy at least.
Indeed.
Touche' :razz:
It's not about punctuation use...
It was not rare. That was taken over on /lit/ and /his/ by Tradlarping somewhere around 2022 and nowadays /lit/ is actually about books, the latter is just /int/ lite. I imagine that the Evola crowd has either grown up or retreated into discord servers where they divide their time between discussing writers they pretend to have read and fighting their porn addiction.
Quoting Count Timothy von Icarus
First time hearing about this guy not shocked considering his 0,2 following/follower ratio , but by his forename and surname I imagine he would be what is called a "barbarian". That surname does not suggest any Mediterranean background even. Why do these people talk about "Graeco-Roman" religion as if they had anything to do culturally, racially, historically with Greeks or Romans? Or as if "Graeco-Roman" is anything beyond a pop-history misunderstanding? It is like folks from Asia or Africa claiming to be Norse pagan.
Interesting. Although I suspect that like religion this may in practice operate at two levels - there are the literalists who believe the conspiracies (they have a simple faith) and there are those who consider them allegorical.
Quoting Count Timothy von Icarus
Can you give me some quotes that demonstrate the belief youre attributing to the alt right that objective history is a myth? My understanding is that the far right is so astonished and incredulous in the face of what they see as completely unfounded liberal interpretations of the facts that they have completely lost faith in the accuracy of anything a liberal says. That's not being anti-realist, thats abandoning the expectation that the other side will be faithful to what is real, true and objective. You seem to be randomly mixing pomo and conservative memes together while providing no evidence to justify this.
Quoting Count Timothy von Icarus
Evola and Fuenon are considered traditionalists. This has nothing to do with anti-realism as I understand its meaning in philosophy. As Joseph Rouse describes them:
Again, your depiction of anti-realism inappropriately mixes mysticism, irrationalism, supernaturalism and other traditional metaphysics with pomo post-realism, which is not related to any of those perspectives.
Quoting Count Timothy von Icarus
Friberg couldnt accurate define what Derridas notion of deconstruction means if his life depended on it. Pomo memes like these have entered the public vocabulary and have now become ubiquitous, but it will be decades before the general public has a clue about their original philosophical meaning. As proof of this, he certainly seems to have you fooled.
Math research is like a giant tree, with a more or less solid core, but with branches upon branches proliferating endlessly. There are so many of these no human can understand more than a fraction of the mathematics represented. So, in a sense, "mathematics" is ill-defined. Postmodernism pushes beyond this surmisal to the point of melting away the rigor of elementary mathematics, allowing the student to play with a subject they know little about, setting aside established principles and rote practices.
So any notion that math is a single connected body of knowledge is muted and an effort is made to disorganize what has barely been organized. Then there are DEI considerations, which may lead to practices that raise one's eyebrows if not their hackles, like ending the practice of grading and testing or manipulating advanced placement policies.
I retired from college teaching twenty four years ago having never been involved in these approaches, beyond being advised to be especially nice to minorities - which I had always practiced. So, it appears to me that PM mathematics is mostly a factor in mathematics education. I have never known or even met a research mathematician who considered themselves post modern. Guess I'm not either.
Hope your leg is improving. Reading your paper.
I will consider this a joke until further notice.
I'd expect that. My original quesion was intended to understand how that rather lose category of ideas called postmodernism might understand maths. Maths interested me because it is an approach which appears to be universal and consistent across cultures. This, I have assumed, is anathema to many postmodern projects. I also thought it would also be an interesting way to see how pomo might deal with the age old quesion - is maths discovered or invented?
I'm fine with granting Descartes to Nietzsche, ala Heidegger.
I'm tempted to say this supports my notion that science and philosophy are distinct.
But I'm uncertain. If I missed something I'd appreciate a clue.
For Heidegger the way that science and philosophy are distinct is that science doesnt think. What he means by that is that a given science works within the bounds of a regional ontology produced by philosophy, but cant escape those bounds without the help of philosophy. Philosophy contributes
To put it in Kuhnian terms, normal science is the way the vast majority of scientists think, whereas revolutionary science requires philosophy. He believes todays sciences (in the very way they define themselves as objective) are still stuck within the metaphysics laid out by Descartes and modified by Kant Hegel and Nietzsche.
Where? An WSJ article? So someone really has the problem with actual arithmetic? If you provide "plain proof", the just give the reference...even if this is just five pages, it's hard to find.
Quoting Lionino
Remember to give the actual quotes, not someone referring to something.
Quoting Lionino
This is an important point here. It's just like talking about leftist thought in general where words that have specific definitions are used as vague adjectives and called "marxist", "maoist" or "woke". Well, in this forum there are a lot of leftist members and usually their views and comments have nothing to do with what is portrayed by Shapiro and JBP (Jordan Peterson?).
In fact, the ignorance of for example Jordan Peterson is clearly when he had a debate with Slavoj Zizek. And naturally that in the discourse of 'leftism' that social democracy isn't discussed shows how shallow this right-wing rhetoric is. As shallow as, well, leftists analyzing the right-wing.
Hence back to the subject of mathematics. The first question is, is it really about the formulas of mathematics or is it about the teaching of mathematics?
Well, I think I can understand what Heidegger means. His stance is that mathematics is a collection of ideas developed over human history, so it is part of the history of ideas, so part of history.
This may help too.
On Joshs's style
Quoting Banno
I can see in a general way that if you are using language to deconstruct language, you are in danger of sawing off the branch you're standing on, which might make your language weird. Do postmodernists understand one another? I do not know.
Perhaps what is required is some kind of neutral, formal, metalanguage so that natural languages can be deconstructed more precisely. Instead of postmodernising mathematics, we should mathematise postmodernism. :smile:
Quoting GrahamJ
Dont know about that. We dont want a repeat of the Principia Mathematica fiasco. As for an Esperanto for postmodernists, that kind of flies in the face of the point theyre trying to make about the relation between language and the world.
Is this one of those No true Scotsman fallacy for damage control? "Woke leftism does not come from Neo-Marxism!". Let me know if otherwise.
Quoting ssu
Oh, so mainstream news is now unreliable? Convenient.
It says in the article "a proposed mathematics curriculum framework, which would guide K-12 instruction in the Golden States public schools". Another manual says that addressing students mistakes forthrightly is a form of white supremacy.
Your dodgy tactic here is that just because I didn't give evidence that people claim that 2+2 can equal 5, it means that there are not people who say that mathematics is culturally relative. It does not matter if nobody said 2+2=5, by the claim that mathematics is culturally relative, you automatically enable the justification 2+2=5. The particular comes naturally from the universal, I don't need to prove the particular after I have proven the universal.
But, alas, I have plenty of evidence of the particular. [tweet]https://twitter.com/Laurie_Rubel/status/1290317564678111232?ref_src=twsrc%5Etfw%7Ctwcamp%5Etweetembed%7Ctwterm%5E1290317564678111232%7Ctwgr%5Eb8d697f051d776bd5426141e55601e0b5cda8339%7Ctwcon%5Es1_&ref_url=https%3A%2F%2Fwww.washingtonexaminer.com%2Fnews%2F68417%2Fmath-professor-claims-equation-224-reeks-of-white-supremacist-patriarchy%2F[/tweet]
[tweet]https://twitter.com/Laurie_Rubel/status/1290554158421073920?ref_src=twsrc%5Etfw%7Ctwcamp%5Etweetembed%7Ctwterm%5E1290554158421073920%7Ctwgr%5Eb8d697f051d776bd5426141e55601e0b5cda8339%7Ctwcon%5Es1_&ref_url=https%3A%2F%2Fwww.washingtonexaminer.com%2Fnews%2F68417%2Fmath-professor-claims-equation-224-reeks-of-white-supremacist-patriarchy%2F[/tweet]
And there is plenty more evidence here: https://archive.ph/Aw8PQ
Your next move is to deny the evidence that I provided by whatever way you can. Let's not mistake ourselves here, your denial of the obvious stems from your political affiliation.
Let us all remember the peak of these people's insanity:
Quoting GrahamJ
Are you conviced now? You should be, I am not going to deny obvious reality because modern leftists don't want the ridiculous consequences of their mis-ideologies thrown in their face.
Lots of noxious examples of woke authoritarianism here, but would you agree with me that Laurie Rubels comment about math and data being non-objective was likely not referring to the logic of calculating in itself but the contested subject matter it is attached to? That many facts in the social sphere are contestable doesnt in itself seem to be an unreasonable assumption. What many do find unreasonable are the sweeping guilt by association tactics (white privilege, implicit bias, etc) used by some on the left.
I accept a distinction now, but I don't think I'd follow Heidegger in saying normal science is not-thinking, and revolutionary science requires philosophical thinking -- or something along those lines. "What is the difference between these crafts?" is hard to answer.
Sometimes philosophy and science works in concert, but sometimes they're orthogonal to one another such that a change in philosophical belief will not result in a change in scientific belief, or vice-versa. So not so much at odds as simply different in what they do.
SOCIAL CONSTRUCTIVISM AS A PHILOSOPHY OF MATHEMATICS:RADICAL CONSTRUCTIVISM REHABILITATED?Paul ErnestUniversity of Exeter
These people are actually right when they say that 2+2 is not always 4. There is a myriad of arguments we can bring up for that. The meaning of the symbols used¹, what the symbols stand for², the arithmetic system we are using³, and others.
1 Of + and =. In the group , multiplication is by definition not defined. For real and complex numbers, the symbol * for multiplication is a commutative operation, for square matrices it is a completely distinct operation (not commutative for one). For vectors, there are different kinds of multiplication, cross product, scalar product, outer product.
2 Two halves added together make one whole. 10 liters of water added to 1 liter of salt does not add up to 11 liters of material.
3 For mod3 arithmetic, 2+2 equals 0. In binary, 2+2 isn't a thing beyond that it is a decimal representation of 10?.
But the problem is that this is not how many (perhaps most) of them go on about it¹ because these relativisms of basic arithmetic are well known and they don't engage with them productively , a broken clock is wrong twice a day, their purpose is not to explore the world and unravel its truths, their purpose is childish, they (and I am psychologising here) must be literal children in the mental sense because they are simply pushing to see how much they can get away with stuff, just like kids break stuff to see how much they can push their parents infinity sexualities, then rocks are racist, segregation is ok if it is minorities choosing when to do it, now math is white supremacist. Why do you think that these same people are so supportive of all things statal regardless of whether it is beneficial? They have a paternalistic idea of the State. Call me Freud 2.0, but these are people who never grew up to impose limits upon themselves and give it to others to do it for them, which is why you don't see them in high-stress professions like oil rigs; they just want people to be pushed to the far-right so that they are finally oppressed, and they are succeeding, it is like a weird political fetish.
Inb4: Someone here will quote the sentence before and say it applies to me.
1 And then comes the naive laureate in mathematics to talk about how these people are right because of the reasons I listed in 1 and 2 and 3 without realising that those people are not engaging in the foundations of mathematics and mathematical logic at all, but in politics.
Quoting Joshs
The way that Laurel goes on about it is completely confused. She quotes an article for interpretation of data (which I assume implies statistics) and then goes on to say that math is not culturally neutral. Even if what she had in mind is that math can be used for manipulation (which I don't agree with, math is not the same as statistics), what she writes comes off as badly thought-out bait.
AND THIS IS MY POINT!
It's about K-12 education.
It's not about mathematics itself, or math being racist or about 2+2=5.
It's about minority students not being so as majority students, and that the current is educative methods aren't good when it comes to them. Or something like that. That is a totally different discussion. And you can make a great argument against this if you want to engage in the actual statements. Not the strawman argument of Oh No! The pomo wokesters want 2+2=5.
Because arguing here the 2+2=5 simply is a strawman argument, lazy and misses the point. There's ample reasons to say just why when teaching math to kids in school, you have do it the way it's been done, but that is an educational debate. One can start from the fact that it isn't a form of "white supremacy"... starting from how mathematics is taught in Asia, for example. In China they haven't been subject to "white supremacy". And you can oppose these views on educational reasons too. That kids who aren't so interested in math, arithmetic is actually good to be taught by doing and doing it again until you don't have to think that 2+2=4. You don't have to start to teach it with first teaching set theory (which was in the 70's taught to me at first grade) or the present woke arguments.
Even if written in Chinese, some of us could do the math:
And when it's not actually confronting the real issue at hand, this kind of argument (2+2=5) can easily be dismissed. You aren't making any point here with 2+2=5 if the argument is about the ways to educate people.
No, that is wrong and you either did not read the rest of the post or ignored it, that much I expected many posts ago.
Quoting Lionino
Mind you, I have had this exact conversation with other leftists, just like I have had the same conversation with numerous other people surrounding other topics and the script and tactics are always the same. I never expected to convince you of anything. My posts don't speak to you or other "hylics" possessed by ideology but to the "psychics" or "pneumatics", I have proven my case and I rest it.
And it simply doesn't mean that mathematics is culturally relative. It's about education of mathematics, not about math itself.
Why is this so difficult for you to understand?
In what way do you regard 'Principia Mathematica' to be a fiasco?
Quoting Gary Venter
I don't have enough maths knowledge to drill down into this, but no doubt axioms or presuppositions (and their justifications) lie the core of postmodern investigation.
Agree on these points:
(1) A theory is categorical if and only if all its models are isomorphic with one another.
(2) First order Euclidean geometry is categorical.
But some points I would put differently:
(3) The incompleteness theorem implies that there is no recursively axiomatized, consistent, sufficiently arithmetical theory that is categorical. But that is endemic not just to set theory but even first order PA, Robinson arithmetic or many other theories for even just basic arithmetic. Roughly speaking, pretty much when you have successor, addition and multiplication, you don't have a categorical theory. But even more basic to the incompleteness theorem, from Lowenheim-Skolem we know that a theory with an infinite model has models of all infinite cardinalities, thus not categorical.
(4) We presume that ZFC is consistent, so there is the proper class of all and only the models of ZFC.
(5) It's not clear what is meant by [my paraphrase] "a theory specifying or not specifying an object". There are two notions of definition:
(a) In a theory, given an existence and uniqueness theorem, we may define a constant symbol. With a model for the language of the theory, that constant maps to a member of the universe, and if the model is a model of the theory, then that member of the universe is the one that satisfies the definition.
(b) Given a model, a member of the universe is definable in the language if and only if there is a formula with exactly one free variable such the formula is satisfied only by an assignment of the variables that assigns that free variable to said member of the universe. (This can be extended to relations too.)
But the class of all and only the models of a given theory is a proper class, so it cannot be a member of a universe. (I think the following is right:) On the other hand, in class theory, we can define the proper class {x | x is a model of ZFC}. Or in ZFC we can define a 1-place relation symbol M by: Mx <-> x is a model of ZFC. But in ZFC we can't prove that that is not the empty relation.
/
In any case, yes, usual formal theories for mathematics are such that each one has non-isomorphic interpretations. That is a mathematical fact. But I don't know that that blocks a realist from reasonably regarding mathematics to be referring to certain objects.
That seems like a good synopsis to me.
So how is the above supporting your claim?
Did they or did they not use the Critical Theory of the postmodern to write their own worldview? Derrida's post-structuralism certainly has nothing to do with critical race theory. So, how in the world did they spin it off to something else?
Pretty much.
Quoting SEP
The confusion comes from the polysemy of terms such as "postmodernism", "critical", and "deconstructivist". Standard deconstructivists deconstruct. The intersectionalists deconstruct to build anew. Their methods may be alike (though surely not identical) but the goals are different.
CRT does not seem to talk about metaphysics, phenomenology or language, barely about existentialism. It does talk about power structures, about subversion, about oppression. In that sense it is clear that CRT has little to nothing to do with Derrida or Deleuze, but everything to do with the Frankfurt school.
{J. Willard Gibbs is definitely pre-post-modern.}
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I don't think so. I still think that their focus is on the societal aspects of mathematics, starting perhaps with the way it's taught.
Postmodernists don't have such knowledge about ZF etc.
What they will (unfortunately) refer to is Gödel's incompleteness Theorems, but... basically I get the feeling that the just mention it to say that they are aware of incompleteness results existing. But that's basically it. If they say something more, it's quoted by Alan Sokal in "Fashionable nonsense".
Or if I'm wrong, please quote the text that shows your point.
Deleuze, Wittgenstein, Heidegger and Husserl have a lot to say about the foundations and meaning of mathematical reasoning. For Heidegger mathematical thinking is inauthentic, for Husserl it doesnt understand its basis in subjective processes of constitution, for Deleuze number is ordinal before it is cardinal, and for the later Wittgenstein it is socially constructed.
You think Wittgenstein's Tractatus Logico-Philosophicus is postmodern thought? I beg to differ. I think that what Wittgeinstein says about mathematics there is quite true philosophy of mathematics.
I'm not familiar with Deleuze, but at least Heidegger and Husserl did have a broad understanding of philosophy before them and that of Francis Bacon, Descartes, Kant. That the 19th and 20th Century continental philosophy had the "linguistic turn" isn't at all postmodernism, but at least they had an understanding of what they were criticizing.
The Tractatus is not post-modern. But Wittgensteins later work, which turns its back on the logical grounding of mathematics put forth in the Tractatus, had a strong influence on many postmodern thinkers, including Rorty and Foucault. Lyotard, who popularized the term postmodern, devoted a chapter of one of his books to the later Wittgenstein. Heidegger was of central importance to postmodern poststructuralists like Derrida, Foucault and Deleuze. Husserl is not generallly considered to be postmodern, but I believe his work on the philosophy of arithmetic and logic contributes ideas that are taken up by postmodern thinkers.
Well, where did Bertrand Russell end up? I think the reason for the "linguistic turn" is obvious: if you find things that are problematic and you cannot find an answer one way, you try to think about it differently.
Yet I think here you come to the real problem of the postmodernists. While Wittgenstein, Husserl and Heidegger (and actually even Foucault) knew what they were criticizing, the older philosophical views, the postmodernist just refer to these guys.
That's the basic problem: if you know only the critique of something, but not study the itself actually, you position is weak.
That's why if you criticize Marxism (or Marxism-Leninism), then you really have to have at least a basic understanding of Marx and Lenin. And obviously it can be frustrating, but it's important. For example I'm very glad that in the economic department in the university, they did go through the ideas of Marx and Marxian economics.
Some of the critical, if you'll excuse the pun, figures in the CRT development (Kimberlé Crenshaw, bell hooks, and Cornel West) cite Derrida as influential on their thinking. And i think its reasonable to use that metric, rather than mentions in textbooks, as a metric for the relevance of ideas.
Commenting on this, I don't think it is quite correct to say that multiplication is not defined in . It doesn't exist in the scope of of course, but whether it is defined or not is not a pertinent question. But the point stands nonetheless.
Postmodern?
No clue what you mean.
Sorry, I missed this discussion. How does this bit about group theory relate to postmodernism?