though the grunt, growl, and purr lack discernable syntax, it could be risky to interpret them as semantically void. — Arne

Indeed. I'm not arguing this. I'm just saying they are not propositional and are not as clearly beholden to local axioms as a more fully developed linguistic system is. My point was a minor one - that between silence and linguistic 'coherence' lies noise.

I maintain that bodily experience can not he reduced to language and culture. Our bodily sense of situations is a concretely sensed interaction process that always exceeds culture, history, and language.

This is an intriguing position and I am sympathetic to embodied cognition. I'm not sure what it means to 'exceed' culture. Does he mean that bodily experince is primary and the others later and derivative? Or is there more of a reciprocal relationship?

It will incorporate the insights of postmodernism and move past the dead end where postmodernism seems to stop. I

Do you agree with Gendlin's account here? Does postmodernism lead to a dead end?

↪Tom Storm chicken or the egg. and with no language to express the axioms, silence. and speaking only for myself, silence is preferable to incoherence.↪Fooloso4 — Arne

I'm quite partial to incoherence, but it depends on the context. I think between language and silence there are also grunts, growls and purring....

I would have thought language depends or is grounded upon the logical axioms: identity, non-contradiction and excluded middle. Without which... incoherence...

As a matter of fact I do. I once heard a story of a fellow who asked a karate instructor how long it would take to get a black belt — HardWorker

That clarifies things. I don't think this example counts as philosophy - unless you are using the word metaphorically. It's an allegory using irony to teach patience. Furthermore, if you are taking this story literally and applying categories of right or wrong to it then you are not understanding it. The allegory is likely intended to teach the right attitude to personal growth and has nothing really to do with karate.

Now back to philosophy. What do you consider philosophy to be? And a follow up question, to what extent are your binary categories of 'right' and 'wrong' useful?

I was thinking similarly. :wink:

If philosophy ever gets around to proving an objective morality, then it would become science. The great mysteries that philosophy has yet to solve are: Morality, knowledge, and (my opinion) art. Perhaps there are others, but those are the big three. — Philosophim

I'm curious - you don't think reality is one of these - or do you have a presupposition about the nature of reality which informs the others?

Is this a serious OP? Would it not be obvious that no one can be familiar with all philosophies, let alone agree with them all? What does it mean to say you 'agree' with a philosophy and what counts as a philosophy?

But do you need a good understanding of philosophy in order to determine which philosophy has merit or not? How does one make such a distinction?

Philosophies have been shown to sometimes be wrong. — HardWorker

Do you have an example in mind?

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. — jgill

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?

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. — Count Timothy von Icarus

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.

Only today there is no one comparable to Plato or Aristophanes. I don't think it was a matter of manipulating the good, but rather, in the absence of knowledge of the good, making images of its likeness. — Fooloso4

That's interesting. How did they consider poetry was able to do this - by aesthetic distraction and emotionality? Poetry as truth's false gold?

:up:

Well I disagree with this antirealist suggestion, Pez – "concepts" do not "change" themselves, we change our concepts in order to adapt. Turning on house lights at night in an unfamiliar house does not change the house, rather you change only your capability for orienting yourself within that unfamiliar house. Likewise, given that we inhabit the world, the 'models (i.e. pictures, maps, simulations) of the world' which we make conform with varying degrees of fidelity to the world and thereby inform our expectations of how we can adapt to the world. For instance, GR & QM were as true about the physical world in Aristotle's day and in Newton's day as they are today even though Aristotle, Newton and their contemporaries, respectively, were completely ignorant of them. Thus, changing our concepts of reality, in effect, only changes us and not reality itself. — 180 Proof

That's very elegantly put. Thanks.

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. — Moliere

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:

You’re 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. — Joshs

This notion of 'mathematical idealizations' which are essentially empty seems a promising direction as per below -Derrida followed by Joshs

“I can manipulate symbols without animating them, in an active and actual manner, with the attention and intention of signification…Numbers, as numbers, have no meaning; they can squarely be said to have no meaning, not even plural meaning. …Numbers have no present or signified content. And, afortiori, no absolute referent. This is why they don't show anything, don't tell anything, don't represent anything, aren't trying to say anything. Or more precisely, the moment of present meaning, of “content,” is only a surface effect.”

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. — Joshs

Derrida, writing in Margins of Philosophy, says:

Every sign, linguistic or nonlinguistic, spoken or written (in the usual sense of this opposition), as a small or large unity, can be cited, put between quotation marks; thereby it can break with every given context, and engender infinitely new contexts in an absolutely nonsaturable fashion. This does not suppose that the mark is valid outside its context, but on the contrary that there are only contexts without any center of absolute anchoring. This citationality, duplication, or duplicity, this iterability of the mark is not an accident or anomaly, but is that (normal/abnormal) without which a mark could no longer even have a so-called “normal” functioning. What would a mark be that one could not cite? And whose origin could not be lost on the way?

I guess I've been curious how this approach applies to maths. What does it say about the certainty and universal reliability of equations?

I hear you. I find the range of ideas which flow around the categories of post structuralism and post modernism very interesting. The antipathy they frequently generate makes it even more fascinating. On this site I’m mostly interested in the conversations we create. If I were of a studious disposition I’d probably just read books and avoid untheorised fora opinions.

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. — Moliere

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.

Socrates wants to banish the poets from the just city. The philosophers and not the poets should be the educators, the myth makers, the makers of truth, and of proper conduct toward men and gods. — Fooloso4

Thanks. I thought Plato saw poetry as immoral, distracting folk from truth. Doesn't he also agree that poetry has a role some later works?

How are we to understand this today - sounds like a culture war. Was it that poetry functioned a bit like sophistry, using its artfulness to manipulate rather than identify the good?

Plato referred to it as 'the quarrel between philosophy and poetry'. — Fooloso4

Nice - can you expand a little?

I’ve met self-proclaimed non-spiritual atheists that uphold this metaphysical worldview but are in practice superstitious and affirm things like “your car was broken into today because you weren’t cordial to person A last week” or, as an example of the flipside, self-proclaimed Christians that adhere to all ritual aspects of their faith and uphold this metaphysical worldview while at the same time in practice being in many a way atheistic (e.g., they fear - and hence innately believe - death to be a cessation of being; or else don’t believe in the occurrence of spiritual realities in the here and now, as contrasted to occurring for biblical figures (e.g., “burning bushes” are OK biblically but not in reality that is lived); etc.) - this to not address the grave hypocrisies in ethical principles relative to Jesus Christ’s teaching that often enough occur (the ontology of values being in many a way metaphysical). — javra

I don't find any of this surprising and I don't think professed worldviews tell us much. I've met many atheists who believe in clairvoyance, astrology and magic. Atheism is just a position on one idea. God or not. People often assume it means Richard Dawkins acolytes.

Materialistic Christians are pretty common too. I grew up in the Baptist tradition in the 1970's We were taught that most of the stories in the Bible were allegories. Most Christians I knew did not believe in ghosts, demons, miracles or anything supernatural. Religion seemed more about community than anything else.

Having worked with people dying in palliative/end of life care, I have noticed how often Christians no longer have faith or any interest in God. Deathbed deconversations seem to be more common than non religious people finding god/s in their pending mortality.

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? — Banno

Yes, I'm interested in this too.

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.
— Tom Storm

Here's the context:
The notion of mathematics as objective and eternal is today being replaced, among mathematics educators, by the postmodernist notion of “social constructivism.” According to “social constructivism,” knowledge is subjective, not objective; rather than being found by careful investigation of an actually existing external world, it is “constructed” (i.e., created) by each individual, according to his unique needs and social setting. Absolutism is deliberately replaced by cultural relativism, as if 2 + 2 = 5 were correct as long as one’s personal situation or perspective required it to be correct.
— Arthur T. White — Banno

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.

It's unclear to me what you are attempting to say other that there are different ways of knowing and that you believe in god because of personal experience. I was talking to a Muslim on Wednesday who put his argument the same way you do, except for him Jesus was a mortal who died and only Allah provides the way to Paradise. How do you measure one person's personal feelings (revelation) against another's, when the revelation grounds utterly different worldviews?

Yes, I was familiar with the Sokal affair.

Pomo was never in high regard among the general population , so there was nothing to recover from. — 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.

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? — 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.

There is a definite tendencies towards "No True Nietzschean," arguments when someone transvalues values the wrong way, towards the wrong politics. — Count Timothy von Icarus

That's an amusing line. :up:

More simply put, my position is ↪180 Proof: nature does not "comply" with "physical laws"; rather our best, unfalsified models conform via physical laws (i.e. generalizations of transformations of phenomena) to the observable, objective regularities of nature. — 180 Proof

I was just talking about this to someone at home. Language does us a great disservice when we use terms like 'laws' of logic or 'laws' of nature in as much as for many this word implies a 'lawmaker', so that anthropomorphic theism is built into the language and infects people's thinking.

I dont agree with this split between feeling and thinking. Pleasantness and unpleasantness are not just meaningless bodily sensations that happen to get tied to different experiences via conditioning. They are better understood in terms of enhancement to or interruptions of goal-directed thought. We are sense-making creatures who attempt to anticipate and assimilate strange new events via familiar schemes of meaning. We strive to make the world meaningfully recognizable and relevant to our purposeful activities, and pleasantness-unpleasantness are meanings that express our relative success or failure in making sense of things. Anxiety, guilt, fear and anger result from our finding ourselves in situations that threaten to plunge us into the chaos and confusion of incomprehension. — Joshs

I’ve come to a similar view. This is beautifully explained.

X 2

Jesus of Nazareth did exist. — javi2541997

There's no good evidence of this but I think it is safe to say the myth came to us via one or two messianic preachers of the time. There were many doing the rounds. This plus borrowing miracle stories etc from other places. Even today we can find living gurus and religious figures who do 'miracles' and have exaggerated stories attached to them.



I don't follow or accept any religion and I'm not a believer in gods or goddesses. I've written here before that (aside from enculturation) I think theism is a preference people have, like their sexuality or an aesthetic appreciation, which may be back filled, ad hoc with reasoning. The notion of god has never supported any of my sense making, nor seemed coherent to me. I haven't 'felt' a need for it.

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. — Fire Ologist

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 we’re able to understand the physical world.

Same goes for logic. Same goes for language. — 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.

:up:

I wish they were more cunt and less post.

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…

Thanks and Christ! It’s a can of worms…

I'm interested in what I might get from member's responses. As I said at the top, time is limited and I have no education in any of this, so I am just wanting to sift through the various views. My trying to read about maths proper would be like teaching card tricks to a dog.

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) — 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.

But a mathematician talking about post modernism... that might be interesting. — Banno

A conversation between both would be interesting (and perhaps incomprehensible).

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. — Fire Ologist

Nice.

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. — 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)?

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. — Count Timothy von Icarus

Could be. But no one is claiming PM is entirely original in this.

So, attacking the grounding would be nothing new — Count Timothy von Icarus

I'm sure, but no one is saying it is.

whereas attacking the reliability seems extremely difficult if we're not talking about applied mathematics — 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.

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. — Count Timothy von Icarus

Does your language here suggest that you take post modernism to be a posturing deceit?

There is already a lot of pluralism and "questioning all assumptions," in the foundations of mathematics/philosophy of mathematics, so it's hard to see what a post-modern critique of mathematics would find worth critiquing. — 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?

AFAIK, no one, including any p0m0, has ever pointed out a 'culture' wherein mathematics does not work — 180 Proof

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.

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. — Joshs

That's what I'm looking for. It's not an easy thing to fully understand.

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. — Joshs

Any thoughts on the unreasonable predictability of maths? Does maths allow us to make any assessment of realism?

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. — javra

Great and thoughtful response: I'll mull over it.

I gave you an example and you completely ignored it: please re-read my previous response. — Bob Ross

Do you mean this below?

let me use a perhaps odd example. A calculator would be hypothetically perfect if my purpose for it is to hold up books and it is flawless at fulfilling this task. — Bob Ross

As you say an odd example.

I think this is just a strange way of defining the idea of flawless. You may as well say that perfection is an erect penis flawlessly being used for hanging up a dressing gown.

The calculator is actually perfect if it is in a state of 100% (flawless) self-harmony and self-unity—i.e., all the parts are in agreement and peace with the other parts. The calculator isn’t broken, it doesn’t have parts that oppose other parts in a manner that brings disunity, etc. — Bob Ross

This sounds like what happens when language is used imprecisely.

I can accept that we might use the word perfect to describe a calculator which does its job flawlessly.

I would avoid talk of parts being in agreement and at peace with each other. The calculator is not Krishnamurti.

What benefit does the word prefect bring you here? Does it not just mean 'working as intended'?

I don't think you are quite understanding pragmatic goodness. It is perfection for some purpose. — Bob Ross

I think if it means pragmatic goodness then leave out perfection. The hallmark of 'pragmatic' is it's efficacy in certain situations (which may change with new information and says nothing about whether it is good or true). It's utility. The moment it is called perfection it suggests the goodness is far from pragmatic and constitutes that which cannot be improved upon.

In terms of actual perfection, the clock is perfect (morally good) if it is in self-harmony and self-unity. — Bob Ross

You have parsed perfection into a kind of dualism - that which is not quite perfection (the physical) and that which transcends the human (Greek philosophy's The Good).

I'm assuming you are joking about a clock being morally good, with self-unity, etc.

:up: This is the matter I'd like to hear more about from someone with more specialized understanding of the subject. It's in the realm of social constructivism, perhaps. And I guess it leads to a subsidiary question, does supposed universal language of maths have to be such as it is, or could it have taken a different form and had the same results? And in this identified difference, does this point to maths being more arbitrary than we think?

But its not the most pivotal of issues to me. — javra

Ditto.

Thank you for an interesting conversation. I've appreciated your approach. :up:

But, if so, then – via pi and so forth – so too is all our modern scientific knowledge of quanta nothing more than concoctions of human imagination. — javra

I am not sure my point leads here but I am sympathetic to this regardless. I am a reluctant anti-foundationalist and consider human knowledge to be contingent. With constructivist leanings, I've often thought truth is shared subjectivity.

If I can remember back to the point of the discussion I think I was arguing that I have never seen an physical example of perfection in the real world. Examples we could proffer like Margot Robbie or George Elliot's Middlemarch or Mahler's Second Symphony or Botticelli's; Primavera, whatever, are using the word perfect to say we like them. The notion of perfection in this kind of context becomes a superlative rather than a precise philosophical understanding.

I suspect only maths offers us what we might dub perfect solutions (but I am no mathematician, so I'm happy to be wrong here) where an equation is the most elegant, prefect solution to a given problem. An equation which cannot be any better. This would satisfy my idea of perfection as that which can't be improve upon.