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. — Tom Storm
what is the relationship of the reality we map maths too (or visa versa)? — Tom Storm
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
Same goes for logic. Same goes for language. — Fire Ologist
This recognizes the issues at the foundations of math but also fixes "math as math" in itself, as a long-form tautology. 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.
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. — Tom Storm
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. — Jamal
↪Tom Storm I suspect that postmodernists talking about mathematics woudl be a dime a dozen. Google supports this.
But a mathematician talking about post modernism... that might be interesting. — Banno
Thanks and Christ! It’s a can of worms… — Tom Storm
Now perhaps we could have a thread on postmodernism and science, differently from postmodernism and mathematics, there is looots of content around that :razz:
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. — Count Timothy von Icarus
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. — Count Timothy von Icarus
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. [...] They tend to be metaphysical, or naive, realists about both ethical and objective truth. — Joshs
As if we haven’t 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. — Joshs
...and points out thatAbsolutism 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 — White 2009,
First of all, cultural relativism is out of context in this setting. When postmodernists claim that a mathematical truth is never absolute, they mean it is to be interpreted relative to a background. Certainly 2 x 5 = 1 is true in mod (3) arithmetic. No sane mathematician or educator would go around redefining addition or any other mathematical construct because his or her “personal situation” requires it to be correct. The Platonic fact that the sum of the interior angles of a triangle being exactly 1800 was challenged neither because the personal situation of Lobachevski nor because the personal perspective of Riemann warranted it, but because the resulting geometries turned out to be no more or no less correct that the Euclidean one. — Ilhan M. Izmirli
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. — Count Timothy von Icarus
"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?" — Count Timothy von Icarus
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. — Jamal
↪Joshs
As if we haven’t 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.
— Joshs
Yeah, what would mathematicians know about maths — Banno
The article I shared was about as sympathetic as you might expect, and more than I expected. It takes an example from the literature,
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
— White 2009,
...and points out that
First of all, cultural relativism is out of context in this setting. When postmodernists claim that a mathematical truth is never absolute, they mean it is to be interpreted relative to a background. Certainly 2 x 5 = 1 is true in mod (3) arithmetic. No sane mathematician or educator would go around redefining addition or any other mathematical construct because his or her “personal situation” requires it to be correct. — Banno
“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.”
Wittgenstein’s early conception of meaning and his commitment to Logical Stoicism drove him to rid the arena of truth and logic of all human interference, which required that the states-of-affairs asserted or denied by a proposition be completely delineated, as we saw with the questions concerning whether the book was still on the table under all possible circumstances. He gave up this dream when he recognized our ineliminable role in
applying the rules. No matter how assiduously we strive to passively obey a rule, we still need to make the phronetic judgment call as to whether this state-of-affairs counts as an instance of the rule: “if calculating looks to us like the action of a machine, it is the human being doing the calculation that is the machine.”
We feel that all possibilities are settled in advance because we rarely step outside the normal circumstances where our footing is so sure we imagine it to be perfect. Wittgenstein spends considerable time constructing scenarios that throw our intuitions out of whack and leave us uncertain about what to say. This doesn’t expose a disturbing, problematic gap in our everyday usage, but rather shows that we get along fine without the propositional omniscience he had previously found necessary. Without meaning-objects’ applications coiled up, as it were, within words or the mind like a retractable measuring tape, Wittgenstein now sees each application as metaphysically unguaranteed by past instances.
“We must not suppose that with the rule we have given the infinite extension of its application. Every new step in a calculation is a fresh step. . . . It is not in the nature of 23 and 18 to give 414 when multiplied, nor even in the nature of the rules. We do it that way, that is all.”
No matter how clearly the world seems to take us by the hand and lead us, it is always up to us to recognize its authority and interpret its commands; neither past usage nor reality forces us to go on in one particular way. We will never get to the other side of the ellipsis of “and so on . . .”—not because of our all-too-human limitations, but because there is no other side; that’s the point of an ellipsis.
Since the notion of infinite extensions occurs paradigmatically in mathematics, Wittgenstein spends a great deal of time on this subject, originally planning part II of the Philosophical Investigations to focus on it. Just
as linguistic meaning occurs in our use of it, so mathematics only exists in our calculations, which means that
“there is nothing there for a higher intelligence to know—except what future generations will do. We know as much as God does in mathematics.”
Mathematics and grammar are inventions, not discoveries. As Simon Glendinning writes, each new application of a rule “is ungrounded or structurally abyssal. That is, it is logically prior to a determined rationality (or irrationality).”Without timeless mathematical truths, the notion that humanity has always followed a rule incorrectly is simply incoherent: how we follow it is the right way. “The point is that we all make the SAME use of it. To know its meaning is to use it in the same way as other people do. ‘In the right way’ means nothing.”This seems to entail the worrying possibility that if everyone began, say, adding differently—getting “6” from “2 + 3,” for example—then that “wrong” practice would become “right”, but this concern hasn’t followed the argument all the way out.
If we see this “new” way as maintaining the same rule of addition we have always used, then it isn’t new at all. If no one (except a few cranks) judges a change to have occurred then we have no ground to say that a change
has occurred. It isn’t so much that our notion of green may turn out to be grue as that, if we all “change” from green to grue without noticing it then no change has taken place—and scare quotes proliferate. If a tree changes color in the forest and no one realizes it, then who exactly is claiming that it changed? We imagine God sadly shaking his head at our chromatic apostasy, but the only way for this picture have an effect would be for Him to make His displeasure known—which would mean, in turn, that someone did notice. Alluding to the most famous modern discussion of skepticism, Wittgenstein asks:
“is no demon deceiving us at present? Well, if he is, it doesn’t matter. What the eye doesn’t see the heart doesn’t grieve over.”
A deception, carried out perfectly, becomes truth.
↪Joshs I respect many of your views, but:
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. [...] They tend to be metaphysical, or naive, realists about both ethical and objective truth.
— Joshs
How is that not blatantly incongruous (this in non-dialetheistic systems, if it needs to be said)? — javra
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. — Joshs
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 am interested in what postmodernism has to say about mathematics. — Tom Storm
Included among the articles that were published were arguments that dogs engage in rape culture and that men could reduce their transphobia by anally penetrating themselves with sex toys, as well as a part of a chapter of Adolf Hitler's Mein Kampf rewritten in feminist language.[3][5] The first of these had won special recognition from the journal that published it.
↪Tom Storm There was the famous Sokol affair, where a postmodern journal published an article arguing that quantum gravity was a social construct.
Unbeknownst to the publishers it was satire, exposing the lack of scientific rigor of the postmodernist.
Not sure they've fully recovered from that — Hanover
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