There is a widespread belief among mathematicians that mathematical truths exist in a context outside of and independent of all human thought, a kind of platonism. What is the Holla Forums interpretation of this? Is this pure ideology, or is it compatible with materialism?
Mathematics
Jason Ross
Lucas Davis
The task of mathematics, like all other sciences, is not to discover any actual "truths" as in facts about nature in itself as these can never be known to us. Their task is to describe what we humans can say about nature, what predictions we can make. In mathematics this becomes extremely clear as there is no illusion of a "true nature" that we can perceive directly, it is a pure abstraction that can be used to describe nature in the eyes of a human and make accurate predictions about this matter. One example of this is that in mathematics one can describe numbers past infinity, while if one accepts that reality can be perceived by humans there is clearly no such thing as beyond infinity.
Now this is speculation on my part, but this "new wave platonism" may stem from the imposed divide between "hard" and "soft" sciences, where mathematicians need to believe they are on the side with the hard sciences. Which to be fair makes a lot of sense, as almost all of physics and engineering becomes impossible without mathematics.
Jaxon Jackson
It's retarded, and possibly the ultimate example of the kind of vulgar materialism that uncritical naive empiricism gets you.
Easton Cook
Yes it is true.
Connor Cox
As I understand it, materialism is literally the opposite. There is nothing outside specific, concrete things. There are tendencies, trends, evolutions, etc. but they are nothing outside of the results that they produce.
Elijah Murphy
As a mathematician myself, I love Platonic numbers.
It probably isn't comparable with materialism, but I am not going to bend by metaphysical beliefs based on my economic beliefs, I'm sorry but that's not happening. For all I know this is all an illusion, and there was never any Karl Marx, but 2+2=4 motherfuckers.
Oliver Bennett
But that is a mere abstraction. It isn't some "truth" concealed by nature in itself. It can only be considered truth if you accept truth as what we can say about how nature behaves. To think that mathematics is grounded in "reality" is quite absurd, as even if we accept that what our senses can detect is reality itself and not just a representation of reality not one mathematical equation can be detected by our senses. They are abstractions which are useful for describing nature and predicting outcomes, and only in this sense they are "true"
Metaphysics isn't like picking which football team you root for
Liam Bailey
Kek. Have you taken any math courses which start with a "3" or "4"?
It's purely about definitions and the logically implied conclusions we then draw from them. It's not reflective of the world, but a world. See Dennett's Higher Order Truths About Chmess.
This is tantamount to saying that doing any philosophy at all is putting idealism over materialism.
The meanings of "1+1", "2", and "=" are all socially constructed, but the truth of "1+1=2" is contingent only on these meanings, and not any objective fact of the world. We're not dealing with metaphysics in the first place when we do mathematics, but the "physics" of mental constructs, which may or may not have been constructed for an abstracted resemblance to or utility in explaining various aspects of the physical world.
Colton Kelly
op do you seriously not understand mathematics? how about you ask on a relevant board?
Caleb Flores
Isnt math just the study of a system of logic based on base truths set by humans?
Ethan Jenkins
>It's not reflective of the world, but a world. But this world doesn't exist, it's an abstraction. It's only purpose is to describe the world. So 1+1=2 is true not because it refers to any real "truth" in the world, or any imaginary world for that matter, but because it can be used to describe reality as we percive it.
This holds true for all scince, not just matemathics.
Bentley Walker
Didn't mean to greentext all that shit
Nicholas Russell
learn2badiou, comrade mathfag
Aiden Nguyen
thanks for those badiou links, highly interesting, going to share these with my advisor.
David Long
m-muh subject-supposed-to-know
Here's more basic intro if you are afraid to go alone, comrade mathfag: 4shared.com
Zachary Parker
You should read Badiou peebs
Kayden Collins
interestingly, my advisor is actually a philosopher but does mathematical modeling work. Therefore this stuff is right up his alley.
Lincoln Miller
Define "exist."
True, and what I'm saying.
It's only purpose is to describe the world.
False. That's far from its only purpose. Intellectual curiosity in its own right is an equally strong impetus which overtakes understanding the "real world" in many places. What implications does classifying the nontrivial zeroes of the riemann zeta function have for our understanding of the universe? Nothing, really, for now.
In the ring of integers modulo 2, 1+1=0. That doesn't readily describe some natural phenomenon observed through sense perception, but rather an abstract concept.
Science is about presupposing there exists an objective "real world" governed by consistent laws which we can approximate through models with predictive capability, math is simply about following definitions to their natural conclusions and need not necessarily have anything to do with this objective "real world." As such, math effectively brackets metaphysics, while science inherently requires some metaphysical position to justify its foundations. The application of math to studying the real world, however, is a form of science which requires such a metaphysical position, and it seems to be this sort of application you're really talking about when you say "math." I feel a distinction is worth making between the two, however. For instance, you can deal with the definition and elementary consequences of Minkowski spaces and explain how the postulates of special relativity imply them without claiming anything about the real world, but justifying special relativity as a useful model of the real world is where you need some empirical evidence, part of which deals with the consequences of the Minkowski space definition. So the leap is not in the structure of the math itself, but rather in the connection of "a world" to "the real world."
Physical science is very much a materialist thing in its foundations. If mathematics was inherently idealist, we'd run into a variety of serious problems in applying it to further a materialist ontology of the world.
Ok
Ryder Scott
Have you read a single line from Badiou?
Landon Thompson
He did not.
Henry Miller
This is very wrongheaded. Non-mathematicians attempting to discuss the philosophical implications of mathematics smh
It's used so heavily in the sciences because the argument structure is perfect and, absent genuine verifiable mistakes, it does not dilute the brand. It is a tool for obtaining the most precise implications of a given theory. What he does here is confuse the "lossless" argumentation style with one which actually adds something from beyond the realm of ordinary, constructed science, seemingly drawn from the ether.
As I say, the definitions in math are arbitrary, even if chosen for specific, highly useful, highly relevant reasons. The "absolute, context-independent objectivity" is in what logically follows from the definitions and foundations themselves, but these must still be chosen, actively, and properly applied to the real world by individuals still apparently subject to all the same epistemological hurdles. He seems to beg the question to avoid directly assuming that observations can reveal information about the material world leading to successively better predictive models, or that this material world is objective and fundamental. Which, while he has some harsh words for radical subjectivism, belies a certain skepticism of "meta-narratives." The need remains to justify the construction of science as a valid approach to the objective. No defense of mathematics as merely internally self-consistent can itself accomplish this.
Henry Ramirez
Wasn't some theorem about mathematics can't being used to prove themselves?
Landon Murphy
It's all fucking bullshit. Math a tautology. It is true within its own given rule set. Math doesn't explicitly relate to reality. There is no such thing as 1 much less 1 + 1 equalling 2. It is a linguistic tool we use to describe the world.
Jeremiah Jackson
What field?
Jaxson Barnes
Unfortunately no amount of mathematics can help a guy parse this sentence.
"Math" is better viewed as the collection of all such conceivable rule sets.
While it is true that the truth of every "A->B" statement comprising "math" is completely contingent on choice of A, for any given B, and not on context or value judgments, I feel this is an impermissibly broad definition of "tautology," seeing as the level of work that goes into most mathematical results is far from trivial. But yes, the view of mathematics as some absolute transcendental reality that precedes and supersedes human existence is not a robust one.
Tyler Jones
Badiou is a trained and teaching mathematician, you ignoramus.
Aiden Hughes
that's not what transcendental means
Caleb Ross
Yeah, not that.
Yeah, seems appropriate.
So your point is, what? "Transcendental numbers" seem to inherit their meaning in the first place from the latter definition, as they're not constructible through ordinary arithmetic, meaning direct personal experience and sense perception.
Funny, because I haven't been able to find any relevant degree or mathematics teaching experience of his. Feel free to prove me wrong, however.
Elijah Barnes
You forgot to mention "within an arbitrary set of axioms" faggot. Of course that takes away all the "beauty" that gives you your sense of acomplishment.
Jaxon Peterson
no he isn't
Luis James
Proofs?
geddit
Jose James