Was mathematics created or discovered?
The system we use to quantify mathematics was created by man.
define 'mathematics' and we'll talk.
>>7531882
>le naive formalist face
now you just have to define what a system is, what mathematics is, and provide empirical evidence that the system was the creation of man
>>7531902
yeah, unlike all those systems that weren't created by man.
>>7531902
You know what those mean within this language game
>>7531916
>language game
my man
>>7531868
mathematics are a man made system, about as 'real' as alchemy or theology. It is only relevant because of its socioeconomical usefulness to existing power structures. eventually matematicians will go the way of paracelsus and trimegistrus, and their whole little game will be forgotten as if it had never existed
Correct me if I'm wrong, but doesn't truth only exist in reality as correct thought? Where does this truth independent of thought occur?
created, like every other categorization of universe
>>7531946
had it been as 'real' as alchemy or theology it wouldn't have aided us with landing on Moon etc
>>7531868
>>7531873
This is the only correct answer.
Mathematics, as in invented formulas to describe relations we can observe, was created.
But Mathematics, as in the relations of the things, exists also. Things have relations, constants we can observe all over the universe.
Why? I dunno, just the way e^pi*i=(-1). That´s just the way the universe works, I guess.
>>7531969
THE MOON LANDING WAS FAKE STANLEY KUBRICK FILMED IT FOR NASA THAT WAS WHAT 2001 WAS ABOUT
>>7531969
also, it's a cheap shot to pronounce mathematics as created if your sole focus is on syntax. had it been syntax only it wouldn't be able to describe the external world at all; and yet it does and yet there are electronic devices, moon-landings etc.
>>7531936
You're assuming there are such things as exhaustive definitions in the world. What do you mean by that?
>>7531946
Nobody can be this deluded, even on /lit/
>>7531969
alchemy produced its share of useful philters and concoctions too, but that doesn't make it 'real' either. Math is not neutral but part of existing structures and ideologies, a tool used to sustain the status quo, much like theological disputes were a tool of political power in the middle ages.
>>7531996
if you use a goddamn word you better know what it means. so--what does 'system' mean?
Created, obviously
>>7532006
Some would say a system is one of the things that's presupposed by an exhaustive definition of something.
>>7531946
10/10, made me laugh and you even got two idiots to respond seriously
>>7532028
he is right though
The fact that it is fucking sophisticated doesn't make it any more real
>>7532005
but that's a shitty comparison for the productions of alchemy fail to succeed in their alleged affects/effects. math does not. math encompasses many formal languages (only the syntax is considered to be constructed or a work of man; there is nothing special about the arabic '1', you could just as well use the roman 'I' to denote the same number), it's considered and instrument in itself, and it's also about the external world aka the entities our agreed-upon terms refer to.
then there's the indispensability argument of Quine and Putnam etc
>>7532050
how the fuck do you know that 1+1=2
>>7532062
Because grouping one thing and another thing gives you two things
>>7532042
He's right, sure. But we've also discovered mathematics to be a much more logical and useful system for our discovery and understanding of the world than, say, alchemy.
>>7532062
1+1=2 is far from an universal truth. In the aboriginal arithmetic of some Papuan peoples 1+1 does not always =2, occasionally it adds up to 3, sometimes 4 or 5, it's al relative.
>>7532081
sauce?
This sounds interesting.
>>7532062
not sure what you're asking; if your concerned about truth of the statement then there are models of peano arithmetic in which propositions like '1+1=2' are rendered true. however, if you're concerned about the grammar of '1+1=2' and whether or not it is well-defined PA-sentence then no, since we take '1', '2' etc. to be conventional abbreviations of the successor function ('2' e.g. is an abbreviation for 's(s(0))' and so on) to ease readability etc.
>>7532078
obsolete disciplines like alchemy was good for its times because it managed to described known phenomenons. Same applies to maths. We will eventually overcome it as we (if) approach more complex understanding of being.I bet my money on object oriented ontology and something that will come out of it
>>7531946
Post-structuralists pls go
>>7532096
since you obviously known far more of maths then me, I was asking about the true-ness of the statement that whether we can know, considering integers, that there is not another value between 1 and 2, that would give the sum of 1+1. (thus
Its just my mumbo jumbo, Im in applied sciences.
Mathematics is based on a few central logical axioms that (thus far) have seemed to map very closely to how the real world operates.
The difference between mathematics and alchemy is that alchemy couldn't survive the central assumptions being updated. If our central assumptions that mathematics is based on (which are certainly created) are proved false, mathematics will change, not die, unlike alchemy. It's too socially entrenched at this point. Literally too big to fail.
>>7532136
>The difference between mathematics and alchemy is that alchemy couldn't survive the central assumptions being updated. If our central assumptions that mathematics is based on (which are certainly created) are proved false, mathematics will change, not die, unlike alchemy. It's too socially entrenched at this point. Literally too big to fail
this might and also might not be true
>>7532081
kek end your life
what the fuck does that mean "occasionally adds up to 3"? a function such as + has only one output for any n-ary input/argument. it is nonsense to say that +(1,1) can output A one time and then output B some other time, while A =/= B. it's inconsistent with the nature of what a function is. just because the 'Papuan peoples' use the very same symbols as we do in western societies, doesn't mean that what WE mean by '1', THEY mean by '1' too. there is nothing special about the symbol '1' as i asserted in >>7532050: it very well may have multiple interpretations. the 'Papuan people' just probably use the same syntax but have it refer to something else entirely.
>>7532005
Can you explain to me how math is a structure of power?
>>7532137
Of course, but bet your money on it still being called mathematics even if it's fundamentally different.
>>7532138
Not the anon to whom you replied, but to give another example, in Oceania 2 + 2 usually = 4, but sometimes = 5
>>7532140
our financial markets depend on mathematical algorithms as does the advertising driven tech-industry. This brings the neutrality of mathematics into question, as they are not just a tool of objective inquiry but one for the exercise of power. Hence, challenges to the system are inherently political, there would be nothing more disruptive to the current system than an uprising of radical post-math theory.
>>7532173
computers deal with mathematics, does that mean the argument you made is therefore invalidated since you made it through the use of mathematics?
youre a fucking moron lmao.
>>7532189
you are retarded and he is right
Just consider that big thing that solitary jap prof published in Nature some months back about prime numbers
Things like that will seriously challenge encryption, algorithms, computational capacity, in a big-scale
>>7532189
what a trite response to an interesting point
>>7532201
You cannot use the Jap proof in this as (and no offence here) nobody actually understands it well enough to say if it is correct or not. They literally had to send people to live and study it with him in order to even get close to verifying it and there is still no definitive answer to if it checks out or not.
I agree with you, but I do think that was a bad example to cite. It's relevance was also played up by the media. Also the proof (as far as the guy has himself stated) supports the basic tenets but fucks with a lot of high level abstract shit, which isn't used in markets etc anyway.
>>7532219
Agree, it wasn't a good example I just though its something quite universally known to imagine such situation
Does your computer work when you stop believing in math?
Do planes fly when you stop believing in math?
Congratulations, you've just proved that mathematics was discovered.
>>7532173
Interesting thought, but I do not think it would be as disruptive as you think. The current models project, predict and control markets well. Any change to this theory will either aid the controllers or not see any kind of implementation outside of academia. But perhaps I'm being cynical.
>>7532243
>>7532173
I think your issue is that leftists just suck at math
>>7532243
My computer works with electric charges, not numbers.
>>7532201
the one he posted 3 years ago that nobody understands?
Even the people who don't understand it can't explain to you what they don't understand about it. It's ludicrous.
There's billionaires with trillions leveraged on the mathematical certainty of predictive and encrypting algorithms. Do you think this guy wouldnt've gotten paid to the teeth or extorted in some way to make sure whatever he discovered if it were applicable in any way to destabilizing world monetary and economic systems would be suppressed or given a heads up so changes could be made?
It's been out there for 3 years now, nobody can understand it because it's fucking bullshit. It's the Finnegan's Wake of number theory.
>>7532294
There just might be something to it maybe.
Besides, I don't think there's much need for anyone to suppress these things. If they don't mesh with the current system nobody will bother using them. If they allow for exploitation of the current system by being better everyone will adopt them. I don't think these things will be as radical as people in this thread seem to think.
>>7531868
It was created. An invention not much better than the belief in god.
>>7532313
there could be a grand shifting of powers involved in adaptations of those theories, that means a lot of stress
>>7532330
Hey, I have faith in mathematics! I don't criticize your anti-mathematical ideologies!
>>7532311
I agree. As to the ontology /lit/ is probably not the place to ask. I can't claim to know anything detailed about the axioms involved and so I can't comment. /sci/ would be a good place to ask if they were into the questioning of the fundemental axions, which they are not, for the most part.
>>7531868
Evoked, I actually read an interesting book on this.
>>7531868
copypasted
>>7532006
A set of elements that interact with each other.
>>7532293
Damn, sonny
>>7532356
So share the book faggot.
>>7532093
languages in most societies before they have a counting system/mathematics only contain words for "1, 2, 3+" or similar.
>>7531916
>language game
Jesus Witty really is the worst Analytic for children to read
>>7531868
I asked my math teacher that in fifth grade.
He didn't know. Can't help you bro.
>>7532138
Probably because they do arithmetic based on approximations, so they don't literally mean 1 + 1 = 3.
>>7532886
What did I say that is wrong?
>>7531995
yeah, but i can use syntax only to describe world once we agree on certain relationship pointing outside the system, say as an ordering of quanties and perhaps with an arbitrary system based on, say, 10.
>>7533907
you spoke at all about that which we shouldnt speak.
>fight club
This is a whole problem within philosophy of mathematics. This problem stretches far back, but most noticeably in Kant, where the ontological status of numbers is raised as an issue, especially in relation to whether or not math is considered as knowledge in the strict Kantian sense, i.e. cognition.
It depends on whether you are a Platonist in regard to math, a fictionalist, an intuitionist, etc., it is debatable. I find points on both sides of the argument, so I find myself torn, but find myself more swayed to the fictionalist position.
I know a topologist and he claims that nowadays mathematicians who are Platonist are in the minority.
Created, it's a social construct. People who believe numbers exist are retarded as hell.
Hello /lit/, it's a /sci/ guy here about OP's question. I will give my opinion, provide a bit of context, and give some serious /lit/ recommendations which a general /lit/ reader ought to be able to approach and appreciate. I am actually a bit happy that this meme-question has been placed on this board where people will be more willing to play with the idea philosophically. And for the record, no, I am not the OP.
The OP post is a common meme (nigh troll-post) on /sci/, but the question itself has enough substance (and its repetitive discussion has enough civility) that its repetition is usually tolerated on that board. To my personal distaste as a math autist, the usual majority opinion there is that mathematics is essentially "created" or invented by man, as opposed to being discovered. Engineers/engineering majors and physics people describe math as a "developed tool" or language, and particularly among anonymously-professed engineers, there seems to be a certain lack of interest in mathematical theory, let alone philosophy.
My personal view is roughly opposite to this. For me, the content of mathematics is not an arbitrary contrivance, but a discovery mapping to and describing the exterior world (with some greater lattitude toward speculation, not needing as much to conform to physical reality in the more abstract cases---though applications are regularly found!) . This discovery arrives in the fact that you can make certain abstract, mathematical, true statements about things, which are exactly the content of mathematics. That is why I maintain that mathematics is (mostly) discovered, and not invented. "2+2=4" goes on being true whether humans are around to appreciate the fact; a prime number's worth of cubic brick-bodies can only be arranged into a rectangular prism in one particular way (again whether humans are around or not), and so on. I maintain that mathematics is substantively exterior to and independent of humans. In other words, my personal view is some flavor of "Platonism" (a la OP's Gödel!), where mathematical philosophy is concerned.
For mathematically oriented lit-izens who are interested in this autism, I have a small number of excellent selections that even name-drop Witty regularly, just to sweeten the cultural pot for you:
Rebecca Goldstein: Incompleteness (Gödel's life and times, the above Platonism etc)
Bertrand Russell: Introduction to Mathematical Philosophy
G.H. Hardy: A Mathematician's Apology
a basic reading list to understand the autist/platonist (my) point of view. Only Gödel can be avowed as a full (mathematical) Platonist IIRC, however.
Is a word heard or uttered? Could there be a word that exists not to be heard, or one that cannot be uttered?
>>7534439
I disagree with your views, but good boast.
Mathematics is like you, it was both created and discovered
Your parents both created you, and discovered you were gay
>>7531902
stop jerking off and go help the world
Discovered
>>7534439
Have you read "The Man Who Knew Infinity"? It's a bit too American for my taste, but it contains mountains of good stuff about Hardy
the axioms were created, the implications were discovered
>>7534511
No I haven't. Please favor us with what you had in mind, while you're at it.
>>7534526
>Please favor us with what you had in mind, while you're at it.
Not sure what that's supposed to mean, I just thought I'd recommend you another book based on the ones you recommended
because I like recommending books
>>7534528
The Hardy bits you mentioned. You have a basic idea of Hardy-highlights based upon the book, and I'd like to know your version of those.
maths describes the noumenal realm
>>7532138
What sometimes happens when 1 woman and 1 man get together?
>>7531868
mathematics are conventions which are created by nerds.
laws are conventions which are created by normies.
>>7532005
>i just read chapter 2 of history of sexuality volume 1
you're doing it wrong my man. read deleuze. we like math, actually.
>>7531985
>But Mathematics, as in the relations of the things, exists also. Things have relations, constants we can observe all over the universe.
>Why? I dunno, just the way e^pi*i=(-1)
no
the rules of inferences are just as conventional as the relations that ''we'' observe.
>>7532138
prove that A always equals A
>>7534337
>I know a topologist and he claims that nowadays mathematicians who are Platonist are in the minority.
>>7534439
>make certain abstract, mathematical, true statements
yes, you yourself decide to make truth. the point is why do you choose to spend you day manufacturing various logical frameworks wherein you feel safe once you define truth and valid inferences.
also, the question is why other people who claim to have chose to have the same goal as you, still disagree with you.
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Thanks for the stackexchange pic. I believe my friend was claiming that most working mathematicians are not Mathematical platonists, not that they are not Platonists.
There are exactly 5 Platonic solids.
Now, we can discuss what it is about Platonic solids that anyone finds interesting. But there is no disputing that, given the definition, there are exactly 5 of them.
Personally I find regular convex polygons (triangle, square, regular pentagon etc.) esthetically pleasing. And I like the fact that when we put certain restrictions on how those polygons combine to form polyhedra, we get only 5 polyhedra. I also find the Platonic solids themselves to be beautiful.
It's like some complex poetic form, like a villanelle or a sestina. With the restrictions, something interesting and beautiful can be created.
I think that this beauty and the esthetic and intellectual interest of the Platonic solids is what motivates people to take notice of them.
It has often been pointed out that if we ever meet an alien race with the same level of development as we do, some of them will know or could be made to understand that there are 5 Platonic solids too. I wonder whether they will have the same esthetic sense as we do, and whether they will care that there are 5 Platonic solids. But I imagine (with no proof) that they will.
>>7531868
>>7534439
I like to think of Mathematics as a cultural artifact.
>>7534439
>Rebecca Goldstein: Incompleteness (Gödel's life and times, the above Platonism etc)
>Bertrand Russell: Introduction to Mathematical Philosophy
>G.H. Hardy: A Mathematician's Apology
those are all pop-math books though. i thought you were from /sci/: don't you know any better? you will never understand what godel's theorems are about unless you study the technical maths behind it
>>7534337
not really. to be even considering the question whether or not you're a platonist one must be aware of foundations of mathematics as a subject and so of the various philosophical interpretations of what maths mean. your average mathematician gobbled up platonism unwittingly ever since his undergrad years and now he merely teaches and researches without thinking about this stuff.
platonism will probably always be the the dominant philosophy of maths (irregardless if it is true or not); same with christianity as the choice of religion for the common man, etc
why are all of you discussing Plato? Hasn't he been shown to be wrong about fucking everything? He just makes shitty strawmen.
>>7535296
But it is not enough to proclaim that Plato "makes shitty strawmen" for Plato does not "make shitty strawmen" unless you actually demonstrate that he does "make shitty strawmen".
>>7535308
Just read one of his dialogues, it's basically
Socrates: Everything is a form durrr
Other Person: No it's not
Socrates: Yes it is
Other Person: Your right Socrates!!!
Face it Plato was a stupid retard.
>>7532542
I was too lazy to look up the name again
A Brazilian guy wrote most of it.
>>7535318
>just read
It is not my duty to read him, it is your duty to explain to whoever calls you out on your bullshit why Plato "makes shitty strawmen" or why Plato was "a stupid retard". I can't "face it" until you demonstrate it. That fragment of yours isn't a fragment of a Platonic dialogue.
>>7531868
Discovered
He numbers too big for he godam head xxxxxdddd
>>7535393
XXDDDDD thiss
>>7535265
G.H. Hardy is not a pop math book and most undergrads can't get through Bertrand Russell without constantly needing to research what he's discussing in laymens terms.
Hardy revolutionized the field of mathematics with that book. He inspired several potential applied math majors to become pure mathematicians -- I'm one of them.
I can't comment on the book by Goldstein.
>>7535412
Yes it is a pop book by any conventional standards. Hardy also openly refers to the reader as a layman in that book.
You must be confusing it with either his 'A Course of Pure Mathematics' or 'An Introduction to the Theory of Numbers'
> most undergrads can't get through
This doesn't mean it isn't pop-math.
>>7532102
>we will eventually overcome it
The thing that will eventually overcome math will bemore math.
>>7535591
I'm not confusing it. A Mathematicians Apology is echoed among grads and undergrads alike as that being the book which inspired them to go into pure math. Have you read it? There's no math in it, just the ardent conviction that pure mathematics is the only true field and that applied math is blasphemy.
Bertrand Russell's book is not pop math. If it were, it'd be either popular or easy to digest; it's neither. Pop math is like what that girl on YouTube does.
>>7535265
not "/sci/ guy" but dont read Godel's original proof.
Newman and Nagel's "Godel's proof" is good enough (~2 pages of actual proof) but it requires you to take for granted that we can work out if "X is a proof of Y" is true, and that we can write that statement in arithmetic.
Since Turing formalised computability, you can prove it from that, much simpler.
>>7532062
Because it can be demonstrated. However it depends on the "thing" because one raindrop plus another raindrop still equals one raindrop.
>>7535265
It's me, the long-poster.
I'm on /lit/, not /sci/. That is why I posted /lit/ tier material. I even made clear what I was going to do in the first few sentences.
If you want to talk about actual /sci/ tier material (as opposed to the closely-related philosophical speculation which we're doing here), go to /sci/. It's like going to the movies board and complaining that instead of just talking about movies, no one happens to be currently having a scientific discussion about optics, photography, etc.
What was under discussion was not Gödel's incompleteness theorems >>7535265 , but OP's philosophical question. The Goldstein book discusses both, but I mentioned it specifically because it gives a helpful lay treatment of "mathematical Platonism", which goes directly to the OP question.
But since OP's picture is of Gödel, and the door's been wide open for a little bit, here: look up "On Formally Undecidable Propositions of Principia Mathematica and Related Systems" - Kurt Gödel. Bear in mind that this is a /tangent/ from the original subject of discussion, your complaint was a /tangent/ to begin with.
>>7534692
A bit snarky, but the last line is the /real/ interesting question. OTOH I can read the latter part of the squishy second line as a vindication of the "math is (mostly) discovered" camp: Your thing starts out roughly "Well um why du U make it be like dis dawg wit dat axioms? Dat's arbitrary." And then I can reply something like "Because this setup better conforms to reality, it "works" better, that is I'm /discovering/ what works and what doesn't."
>>7532014
kek
Real numbers like φ or π were discovered. Integers were created.
>>7531868
In my reasoning I'll conclude in the same way as >>7534439 did, however the road I'll take is less object-oriented (like '2+2=4 whether you're here or not'). I really like Hegel and from what I read it is easy to understand that, since the world and reason (or reality of you want) is what is - i.e. the Totality - you can see that the human existence is a condition for it to exist (not a necessity).
Therefore as an object of study mathematics have been found/discovered by men in their own representation which is where one could argue that they (by definition) have been created. However as a contigency of Reality man isn't able to create but only to find, discover and use.
>>7534482
And what did you do today?
