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After a fairly robust conversation with one of my learned chums, I asked him wether he thought that maths was discovered or invented. He thinks that it was invented whereas I think that it was discovered.

What followed was a pretty heated debate from which neither of us persuaded the other to change his mind and to my astonishment, I found out that this very same matter has been the cause of a lot of debates for many years and has split the science community right down the middle.

Think about it. Maths is a truly universal language that (in my opinion) should be discovered by any alien life that resembles our carbon based selves. Sure they will call it something else but the under-laying principles will be the same.

We most certainly exist inside a mathematical universe with maths being the language of creation, the blueprint of existence itself. I just cannot see how someone could believe that maths is simply an exclusively human achievement like English or Spanish or Mandarin for example.

I would like to see what you guys thought on the matter.

You're, like, TOTALY blowing my mind, maaaaan.

A bit of both i guess...
The stuff Maths deals with was discovered but the way we deal with it was invented...

It was invented by a Zionist Conspiracy.

I think it was invented.

Mathematics is an invention. It's a way for humans to quantify their environment. Amounts of things only exist because we ascribe them to things.

TheRobotLol wrote:You're, like, TOTALY blowing my mind, maaaaan.

Robot, you need to lay off the weed, itll help you with that problem




I really could see this being argued in favor of either side. But I like the thought of it being discovered, it sounds better

Mathematics is an invention. It's a way for humans to quantify their environment. Amounts of things only exist because we ascribe them to things.

Completely false. Epistemologically, mathematics aren't a science, they are multiple systems of quantitative truth functions. Wittgenstein described it best in the Tractatus logico-philosophicus, mathematics, just as logic, show us what structures of truth-relations needs to be respected for something to possibly be true or false. The ''science'' of mathematics are the collective research on those truth functions.

Maths are discovered, if anything. In truth the relation is much more complex.

On one hand, maths existed in the laws of physics before we knew of it, therefore it was discovered. For it to be invented would imply that humans made it.

However, one could argue that maths is simply a way of expressing these concepts that existed before hand; therefore it is a system devised by humans to explain and prove the laws of physics.

It is indeed a tough question... it all comes down to "what is maths" basically. If it is the underlying principles of the universe then it was discover. If it is the way humans describe, explain and prove the laws of physics then it was invented.

Maths is only important to us cos it's a way to make sense of the world around us, if we hadn't made math, we'd have made something else.

So math is invented. XD

NOm

Mathematics is merely a philosophical construct with which humans can quantify their environment and predict the effects of change, therefore it is an invention.

Kovnik Obama wrote:Mathematics is an invention. It's a way for humans to quantify their environment. Amounts of things only exist because we ascribe them to things.

Completely false. Epistemologically, mathematics aren't a science, they are multiple systems of quantitative truth functions.

I know you probably expected to blind me with your terminology, so I'm sorry to disappoint. Quantification is a human exercise; a product of our culture. It cannot exist without us. There is no essential mathematics, only what we percieve and our interpretation of it.

I find it odd that you cling to absolutist statements about truth, and ignore the near-century of work that came after, pretty much destroying it. There is no mathematics without us, because it arises from us. I mean, what is an amount?

Mathmatics came in to being organically. Essentially, enough Orks believed in it one day, and BOOM. Math. Now, you might ask why Orks would bother to believe in something like math to begin with, given their tech base. However, taken in the context of Gork and Mork, it falls nicely in to place. Math is the Ork's "great evil" to counter balance Gork and Mork.

Without a 'mind' in which to calculate them maths cease to exist. So invention.

Kovnik Obama wrote:Mathematics is an invention. It's a way for humans to quantify their environment. Amounts of things only exist because we ascribe them to things.

Completely false. Epistemologically, mathematics aren't a science, they are multiple systems of quantitative truth functions. Wittgenstein described it best in the Tractatus logico-philosophicus, mathematics, just as logic, show us what structures of truth-relations needs to be respected for something to possibly be true or false. The ''science'' of mathematics are the collective research on those truth functions.

Maths are discovered, if anything. In truth the relation is much more complex.

First, just a piece of advice: use the quote function. It makes it easier to see who you're referring to, and what words are your own; especially as most people (myself included) don't expect the use of italics in such a context here.

Now, on to business: I have several problems with your statements, which I'll bullet point for my own, and possibly your, convenience.

1: Whether or not math is a science comes down to what particular philosophy of science you subscribe to. I'm biased here, because I generally think the "problem" is a non-problem, and am broadly willing to give people claiming that a thing is science the benefit of the doubt so long as they aren't blatantly incorrect. For example, claiming that I have scientifically proven X is in fact Y because I feel really strongly that X is Y is not science, but being able to demonstrate that there is a sound argument for X really being Y, by way of material evidence, is science. You might think math cannot rise to this, but it can, and has, done so. Though, admittedly, the physical evidence lags well behind the theoretical evidence (though that's arguably true of all science).

2: Like truth functions, mathematical postulates are necessarily falsifiable. Sure, at a fundamental level they are not, as shown unintentionally by Russell, but the same is true of everything. You cannot falsify the claim that you exist, because existence is defined by, essentially, itself; ie. "I exist because this thing I am doing is existing."

3, and this is only sort of an objection: The question of discovery versus invention is essentially moot, because they are freely interchangeable. When we invent things, because we are, ultimately, just as much a part of reality as anything else, we are also discovering them. To invent a thing is to discover it can be done, or that a certain set of concepts can be associated with a certain other set of concepts. Its simply a question of emphasis, which has more to do with an emotional response than any question of truth.

I know you probably expected to blind me with your terminology, so I'm sorry to disappoint. Quantification is a human exercise; a product of our culture. It cannot exist without us. There is no essential mathematics, only what we percieve and our interpretation of it.

Sorry if I passed for an douche, but if you are going to pronounce yourself over an epistemological subject, expect those who study epistemology to argue, and to know and use the proper terminology. BTW, it's nothing you can't completly acquire throughout 2 wiki searches.

Epistemology : discourse over the definition and value of truth, and it's implication toward knowledge
Truth-function : A structure depicting a basic logical relation. For example, the truth function of non-contradiction is [if A = True, then -A /= True]

Your reduction to the necessity of an organic support is simply ridiculous. By all accounts, it would means that nothing is discovered, all is invented, even objects of perception. Semantically, it erase the definition of 'discovery'.
And quantitative essences are a priori in existence, however much I loath to use Kant's terms. Things exists as cohesive unit before we subjectively can do the operation of calculus.

Dogma reveals himself to be an existentialist!

I'm going to follow this thread with keen interest.

Thanks for that post Dogma, enjoyed reading it.

Mathematics crosses boundaries of discovery.

It is not an invention, neither is it a discovery, its both and neither or something else. The point is discovery refers to a preexisting concept or item, wheras invention is solely sourced by the human imagination.

Mathematics includes fundamental themes which are pre-existant, such as numbers and geometry what were either perceived or otherwise revealed by a process of discovery.

Other mathematical concepts are entirely of human invention. Plainly put if we discover a pretty pattern in mathematics (which is what most theorems are) we in fact invent, because the observers choose the criteria and how the criteria are observed and quantified wholecloth.

nomsheep wrote:Maths is only important to us cos it's a way to make sense of the world around us, if we hadn't made math, we'd have made something else.

So math is invented. XD

NOm

If that was true then how come we cannot simply 'invent' a way for 5 + 5 to equal 15? Without mathematics modern life would be impossible. Why do we need to quantify things in order to make sense of the world? Think about that, think really hard for a moment.

To understand the universe and to even be able to work out how something should behave that we have no direct experience of we need mathematics in order to make that possible.

There is something really profound about that.

If anyone simply thinks that it's just a way that we humans make sense of the world then they haven't thought deeply enough on the matter. Mathematics taps into something that links everything and everyone from the beginning of time and beyond. All the greats in history that have offered any true insight to the mechanics of the physical world (Newton, Einstein, Hawking, Penrose to name just a few) have done so through the abstract language of mathematics.

Newtons Inverse Square Law simply could not be explained any other way (a way in which could be applied to other planetary bodies in order to gain an accurate result that is) except through mathematics. You could communicate speaking English, Japanese or even French but that mathematical content would be the same.

I wanted to use the quote function, sorry ^^
Yes, I pronounced myself quite specifically, this isn't the place for a complete course on epistemology, and even less on epistemology of philosophy (which would be needed at first). But Wittgenstein's exposition of the comparable emptyness of truth-content of logical and mathematical axioms is currently pretty much considered the highest level of epistemological study at my university. Quine would be the other top figure, but I know next to nothing about him. Even then, its true, there are other very well developed opinions about the question, but none that comes down to "well, humans are needed to think, so maths were invented".

On the other side, my main interest is Husserl, who started as a mathematician, only to turn to descriptive psychology and later on phenomenology. Even then, he maintained that it would be impossible for us to have evolved a categorical attitude if naturally the quantitative aspect of objects didn't, in a sense, come from the object to the subject, in an existential kind of way.

And on to 3. I perfectly agree with you. Most of the problems are linked to the application of the term 'science' unequivocally unto different forms of knowledge. Yes, they are all sciences, in the broad sense of knowledge, but they aren't all sciences according to the same objectivity. Mathematics, like logic, and certainly the meta-language do not pronounce truths, but structures of truth, and those 'sciences' are usually recognized as those we called 'a priori' (even tho the term doesn't exactly mean 'pre-existing')

Its invented.

starting with basic counting, we have 10 fingers we use a base 10 system for counting. is we only had 8 fingers our base would be 8.

all measurements are invented, someone looked at his foot and walla we have a unit of measurement. But that was to easy so someone else invented a metric system. Gravity might be a constant we discovered, but it is expressed by the measurements we make up.

just because we can measure the distance to the moon, you could say we discovered the distance, but the distance is still expressed in our invented system.

while we figure out some impressive formulas to measure and calculate various things, its not really discovering it. If math was purely something we discovered like say Pluto, then PI would probably just equal 3 Pi is only the number it is because of the number of our fingers, in any other base its a completely different number.

starting with basic counting, we have 10 fingers we use a base 10 system for counting. is we only had 8 fingers our base would be 8.

all measurements are invented, someone looked at his foot and walla we have a unit of measurement. But that was to easy so someone else invented a metric system. Gravity might be a constant we discovered, but it is expressed by the measurements we make up.

We aren't talking about how we count, what overall shortcuts we use, but about the actual essence of quantity. The act of counting presuppose unity, then multiplicity. In a sense, Math isn't measurements, it's what allow measurements.

I believe math is what we use to describe facts, so it's an invention.

Relapse wrote:I believe math is what we use to describe facts, so it's an invention.

Very well put.

I believe that mathematical objects really exist, located not in the physical world of appearances but in an abstract realm of idealized forms, accessible to the intellect. Theoretical physicists, who express the laws of physics as mathematical equations, tend to follow this tradition. They prefer to envisage the laws of physics as having real existence, but transcending physical reality.

I like what Galileo had to say on the matter: "The great book of nature can only read by those who know the language in which it was written. And that language is mathematics." Or to be put more bluntly, here's what the English astronomer James Jeans said three centuries later: "The universe appears to have been designed by a pure mathematician."

Seriously, if you think it was invented then you ain't thought hard enough. If anyone does think this then can you give a good example of why you think this rather than the bland statement of: "It was invented," or: "It's how we make sense of the world." Something a bit more persuasive please.

I believe that mathematical objects really exist, located not in the physical world of appearances but in an abstract realm of idealized forms, accessible to the intellect. Theoretical physicists, who express the laws of physics as mathematical equations, tend to follow this tradition. They prefer to envisage the laws of physics as having real existence, but transcending physical reality.

That might be a bit too idealist for my taste. The 'mathematical object' could simply be the character of the unity of an object, in which case it's a synthetic character, revealed by our Gestalt-oriented perception. Hence the 'discovery'.
You don't need to believe in a metaphysical 'final cause' to have the same position, and I do not find that most physicists would agree with a 'final cause' argument. Could you provide source? I always was under the impression it was quite abandoned.
Anyway, the important epistemological fact is that claiming it's invented is absolutely false on all accounts.

Kovnik Obama wrote:

I believe that mathematical objects really exist, located not in the physical world of appearances but in an abstract realm of idealized forms, accessible to the intellect. Theoretical physicists, who express the laws of physics as mathematical equations, tend to follow this tradition. They prefer to envisage the laws of physics as having real existence, but transcending physical reality.

That might be a bit too idealist for my taste. The 'mathematical object' could simply be the character of the unity of an object, in which case it's a synthetic character, revealed by our Gestalt-oriented perception. Hence the 'discovery'.
You don't need to believe in a metaphysical 'final cause' to have the same position, and I do not find that most physicists would agree with a 'final cause' argument. Could you provide source? I always was under the impression it was quite abandoned.
Anyway, the important epistemological fact is that claiming it's invented is absolutely false on all accounts.

Theoretical physicists who are steeped in Platonic tradition will think in a similar vein as my own. From the sense of it originating from Plato you are quite correct in saying that it is outdated but the fact that it is still given a healthy amount of credence by a number of theoretical physicists, I think, counts for something.

Having said that, I think that it is an enjoyable experience to have a debate like this when people like yourself add what they do to it. In many ways, I think that you are someone who, in some respects, think in very similar ways to myself. Glad you joined the thread Kovnik.

Math is an invention-we gave each number value. 2 can mean a single object plus a single object, or it can mean Glorp. We determined it to have the value of a single object plus a single object. Now, multiple objects having the ability to be combined, hetero- or homogeneously, has always been possible, but the formulas had to be created. Do you think the universe decided "I'm going to make A^2+B^2=C^2 equal the formula for the area of a right triangle and see how long it takes people to figure it out?" No. We assigned a triangle to have a value of 180 degrees (a human conception) and over time built up a formula that would always give us an answer to side lengths, with the foundation based on the angles of the triangle. We assigned value, then built the formulas. Nature didn't do that. We had to "discover" the formula, but it was a formula discovered out of our created value for each piece of the puzzle. Combinations were discovered to make it easier to utilize our invention.

Glad you joined the thread Kovnik.

Thanks, a pleasure!

Math is an invention-we gave each number value. 2 can mean a single object plus a single object, or it can mean Glorp.

No. Each individual numerical values where named, yes, but there essence all descend from unity (0 or 1) or multiplicity (2,3,4, etc...). The name doesn't matter, the value is essentially there. It would've been there for a peasant looking a three cows even if he didn't know the number three. That's one aspect of the higher degrees of discrimination of the categorical attitude.

We determined it to have the value of a single object plus a single object.

Unity and multiplicity are given to anyone, anything capable of higher levels of perception. The conceptualization of those in numerical concepts is just a exercise of organization. We act on quantitative essence way before we can conceptualize them (like the cavemen who decides to run after the one beast he has isolated, instead of the pack). So again, 'discovery'.

Now, multiple objects having the ability to be combined, hetero- or homogeneously, has always been possible, but the formulas had to be created.

Same thing with the meta-language and natural language ; the meta-language is the necessary structure for the development of higher languages. Even formulas aren't truly created, but more balanced on previously established grounds.

Do you think the universe decided "I'm going to make A^2+B^2=C^2 equal the formula for the area of a right triangle and see how long it takes people to figure it out?" No.

Of course no. But it's easy to counter with the argument that however else you decide to express the formula for the area of a right triangle, it would be directly translatable to our formulation, hence suggesting its relative to an underlying structure.

We assigned value, then built the formulas. Nature didn't do that. We had to "discover" the formula, but it was a formula discovered out of our created value for each piece of the puzzle. Combinations were discovered to make it easier to utilize our invention.

I have no idea how you can conceive that we discovered formulas but invented values. I could almost understand the contrary. Could you elaborate on what you mean?