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/sci/ - Science & Math

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5035569 No.5035569 [Reply] [Original]

Is math a discovery or an invention?

>> No.5035580

the axioms are an invention, the properties where then discovered. the axioms were invented after the need for such a system was found in physics (how many cows you have is physics now) so the first math was kind of backwards with the properties of a set of numbers being assumed to be the same as a set of physical objects, which properties were discovered and the set then invented that had those properties.

>> No.5035584

It's a bit of both. The results always exist, we just have to decide the axioms. If there were an alien race that came up with the same axioms, they would always get the same results. For example, any alien race that came up with naive set theory would eventually stumble upon Russel's paradox. Any alien race that produced the axioms of ZFC would discover the Banach-Tarski paradox, etc.

Mathematics is fairly unique, in this regard.

>> No.5035585
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5035585

Discovery.
But we had to invent a language to describe it.

>> No.5035589

It is an invented system that correlates with reality, and leads us to discoveries.

>> No.5035593

>>5035589
>correlates with reality
nope

>> No.5035594

>>5035593
yes

>> No.5035595

>>5035569
I would be of the opinion that it's a combination of both.

>> No.5035597

>>5035594
Sometimes it approximates it if we make certain assumptions.

>> No.5035603

>>5035597
>>5035594
what the fucking fuck
describing reality is the role of physics and modelization, not maths.

>> No.5035609

>>5035603

Inb4 define reality

>> No.5035610

Invention.
The results are discovered, but the axioms are invented. Not in arbitrary fashion, mind.

>> No.5035612

>>5035603
>implying physics doesn't use math

>> No.5035614

>>5035594
whats does the Z_6 × Z_2 group correlate with in reality?

>> No.5035619

>>5035603
Maths is an abstraction of the real world. Without the real world there would be no maths.

>> No.5035618

>>5035612
>implying that contradictory with my claim

>> No.5035622

>>5035614
are you suggesting that groups are fictional
we may not be able to say that they correlate with a form in reality, but they correlate with the operation of reality

>> No.5035625

>>5035614
The concepts of 6, 2 and symmetry are all found in reality. That group is an abstraction thereof.

>> No.5035627

>>5035622
so we can define any binary operation and reality will follow it?

>> No.5035630

>>5035627
no, we can define any binary operation and say reality COULD follow it

>> No.5035638

>>5035622
>>5035625
so you arnt arguing math isnt an invention, you are arguing that inventions dont exists?

>> No.5035639

>>5035638
what.

>> No.5035642

>>5035638
I'm saying maths is an invention...

>> No.5035658

invention

faggots say otherwise

>> No.5035691

its an expressive mean, just like language. neither an invention nor a discovery.

>> No.5035692

>>5035691
but languages were invented

>> No.5035703

>>5035692
some evidence show that it is an inherent capability; sort of an instinct. so in that since it can be looked at as a form of discovery.

>> No.5035709

>>5035703
please tell me you're joking.
there's a difference between a capacity for a language and a language.
are you going to suggest that the vocabulary, grammar, and syntax of the english language are innate, and not invented forms?

>> No.5035722

>>5035709
i'm not joking, but it's hard to tell really. otherwise hpw would you explain the syntactical and grammatical identities between different languages which developed independently from each other?

>> No.5035747

Mostly invention, but cannot be 100% invention.

As a formalist, I believe that things such as "the integers (which satisfy the axioms of PA)" are an invention. However, in order to invent things, we need axioms and rules of inference, and in order to know that a proof is valid, we need a certain subset of mathematics to define a valid proof. However this subset can be shown to be much smaller than even Peano Arithmetic.

>> No.5035753

>>5035722
source?
also if true, my first guess would be: same needs.

>> No.5035754

>>5035709

Noam Chomsky has theories that language is indeed natural

>> No.5035755

People often separately invent the same things in parallel. Evolution converges on the same designs despite completely different genetic histories.

Could it be that all inventions are really just discoveries?

>> No.5035772

>>5035754
There are Chomskyists and there's everyone else, and both groups are pretty big. The matter is not considered settled.

>> No.5035787

>>5035772
How else would language be possible if not through the natural systems in the neocortex?

>> No.5035794

I think it's an invention we have crafted to model the universe. We choose the axioms because they are what we intuitively observe in reality. It's very successful for some reason.

>> No.5035795

>>5035753
take creole as an example

http://en.wikipedia.org/wiki/Creolistics

>> No.5035801

>>5035787
You don't need, e.g., specialized systems to use a hammer to pound a nail. I personally don't really have a favorite one way or another, but a common counterpoint to Chomsky is the view that language is not innate, but a learned behavior and just another part of the human toolset.

There's also the median viewpoint, itself pretty common, that our brain co-evolved with language.

>> No.5035803

>>5035753
think of creole

http://en.wikipedia.org/wiki/Creolistics