Mathematics is a group of rules and seeing what can be made as long as they are followed

set of axioms expressive, rigorous and consistent enough to be applied for nearly everything. every other philosophies don't have this.

Uneducated

But it is philosophy. That's okay with me.
t. computer science and applied math undergrad

If you take mathematics and you zoom out then it looks like philosophy. But then zoom out even more and philosophy looks like math.

Take any philosophical position. Those always start with some unproven premise to guide the debate. (In the philosophy of feminism axiom number 1 is men=bad). And then they deduce whatever follows from those axioms.

All of this could be framed in terms of a first order theory, with some axioms and then deductions would come in terms of sentences in that first order theory. So basically philosophers do logic light. They do deductions in very simple theories, with finitely many axioms. (In contrast, a first order theory of arithmetic needs infinitely many axioms).

So philosophers are simply mathematicians who aren't smart enough. Furthermore, while mathematicians do debate about which axioms should guide them, there is an almost universal consensus around ZF. With people (like Wild) having problems with one or two axioms at best. (In the case of wild, the axiom of infinity)

In contrast to that, philosophers have never decided on what axioms really guide reality. Every century brings some new movements that is as retarded and wrong as the previous movements. Philosophers will never settle any argument.

This is the best answer

The language we use to describe logic and math was made up for communication purposes, but the meaning and mechanisms it describes are inherent and necessarily true. You're already using logic to go against logic.

Non-formalisation =/= untruth. There may be certain truths that we may never be able to formalise at all. There's also no such thing as "inherently, objectively true", as in, you can't prove it.

How have you not already combined the two?

That is not math. The axioms just exist to keep rigor while trying to get at objects that exist independent of the axioms. A sphere is a sphere, we can encode it in sets but the platonic ideal exists independent of set theory. Math existed before Cantor.

Your whole post really demonstrates the Dunning-Kreuger effect

Yes OP, you're actually right. The general goal in mathematics is to apply the formalisms of philosophy and restrict them to a strictly logical framework.

Hence, there is a lot of overlap between Analytic Philosophy and Mathematical Logic.

The core difference is that in philosophy, we agree that Logic is not the only tool. (For example, non-logical argument examples include Pathos and Ethos.)

The result is that we cannot argue in mathematics. We may dispute the assumptions (axioms) and start from a different vantage point. However, there is no such thing as disputing a proof.

In Philosophy, due to a more powerful argumentative toolkit, we may dispute something even if our interlocutor has come up with definitive evidence. From an academic perspective, this is intriguing. From a practical perspective, this is troubling.

t. math grad student

ITT: ugly virgin nerds relying on Platonism to justify why mathematics is better than philosophy

>muh math is reality
>*cocksucking intensifies*

How are you helping your case that mathematics is separate from philosophy?

>How are you helping your case that mathematics is separate from philosophy?
Can philosophy make accurate, quantitative predictions about the real world?
Is mathematics trying to get answers to metaphysical questions, which lie beyond logic?

Because that is exactly what the argument here is. Mathematics can build a model of reality with predictive qualities, can philosophy do that?

>Can philosophy make accurate, quantitative predictions about the real world?

Whenever this happens, "natural philosophy" becomes science, and the goalposts are shifted again. Not interested in this type of question because it covers up the fact that philosophy and mathematics cover different kinds of concepts with the same focus on problem-solving and proofing.

>Is mathematics trying to get answers to metaphysical questions, which lie beyond logic?

This makes no sense. All philosophical questions, if solvable, would be solvable through logic.

>Because that is exactly what the argument here is. Mathematics can build a model of reality with predictive qualities, can philosophy do that?

Most of mathematics is totally irrelevant for building "models of reality", and even that is dubious proof of anything but coincidental correspondence. You're relying on a lot of philosophical assumptions to dismiss philosophy.

>it covers up the fact that philosophy and mathematics cover different kinds of concepts
Exactly they are different.
Contrary to what you said here ">How are you helping your case that mathematics is separate from philosophy?"

>This makes no sense. All philosophical questions, if solvable, would be solvable through logic.
Really, that is not what I was taught. Even the infamous "trolley problem" can't be answered with logic and as imo rightfully pointed out > we agree that Logic is not the only tool.

>Most of mathematics is totally irrelevant for building "models of reality"
That is plain wrong. Provide one field of mathematics which isn't in some way relateable to the real world.
> and even that is dubious proof of anything but coincidental correspondence.
This also is complete nonsense. How can you explain most of our understanding about science relying on the "coincidence" that it can be modeled by mathematics.

The reason being that mathematical axioms are chosen with respect to reality, which gives them the ability to create models of reality with accurate predictions.

> You're relying on a lot of philosophical assumptions to dismiss philosophy.
Stop strawmanning. I never dismissed philosophy. I argued that it is a disciple different to mathematics, aside from that it is clear to see which one is more useful for out world.

>how is this not just philosophy?
who said it isnt?

>who said it isnt?
people who know what these disciplines are.

The best philosophy is mathematical.

>how is this not just philosophy?

It IS philosophy, specifically, it's a branch of logic.

It's not philosophy, it's math
Literally anything is philosophy if you get loose with the definitions.

No. Mathematics has made the step philosophy hasn't made.
It is completely formalized to point where the rest of philosophy (and reality for that matter) can be modeled with mathematics.

It is true that mathematics used to be a sub field of philosophy but that changed, mathematics nowadays is powerful enough to completely contain philosophy.

>Exactly they are different.
Contrary to what you said here ">How are you helping your case that mathematics is separate from philosophy?"

If anything, it's quantitative philosophy as opposed to qualitative philosophy that we normally just call "philosophy". Methodology and epistemology is still the same.

>Really, that is not what I was taught. Even the infamous "trolley problem" can't be answered with logic and as imo rightfully pointed out > we agree that Logic is not the only tool.

The trolley problem isn't a problem. It's a hypothetical scenario that's used to test ethical theories to see if they can handle complex cases.

>That is plain wrong. Provide one field of mathematics which isn't in some way relateable to the real world.

inter-universal Teichmüller theory (IUT)

>This also is complete nonsense. How can you explain most of our understanding about science relying on the "coincidence" that it can be modeled by mathematics.

>The reason being that mathematical axioms are chosen with respect to reality, which gives them the ability to create models of reality with accurate predictions.

Most mathematical theorems were not proven by going into the world and looking for corresponding patterns but rather by delving deeper into abstractions in the comfort of indoor study. I.e., math for the sake of math.

Where exactly is the "respect to reality" portion you're trying to get at? Because with that kind of definition, it's no different from philosophy.

>Stop strawmanning. I never dismissed philosophy. I argued that it is a disciple different to mathematics, aside from that it is clear to see which one is more useful for out world.

Fair enough. But I did view your criticisms as a dismissal of philosophy because you haven't proven the methodological difference between math and philosophy.

>the rest of philosophy (and reality for that matter) can be modeled with mathematics
lol

Mathematics derives from philosophy.

>inter-universal Teichmüller theory (IUT)
Are you seriously suggesting that number theory is NOT applicable to real world scenarios?
The theory is extremely complicated, but its purpose is to solve an open problem in number theory which itself is not very hard to understand.

>Where exactly is the "respect to reality" portion you're trying to get at? Because with that kind of definition, it's no different from philosophy.

Read again what I said. The axioms of mathematics are carefully choose based on our understanding of the world, with these axioms definitions are made which also correspond closely to how we understand the world.

As an example: in linear algebra you have something you call "perpendicular", which is defined as=0 but that term also has meaning in reality. But the abstraction of mathematics describes exactly what we understand as "perpendicular" and the conclusions drawn from this definition "=0" also correspond very closely to what we can experience about perpendicularity in our lives.

This is not "math for the sake of math" (at least not only) but it helps us actually understand our world better, especially when problems get a lot more complicated.

>lol
great argument, are you calling me "cuck" next?

Not him but I'll call you a piggot

Nothing is more "real", everything is simply a construct of the symbols we humans lend meaning to. Math makes sense because the reactions connect like a chain and the links seem reliable.

Stop trying to push your shitty meme. You can't force a meme and expect it to be good. It has to come naturally, most likely from the places you least expect.

It doesn't even rise to the level of philosophy. It's basically D&D for people who can't make friends.

>Read again what I said. The axioms of mathematics are carefully choose based on our understanding of the world, with these axioms definitions are made which also correspond closely to how we understand the world.

You are using the word "world" so loosely that I have a hard time believing that you can make a serious distinction between mathematics and philosophy with your understanding.

>As an example: in linear algebra you have something you call "perpendicular", which is defined as=0 but that term also has meaning in reality.

What do you mean by "reality"? I don't see exactly perpendicular lines in my life, nor does any particular notation arise from structures that I encounter in everyday activities.

>This is not "math for the sake of math" (at least not only) but it helps us actually understand our world better, especially when problems get a lot more complicated.

Plenty of "math for the sake of math" helps us to understand mathematical nuances more clearly. They are not mutually incompatible goals. In fact, that's usually a recent why somebody does math for the sake of math... to see how far the rabbit hole goes. Not sure why you needed to justify that.

Math is philosophy that has to be universally accepted, and if proven false in one instance rejected

Math is a logic game played by mathematicians.

It is up to scientists, and perhaps some philosophers, to decide if math reflects reality.

Oh user, you couldn't be more wrong.

You don't need a set theory system to start, you could use topos or something else

A topos is a set theory, bitch.

Because we tend to focus the rules on objective ideas and usefulness instead of feelings.

The degree to which a pair of material objects lend themselves to material operations analogous to immaterial Mathematical ones is almost negative. Also, the world models associated with Mathematical thinking preclude any Ideal/Platonic plane in which Number and/or Mathematics can operate in any capacity outside of their current one - that of a random Symbol-based construct.

It shouldn't be this easy to make fun of you.

>how is this not just philosophy?

It is. Bad Philosophy.

No argument here. Philosophy proceeds without empirical knowledge- it isn't disproved by experiment or observation. That makes it a philosophy.

>It is. Bad Philosophy
Philosophy has not contributed one meaningful thing in the last 1000 years.

On the other hand mathematics is the reason for all our scientific advancements, how exactly is the greatest human achievement "shitty"?

It is philosophy. Thats why they call you a doctor of philosophy if you do it successfully for long enough at an institution.

>mathematics is a group of rules
no, you're thinking about law

Advances in mathematics might account for advances in modern physics, but its far from advancing most our tech.

Most advances in tech came from advances in material science which has only started to get influences from math and physics. And if you look at any decent material science book you'd be lucky to find a derivative.

How's it feel to be barely noticed for 300 years?

Are you serious?

Half our world is calculus it comes up in most parts of engineering, from basic mechanics to fluid mechanics. Even modern material science makes heavy use of FEMs.

> doesn't know the difference between solid mechanics and mat sci
> continues posting anyway

>The axioms you described are not chosen at random, but very carefully selected with respect to our real world.
>Axiom of infinity
>Carefully selected with respect to our real world
That's hilarious.

>> doesn't know the difference between solid mechanics and mat sci
I was just saying that VERY important engineering disciplines who are not mat sci make heavy use of calculus.

I FUCKING LOVE FLYING LOTUS OP

The whole scientific method and science itself was and is changed by philosophy if it's not based on it. Read Thomas kuhn as example. It's more appropriate to call science a philosophical construction than anything.

>nothing meaningful
>all cultural watershed moments that made the spread of new material objects possible were top-down ideas triggered by thought alone
>nothing meaningful

>He believes a line going through a circle can possibly not touch it.
Even Euclid had more advanced mathematics then that.

>physicists have a theory about the aether
>it isn't borne out by experiment
>welp, time to make a new theory

>mathematicians have a theory about lines intersecting circles
>it isn't borne out, turns out there are gaps
>welp, time to make an infinite infinity of infinities

>>it isn't borne out, turns out there are gaps
But that is inconsistent with reality. The observations dont't match wildbergers theories.

And unless he provides a circle where shit like that does NOT happen his theory is worthless.

was meant for

Couldn't be more wrong. Jesus Christ.

>Couldn't be more wrong.
nice argument. You couldn't even point out 1 thing wrong.

Ok.
>Because math is based on reality.
There is no such thing as the true nature of the world. Science doesn't tell it to us, nothing tells it to us. The whole question about what is reality and what is apparent is a bad question.

>There are no axioms on which most of Philosophy is build, so there are no objective facts to be drawn from philosophy.
There are Platonic forms and other rules just like in Maths.

>There is no such thing as the true nature of the world. Science doesn't tell it to us, nothing tells it to us. The whole question about what is reality and what is apparent is a bad question.
Math is based on the facts we see in our every day lives.
Euclid's axioms were things like "if a is the same as b then b is the same as a". These are the basic truths about the reality we are living in.
For any reasonable being reality is the sum of all our everyday experiences (except he is a philosopher), on these experiences math is build.
This is not even debatable mathematicians transformed the things they though were "self evident" truths into axioms which then are able to model reality (model is the important word here at no point is it certain that they actually ARE reality). This already happened 2000 years ago and while the axioms have changed the basic Idea has not.

>There are Platonic forms and other rules just like in Maths.
Tell me about them. Is philosophy the logical deduction of a gives set of axioms?
That certainly is not what I was taught.

> modern mat sci uses fem
> wasn't talking about mat sci
Uh huh...
Too bad the other engineering disciplines continue to bow to the limitations mat sci gives them.
Just face it, you're all mat sci's bitch.

There's a reason we name eras of tech based off the newest developed material.

>Too bad the other engineering disciplines continue to bow to the limitations mat sci gives them.
They also bow to the limitations that mechanics gives them.

And as I said. Modern mat sci heavily relies on modern mathematics, so we have engineering also relying on mathematics.

It doesn't tho lol.
You keep thinking mat sci has anything to do with mechanics and acting like you never read a text on mat sci

>It doesn't tho lol.
The professor at my university working on mat sci told me something else.
Apparently his research is about using FEMs to predict the behaviors of materials.

>You keep thinking mat sci has anything to do with mechanics
They are both important engineering disciplines, which heavily influenced our world. And I know that at least mechanics utilizes a lot of mathematics.

>The axioms you described are not chosen at random, but very carefully selected with respect to our real world.

The people who chose those axioms were primarily analytic philosophers of the 20th century. Their philosophy was pretty close to math, but their methods of reasoning were based on philosophy. They were philosophers doing philosophy.

> but wild thoughts scattered without anything bringing them together.

This is what brainlet engineers actually believe.

0/0 you tried

>0/0
So you mean the quality is not defined?

Is it because it is far over your head?

>but their methods of reasoning were based on philosophy.
You may actually be right there and I am quite willing to admit that at the basis of mathematics philosophy lurks.

>This is what brainlet engineers actually believe.
But I am no engineer. I am studying mathematics.
Although the "brainlet" part is probably right, but that really applies to everyone her, more or less.

I liked your album and all, dunno why you created a bait thread man.
Mathematics is philosophy

>he doesn't know what philosophy is

Math has no connection to reality. You can imagine infinities, 250 dimensional tesseracts, Klein bottles, pretty much anything and everything. It's a language used to reduce things to the tiniest bit of information the human mind can meaningfully communicate and analyze, and more disconnected from reality than any other language - which, at least when describing things outside of reality, all rely on synthesis of things that actually exist.

Philosophy, on the other hand, revolves around defining axioms and logically testing them against reality as well as other philosophies. If it can't survive the litmus test of reality and critique, a philosophical concept is defeated, save perhaps as an educational tool as to typical follies (such as Zeno's paradoxes or Anselm's ontological proofs), whereas mathematical models remain relevant forever, whether applicable to reality or not.

Granted, when boiled down to core dialectic, philosophy becomes math, but in the end the debate is as to how the axiom reflects and functions in reality, where as the axioms in math have no such hurdles to overcome. So long as the calculations work out, it's golden.

Math absolutely is philosophy, specifically its a branch of logic

Since however it deals with rigorously defined concepts that in some cases translate very well into reality it is extremely useful

>Math has no connection to reality.
How do you explain that math is able to model reality then?
It is completely insane to assume that something which is axioms and definitions heavily based on reality would suddenly be completely removed from reality.

>You can imagine infinities, 250 dimensional tesseracts, Klein bottles
Klein bottles in 3D are a REAL THING. How can you claim math is unrelated to reality and in the next sentence point to something IN REALITY that is about mathematics.
Stop your contradictions.

>It's a language used to reduce things to the tiniest bit of information the human mind can meaningfully communicate and analyze
No, this only demonstrates your lack of knowledge about mathematics. It is no wonder that you are spouting such stupid bullshit if you haven't even taken high school mathematics.
Mathematics is about ABSTRACTION. Breaking down reality to its most fundamental truths and then building from that.

>whether applicable to reality or not.
Completely wrong. A mathematical model is physics. A field in which traditionally many models have been discarded.
Mathematics provides the ONLY way to argue about reality in a quantitative way and the study of these quantitative models of reality is called physics.
Frankly, you have no idea what you are talking about.

>where as the axioms in math have no such hurdles to overcome.
You are insane. The axioms of mathematics are obeying the most fundamental realities of our world.
They are CHOSEN BASED ON REALITY.
Read about ZFC or Euclid's "elements" the axioms are not "the part is greater then the whole" but the exact opposite.
That someone with so little clue about the foundations of mathematics is making such outrageous claims is pretty sad, you obviously are talking about something you don't understand in the slightest.

>So long as the calculations work out, it's golden.
Again, you have no clue about mathematics. Even implying that mathematics is about "calculations" is disturbing.

jesus fucking christ engineering faggots should be banned on sight

go read a couple of books on set theory, model theory, type theory, and large cardinals and get back to me on how math is totally based on reality

>non-euclidean geometry
>axiom of choice
>n-dimensional manifolds
>non-differentiable surfaces
>the entire field of algebraic topology
>IUTT
>not to mention the entirety of set theory and mathematical logic
no yeah dude math is totally like SO based in reality man haha remember calculus 1? yeah dude i took physics in high school too

>engineering faggots
I am a mathematics student...

>go read a couple of books on set theory, model theory, type theory, and large cardinals and get back to me on how math is totally based on reality
Are you retarded?
Just because a subset of mathematics doesn't have immediate applications to reality (set theory and type theory are awful examples because they play an important role in modern programming) doesn't mean that the axioms on which mathematics is build are not based on reality.

>Category theory
>based on facts we can see in our every day lives
oh my god user don't make me laugh so hard i'm eating

you clearly don't know shit about set theory or type theory
reconsider your major; your posts are embarrassing

t. large cardinals & ultra filters phd student

>a subset
It's the FOUNDATION of all of mathematics, unless you take something like category theory for a foundation you incredible faggot holy christ

which set of axioms?
if you're thinking ZFC, there are an incredible amount of sentences that can't be proven nor negated, which makes it very limited and has lead to countless alternate axiomatizations

i hate you retards who don't know shit but pretend to

>no yeah dude math is totally like SO based in reality man haha remember calculus 1? yeah dude i took physics in high school too
why are you ignoring 90% of mathematics?
Just because some theories have no immediate applications (you provided some rather weak examples of them) doesn't mean that the rest of mathematics have none.

DEs
PDEs
Calculus
Functional analysis
Numerics
and many more

play a giant role in engineering and physics.

>oh my god user don't make me laugh so hard i'm eating
Can you read? I talked about the axioms

>>>>>>>>type theory is not used in programming
consider suicide, you clearly fucked up your life.

And the foundations are unrelated to reality. Was ZFC chosen at random, because Frankel "felt like it"?
And don't lead the foundations to things applicable to reality?

t. engineer

>i know about haskell therefore type theory is totally le wacky programmer maths ;P
stop posting whenever faggot
i suggested you read up on precisely the topics which would show you math is fundamentally ungrounded in reality, but you'd rather keep your head up your ass with a bunch of (essentially) applied math while feeling superior and claiming it accounts for 90% of math fucking lmao

truly the quintessential undergrad

>>>>>>>>>>>>>I have been proven wrong so now I start spouting bullshit
We both know you fucked up and we both know that you are an undergrad in philosophy trying to defend is value by posting some shit he read on Wikipedia once.

Don't make it even worse, stop posting.

whatever you say honey
stay in denial; you'll make a great adjunct someday teaching precal and remedial finite maths

>After I have been proven wrong I proceed to call my opponent names.
I don't think it will be me who slaves his life away in a shit job...

>how is this not just philosophy?
Philosophy is about having no rules, as you wonder which rules have to be and which don't.

>math is real
then how much is square root(-1)

Any language has application to everything - it doesn't necessarily follow that everything described by language reflects reality.

Math can describe anything, real, or unreal. It thus has no more bearing on reality than, say, English, save that you're much more apt to come up with descriptives completely unrelated to reality from a process that spawns its own by interacting with itself.

Math is merely a language consisting of the finest units of self-referencing logic that you can communicate. Logic, in and of itself, does not necessarily reflect reality. Any number of entirely fictional systems can be entirely logical within their own scope.

Every computer game out there works with flawless mathematical precision. Nonetheless, vidya game physics only mimic reality enough to provide immersion to the user - and for all its mathematical perfection, Halo isn't real.

Or, mayhaps more to the point, as has actually been demonstrated, you can create mathematical models that predict every output a Vic20 CPU might make based on every input you can give it and response you can get from it - and still be entirely wrong as to what's actually going on inside the CPU, even though the model simulates it perfectly in every way.

...and, as has happened time and again, the same is true of reality. The labyrinth of logic can check out from every conceivable angle, and still turn out to be entirely alien to the actual activity, once some new piece of information comes into the picture.

The guy arguing that mathematics axioms are grounded in reality clearly hasn't taken more than calculus.

His arguments are so juvenile, fallacious and wrong, you could classify them as "not even wrong".

Stop replying to him

As for OP's question, mathematics is philosophy. Godel seems to have made this clear by showing that mathematics has inherently unanswerable questions. You can't "solve" mathematics any more than you can solve philosophy.

Albeit, it's a highly interesting and abundantly useful form of philosophy and the fact that we can model our observations with it is a bonus

you guys are all genuinely retarded.

Is this bait