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/sci/ - Science & Math

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6038136 No.6038136[DELETED]  [Reply] [Original]

Is math just formalized philosophy?

>> No.6038142

>>6038136

No.
People who have not studied philosophy should not waste time talking about i.

>> No.6038146

>>6038136
No, it isn't a philosophy, not even a science. It is a language. Just like with language, you can express ideas with it or spew out crap.

>> No.6038151

What is philosophy?

>> No.6038155

philosophy redefines itself constantly

>> No.6038157

What is math?

>> No.6039548

>>6038151
We just don't know.

>> No.6039561
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6039561

Philosophy is supposed to be formalized and subjective. Math is formalized language. Let me go brighter. Mathematics is for quantity abstraction and Philosophy is for quality abstraction.

>> No.6039565
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6039565

Yes.

>> No.6040851

No, math is science. Math is discovered and not invented.

>> No.6041314

>>6040851
"Imaginary numbers" certainly do not fit this criteria.

>> No.6041360

>>6041314
Imaginary numbers exist in the nature though

>> No.6041363

>>6040851
I think it's more like math is a formal system that we invent to describe how reality behaves. For example, it is a discovered fact that objects in reality act like the natural numbers. This is true no matter what anyone believes or how much math they happen to know. Our mathematical models of natural numbers, sets, etc. are useful because as near as we can tell the behaviour of these things is isomorphic to the behaviour of reality.

>> No.6041366

>>6041363
The same is true for the systems of logic that we use to build our mathematics. As near as we can tell, reality is logical. There are no states of reality that are both the case and not the case simultaneously, for example.

>> No.6041374

>>6039561
I really dislike it when somebody calls math a 'language'. Math is inherent to reality, its not a language but a property, notation is language used by people to represent such property

>> No.6041395

>>6041374
The notation of math is a formal language, that formal language models abstract entities like sets and the natural numbers, those abstract entities are attempts to describe properties of reality, properties like the fact that objects in reality act like the natural numbers.

The word 'math' is used to refer to all of these. The notation, the abstract mathematical entities, the mathematical properties inherent to reality.

>> No.6041463

Philosophy is the explanation of humanity. The excuses for humanity. Math is the bridging of the gaps between the many excuses we have made more abstract. This way we gain some insight from our mistakes in the form of recognition. Further generalized to suit our unheeded desire to "control" everything, as if controlling something could ever really help us truly understand anything. Physics.

>> No.6041466

>>6039561
This is a great description. I'm sorry I didn't see this before having posted. The posts up to this one just really ground my gears.

>> No.6041810

Maths is a less abstract form of logic.

>> No.6041925

Nobody knows what mathematics is, we can only observe its effects. Some people believe that scientists used mathematics to send people to the moon and others think that mathematics is something to do with counting the number of fingers you have.

The only "proof" that mathematics is real is that some people claim it is a language, but if it was a language then how come signs aren't written in mathematics?

>> No.6041928

>>6041925
>how come signs aren't written in mathematics?
oh but they are.

>> No.6043623

>>6041810
Is logic just formalized philosophy?

>> No.6044049
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6044049

Dude do not include me in your 'we'.

Reality isn't logical that is the whole reason why people waste time with virtue-ego stroking because they erroneously try to conseptualize reality in terms of philosophy(logic) and mesure it in terms of math.

Logic and causality prevent free will.
However, logic and casuality do not explain all there is. Therefore, free will is possible.

Quantic captcha:
ingdffi purpose

>> No.6045372

>>6044049
>logic and casuality do not explain all there is
What do they not explain?

>> No.6045948

>>6041925
Wat?

>> No.6045969

>>6039561
But with math you can quantify qualitative abstractions.

>> No.6045971

>>6041366
wat about quantum physics bru?

>> No.6045973

>>6041374
Math is inherent to reality? That's a pretty bold claim man, wouldn't it be better to say math is the most reliable tool humanity has for understanding reality?

>> No.6045980

>>6045372
Logic and causality do not explain everything as far as we know.
The origin of the universe is the quintessential proof against causality. Sure, we know the big bang led to the current universe but we can only speculate about what was before that, if there was anything.

I love science and math, but believing we know the truth is a claim I will not accept until we either meet god or become god.

>> No.6045994

>>6038136
Each is a form of logic, formal and informal, respectively.

>> No.6046500

>>6045971
What about it? The mathematics of quantum physics, being math, is deterministic. There are two major interpretations of that math, copenhagen and relative state. The former says that a space of possible outcomes collapses into just one, so no two states are both true and false at once. The latter says that the entire space of outcomes occurs, each in its own world, which is still not saying that any two states of reality are both true and false, it's saying that reality is a larger place than we thought and includes many worlds of which we are at this moment in just one.

>> No.6046506

>>6045973
It sounds about right to me. Adding 2 apples to 2 apples gets you 4 apples no matter what you believe or don't believe, no matter whether you know math or don't know math, no matter whether you're a human or some other intelligence.

>> No.6046522

>>6046506
The problem is the concept of a number. Numbers don't exist in nature, since inherent in a number is an abstraction.

Even more difficulty to justify are real numbers, irrational numbers, and continuity. If you care to try, give it a shot.

>> No.6046536

>>6046522
Numbers are an abstract concept, but the reason we care about this particular abstract concept and not some other concept we could define is that things in reality that can be counted, like apples, act like the natural numbers. And that's not an opinion, that's just a fact. No one who has ever manipulated things in reality has ever found otherwise.

And the natural numbers, as defined axiomatically through peano or through sets, are the foundation of the rest of mathematics. Do things in reality also act according to the abstract concepts of real numbers, irrational numbers, etc.? Yes they do, that's why you'll find these things in a physics textbook.

>> No.6046554

>>6046536
>Do things in reality also act according to the abstract concepts of real numbers, irrational numbers, etc.?

No, they don't, out model just works (and that is not even true for all cases), but it doesn't mean it is actually true, so it does not mean that there is an epistemological connection between numbers and reality.

lrn2more epistemology

>> No.6046575

>>6046536
>>6046554

When you take "two" apples, you don't have "two" apples, since no "two" apples are exactly identical. This is where the abstraction comes in. When you have "two" apples, you really have one thing that looks an awful lot like another thing, so you create the concept of an "apple" so you can say you have 2.

>> No.6046608

>>6046506
except the way we interpret reality is based on a very small number of parameters. its proven there are things we don't see. spectrum stuff our physiology makes us c 2 apples but is there even an apple futhermore this is backed by physics sum-what and einstein

>> No.6046623

math is just logical operations
and logical operations initially falls under philosophy jurisdiction
so yeah

>> No.6047370

>>6046623
That is indefensible and idiotic. Anti-intellectual "u cannot know nuthin" bullshit does not have any jurisdiction over science and maths.

>> No.6048554

>>6038136
yes because u cannot know nuthin

>> No.6048556 [DELETED] 

>>6038136
No math is fucking horrible

>> No.6049212

>>6048556
How so?

>> No.6050398

>>6049212
Because solving for x and finding the derivative.

>> No.6050769

>>6038136
makes sense
but it also makes sense the other way around
so i suppose they are the same thing
/thread

>> No.6050952

>>6050769
>makes sense
You must not understand either of the fields.

>> No.6051134

>>6050952
how about you write a book about how different they are

lmao

>> No.6051139

>>6050952
i mean, you must only know the surface of both fields to say something like that

>> No.6053511

>>6051134
I do not have time to do that.
>>6051139
non-sequitur

>> No.6055055

>>6051139
Not that poster, but I know both fields indepth and they are very different.

>> No.6056338

>>6050398
Why do we need those?

>> No.6056369
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6056369

>>6038136
Nope. No such thing as philosophy. Every philosopher is either fraud or delusional. Sometimes both.

>> No.6057859

>>6056338
We don't need them anywhere. They were invented only for the design of homework problems.

>> No.6057996

>>6040851
Math is not science m80, no mathematician will use anything as retarded as the scientific method

>> No.6058088

>>6057996
Of course, because that would mean that you are able to actually benefit the humanity, which is a big turn off for mathematicians.

>> No.6058097

>>6058088
99% of science and 100% of math does no benefit

so well done science for that astonishing lead

>> No.6058122

>>6058097
99% of science is actually a lot less and is responsive to the current highest progress point. In the future it all will be manifested in a ways theoretical scientists already can see. And then there'll be another 99%. Only these ninety nine percents are responsible for our technological progress. We made our way from caves to high-teck homes in less than 10 kyears, I say it's not bad.

>> No.6058127

>>6058122
nope

99% of science will never benefit mankind. go look at published science in journals. almost all useless forever

>> No.6058129
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6058129

>>6058097
maths is enormously real world useful you faggot

>> No.6058140

>>6058127
How much of it's just people trying to find something new to get their Ph.D?

>> No.6058145

>>6058140
>implying you can find something new without benefiting mankind
Phd is the ultimate test of scientist. It challenges you to create something, to discover.

>> No.6058154

>>6058145
if stupid physics discoveries about adding another sig fig to the latest estimate of how much angular momentum interstellar dust possesses is a benefit, then so is some math discovery of a weird property of a topological space

>> No.6058169

>>6058154
You are not seeing clearly, when you believe you are. And that makes you even more deaf, I'm afraid. Yes, the benefit which go along with phd's study is often close to null. But it is not. And if you sum them all you will eventually get quite a big benefit. Of course, they could be harder, but why? It was proved to be enough.

>> No.6058179

>>6058169
>whiny bitch with added self importance

>> No.6058201
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6058201

>>6038136
It's fun to read /sci/entist arguing about philosophy.

>> No.6058223

>>6058201
what is philosophy?

>> No.6058235

>>6058223
formalized math

>> No.6058247

>>6058223
Unformalized maths, If you ask me, that's what it is.

>> No.6058255

>>6038136
>Is math just formalized philosophy?

Well, there is a bit of an overlap.

For example, symbolic logic is a topic that's often taught in both Philosophy departments and Math departments.

I view philosophy as being broader than Math. Math really just concentrates on symbolic pattern analysis. Philosophy tends to include topics in a broader range of fields like politics and so forth.

>> No.6058261

>>6058255
Too bad it doesn't work.

>> No.6058273

>>6058261
>Too bad it doesn't work.

What, philosophy doesn't work?

I don't think it's intended to "work". When I took a few philosophy courses in college, the overall impression I got was that the purpose of academic philosophy was to assign standard terminology to various concepts. For example, in philosophy you can mention the "T.S. Kuhn view of science" and quickly communicate what you're talking about. Academic philosophy mainly just collects all those views together in a catalog and assigns standard terminology and names to all the ideas.

(Actually, math takes the same approach too. Math is really nothing but a catalog of mathematical objects and their properties. When you study "math", an important part of what you're doing is learning the standard terminology used in that catalog, so you can quickly discuss things in an efficient manner.)

>> No.6058284

>>6058273
Except "views" of philosophy bother no one for they are useless in science and useless logically in principle.

>> No.6058285

>>6058247

wut

explain Kant's Categorical Imperative using maths

>> No.6058291

>>6058285
Would love to, but it's an illogical concept, hence inability to formalize it. It's not only unformalized maths, it's also unformalizable maths, which is even more important.

>> No.6058295

>>6058291

How the fuck is it an illogical concept?

Or more importantly, what does philosophy have to do with mathematics?

>> No.6058301

>>6058295
Nothing. That's the thing, you see. Maths is about logical half of science, philosophy is about intuitive (illogical) one. Naturally, philosophy burned out long ago.

>> No.6058313

>>6058284
>implying philosophical motivations aren't taken into account when generating new systems of math/physics

You never go full retard.

And just as an example of what I'm talking about before you start sputtering 'b-b-but philosophy is never ACTUALLY used in science' where do you think Issac Newton's absolute notions of space and time came from? It sure as shit didn't fall out of the math: the math was built around the ideas, not the other way around.

>> No.6058317

>>6058284


>Doesn't know what philosophy of science is

>> No.6058320
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6058320

1=1

>> No.6058327

>>6058284

>Implying the definition of science doesn't come from philosophers
>Implying the formalization of the scientific method (and any critique of it) doesn't come from philosophy

>> No.6058340

>>6058284
>Except "views" of philosophy bother no one for they are useless in science and useless logically in principle.

I can't agree that philosophy is "useless logically in principle".

Philosophy actually encompass logic as one of its subject areas.

Your statement seems to imply that philosophy is not equipped to explain logic. A lot of us who successfully took logic courses in philosophy departments would take exception to that implication.

>> No.6058354

>>6058313
Philosophy at the time was a wholly different subject. It was some kind of set of knowledge, to which physics and maths were subsets. But then everything came to their places, except there was no place for philosophy. So now it's fucking around while being pretentious.
>the math was built around the ideas
If you read on some quantum gravity theories you'll realize it still is.
>>6058327
>>Implying the definition of science doesn't come from philosophers
> Implying the definition is something of importance
>>Implying the formalization of the scientific method (and any critique of it) doesn't come from philosophy
> Implying it's of any use now when psychology isn't yet an accurate science, so it can describe conscious and unconscious processes rigorously. Basically it all comes down to creating hypotheses and verifying them. We can't really rationalize this process, as philosophy claims it does, because it's just a hunches, based on accumulated knowledge, we know nothing more about. We have a lot of ages to go though until we know what mind is on quantum level. Then philosophy will finally die and social sciences will prosper as legit applications of biology. Until then it's just better to continue doing what we do as we have been doing it since the death of the old philosophy. We are kind of in the similar position to the 17nth century chemistry scientists.

>> No.6058360

>>6058354
There are still viable branches of modern philosophy, don't discount the subject just because the majority of it is a stagnant cesspool, it contains the occasional oasis still.

>> No.6058366

>>6058340
> Philosophy actually encompass logic as one of its subject areas.
Supposedly, but not actually.
> Your statement seems to imply that philosophy is not equipped to explain logic
It is not.
> A lot of us who successfully took logic courses in philosophy departments would take exception to that implication.
So then if I'm a cook and I've successfully taken logic courser, it means that cookery is equipped to explain logic? Or what are you saying exactly?

>> No.6058367

>>6058360
I would like an example of that.

>> No.6058373

>>6058367

ethics

>> No.6058375

>>6058366

>It is not.

Why not?

Logic is a brach of philosophy

>> No.6058376

>>6058375
You cannot really explain logic. Some minds have created the fundamentals of it and it proved to be true 100% of the time. It's not luck though as some might start to think.

>> No.6058426

>>6058366
>> Philosophy actually encompass logic as one of its subject areas.
>Supposedly, but not actually.
>> Your statement seems to imply that philosophy is not equipped to explain logic
>It is not.

You're expressing a view that would be extremely unpopular among academic philosophers.

I'm not saying you're wrong, but you're going to face some ferocious headwinds if you actually try to air those ideas to the mainstream philosophy community.


>> A lot of us who successfully took logic courses in philosophy departments would take exception to that implication.
>So then if I'm a cook and I've successfully taken logic courser, it means that cookery is equipped to explain logic? Or what are you saying exactly?

I'm saying that the faculty who work in philosophy departments can successfully teach students logic. And those faculty members almost always consider themselves as being teachers of philosophy when they teach logic.

Maybe you disagree -- if so, that's your right. But, again, you would face some very stiff resistance if you waltzed into a philosophy department and whipped out your "supposedly, but not actually" comment from above.

>> No.6058438

> if you actually try to air those ideas to the mainstream philosophy community.
So am I, if I'm going to air some ideas on religion community, but why would I engage in such illogical activities? As my vulcan uncle used to say: "if you can't change it, deal with it (rather than deceive yourself doing something that's not gonna work)".
> I'm saying that the faculty who work in philosophy departments can successfully teach students logic
What is the basis of this statement? Students successfully study logic in philfacs? So are all the other students, because it's a fundamental subject, you don't need background knowledge for such.
> And those faculty members almost always consider themselves as being teachers of philosophy when they teach logic.
Oh, that changes everything.
> But, again, you would face some very stiff resistance if you waltzed into a philosophy department and whipped out your "supposedly, but not actually" comment from above.
Yeah, it's not hard to deduce philosophers prefer the path of the least resistance.

>> No.6058452

>>6038146
>It is a language. Just like with language, you can express ideas with it or spew out crap.
Why do people say this? Its stupid.

>> No.6058455

>>6058452
It's the truth.

>> No.6058506

>>6058455
Can you support it at all with some reasoning or something like that? Languages are mathematical objects after all, so if maths is a language its not so by definition, you need to show it to be so.

And if mathematics is a language, what is the language of mathematics? A language defined on a language? Very strange. Its simply not the case that mathematics is a language, its just an old metaphor gone too far.

>> No.6058511

>>6058506
Yeah, no.
Nice try though.

>> No.6058546
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6058546

>>6038146

>> No.6058566

>>6058367
Politics
Ethics
Scientific Philosophy (The scientific method is not inherently perfect, and will always need more and more fine tuning)
Historiography
Almost any philosophical discourse that hasn't been infected by post-modernism

>> No.6058567

It's sadly the case that mathematics relies upon a foundation of a priori knowledge that we call axioms. Never mind the fact that we can never precisely define these axioms without room for interpretation (the words we use to define things in turn require definitions themselves) - the axioms themselves are either incomplete or inconsistent. This is a well known phrase, but I find that nobody actually understands what the significance is. To go over it briefly, when we say a set of axioms are incomplete, we mean that there will exist problems that this particular set of axioms will be unable to prove. When we say a set of axioms is inconsistent, we mean that there are contradictions.

The ramifications of this are under-appreciated. If any contradiction exists of any sort, anything can be proved from that system of axioms (I encourage any junior mathematicians to try the proof for this themselves - it can follow from vacuous truth). So we really hope that our axioms are not inconsistent, but merely incomplete. This is no less heartening - it means a mathematician can work on something his whole life, and simply not have the tools to reach the results he hopes for. Some propositions are unprovable, and we can't tell ahead of time which are which. This assumes that a contradiction isn't lurking somewhere, which would absolutely destroy mathematics as we know it. Not a single theorem would be salvageable.

What I'm getting at here, is that anybody who thinks that math is some kind of universal embodiment of truth really hasn't had that much experience with the subject. There's an enormous amount of faith involved, and nobody in contemporary mathematics would dare make that kind of claim. How could you, when it's been demonstrably proved that alternate systems of description exist? The universe doesn't consult your calculus textbook every time a rock rolls down a hill.

>> No.6058572

>>6058566
> Politics
> Ethics
You kidding.
> Scientific Philosophy (The scientific method is not inherently perfect, and will always need more and more fine tuning)
I have already establish, that philosophy in incompetent of making any useful judgements about anything, because of it's non-existent methodological inventory. Everything that could be deduced by logic was deduced long ago. Same goes for everything else, except it's almost always some useless illogical bullshit, so you don't even need to talk about methodology.

>> No.6058574

Why are you people arguing about stuff like this?

>> No.6058576

> How could you, when it's been demonstrably proved that alternate systems of description exist?
Because it has nothing to do with it? Any linguistic language is an alternative to maths. Yet they all mean the same thing. It's just that maths always provide one meaning to each mathspiece.
What usually is meant by "maths" is not "current level maths", but the "ideal maths" - set of everything there is to know with no inconsistensies and complete. It's also can be called maths because it shares principles it's based upon with current maths. Principles, not necessarily axioms.

>> No.6058578

>>6058574
Takes the head off of my perfect gf I never had.

>> No.6058607

>>6058567
Disproving mathematics, while awesome, would in no way disprove all progress accomplished thanks to the 'discoveries' of mathematicians.

>> No.6058628

>>6058567
>It's sadly the case that mathematics relies upon a foundation of a priori knowledge that we call axioms.

No it doesn't, axioms are assumed to be true. They're not believed to be true, no one thinks they're actually true statements, you just say "If this is true, then so are these other things", and mathematics goes no further than that. Its the application of science that takes the axioms as a priori knowledge.

>Never mind the fact that we can never precisely define these axioms without room for interpretation
If someone interprets your axioms wrongly they just end up doing different maths to you. The more interpretations the merrier, doesn't affect the actual mathematics.

>the axioms themselves are either incomplete or inconsistent.
That's not true. Systems which're axiomatically defined are either incomplete or inconsistent, not axioms themselves. Incompleteness isn't really a big deal. You completely misunderstand the incompleteness theorem.

>The ramifications of this are under-appreciated. If any contradiction exists of any sort, anything can be proved from that system of axioms
That isn't underappreciated at all. Its covered in any undergrad maths course. Its not such a big problem as you seem to believe though, and I don't say this because I under appreciate it, I say it because we define systems that're incomplete, rather than inconsistent.

>What I'm getting at here, is that anybody who thinks that math is some kind of universal embodiment of truth really hasn't had that much experience with the subject.
No one thinks its a universal embodiment of truth, everyone knows its the closest thing to that that human's have achieved, and most likely ever will though. You get truth under assumptions, its not the mathematician's job to say whether the assumptions are true or not, but to find what's true when they are.

You're not really talking about mathematics here, but instead are talking about the popular view of mathematics among high schoolers.

>> No.6058650

Arithmetic is what happens when you take counting and apply logic to it. Mathematics is the abstraction of arithmetic processes.

>> No.6058655

>>6058650
Prove arithmetic even exists.
Amirite guise??

>> No.6058668

>>6058567

I believe this is called Godel's Incompleteness Theorem, friend.

>> No.6058677

>>6058668
Its called misinterpretation of Godel's incompleteness theorem more specifically.

>> No.6058685

>>6058668
I am no friend to you for I do not believe.

>> No.6058686

>>6058567
>How could you, when it's been demonstrably proved that alternate systems of description exist?
It's just a matter of time before those alternate systems of description are generalized into a more abstract theory that captures all of it.

On a sidenote, I personally like axiomatization but I don't believe it is inherent in mathematics. I see it more as a convenience for keeping everything consistent and provable. The fact that there are unprovable truths in an axiomatic system doesn't make those truths any less true. To modify an analogy from that awful book about a tortoise and a hare. Just because your stereo can't play the resonant sound frequency of your stereo without breaking doesn't mean that sound doesn't exist. The real question is,
>is it even necessary to play the sound to know it exists?

>> No.6058764

>>6058655
It is proven by measuring the objectively observable brain activity of a preschool kid.

>> No.6059695

>>6038151
>>6038157
/thread

>> No.6059833

philosophy and math relate to each other. However I think math would be the correct way to approach philosophy and not vice versa.

Math is a tool which you can prove things right or wrong. Philosophy is basically saying "it could be right or wrong ".

>> No.6059842

If you want to see it that way, it's the only field of philosophy that accomplished shit in helping us understand the world AND in helping to understand "transcendent" truths of mathematical entities.

>> No.6059846

>>6038146
No ass hole. The symbols are the language that lets us describe math, something that is much more than just symbols or a language.

>> No.6060775

>>6059833
>Philosophy is basically saying "it could be right or wrong ".
No, what you meant is "u cannot know nuthin".

>> No.6060902

>>6038136
Is science not just formalized religion?

>> No.6060936

>>6058375

>Logic is a brach of philosophy

Historically this isn't true. Go read the Analysis article on the SEP. Especially the history section. Greek philosophers borrowed logic as a tool from Greek geometers due to its success as a method of analysis. Not vice versa, as everyone here on /sci/ or /lit/ seems to think. While it is true there is a large field of logic in philosophy; historically, the branch itself arose from mathematics. There is also a large field of mathematical logic that encompasses model theory, proof theory, and computability theory (recursion theory). Now there are philosophers who dabble in these fields (like the guys at CMU, or that German university that did the mathematical philosophy course on coursera), but most of the research is inward directed at mathematics, and rarely have anything to do with philosophy. You might also counter what about Frege, Russell, and the turn of the century logicians? I'd reply that you are stuck in the past. I mean seriously, what is it with philosophers and their fetish for resting on their laurels? You guys realize that there has been a hundred years of research in mathematics beyond Frege and Russell that has turned up a ton of interesting tools beyond logic right? We've had topos theory, category theory, graphical models, k-theory (and its major implications all over the place from surgery theory to physics). Yet you guys are stuck on logic. How about you make like the Greek philosophers (or their contemporaries like the CMU and GMU guys), and you know, look into the field a bit more rather than resting on your laurels and dismissing it? Whoops, I forgot, we are on 4chan, where it is easier to reply to people with the skeptical equivalent of "you don't know nuffin!"

>>6058373

>ethics

LOL. Google experimental philosophy + ethics. Philosophers are no better at ethics, than the average person. See this paper for instance: http://www.faculty.ucr.edu/~eschwitz/SchwitzPapers/PowerReason-130204.pdf