Mathematical Analogies for Philosophical Concepts

As is currently fashionable, I'll namefag for the sake of this thread. I tend to learn about philosophical concepts by relating them to mathematical concepts - for example, with tautologies I refer to constants in polynomial graphs given that when looking at meaningful changes in the world tautologies are useless. My level of mathematical knowledge is extremely limited and the best I can do is basic integration and differentiation though mathematical analogies (preferably visual like those autistically-detailed dialectics.org images) have helped me infinitely more than reading. What analogies can I use for the likes of dialectics and other relevant topics?

Other urls found in this thread:

ncatlab.org/nlab/show/Hegelian taco
ncatlab.org/nlab/show/Hegel's "Logic" as Modal Type Theory
globalcenterforadvancedstudies.org/course/d114-category-theory-and-philosophical-dialectics/
cairn-int.info/article-E_SCIE_161_0153--mathematical-practice-and-hegel-s.htm
scribd.com/book/154695520/Picturing-Hegel-An-Illustrated-Guide-to-Hegel-s-Encyclopaedia-Logic
arxiv.org/abs/0810.1279
academic.oup.com/bjps/article-abstract/32/4/349/1516894/Category-Theory-and-the-Foundations-of-Mathematics?redirectedFrom=PDF
situation.ru/app/j_art_1078.htm
gen.lib.rus.ec/book/index.php?md5=4405C8DD8F614A379E5772AC9DE7E665
4shared.com/office/eRApAsRice/Introducing_Alain_Badiou__A_Gr.html

it's futile with dialectics.

what can i tell you is that dialectics can't be formalized as every other scientifical subject.
because dialectics is the method in which an axiomatic system and it's contradiction(in the dialectical terms) are merged into a new, more complete one.

if it wasn't enough, modern logics proof how it is impossible to reach the absolute spirit through a finite dialectical steps.

Literally fucking clueless as usual.

ncatlab.org/nlab/show/Hegelian taco
ncatlab.org/nlab/show/Hegel's "Logic" as Modal Type Theory
Even a graduate course on it:
globalcenterforadvancedstudies.org/course/d114-category-theory-and-philosophical-dialectics/
cairn-int.info/article-E_SCIE_161_0153--mathematical-practice-and-hegel-s.htm

even
scribd.com/book/154695520/Picturing-Hegel-An-Illustrated-Guide-to-Hegel-s-Encyclopaedia-Logic
could be considered a prototypical graphical algebra of sorts.

That would be the shit I need if I understood topology and other fields. Again, the best I have is knowledge basic calculus. WRT dialectics all I know is that Fichte's methodology ([T-A]-S) is insufficient to understand dialectics. I cannot even determine whether I am thinking 'dialectically', as it were.

Here you go, now you understand dialectics.

Wrong.


Check out Picturing Hegel, it's actually awesome and not mathematical at all like the other ones. I don't have a PDF handy, not sure if that's the full copy on Scribd, but if it is you can scrape it without a subscription pretty easily.

Except that's wrong, you fucking retard. An elliptical orbit does not allow an object to approach another and recede from it *at the same time.*

The book's not on b-ok.org, scribd, academia.edu and Library Genesis is down.

Damn, yeah I remember it being a bitch to find. Will share if I can find it again. Best you can do is google books probably, I think the first couple chapters are previewable.

I tend to be very, very, suspicious of analogies, especially when you combine an hard/exact science with a human science like philosophy.

First you're using these small analogies and next you're a Lacan-tier charlatan using advanced topology you know nothing about to describe the science of benis.

I might be the brainlet here, but I'm 3 years in STEM and I have no fucking clue what the fuck you're talking about.
Tautologies are just things that will always be true. In particular, something that will never happen will always imply everything, and something that is always true is always implied by everything.

Lacan did it better than most. He wasn't half bad.

Besides, these assholes never explore anything beyond multivalued logic. God forbid paraconsistent

Well isn't that a depressing thought. I'm French and he makes more sense translated than in my native language.

You're probably 15 and I respect your curiosity, but what you're assuming is complete shit.

This is 100% horseshit, and it's quite the load of horseshit too, so let me unpack it and get shit all over my hands:

1. A tautology is a statement in a logic that is always true, regardless of the values you assign to the free variables occurring in it. It has nothing to do with polynomials whatsoever. It has nothing to do with real or complex numbers either.

2. Tautologies are by no means useless. What you are trying to grasp by calling them "useless in the world" is that you cannot infer the value of any variable in them from the knowledge of their overall truth-value. An example:
"A or not A" is a tautology (in classical logic), but clearly, you cannot infer whether A is true or not from that, since, by definition, A tautology is true regardless of the value of A. If you want to translate THAT into the real world, which you can, it means that you cannot "gain" any knowledge from a tautology, "knowledge" referring to the value a variable must have.

Let me illustrate this, because you'll very likely misunderstand (variables in bold):
>It is raining = true
From this, we can infer that it is, indeed, raining, because the value of "It is raining" has to be true. The statement would NOT be compatible with It is raining being false.
>(If it is raining then I will masturbate) and I did not masturbate
From this, we can infer that it is not, in fact, raining. If this statement would be compatible with any variable assignment, we could not infer the value of any variable from it being true (obviously).

This does not mean that tautologies are useless. Here is an example of a tautology:

>If standard arithmetic then for all x,y x+y = y + x.
This statement does not have free variables (like It is raining) but it's true, hence it's a tautology - and it proves that addition is commutative. The fact that a set of assumptions (standard arithmetic) logically implies some meaningful statement is very useful, and, in fact, this is how all mathematical proofs work.

Tautologies are also useful in the presence of free variables:
>(If A then B) = (if not B then not A)
This is a tautology because it's true, no matter what you assign to A or B, and it yields genuine insight: what this is is a schema for reasoning, a form of inference rather than a concrete inference about concrete A and B.

3. "I refer to constants in polynomial graphs given that when looking at tautologies are useless." is a completely bullshit subjective statement. By what measure are constant functions "useless"? Does a function's shape have look at least this funny to be useful (it has to have at least X funnity, if you will)? You're imposing an arbitrary and ill-defined standard of "usefulness" that probably comes down to you personally thinking that the function is hard to understand.
Besides, "meaningful" changes in the real world seldom follow polynomial patterns either. Most processes (population growth, interest) are exponential, logarithmic, or in fact constant, and even then only as approximations.

sounds about as comprehensible as Hegel, I think they might be onto something.

You just don't understand!

lol. Not even close. If you're French speaking read like Deleuze at least. DeLanda is pretty good for placing him into more a dynamical frame.

Haha, nice, you do realize category theory is the foundation of mathematics and Lawvere, one of its main founders, is probably one of the greatest mathematicians of all time. Holla Forums is really self-parody at this point.

There is no "the" foundation of mathematics. You could say the same about ZFC or HTT or FOL or Peano arithmetic, though I strongly suspect you know nothing about any of those and have all your "nolej" from wikipedia articles you thought sounded cool.

The claim of mathematics having a foundation at all is spurious. Mathematics is just mental construction and deduction, and one theory being a superset of the other does not make it "foundational", as if more powerful theories had been unwittingly used throughout the millennia.

Sure, you're technically right here, but you also missed the entire point of their post, which was that category theory is important and not just obscuritan bullshit.

The point of HIS (sorry, liberals) post wasn't about category theory being important, but about Hegel's bullshit theory being important because Lawvere jury-rigged some category-theoretic formalization of it.

lol you can't found it on Peano arithmetic you idiot. Set theory can found most of it, category theory is the modern foundation, only people who still disagree is a booty blasted set theorist brainlet who insist categories are just sets anyway.

Oh yeah you're a mathematician?
nahahaha

You're a fucking idiot. The concept of a foundation of mathematics is totally valid and accepted it doesn't mean it's some deeper underlying Platonic true structure although category theory, if you knew anything about it, is actually strongly suggestive of such structure.

Shut the fuck up.

Clueless nazbol calling others idiot, that's rich. Go kill yourself retard

It's funny how often you people have to call me dumb, when I crush you in every debate, on every topic, every single time. Really never gets old.

Just because you are too retarded to admit defeat does not mean you are not constantly destroyed

When have I ever lost? Can think of like 2-3 times maybe.

Read Grothendieck

Lawvere is more accessible I find fam, he really tried to expand it to a general audience and did a lot of groundbreaking work in applying category theory to philosophy, logics and formal systems in general. Grothendeik is like an alien, best working mathematicians in the world still combing thru this nigga shit finding new gems

Yes.

Yeah, too fucking bad you can embed category cheory in ZFC+I, meaning that your hated set theory is at least as strong.

arxiv.org/abs/0810.1279

I quote for your faggot-ass:
>Let us pause here briefly to compare the ‘category-theoretic foundation’ for mathematics offered by etcs and its relatives with the ‘set-theoretic foundation’ offered by zfc and its cousins. This terminology is common, but one can also argue persuasively (see [Law05]) that etcs is itself a set theory, meaning a theory about the behavior of sets. What distinguishes it from zfc is not its objects of study, but how it studies them: by taking functions as a basic notion rather than global membership. Perhaps a more correct distinction would be to call etcs a categorical21 set theory and zfc a membership set theory. I mentioned in §13 that etcs is equiconsistent with bzc. In fact, if we add axioms to etcs and bzc saying that every set is contained in a transitive one and that transitive collapses exist (§11), then we can obtain a full equivalence between models of the two theories
>a full equivalence between models of the two theories
>a full equivalence between models of the two theories
>a full equivalence between models of the two theories

You say this as if some conference were held somewhere that decided this. category theory is a niche subject and while it's accepted that you can formalize many structures in it, it's not held to be the foundation of mathematics". What would such a thing even mean? That it's uniquely stronger than all other competing theories? That it's more popular? If anything, that's ZFC, and maybe''' some stronger set-based theories NBG.

Not even proponents of category theory claim that it's "the foundation of mathematics". I literally don't know what the fuck you're talking about.
academic.oup.com/bjps/article-abstract/32/4/349/1516894/Category-Theory-and-the-Foundations-of-Mathematics?redirectedFrom=PDF

Yes, a foundation, not the foundation. You can derive arithmetic, analysis, recursion, predicates, and infinities (the only things you need, really) by multiple means, but you're insisting that category theory is the only trve path, ordained by God.

I didn't say there wasn't a (many) full formal equivalences, but syntax informs semantics and vice versa. There's an equivalence between binary and ASCII, doesn't mean reading the former means anything to pretty much everyone. Similarly you can do shit that took a chapter of Bourbaki to build out of atomic sets with just a few diagrams. Adjoint functor has been extremely fruitful. This is literally the whole point of category theory. It's constructive and illustrative and useful in a way that set theory just isn't. That it allows you to see the deep structure and similarities and interrelationships between what otherwise might seem like totally different fields. Like how you can astonishingly easily see deep links between Hilbert spaces, n-cobordisms, string theories, Feynman path integrals etc.

Plenty do. I dunno why this has you so rustled?

If you are a mathematician, why did you claim that you can found mathematics on Peano arithmetic when you obviously can't due of course to one of the most famous results of all time which specifically refers to it. And you at LEAST need the Axiom of Choice for most of it.

Yeah, well, you didn't say that. I very much remember you saying
The first part of that is false right off the bat.
The second part is tendentious and unfalsifiable. If you had said that it was the most convenient foundation or the foundation you liked best, this wouldn't be an issue.

I hope you're not referring to Gödel's Incompleteness Theorem, which applies to any system that's at least as strong as Peano arithmetic. It's not a statement about the deficiency of Peano arithmetic specifically.

Well I stand corrected, I didn't know about the result you posted.

I just think it's too deep to not be considered the foundation at this time. Will it be The Foundation forever? Nah. But it seems to say some shit about what mathematics is and what we do when we do mathematics on a level hidden prior. And the links to logics and formal systems in general are insane. Unfortunately not that much work has been done here since Lawvere. Plus it's helping blaze the trail into new fields beyond classical.

The work on set theory foundations kind of fizzled out after initial interest in Bourbarki as well, and they're still releasing new chapters. It was just kind of assumed that ZFC or similar could found it all until cat theory started to take the front line.

Your statement re Godel is true but you still can't found much on PA alone, just found this a strange statement you made.

You're correct, that is what I was getting at. That's the standard which you try to critique in the third part of your reply.

This seems far more like programming and I think that it would be better suited to making analogies. As for the rest of the thread I have no idea what's going on.

Smelly dumb nazbols scum.

Try reading this fam, DeLanda on Deleuze: situation.ru/app/j_art_1078.htm

...

Post your faggot critique now.

It's ok, we're all friends, good nazbol.

I actually like category theory as well, but you have to be careful not to read more into these things than what's there. It's a very cool theory with interesting results, but not quite esoterick magick from the star gods.

Gödel's incompleteness theorems weren't about Peano being shit, they were about the lack of guarantees you can give. What Gödels meant to show that, even in such a simple theory as Peano arithmetic, you could construct unprovable statements, which was a huge shock at the time. Geometry had been formalized some years prior with Galois theory (which is weaker than arithmetic, as it only deals with 1st and 2nd degree polynomials), and Hilbert hoped that the same could be done for arithmetic. Gödel proved that addition and multiplication alone already led to runaway complexity. Stronger theores like ZFC have even less guarantees. If you can express more, you can prove less.

What's that book on category theory you read, by the way? I might get it.

He won't post shit but a disguised shitpost. He'll probably ask you what you've read then do some mocking game before saying anything useful to hide that he is a goddamn hack.

gen.lib.rus.ec/book/index.php?md5=4405C8DD8F614A379E5772AC9DE7E665

Read anything by Lawvere, he has a lot of short articles which are really good, can post more if you're into it, ncat cafe which I linked before is the main wiki, and check John Baez who's team is doing phenomenal work with network theory on the physics side. Lawvere did all the heavy lifting on topoi as well, far more fruitful going to the source than reading some pretentious nonsense like, oh, say Badiou.

Why would I do something nice for you when you've been so rude?

Oh libgen still down, the book is Lawvere and Schanuel - Conceptual MAthematics: an intro to Categories

You have refused to post the critique of Badiou. You said you'd post it today, yet I'm seeing nothing but you throwing names around.

or i have a better idea, how about, instead of me carefully preparing an effortpost for salty little bitch ingrates like yourself about a minor figure in leftism… a salty little bitch who, apparently, is still mad like 8 hours later, after you got caught lying about knowing anything at all about philosophy, like no one saw that shit go down, how about you just slit your wrists and never post again?

I win.

okay guy i see it means a lot to you to "win" against muh nazbol boogeyman so you can have this one, be sure to tell all your friends what transpired here today

Hey man, did you see how I BTFO that dumbass nazbol on Holla Forums today? It was so epic lol. It was even easier because he never once bothered arguing and resorted to just being smug.

what are you fucking autists even on about?

does it really make you THIS insecure that i dominate you in every way possible? well come to think of it, i guess it would. that's bad luck. :(

Nazbols are truly the worst posters on Holla Forums. I wish they were banned already for being this useless and annoying.

Oh- congrats and commiserations! Your penises have been stroked and burned while someone here is trying to learn only to be confronted with this. I'm still struggling through the article on Deleuze though I'm not entirely sure what it has to do with dialectics or even the original topic I raised: philosophical analogies. So much of the material that I encounter isn't suited for my learning style and I'm practically fucking locked in this mentality and state of ignorance (I can't learn to think using new modes of thought and I'm gradually becoming more discouraged).

I mean, seriously, are you guys all fucking COINTEL niggers?

Is this mathematical formal enough for you, op?


Not Hegelian dialectics, and the picturing dialectics book is a crutch that is, as the author themselves admit, not capable of being faithful to the purely conceptual content. Picture thinking is >not< conceptual thinking, and the point of the Logic is thought free in itself, a pure construction of language.

I don't know how the category theory thing works, and I will give it the benefit of the doubt that maybe it is a possibly a "dialectical" mathematics (albeit, I don't see why you wouldn't be using the quantity and measure categories instead for actual math instead of pseudo-math form with metaphysical categories, this shit reminds me of Badiou's shitty Pythagoreanism).

Familia, sorry for shitting up your thread. Since you ask for philosophical analogies, I have one book which might be of help but it deals with a specific philosopher's system. I know shit about dialectics right now.

Here it is, it contains analogies and mathemes for certain parts of it: 4shared.com/office/eRApAsRice/Introducing_Alain_Badiou__A_Gr.html

why everything has to be so complex

bump

Did you even read,
Oh so you didn't.
Why

While Hegel himself was adamantly against picture thinking with dialectics, there are arguments to be made for it which I obviously agree with.
It's a proto graphical algebra which I think is very useful as a learning tool. Considering most people can't even get through the most basic Hegel shit, let alone ever try crack Encyclopedia Logic, I find it very valuable to help teach people new concepts. They are free to read the original material when they are more familiar with it. The shit's a gold mine and has vast tracts still basically unexplored by philosophers since due to the learning curve. So what's your problem?

No need to be a dick, I was only trying to help. :v) Deleuze is all about ontological analogies with dynamical physics, which is all about calculus and not that much harder. While it's not dialectical, and even somewhat anti-Hegelian (Deleuze himself claimed Hegel was Evil, but he covered up how much he was influenced by him imho), it's a radical way of thinking that is at least complementary with it, and updated with much more modern references presentation. Calculus of course was in its infancy when Hegel wrote, and his analogies with science are obviously dated as hell.

n-nazbol sensei, you seem to know your shit.
i've never been good at learning philosophy, but i was quite good at math.
i just wanted to know if those matheme-looking pictures like the ones of are legit or not.

thanks

That guy is a bit of notorious crackpot but I really like it on an aesthetic level. Tickles my fancy. Some of it seems like a real stretch, but I really haven't delved deep enough into it to confirm any deeper validity tho tbh sorry

also are you truly a nazbol or are you just memeing?

Where's the fun in that. Lurk moar and find out my dude

i ask because im sure something around 90% of the people that get buttmad at you are because they can't hold up the fact that someone with a nazbol flag btfo them.

Seen this already. The combination of new symbols and logic is way too much for me to comprehend though I do see patterns. If I explore the image enough I'll be able to figure it out but I have to counter the mental resistance I feel every time I do so.

Mind is gonna kill me for this, I'm gonna need to think.

There is a cypher, it actually has a logic behind it. It's based on Boole's first logical calculus of concepts, which I had never heard of and is strange.