In your opinion, how essential is it for a philosophy enthusiast to learn the foundations of mathematics?
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In your opinion, how essential is it for a philosophy enthusiast to learn the foundations of mathematics?
You need to actually study mathematics in order to learn the foundations of mathematics
It's extremely complicated
Pishposh, poppywiener, and cumdrizzle.
Absolutely critical. A mathematical background is what separates serious philosophers from the dude weed lmaos.
nothing wrong with smoking weed.
Nothing wrong with it. In fact I enjoy it occasionally myself but I don't think the ruminations of a crippled brain are adequate foundations of good philosophy.
yeah well, that's just like, your opinion man
which is probably a by-product of your environment and other factors that have influenced you that you haven't really analyzed in excruciating detail
but i don't fault you for it, because no human being has the time to do so - we'd never look to the future, just be stuck analyzing the past
>I need to look intellectual and refined at all times
insecure midwit
homosexual
Maybe for you, my writing tends more towards history, anthropology and sociology than metaphysics
>anthropology and sociology
A meme discipline and an even bigger meme discipline.
well i like memes, so, yeah what of it?
Pythagoras would enthusiastically say yes.
This board despises Russell and he's the only philosopher I can think of that would have a real claim to understanding the foundations of math and even his understanding is obsolete at this point. A general understanding of deductive reasoning and formal logic is absolutely necessary for a philosopher though.
Not important at all unless you want to learn about the philosophy of math. Don't know why you would do it.
Any mathematical proof you get that 1+1 = 2 is less convincing than your intuitive apprehension that 1+1 = 2. The best proof you got was when your kindergarten teacher or mother told you what 1 was, what it means to add another, and told you to count things up with your fingers. The Peano axioms will just give you a formalized way of describing your intuitive belief. And constructing natural numbers within Zermelo–Fraenkel set theory out of nested empty sets is only interesting for theoretical reasons, not for apprehending why 1 + 1 = 2.
Now learning math generally? Very helpful in a lot of ways. Know about probability theory, know about statistics, know about mathematical formulations of logic.Learning ZFC set theory or alternative formulations of the foundation of math? Nah bug off with that.
smart answers receive no replies here, comrade
I must be the smartest one here then because I hardly get (You)s
Or you're on the shadowban list like me. We can see each others post and the dumbest the low quality and trolls who be elsewise shadowbanned but most posters and lurkers cannot see our posts.
Some of us just suck at math so we have to work around it
To be fair, a lot of foundational mathematics is the study of the properties of formal systems in general, which is useful to know, because most epistemologies involve some kind of evidence calculation and formal structure. Also, it's just useful to know how our fundamental ideas hold together, even if their premiss is only intuition.
How would you apply insights from the foundations of mathematics (in the technical sense) to some epistemic system? I would be swayed if there's actually an example where we derived interesting conclusions about an epistemological framework using such methods.
Gödel’s incompleteness theorems
I can't think of much relevance to Godel's incompleteness theorems other than there being a limitations on what we can demonstrate through formal systems. There's not an epistemic question people really care about where Godel's theorems explicitly come in to say "you don't get to know that."
These are all interesting questions. Constructing the natural numbers using nested empty sets within ZFC set theory won't answer any of them. It'll tell you that if ZFC is consistent that the Peano axioms are consistent, though.
>Constructing the natural numbers using nested empty sets within ZFC set theory won't answer any of them.
Proof? Or is this more citation: muh intuition?
I'll frame it a way you can understand.
No one has ever used the ZFC construction of the natural numbers to prove:
- An explanation for why we have the intuition that 1 + 1 = 2. There are proofs that 1 + 1 = 2, but this is district from providing a psychological account for why it's intuitive.
- An explanation for why mathematics is able to describe the universe well.
- An explanation for why computers are able to surpass human achievements in many domains now.
If you believe there is a construction, feel free to state the relevant axioms of ZFC set theory you need for your proof and use valid rules of inference to demonstrate one of these.
If this formalism fails to adequately address the foundations of mathematics, then it is off topic. (If we could satisfactorily explain mathematics, what would be the point in studying it?). The existence of one inadequate answer does not unask the question.
So you don't know what the foundations of mathematics actually means within the field of mathematics.
The foundations of mathematics means the foundations of mathematics, which is not necessarily identical with the prevailing theory at time t, even if t= today.
Mathematicians should study philosophy as well.
Sure, and there are alternative texts that don't use ZFC. When someone asks if they should study a topic, I'm going to tell them what they would learn about if they sought out a standard treatment of that topic. It sounds like most people would be more well served by reading a textbook on the philosophy of mathematics than taking a course on the foundations of mathematics at a university mathematics department.
Its simple to answer why its intuitive, just use proof by contradiction you don't even need set theory for that. Its intuitive because we perceive many distinct things instead of just one thing. Math would not work if there wasn't any distinctness.
Computers are like wheels, they can surpass running, doesn't make them any more special when they barely make any progress in the non linear analogue computations that make us human, like recognizing faces, emotions, states of mind etc. Also math describes the universe well because of logic, not because of any special trick only found in math. You are trying to frame these questions into intractable impossibilities, the sort of thing that impresses teenagers.
Ok but these aren't really philosophical questions either.
They are philosophical questions, but this guy has a hard on for ZFC, and presumably Peano and Frege and Russell, so we get these random complaints that this fork isn't a very good spoon. The foundations of mathematics is a broad topic, and philosophers should be educated about it (and about mathematics as a discipline, which has deep historical ties with philosophy to put it mildly), and should probably take regular mathematics courses too because it's very very sophia and you have no excuse not to philo it. The truth is that most "philosophers" h to say nothing of philosomeme IQfy mega posters - are dumb and get filtered brutally by arithmetic.
OK, where does this "intuition" come from? Why does the world obey it? Why does formalizing it in calculating machines now produce "intelligences" which can mimick or in some ways outstrip our own "intuitive" knowledge which transcends formalism?
>where does this "intuition" come from?
Various aspects of human cognition ranging from something like the Kantian transcendental aesthetic to gestalt psychology and the ability to "see" the analogical truth or adequacy of metaphors in non-discursive ways / in ways that discursive thought can only follow and formalize post festum
>Why does the world obey it?
It doesn't always, there is a complex relationship between our intuitions, our post-intuitive formalisms, and the world-interacting practices and mechanisms we build by means of these. Many, perhaps infinitely many possible forms of mathematics accurately model the world and thus allow us to interact with and manipulate it, which can give the illusion of "obedience." Modern logicism on the other hand has actually occluded interesting possibilities for explaining what sort of mathematical structure the world could ACTUALLY have -- for example it is extremely difficult for us to recover and "think with" Platonic/Pythagorean understandings of ontologically real numericity and geometry precisely BECAUSE we have substituted modern algebraic/symbolic notions of numericity which have their foundation in being non-ontological, viz., being agnostic with regard to the adequacy of their objects (e.g., the infinitely divisible continuum) to the real world (but then, confusingly, we went ahead and reified all these schemas after the fact).
>Why does formalizing it in calculating machines now produce "intelligences" which can mimick or in some ways outstrip our own "intuitive" knowledge which transcends formalism?
It doesn't, these computers are just pseudo-random stacks upon stacks of things that make us say "Yes, do more of that." We can only ever get out of these machines what we put in, but their pseudo-infinite pseudo-complexity makes us think they are capable of producing novelty, which is dangerous. Compare this to Coleridge's concepts of fancy vs. imagination. Today's AIs are a poor response to the abject failures of GOFAI (good old-fashioned AI), they are just a quantitative response to a qualitative problem that "blurs" the problem and thus obscures it. And just like how we buried the ontological and intuitive agnosticism of modern mathematics, which was initially a rebellion against the old, stifling, Greek way of seeing geometry and number, by turning it into a new, even less self-aware and even more stifling ontology (with hideous metaphysical implications woven into it), we are now burying the mystery of thought and the possibility of inquiring into its nature under mountains of LLMslop pseudo-random bullshit. Coincidentally, this is happening just as physics is realizing it's in a dead end and needs to radically redraw itself, and just as mathematics is realizing the same thing and becoming open again to epistemic pluralism and neo-intuitionism.
Very good, anon. It's nice to see critical ability in bait threads like these.
>Various aspects of human cognition ranging from something like the Kantian transcendental aesthetic to gestalt psychology and the ability to "see" the analogical truth or adequacy of metaphors in non-discursive ways / in ways that discursive thought can only follow and formalize post festum
Non responsive. Whether or not you can formalize your thought ahead of time has no bearing on whether your thought is, at root and prior to any analysis, the operation of a formal logical system.
>It doesn't always bligglidy bloo blah
Muh intuition. Citation needed for objective physical phenomena which fail to follow physical law formalized mathematically. "There's no physics of history!" - tier responses can be posted directly to trash can.
>It doesn't, these computers are just pseudo-random stacks upon stacks of things that make us say "Yes, do more of that."
They are unbelievably crude, and yet in many ways completely beyond our capabilities already. The goalposts move every few months now, and at an accelerating rate. Formal systems can replicate (and improve on) "intuitive" mental processes we would never have believed 2 years ago. Covering your eyes even harder does not answer the mail, except from your intentionally diminished pov
Totally, bro. Tell me, you still shitting in the street?
How do you know the world obeys it or that transcending formalism is happening? You are making a lot of unfounded assumptions here.
No, I'm noting the many cases in which this is observed, and not accepting "yeah, but not really" as an adequate explanation. A single basic physical phenomena which violated mathematics would be sufficient to at least bound the question, but there are none.
Blackholes violate math, they are singularities in space time and yet have already been observed. The stability of the solar system violates math, there is no math that can resolve the chaos of the n-body problem when you slightly change the initial conditions.
The irony of your statement about the solar system is that the mathemacial theory of chaos knows that chaotic systems can be bound. In other words, the solar system can be 'stable' even though any error in calculation propagates exponantialy. What people fail to know is that there is a a middle place between chaos and order, so to speak. A transition between the two where some stability existist, but borders complete chaos. So no, the solar system doesn't violate math. In fact, math can to some extent describe it. And that is how you know about the chaos in a n-body system. Because math concluded it.
My point is that chaos is still mathematically unresolved. Chaos is what you call differential equations that have no well behaved analytic solutions. The inability of math and physics to create better models, essentially.
Your point was that the solar system violated math.
Also, you don't know what you are talking about. An analytic solution is not necessary for the system to be chaotic. Case in point, Navier-Stokes and turbulence. A system doesn't need to be described by differential equations to be chaotic. Case in point, the logistic map, which is discrete.
Lmao. So another reason to study mathematics (and physics) is so you don't sound like this.
>Singularities
>Observed
Wordcels, when will they learn?
>be "philosopher"
>don't philo sophia enough to learn her mathematics
ngmi
She must be browsing IQfy
I fell in love with this girl after watching her quantum physics rant, the one that made her channel blow up I guess. I would give literally anything for women like that to be at least 2-5% of women. Instead they're like 0.000001%. She's not even that impressive, I didn't like any of the other stuff I looked at on her channel or anything. It just made me think, god damn, imagine going on a date with a b***h and she starts mansplaining what she actually cares about and/or does for a living, instead of just being an empty husk that "likes food" and watches / talks about the same shit every other normie hipster moron watches / talks about lately.
If she was the baseline for a certain type of woman, even a relatively rare one, life would be completely different. Instead, I was around women who were supposed to be like her for ten years, academics and scientists, and I aggressively tried finding even one of them who enjoyed talking about her research or who cared about what she does, cared about anything for that matter, and they don't fricking exist. Autistic women have been stamped out of existence by internet and smartphone culture because something innate and primal in the female mind, some terror of "standing out," "being weird," and thus repelling Mr. Right when he comes along, has formed a symbiotic relationship with the algorithm and turned them all into the same person.
Women with PhDs in Physics and Maths are the most boring sacks of shit in the universe now. Where are all the stinky autistic women who actually care about things? Where are all the man-like frumps with high IQs and deep interests? Nowhere, that's where. They're fricking DEAD. Even IQfy is a bellwether for this. Used to be that certain boards on IQfy were like 20-40% autistic hags, some of whom had souls. Now the female contingent has dropped to 2% on IQfy. Why? Because half of them get absorbed by normie Twitter and Instagram and other oversocial media and pounded into moron cubes, and the other half gets absorbed by lunatic social media and concludes that because it isn't a moron cube the only possible choice is to chop their breasts off and grow their clit out like a hyena.
How many years did I waste looking for women with souls? This Physics lady was just a glimpse of the 0.0001% that still exist by some fluke, not enough to sustain the male autist population, and even she is not that great, you can tell she's still a normie and probably eats her pornsick husband's butthole because he saw it on Brazzers. I would be willing to wage a global crusade to save autistic women from the normalgay oversocialization meatgrinder.
I liked her string theory video
I think that was in fact the one I liked as well, and I got confused.
She fricking annoys me because she made me remember that if you have sex with a woman you admire and respect, sex is actually good. I had spent so long having sex with women I see as morons and just feeling bad about it afterwards that I had peacefully concluded that sex is shit. Then I remembered, oh yeah, you're supposed to think things like "wow she's so smart, I'm lucky she's my gf" while sexually appreciating a woman, not just "Why did this moron let me put my penis in her? We have nothing in common"
To be tbh I didn't get that at all from the few videos I watched of her. She just seems like a generic academic, with the same mainstream/vaguely centre-left opinions.
>She just seems like a generic academic, with the same mainstream/vaguely centre-left opinions
And that's 0.000001% tbh
AHAHAHAH
I have the complete opposite experience re:sex with those 2 categories
Different Anon: I like her silicone alien video, the humanoid robot video (though her opinion on robots is very telling of her gender), and her "Gell-Mann Amnesia and Michio Kaku" video is also good.
What about her?
>3 hours of arab prostitute ranting about nothing
TL;DW
*deep breath*
have you ever heard of the phrase...
*pregnant pause*
the banality of evil?
lol Im kinda delighted at the return of good old fashioned anti colonial nonsense. I feel a lot more at home there then in all this troony everything is social construct bs. It's fun seeing these people discover ideas i've read when i was 14.
also why is everyone doing costumes now? it's a trend im sure of it.
I just watched one of her vids and this is one of the books on her bookshelf kek
https://www.goodreads.com/book/show/16280.Why_Are_All_The_Black_Kids_Sitting_Together_in_the_Cafeteria_?ac=1&from_search=true&qid=WBOHA5Laaf&rank=1
She's likely insufferable. The closest thing to what you describe on youtube might be Rose from decades back
https://www.youtube.com/@TheRoseArchive/videos
As far as I know she has a physics B.S.
she is a lesbian though
source?
There are more autistic men than autistic women. Something to do with X and Y chromosomes, how because men have one X chromosome are more likely to have autism than women. I think its something similiar to reason why majority of orange cats are male, because of the sex chromosomes. Its disheartening to think about it from a romantic point of view. Statistically most men will never match with a woman who matches their sperging out and the few women who do sperg out are so overwhelmed with choices they just end up cat ladies instead due constant overstimulation of potential partners.
Tfwno Sabine Hossenfelder gf
I just watched her string theory rant video. Almost all the accused "liars" in her video (e.g. Brian Greene, Avi Loeb, Ed Witten, Weinberg, Susskind etc.) are israelites. Why can't they connect the dots?
She seems like a hick turned city girl in the cutest way possible and the only reason she turned liberal instead of her usual kentucky republican background is because she got to study physics in a big liberal city and also because she is a lesbian. She even lost her southern accent.
>autistic
having particular interests isnt autistic you moron.
The plaque over the entrance of Plato's Academy read the famous phrase “Let no one ignorant of geometry enter here”
It didn't exactly mean what a modern mathematician would take it to mean.
I suppose like how art and music wouldn't either. What did geometry mean to him? not being moronic?
>IQfy raid thread
How essential is it for IQfy users to actually read books?
What is IQfy? There is no such thing as IQfy
I'm not gonna watch your E prostitute. What did she say that you found so thought provoking?
Math is a philosophy
Phenomenologically speaking, math has more in common with speedrunning than it does with philosophy. The highest level mathematicians are usually just sweaty autists chasing clout by eking out a 1% better performance in something utterly meaningless.
There are rare exceptions but that's the norm.
And that's different from philosophy how?
Philosophy is not a performance, it has no productivity goals unlike math with its millennium problems and completeness dilemma
Uhh you still need to present your ideas in a logically rigorous fashion my dood, only philosophy overall covers a wider range of thought than pure math
Are you really going the route of comparing the practical applications of math and philosophy?
t. doesn't even understand basic calculus
t. thinks it's impressive that he understands basic calculus, which a child could do
Let me guess, engineer or CS?
Electrical engineering. What about you?
Commutative algebraist and rapist.
But why? You could learn logic without studying math.
you should learn logic at least. if you want to do sophisticated thinking about mathematics then it is beneficial.it is also beneficial if you want to be employed
very essential
don't know if you'd include this in math but you also need theory of computation
and finally natural sciences
Watched her videos she's very cute. I also like the Australia/NZ one that dropped out of her PhD and has a calm ASMR voice.
God I’d love to have sex with her
>foundations of mathematics
is too broad to understand what you mean. do you mean calc I-IV? linear algebra? diff eq?
symbolic logic is within the umbrella of philosophy and could benefit from some mid level math, but otherwise the only thing math will help with is disciplining your thought for correctness and problem solving ability, which admittedly is pretty important
Of course mathematics helps philosophy, I suggest euclids elements as a most foundational text
I want to cave her face in mit meiner Faust. Backpfeifengesicht
Why don't mathgays use 2nd order or even third order logic if its so powerful?
Because ur gay
Don't see why.
What kind of math background did Foucault or Derrida or Butler or Mbembe have?
Who?
My mathtuber could totally beat up your mathtuber.
My mathtuber would bully your mathtuber
Well, here are my thoughts on why it would be essential to learn some mathematics. I am more of a math dude with some interest in philosophish things, by the way.
I consider that mathematics is the birth place of abstract concepts that only live in the collective mind of humanity. Most thoughts we have are mostly just remixes of things that we perceive from the natural world. We cannot think a new color, because we haven't seen it, but to imagine an purple apple - if your visual thinker - is completly possible. More abstactly, once we have counting, is not hard to count different kinds of objects. Remixing the concept of counting with different things from the outside world. But counting had to first be created as concept by someone. In other words, who was the first man who learned to count and how was that dissiminated? There is nothing in the outside world we can point out to and say, this is counting. Unity, what is unity? Who though it first? I perceive much of human development as birthing from mathematics. Once we create in math new concepts, we than started applying to other fields. Physics, chemistry, biology, and so on. The most revolutionary mathematics is always the one that come with new revolutionary concepts, that then can dissiminate into other field of knowledge. It takes a long time, but that is the dinamic I see. Philosophy doesn't seem to me to be mich different. It is a place where new concepts are born, but from a different kind of mind. If so is true, wouldn't the philosopher gain from learning from an essentially equal field? As long as I can remember I have been facinated by the birth of original ideias, and there is no field of knowledge more fascinating than math for it. There is also the true factor on it. In mathematics there is no room for personal preference. In mathematics we cannot trick people into believing something with cleaver or nebulous words. Understanding what makes mathematics true might help discern good from bad philosophy.
Another thought I would like to spew. In mathematics talet recognizes talent. The good mathematician can recognize the mathematical prone kid from the one that can just follow the algorithms already set by other mathematicians. The one who can create new counting systems from the one who can count well. Think Ramanujan. The only other example of this mechanic - where a kid is clearly identified as a talent, even without previous learning - is music.
Did any of you study the foundations of mathematics
I have a bachelor's in math tbh.
Beyond watching Wildberger and doing a presentation on the philosophy of mathematics for a class -- no. If by foundations you mean ZFC and the like.
ZFC is not the foundations of mathematics, ZFC is the foundations of ZFC and being a moron
I will let Goethe explain it to you.
I've actually never read this guy before he's amazing !
frick you op for posting an annoying lust provoking image that flares like a sore thumb in the catalog
I hope your shit thread dies soon