Is philosophy of mathematics an interesting subject? I've

Mathematics is natural philosophy.

filename?

>>8428997
Pure philosophy. Natty philosophy is what we used to call science.

>>8426570
>Is philosophy of mathematics an interesting subject?
no

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He lived up to his name, his head was white.

>>8426570
Incredibly interesting to me.

what are numbers? Do they exist? Is it a mere abstract concept? Can animals count? Can you taste it?

>>8426570
It's good.

>>8429853
questions concerning what the "essence of mathematics" is might be interesting

Yes, both philosophy of mathematics (ontology of mathematics, epistemology of mathematics, even the ethics of mathematics) and mathematical philosophy (philosophy is locally rigorous, mathematics is globally rigorous, so application of one to the other should yield interesting results) are interesting. I think every good mathematician is secretly a good philosopher, and that every good philosopher has mathematical potential.

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>>8426570
logic is for people who cannot find rationality outside very tight contrived inference rules

mathematics is for normies

philosophy is like running wild across the field, where you are all alone with your thoughts but still cling to your fantasy of finding rationality in them

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>>8429893

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>>8429896

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Why should I learn phil math when I can just sit back and watch my gf having orgasms from a man I selected for this.

>>8429880
+20 Respect
Been my thoughts since Junior year and I'm just a recent grad.

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>>8429880
>>8429893
>>8429896
>>8429898
Yes. You get it.

>>8426570
One major question in the critique of pure reason, one of the most influential books in western philosophy, basically asks how it is possible that we can infer truths from mathematics/numbers.

Yes, the subject matter is extremely interesting and has caught the attention of philosophers from Plato through to Russel. It is not a coincidence that many mathematicians have been philosophers (Descartes is perhaps the most famous for both)

Following Goedel many questions that remain after a 2000+ year history still remain unclear.

>>8431266
It's spelled fucking Russell holy shit man. Grind my gears more

>>8431266
there is not truth in math nor logic. there is a notion of truth value and it is just a label for the notion

>>8426570

Yes.

How do two people develop an almost exact form of Calculus at the same time?

It was in 1666, I habeeb.

It's in human nature to want to measure things and in order to do that we had to come up with a way to quantify those things hence math was born.

I think once you get past Calculus 3, it just starts getting too abstract to be useful except in very particular circumstances.

>>8426570
Learn mathematical logic and you will know basically everything you need to know about what is normally called philosophy of mathematics.

>>8429880
>I think every good mathematician is secretly a good philosopher,

Such youthful innocence. You haven't met many of the "problem solvers" it seems.

>>8431673
I think many (all?) mathematicians are doing philosophy and don't know it. When we use our intuitions to draw deep conclusions, we are philosophizing over the concepts that the mathematics is meant to represent. This is imperfect, as our systems may miss the deeper nuances that we intended to encode. Unfortunately, the climate of the community has most always been negligent toward this aspect of doing math, and it doesn't seem to be improving. With that said, I still think a truly good mathematician must be doing good philosophy to make progress, even if it is left unacknowledged.

As a side note, this is why computer programming lacks the mathematical "flair:" everything is a priori rigidified beyond the point of being inherently philosophical, except when greater questions are posed about how a better language might work or how theoretical architectures might be designed. Within a fixed language, however, the only philosophy going on is examining the different paths (algorithms) that lead to a result, and how these paths can be compared and optimized for our computational needs.

All in all, I think philosophy is a very important study which is left mostly untouched by the majority of both communities. It would do us a lot of good to adopt a more wholesome stance, but that seems out of reach right now.

>>8431684
>When we use our intuitions to draw deep conclusions, we are philosophizing over the concepts that the mathematics is meant to represent.

That's a bit of a stretch. I would say that most mathematicians only have the dimmest idea of what the actual meaning of the structures is. The rest of what they do is based on formal manipulations and/or lucky guesses.

>>8431694
I may be romanticizing things and projecting my own mode of study. I definitely agree that a lot of mathematics research is mere rule manipulation, but I still maintain that this manipulation is guided by something deeper going on upstairs. I don't think we can reduce mathematical knowledge seeking as pure manipulation of rules; that fails to account for the meaty stuff like the Langlands program, arithmetic topology, or the Goodwillie calculus.

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Why do you do not write numbers as marks on the board ?

>>8431713
Let me refine what I said. Good mathematicians certainly do often have intuition. It's just that their intuition is for the structures as abstract structures that they have gotten used to somehow. My philosophy is that consistent abstractions should have some relationship to real things, in this plane of reality. Like viewing morphisms in a symmetric monoidal category as processes, for example. It is this kind of intuition that is extremely rare.

>>8431769
>consistent abstractions should have some relationship to real things, in this plane of reality
How about [math]\mathbb{R}[/math] then?

>>8431777
That's a big question. I think if you could figure that out, then you would probably solve a lot of outstanding problems in fundamental physics. My understanding is that it somehow represents a universal/limiting informational object. Freyd's universal characterization of the interval is a good step towards this interpretation:

http://www.mta.ca/~cat-dist/catlist/1999/realcoalg

>>8431684
So basically what you say is using intuition is doing philosophy? Isn't it a too broad definition of a philosophy?

I suggest calling a philosophy something that philosophy grads do better than non-philosophy grads. And whatever they do better doesn't seem to help mathematics much.

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In this picture, find
-the mathematician
-the philosopher
-the logician

>>8431904
plz dont post naked men on a blue board

>>8431784
Honestly, now that I think about it, it probably doesn't make sense to talk about doing subconscious philosophy. It's a conscious process and you are right that my definition seems too broad.

>>8429068
>filename?
>toofunny.jpg

>>8431753
>what is trivial

>>8426570
Then read it?

>>8429669
>>8432640
kek.

>>8431141
Where is that (pic) from?

>>8428997
Natural philosophy is old-timey talk for physics m80

>>8426570
>pic
Is it just me or he looks like Putin a bit?

>>8426570
Philosophy of mathematics is a meme

>>8429896
>cult of complexity

What did he mean by this?

>>8429880

Hardy weighs in on the ethics of mathematics insofar as he derides mere "ballistics" in his /Mathematician's Apology/, his general thrust being that the less applicable, the better the theory may avoid making life unpleasant for humans.

The pushback being that of course, over time, abstract mathematics tends to get applied, one way or the other, however abstruse the initial results may be.

>>8426570
Personally I find philosophy in general interesting. I think all scientists should at minimum take a course in classical philosophy focused on Socrates and Plato. Socrates invented the scientific method and first proposed that the language of nature is math. Bottom line any philosophy will challenge standard though patterns and processes and make you a better critical thinker.

>>8435654
>Socrates invented the scientific method and first proposed that the language of nature is math.

Are you retarded?

>>8435615
That seems like a reasonable stance to take. I mostly agree. However, I don't think an individual's work warrants that they answer to anyone for the consequences other than to themselves. So, while I would personally feel dreadful if my work brought harm to anyone, I would never judge another person in the same position.

All told, ethics as a field must fail, just as law must, and really all normative fields of knowledge, as humans must try to find linguistically- and temporally-static models for the complicated dynamics comprising reality. I'm still uncertain whether we can even rightly judge any actions which aren't our own, especially those which do not involve us. But this is a digression from the discussion. I think I agree with Hardy, to the extent to which his ideas on the matter apply.