Math

[Anonymous No.16722870]

I just read a string of bad secondary math books and, after looking up on goodreads, realized I downloaded a lot more. Our Mathematical Universe is some multiversal nonsense and I read a continental intro to math which was about as horrid and one-dimensionally formalist as you can get. Is there any intuitionist or platonist overview on math?

[Anonymous No.16722911]

Your OP image is un-serious which indicates that this is just passing chatter. Your questions are vague. You sound young. I would suggest reading actual math textbooks rather than secondary pop-sci shit.

[Anonymous No.16722933]

>>16722911
I'm reading Reverse Mathematics by Stillwell but I need some good secondary to keep giving me fodder for ideas but formalist and existentialist math is over-published and the last book drove me up the wall with "Ethnomathematics" supposedly being a perfect ethnonationalism of math which it apparently tries to differentiate by asserting European women weaving is indicative of them developing algebra. I can deal with a platonist or intuitionist math interpretation considering formalist math has done nothing but ass these past two centuries but give existentialists justification for capitalism and wine-socialism.

[Anonymous No.16722936]

>>16722870
all mathematicians are logic babies addicted to ZFC and do not give a shit about sets and cats, and they are all platonist, ie ''numbers are real bro not social construct''.

The intuitionist version of maths is not about intuition at all

Today maths is just logicized maths and you have to be a mathematician to first go by intuition, then formalize whatever claims you think hold ''true''.

By the way truth is not found in logic. Logic is just a field by autistic pedants about well formed formulas and valuations, ie sending a formula to 1 or 0 and asking what are those valuations which are stable under inference rules. Zero truth in this, especially truth in the casual sense. Tarski truth is moronic, meaningless. Peak atheist.
Just like there is no truth in science, just some stats and a stat convention for saying ''if p value is XXX then the result is''true''''


If you want to learn, you have to follow the formalized maths and get a teacher, and most math teacher are average, and put a lot of work int it.

you can start here for books

baby logic
baby set theory
baby category theory
baby maths


https://boards.fireden.net/sci/thread/11929176/#11929187

[Anonymous No.16722939]

>>16722870
What you do though is reading biographies of mathematicians.

[Anonymous No.16722941]

>>16722939
Yeah but that's preferably my last resort.

[Anonymous No.16722943]

what the hell is this thread lol

[Anonymous No.16722955]

>>16722936
Platonic math lends itself towards a denial of negations, foundations for fields (vs the ramification of it into millions of oh-so-special pluralist genders, or fields, or intelligence or who can ever know).
I'm interested in intuitionist logic for their denial of infinity of which many books pay ear-note.
I've already a good grasp on math and logic and continue to dive forward. I'm interested, particularly, in an overview on constructive vs non constructive proofs preferably in either of those interpretations. Russellian interpretation of math or logic drives me more up-the-wall than postmodernism politics (of which I may say I'm finally free from).

[Anonymous No.16723050]

>>16722943

Some teenager or a bot, now crossposted elsewhere (can't fault him for trying).

[Anonymous No.16723056]

>>16723050
Just looking for good secondary preferably on constructive vs non constructive maths in platonic or intuitionist metaphysics

[Anonymous No.16723063]

just read brouwer

[Anonymous No.16723121]

>>16722933
That sounds fucking retarded. Ethnomathematics? Just read a normal textbook for fuck's sake.

What area of math are you interested in?

[Anonymous No.16723139]

>>16723121
This is my review of the book https://www.goodreads.com/review/show/3631186310
Logic, number theory right now. I'm trying to found math. I have a non constructive proof system for completeness which I adore after having read so much filth. I think I can found math in predicational monism. I'm working on developing a good reverse proof then I'm going to just start tearing shit up all the way down to science.

[Anonymous No.16723171]

>>16723139
How much math have you studied? Do you have a PhD or a postdoc?

[Anonymous No.16723215]

>>16723171
I study 6-8 hours a day. I've studied model theory a bit and proofs. I was going to work into analysis but I'm going back into proofs.
No degree whatsoever

[Anonymous No.16724645]

>>16722933
You sound insufferably autistic and snide

[Anonymous No.16724812]

>>16724645
I can get way more of all 3 of those if you're disingenuous enough and we have time. That sounds like a you-issue, not me.

[Anonymous No.16724821]

Morris Kline my nigga. Kline's thesis is that formalism killed maths because it destroyed the real referents of the formal structures and tried to turn them into a self-relating lattice tended by a cult of set theorists. He wanted us to go back to remembering the real referents, the real circumstances and concrete things that mathematical systems were created to model. He is effectively a soft intuitionist although he would probably not say this. He may not be the kind of intuitionist you want, if you are looking for hardcore Brouwer-esque platonic/kantian transcendental intuitionism as the foundation of a pythagorean maths. But it's a step in the right direction.

The detachment of calculus from the real world and its transformation into a self-justifying universal omni-tool, and non-Euclidean geometry leading to masturbatory formalism, are Kline's biggest examples. The Loss of Certainty is one of the best books ever on mathematics. But he also has a general history of maths to the present day, probably the single best history of maths.

You may also like Poincare's occasional essays on mathematical intuitionism, since he was not a transcendental intuitionist, more of a common sense realist about the fact that mathematical logic cannot be self-enclosed but only makes sense as a subset of language and thought in general (hence his "intuitionism," which is really a way of broadly designating "those moments in maths where we supply what the logic doesn't 'in itself' supply"). It's usefully general and suggests a lot of Wittgenstein's theses.

Wittgenstein's Remarks on the Foundations of Mathematics might interest you if only for how it knocks down the logicist pretensions of radical formalists. Again like Poincare it will not give you the platonic/transcendental intuition you are looking for, but it will indicate that domain in a negative way by positively pointing out the insufficiency of formalism/logicism.

Ultimately if you want to get into this stuff in a nitty gritty way you will have to study the transition around 1900 to functional/nonmetaphysical maths. Many many many things were left on the cutting room floor, because mathematicians got so mentally and morally exhausted of trying to find an ultimate and firm ground for mathematics that they eventually gave up and took the first "good enough" formalist consensus that came along. They thought they were being realistic and hard-nosed by embracing the function concept and object/ontology-neutral formalism, but they were really coping for their failed quest for the transcendent root of maths. If you want to recover that root, you will have to understand why logicism can't provide it, and then go looking for people who were at least trying to get beyond logicism, like Brouwer.

[Anonymous No.16724845]

>>16722936
Great post, hope you keep spreading the truth. Mathematics is due for a renaissance imo. Listen to this guy OP.

[Anonymous No.16724846]

>>16724645
No but fr this shit got published https://imgur.com/a/mMzEEku

[Anonymous No.16724883]

>>16724821
I have his history book but just dled loss of certainty. Is he a physicalist?
I just ended up downloading a lot of platonist math secondaries and Shapiro (whose ante rem intuitionism might work well). I'm pretty anti constructivist desu but intuitionism is a better claim than "there's nothing at all".

[Anonymous No.16726238]

>>16722870
you seem confused about what you're looking for in the first place

[Anonymous No.16726247]

>>16726238
In what sense?

[Anonymous No.16726553]

bunp

[Anonymous No.16727452]

sjruuu

[Anonymous No.16728590]

bump

[Anonymous No.16729133]

>>16722870

Matematician here.

How about reading some actual maths? Pic shows a Socratic dialogue between a tutor and pupil, explaining some concepts in introductory analysis. It says for high schoolers, but this is the kind of high schooler who goes to math olympiads, so don't be fooled.