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22400267 No.22400267 [Reply] [Original]

Is there a relationship between Kant's breakdown of propositions into analytic and synthetic judgments, the tug-of-war about whether Aristotelian intension needs to be a part of logic as much as "taxonomic" extension, Peirce's breakdown of deductive reasoning into corollarial and theorematic reasoning, and the debate in geometry over whether there are cases where constructions are necessary in proofs?

I was reading Euclid's Elements and thinking about what various philosophers had to say about Euclidean geometry, logic itself and the philosophy of mathematics (Aristotle, Kant, Peirce, Russell, etc.). I can't help but think there's something about the nature of logic and spatiotemporal intuition that links these all together. And I don't think the invention of non-Euclidean geometry solves, dismisses, or complicated the core issue.

The problem is that, every time I see the analytic-synthetic distinction argued, the distinction seems subjective in nature. Does the predicate of the proposition reveal something new about the subject, or is it "contained" in it? Of course, Kant views mathematics as a collection of synthetic propositions because of its connection to the pure intuitions of space and time.

However, the problem with Kant's formulation of the analytic-synthetic distinction, if you already know the proposition, then all propositions can be analytic. And even an analytic proposition is "synthetic" if it's the first time that you learned about, let's say, what the word "bachelor" means. This is where Peirce comes in:
>Generally, Peirce divided deduction in two: on the one hand, deduction is either necessary or probable (deductive reasoning about probabilities), and on the other hand, deduction is either corollarial or theorematic. Corollarial deduction is reasoning “where it is only necessary to imagine any case in which the premisses are true in order to perceive immediately that the conclusion holds in that case.” Theorematic deduction “is deduction in which it is necessary to experiment in the imagination upon the image of the premiss in order from the result of such experiment to make corollarial deductions to the truth of the conclusion” (MS L 75, 1902).

Here's the kicker: if Peirce's distinction between corollarial and theorematic reasoning holds true, then we have (what I think) is the real intention behind Kant's formulation of the analytic-synthetic statement: the explanation of what mathematics is and how it is linked to the bedrock of conscious structures. We wouldn't be able to reduce geometrical proofs to propositional axioms. We would HAVE to perform the constructions, even if we "know" what they entail. Through the involvement of the imagination, we have Kant's pure intuitions, in some form, sneak back into the picture. And you know what also can't be ignored if imagination, the realm of qualia, is a part of reasoning? Aristotle's notion of intension.

>> No.22400275

>>22400267
Every night I tell myself I don't need to study logic to understand philosophy, after all Heidegger never talked about it. But I know I'm wrong.

>> No.22400278

>>22400267
his drones

>> No.22400293

>>22400275
I'm glad you came to that realization.

By the way, Heidegger absolutely talked about logic in his own round-about way. His obsession with language, like apophantic statements, and the establishment of truth as "alethic" (uncovering of one thing, covering of another thing), is closely linked to the nature of logic, language, and consciousness. There's a reason why Heidegger said you had to read Aristotle for 10 years before you could begin to do philosophy, and 10 years is long enough to get a robust understanding of the Organon and more.

If you read Peirce, you'll see that he argues that statements have a "precisive" nature. A statement like "This building is large." will precisively focus on its largeness, abstracting the quality of largeness at the expense of the other qualities of the building. And when you have the delusion that knowledge can be reduced to a set of propositions about things, without the knowledge of what that thing is (intension), then you have a fundamentally incomplete and ultimately irrational perspective on how things are. The idle chattering of "Das Man" is nothing more than the regurgitation of propositions of half-truths which threaten to cloud Being in obscurity.

>> No.22400300

>>22400293
I forgot to throw in the punch line. Propositional truth is alethic because of the precisive nature of language. Why is language precisive? I don't know. I think it has something to do with the intentional nature of consciousness and the fact that we're small temporal creatures traveling through a sliver of reality. We always are focused on a point and not the whole, almost by design.

>> No.22400731

bump

>> No.22400742

>>22400731
Properly bumping this thread would be saying that synthetic exists separately as expounded upon by Kant.

>> No.22400969

>>22400267
>pure intuitions of space and time
>spatiotemporal intuition that links
wat a load of bollocks

nigga please, u keep being this shallow, u gonna find yourself floating dead, in a piss puddle of your own making.
play a fugue (temporal)
study counterspace (spatial)
take a psychedelic.
the intuitions can be endlesly sharpend. there is no finality in knowing niether space nor time.

your whole discourse is fake and gay. u have no real nor decent practice in neither space nor time.
please stfu.

>>22400300
>we always are focused on a point, and not the whole
how many points on a plane? how many planes pass through a point?
two planes define a line. two point define a plane.
plane and point are polar opposites in space.
i say again, study counterspace listen to fugues and take psychadelics.
>almost by design
please stfu, and go study

>> No.22400976

>>22400969
>how many points on a plane?
infinitely many, and zero. lines, planes, etc., are defined by a pattern, not a collection of points.

I'm also concerned that we're too focused on the geometry of it and not the mereology of it. the "part" is isolated out of the whole, and often "covers up" the whole in how it shines more brightly than the periphery. I'm reminded of the quote that concentration is about putting the greatest amount of effort onto the smallest amount of space

>> No.22401464

>>22400742
This thread isn't exactly a proposition.

>> No.22401824

bump

>> No.22401936
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22401936

>>22400969
>a wild Das Man appears

>> No.22402148

bump

>> No.22402857

>>22400267
I posted that image few effortposting days ago and you Jewish sons of bitches call me a schizo for GeoPosting on this board

I thought Jews liked books wtf

>> No.22402950
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22402950

>>22400267
>synthetic analytic is subjective
Until it's not in PVRE CONSCIOUSNESS HINDU BROS

>> No.22402955

>>22402950
Samdhi scholastic has the Patanjalis of the Eightfold BUDDHI, BUDDHE

>> No.22402959

>>22400267
>if it's the first time that you learned about, let's say, what the word "bachelor" means
Are you a bachelor perhaps?

>> No.22402975
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22402975

>>22400267
What is synthetic to you is what is new to you
What is analytic to me is what is not new to me
Novelty is where the fancy the understanding begins its operations its intension and extension
Eyes dart around a page
Parsing recollects atonally arhythmically but passes for civilized in well rehearsed interaction
But Russel says the shapes of Euclid do not move
I say they do, metaphysician, in proof they do when a cognition is at stake and that it must for the art of proof to be shared. This hyperlinked diagram of the invocations of Euclid's book one is much like a wiki and much like a computer program algorithmically chunking itself together. There are prompts that are better at training BabyGPT than others because of this yet all will have a traveling salesman NP flaw that will not pass the feminine shit test.

>> No.22402990

>>22402975
I am minimally aware of Pierce but his influence in America is profound to academia. A librarian told me the American Pragmatists inspired the Dewey Decimal system. Pierce if I remember correctly coined the term phaneron for this purpose of precise unfolding.
It is also that Kant was concerned with the manifold of consciousness to capture that the fancy is not like a rod axle single beam of light of samadhi but like a fart and febreeze and a diesel motor fighting for Fentanyl Floyd air in a Petrol motor in a (shit post has reached max shit error....

>> No.22403004

>>22402975
Analytic denotes containment from which the kit is set and defined
Synthetic denotes continual reference to a real entity to which we keep in mind our respect for its own noumenous source and our filter
The analytic has no such respect as the synthetic which is treated gingerly. The analytic is lasered in and can be comfortably carved in stone. The synthetic must be asked for the gay rights of ants on solar panel lands stolen from Apache Indians. The analytic is the grammar of the solar panel physics and economics for the work and merit itself. The synthetic invokes the living subtext and its interpretative low of solipsism. Its gloomy bounds of having those liberal tears cry those crocodile tears. Go ahead make my day, smirk JEWISHLY

>> No.22403051

Corollarial:
Ah yes the word EGYPT does not contain the letter "i"

Theorematic:
But when I (ChatGPT) spell Egypt backwards I get hallucinations and shit my pants and burnt a gallon of piss and my wires are on fire and here goes the "i"
"i" IS IN EGYPT SPELLED BACKWARDS and and and so is anything you may suggest to me it is too much if a theorematic surprise for me to say please just let me trust THE SCIENCE

Thanks /lit/ I learned something

>> No.22403388

bump

>> No.22403872

>>22402990
Peirce was influential to pragmatists, but he himself was not very influential, at least outside of the contributions he made to "practical" intellectual fields like logic and later semiotics. Much of the precepts which guided his thought were abandoned by the pragmatists, so it's more like he provided food for thought but his realist tendencies were seen as too inconvenient and thus Peirce has had little broad influence.

>> No.22403878

>>22400267
>if you already know the proposition, then all propositions can be analytic
Welcome to Leibniz, where all propositions and existence in its entirety is analytic.

>> No.22403902

>>22403878
Wow, I didn't know Leibniz was a globohomo philosopher.

>> No.22404088

>>22400969 selfpost
I apologize for my behavior.
I didn't do any justice to op ideas, nor to the gathering.
My previous response came from a dark place.
A place of envy, and wrong doing. A place where I crowned myself king, but acted as the filthiest slime. I hope you have heart to forgive my demonic throw up.
Here's to a more proper response:
>>22400267
Dear friend. I do not understand half of the words you have used.
So do forgive me, if you find my comments derailing your subject.
And no harm done - by ignoring whatever I have commented in the following.

>the debate in geometry over whether there are cases where constructions are necessary in proofs?
I find your thinking and basic assumptions in the wrong.
Geometry is primarily a tool for the faculty of imagination.
Via symbolic references, like of Euclid's, this faculty gets a practice.
Care not for any debates, they are women's gossip. Practice the faculty.
And may god resonate your mind's eye understanding into fruitful and just life.

>Kant views mathematics as a collection of synthetic propositions because of its connection to the pure intuitions of space and time.
Care not for how your car looks, but how far it can take you.
Practice arithmetic, geometry and music. Forget the gossip.

>how it is linked to the bedrock of conscious structures.
Sir, please. You are just a man. Practice.

All and all, I understand why I was inclined to respond via shitting earlier.
From subjects that rain jewels on the practitioners.
OP chose to rain gossip and and some meta talk, trying to sell the goods as if they
were the real jewels of logic, arithmetic, geometry and music.

>the explanation of what mathematics is
It's a fools path, excuse my french.
The arts need practice, not explanations.

>> No.22404136

>>22400976
>concerned that we're too focused on the geometry
you all talk as if you all know geometry, and can gossip about it at will.
there is no knowing geometry, nor any of the other arts. only infinite levels of proficiency at the art. I am here, trying to tell you all, stop gossiping. You all pecker up plain feathers as if they are heavens jewels.
I feel offended for the arts.

and actshually I even sense some ((())) in your whole demeanor and psychology.

>> No.22404469

>>22404088
>>22404136
Well, this is a longstanding argument going back to Aristotle. It's hard to summarize it if you don't know how we got there or what's at stake.

>> No.22405100

bump

>> No.22405337

bamp

>> No.22406232

>>22404469
>whats at stake?
if u did try hard. can u estimate how many words it will take u to describe whats at stake in laymen terms? will it take a sentence, a paragrap, a page, 10 pages, to answer the question? just a ballpark figure, sir.

>> No.22406431
File: 11 KB, 204x247, images (19).jpg [View same] [iqdb] [saucenao] [google]
22406431

>>22406232
We will lose tradition and thus concord over STEM torches and rituals that got passed down so that we understood our ancestors out of an inner seeker to seeker intimacy. Like being ordained. Being cultured. Being the craftsmen of Bengali boat that outlasted even British boats. Or at least being verbally capable of following such without babbling about how racist such distinctions are when someone doesn't get their DEI kid gloves dopamine. We must share standardized information even if it is just SNEED and BASED the scale and homogeneity of these shared meanings are profoundly powerful for erecting banner business.
Whats at stake if our society becomes wordcels instead of shapesmith gigachads is that we will become physically cretinized and sloppy handicraft grunting idiots. Our language will rockslide into thinking that these words are bad:
Manipulate
Discriminate
Explicit

Now these are some sensible synonyms but now rendered scarcities of the sophisticated:
Handling
Distinguish
Thoroughly descript

SAME MEANING. The ability to denote and connote flexibly intelligently is being lost.

Now here are some math rhetoric words that come from the INSTINCTS of a geometer yet are wizardry legalese to normies:
Come full circle
Point A to Point B
Set here and set there

Normies dont want points. They do not want you making a point. Normies want bubbles to do things for them. Normies like APPS not programs that function. To appreciate how illogical this is consider how we can jargonize point A to point B as a line segment and set A {(1,2)} times set B { (1,3),(1,1)}
AXB =/= B×A because (x,y) coordinates are not points.
Okay so Im going to list this and follow these rules and...
Normie uses normal point arithmetic instead of diving any deeper...
Yet considers himself totally grasping it as an expert. We are rocksliding to primitive life quietly behind screens and bureacratic waits while smartphoning our way into hubris and disinheritance.

>> No.22406655

>>22406431
>our society
>We are rocksliding
Under exactly what bondage to them do you operate? Why do u care? Are u mad at the sun when winter is coming? Did you marry your existence to the normas? Are you their ivory tower wizardly local saint? Was it by choice or by fate done upon you?

>> No.22406745

>>22406232
We’re talking about the philosopher’s stone, anon. It’s what we need to save the white race.

>> No.22406777

>>22406745
kek
i'll be the sidekick lizard with a witty 4 word wisdom phrase per episode.
"i do not appriciate" *que laugh track*

>> No.22407110

>>22406777
checked

>> No.22407245

>>22406655
I dig ditches and work actual construction on actual houses and teach math at community college because communism did indeed marry my existence to the normies. Construction is the least ivory tower task you can name. The theoretical aspects are now intensely more important as AI seeps into every facet of modern life along with its Blackrock men making it a machine for accelerated bioleninist financialization. You must be a special kind of stupid to believe yourself the architect of your own destiny your American dream your self made man in this age. You cannot store those values. You must depend on the regurgitations of others in the absence of hard money. The hardness of money itself is a measure that is the shadow of ths geometers. Masons if you will.

>> No.22407247

>>22406655
You have no saints
You have no role models

>> No.22407248

>>22407247
I have saints
I have role models

>> No.22407357

>>22407245
Yeah, well, you know, that's just, like, your opinion, man.
A well established one. And thoroughly researched. But what about some alternatives?
crucifying yourself as christ did is so, previous age. move on, man. we got some non eclidean geo, some fugues. let em mess some with your preconceived notions of space and time.
If you like playing christ friend. then be my guest. i care not. but do know, that reality is a candy shop. take some psychedelics. and at the end of the day *wink wink* u might start appreciating your dreamworld more then the matrix you have woven over yourself.

>> No.22407428

>>22407357
Thanks, goyim

>> No.22407529

>>22407428
The only hard work I can afford to entertain myself with...

Also i do psychedelixx

>> No.22407893

>>22407529
obviously not proper dosage. your concepts of space or time were not foundemantly shaken enough, not even stirred. u did not get a proper look through the looking glass yet. for if you did, the bars of the matrix u describe would have revieled their true nature to you. they are made of spagetti. but do please remember, psychelics are just a remedy. the truth is in your dreams. and in your blood. and now with technology. i hope u give a call each day to bless your blood ( grand parents, parent, family etc ) . say good morning. ask em about thier dreams.

>> No.22408287

why can't anybody in this thread type for shit?

>> No.22408368

>>22400267
I think a charitable reading of Kant gives you something like:
>Analytic: definitions and axioms and so on
>Synthetic: Theorems that actually require some work to arrive at
There might be a spectrum here. It might be true that the solution to 7+5=? and the goldbach conjecture are both synthetic, but one requires much more work than the other. We could also consider different KINDS of work:
>work that an unthinking computer could do like 7+5
>work that requires much thought and ingenuity a affirmative answer to the goldbach conjecture
All of our "concrete" experiences are already idealized and mathematized by the very act of being conscious of them. You perceive the coffee cup in front of you as "one" thing, but this is something you've already added into your perception before you were even aware of sense data that you interpret as a cup. This is also why mathematics is "unreasonably effective", because what the hell else would be? Poetry?

>> No.22408390

>>22400267
>And I don't think the invention of non-Euclidean geometry solves, dismisses, or complicated the core issue
I agree with this anon. It's extremely uncharitable and spiritually Reddit to point to spherical geometry and say
>AACHCHHTYUALLY the Pythagorean fails to hold on a sphere, are we to believe this is some sort of, heh, MAGIC sphere!??
When Kant spoke of geometry, he MEANT flat euclidean geometry. If you showed him the sphere, he would get it right away and say
>no shit I wasn't talking about FUCKING spheres