KANTBROS, NOT LIKE THIS--

[Anonymous No.22810219]

>The proof that all pure mathematics, including Geometry, is nothing but formal logic, is a fatal blow to the Kantian philosophy. Kant, rightly perceiving that Euclid's propositions could not be deduced from Euclid's axioms without the help of the figures, invented a theory of knowledge to account for this fact; and it accounted so successfully that, when the fact is shown to be a mere defect in Euclid, and not a result of the nature of geometrical reasoning, Kant's theory also has to be abandoned. The whole doctrine of a priori intuitions, by which Kant explained the possibility of pure mathematics, is wholly inapplicable to mathematics in its present form.
-Russell, Mathematics and the Metaphysicians

[Anonymous No.22810238]

>>22810219
kantsisters…

[Anonymous No.22810246]

>>22810219
Kantian epistemology is more about the nature of experience than it is about the nature of logic, although there is a connection. Logic does not provide us with knowledge; it only gives us a framework for expressing thoughts.

Geometry, on the other hand, gives us a framework for expressing concepts that exist independently of our subjective experience. The rules of geometry are not derived from experience; they are true a priori.

Kant's critique of pure mathematics would acknowledge the independence of mathematics from the human mind while also emphasizing its dependence on the existence of a priori ideas.

Kant believed that the rules of geometry reflect the structure of reality, not of human experience. This means that we can know synthetic truths about the physical world through pure mathematics, without reference to experience. For example, we can prove that the interior angles of a triangle always add up to 180 degrees, regardless of the size or shape of the triangle. This is an a priori truth because it is innate to our understanding of space and not derived from experience.

[Anonymous No.22810249]

>>22810238
ywnbaw

[Anonymous No.22810318]

>>22810219
Both Kant and Russell are clearly wrong here. Contra Russell, no mathematical facts follow from abstract logic. And Contra Kant, mathematical facts are known a posteriori like everything else.

[Anonymous No.22810378]

>>22810318
>clearly
no

[Anonymous No.22810392]

>>22810318
>contra
kill yourself

[Anonymous No.22810484]

>>22810219
>The proof that all pure mathematics, including Geometry, is nothing but formal logic
there is no such proof

[Anonymous No.22810534]

>>22810219
>Spends 40 pages trying to prove 1+1=2
>Fails
And we should care about his opinions why exactly?

[Anonymous No.22810540]

>>22810318
>And Contra Kant, mathematical facts are known a posteriori like everything else.
Please read fucking Kant before you embarrass yourself like this

[Anonymous No.22810551]

>>22810484
PRINCIPIA MATHEMATICA

I kid I kid. Russell wrote OP before Gödel crushed his life's work.

[Anonymous No.22810579]

>>22810484
>>22810534
>>22810551
>All pure mathematics—Arithmetic, Analysis, and Geometry—is built up by combinations of the primitive ideas of logic, and its propositions are deduced from the general axioms of logic, such as the syllogism and the other rules of inference. And this is no longer a dream or an aspiration. On the contrary, over the greater and more difficult part of the domain of mathematics, it has been already accomplished; in the few remaining cases, there is no special difficulty, and it is now being rapidly achieved. Philosophers have disputed for ages whether such deduction was possible; mathematicians have sat down and made the deduction. For the philosophers there is now nothing left but graceful acknowledgments.
-Russell, Mathematics and the Metaphysicians

Russell BTFO philosophylets.

[Anonymous No.22810642]

>>22810551
based platonist chad.

[Anonymous No.22810650]

>>22810642
The future belongs to empiricists. Sciencechads are winning. Experimenting is the way to truth.

[Anonymous No.22811008]

>>22810650
>Experimenting is the way to truth.
lol sure bud

[Anonymous No.22811016]

>>22810246
What about triangles drawn on a non-Euclidean plane? Such triangles exist (insofar as any triangle “exists”) in the real world, but don’t have angles that add up to 180 degrees.

[Anonymous No.22811059]

>>22810246
>Geometry, on the other hand, gives us a framework for expressing concepts that exist independently of our subjective experience.
stfu you didn't Kant you pseud

[Anonymous No.22811115]

>>22811016
that's a wordplay. a non-euclid triangle is not a triangle in the sense we know but something else, hence the necessity arises to use "triangle in non-euclidean plane".

for all intents and purposes I can devise my own plane where a square don't have to have angles that add up to 360 degrees. it does nothing to hinder any logical proposition that concerns a square. it is meaningless.

[Anonymous No.22811119]

>>22811115
this

[Anonymous No.22811552]

>>22810219
Yeah, basically Kant thought the axioms of geometry were apodeictically certain when in fact they were arbitrary.

[Anonymous No.22811584]

What do the platos meno bros think

[Anonymous No.22811622]

Badiou posters redeemed!

[Anonymous No.22811625]

I've never read kant or Russell but for some reason I'm pleased when kant gets shit on, anyway, I've read euclid and I'm a believer in the a priori because like in meno I find I intuit most of what euclid is saying, the elements is a book that you need no previous education in mathematics to read, you're just gonna sort of get it especially if you get past proposition 5

[Anonymous No.22811671]

>>22811625
Also I have thoughts while studying euclid such wonderful thoughts come to me and they then appear latter in the book, even after the first proposition many people will simply play around with the compass and make a hexagon and then a priori a cube or something that doesn't get mentioned until later

[Anonymous No.22811688]

>>22810579
Refuted by Gødel

[Anonymous No.22811701]

>>22811115
What makes a triangle drawn on a sphere "not a triangle"? It meets the definition: a polygon with three sides and angles.

If you want to derive truths about, for example, a triangle drawn on a soccer ball or the planet earth, then you'd better do some non-euclidean geometry.

Why are triangles on flat planes privileged over triangles on other surfaces? What makes them normative?

[Anonymous No.22811723]

>>22811701
>a polygon with three sides and angles.
not a triangle. A triangle: plane enclosed by three straight lines

[Anonymous No.22811726]

>>22811701
>a polygon with three sides and angles.
not a triangle. A triangle: plane enclosed by three straight lines

>>22811701
>Why are triangles on flat planes privileged over triangles on other surfaces?
>privileged
stop

[Anonymous No.22811745]

>>22811726
retard

[Anonymous No.22811746]

>>22811701
Privileged triangles, lol you seem like the kind of person that thinks an obtuse and an acute are congruent and that a woman and a trannie are also congruent

[Anonymous No.22811750]

>>22811746
obsessed

[Anonymous No.22811755]

>>22811750
I like triangles like in Pic related

[Anonymous No.22811760]

>>22811755
Lol forgot pic, it's eucluds definitions,

[Anonymous No.22811764]

>>22811760
>euclidian geometry
kek

[Anonymous No.22811776]

>>22811764
Look at yourself

[Anonymous No.22811777]

>>22811776
mathlet

[Anonymous No.22811796]

>>22811745
>>22811750
>>22811764
>>22811777
Everyone can see that you are a clown and that this thread boils your black perverted soul

[Anonymous No.22811797]

>>22811796
>non-euclidian geometry isn't real! it can't hurt me!

[Anonymous No.22811813]

>>22811797
That's right, pure mathematics is not really a tangible thing and pondering upon it will do you no harm

[Anonymous No.22811822]

>>22811813
cope

[Anonymous No.22812618]

>>22811723 based on Euclid's own definitions (see >>22811760), a triangle is a figure with three sides, and a figure is anything contained by boundaries. There's nothing indicating that figures must be drawn on planes.

>>22811813
We can draw figures on surfaces other than planes ourselves, in the real world, without needing any "pure" theoretical constructs. Buy a ball and draw a triangle on it, then measure the angles of the triangle.

In fact, to accurately make predictions about the real world, we need to understand how shapes on spheres work, because the Earth is a sphere. Non-Euclidean geometry made maritime navigation more precise than previously thought possible, and we continue to use it today for that purpose.

If case "getting ships to port" is too theoretical and high-flying for you, you may be a retard.

>>22811746
Rent free.

[Anonymous No.22812665]

>>22812618
draw a triangle on a sphere that doesn't exist in a plane, do it

[Anonymous No.22812681]

>>22812665
https://blog.richmond.edu/physicsbunn/2014/02/01/spherical-triangles/

[Anonymous No.22812698]

>>22812681
Those triangles exist in planes retard

[Anonymous No.22813001]

>>22810579
that's from before godel

[Anonymous No.22813015]

>>22811016
>but what about imperfect triangles
Lmao

[Anonymous No.22813016]

>>22810219
Bertrand Russell was a fucking faggot who despised himself and despised life. Idc about his ideas.

[Anonymous No.22813070]

>>22810579
>>22810246
>>22810219
One man already discovered the secret to grounding math and being, without any dualism or atheism. Unfortunately, Russell, by his own admission was badly filtered by him.

[Anonymous No.22813391]

>>22810392
Drop the club and grab a dictionary. This is a literature board, Grog.

[Anonymous No.22813402]

>>22810540
Nope, you are the one embarrassing yourself here.

[Anonymous No.22813483]

>>22813001
>godel
literally who?

[Anonymous No.22813557]

>>22810246
>The rules of geometry are not derived from experience; they are true a priori.
That doesn't make any sense. The rules of geometry are an arbitrary abstraction of some aspect of experience that "works" because it is logically coherent, that is, it is a truism

[Anonymous No.22813574]

>>22813557
>The rules of geometry are an arbitrary abstraction of some aspect of experience
Can you even into Kant?

>though all our knowledge begins with experience, it by no means follows that all arises out of experience. For, on the contrary, it is quite possible that our empirical knowledge is a compound of that which we receive through impressions, and that which the faculty of cognition supplies from itself (sensuous impressions giving merely the occasion), an addition which we cannot distinguish from the original element given by sense, till long practice has made us attentive to, and skilful in separating it. It is, therefore, a question which requires close investigation, and not to be answered at first sight,—whether there exists a knowledge altogether independent of experience, and even of all sensuous impressions? Knowledge of this kind is called a priori

[Anonymous No.22813598]

>>22812618
>triangle is a figure with three sides
three STRAIGHT lines retard. holy shit I already told you that.

[Anonymous No.22813603]

>>22813598
Straight relative to what? Presumably the surface it's being drawn on.

[Anonymous No.22813616]

>>22813603
>Straight relative to what?
>relative
it's not relative retard. it's a priori, i.e., NECESSARY TRUTH.

[Anonymous No.22813622]

>>22813616
But Glaucon, what is straightness?

[Anonymous No.22813634]

>>22813622
>what is straightness?
not being an absolute faggot like you are. also Euclids 4th definition.

[Anonymous No.22813645]

>>22813634
>any line which lies evenly with points on itself
Remarkable, my friend. Now tell me, what does it mean to "lie evenly?"

[Anonymous No.22813652]

>>22813574
>whether there exists a knowledge altogether independent of experience, and even of all sensuous impressions?
Independent of all sensuous impressions doesn't mean not derived from sensuous impressions. You can (it is not obvious and it may be false but that's another story) know all geometry without having sensuous experience but you need at least the axioms. And where do the axioms come from? Experience. Geometry is an arbitrary set of axioms and its logical consequences, that's all. You could have called geometry to a different set of axioms and, having no sensuous experience, it would be the same to you because you have no way of telling if it corresponds to something external or not.
Basically, independence is one aspect and origin or inspiration another

[Anonymous No.22813655]

>>22813645
what do you think pseudo-socrates? get a point, get another point, draw the shortest line possible between them. no curves numbnut since then that wouldn't be the shortest line.

[Anonymous No.22813659]

>>22813652
>doesn't mean not derived from sensuous impressions.
yes it does dummkopf. You have not read Kant and it shows.

[Anonymous No.22813660]

>>22813655
>no curves numbnut since then that wouldn't be the shortest line.
nta but holy shit you're retarded

[Anonymous No.22813661]

>>22813655
Whence the connection between "evenness" and "shortness"? It seems to me, my friend, that evenness refers to a surface on which the line is drawn. But perhaps I'm merely unenlightened. Spell it out for this poor fool.

[Anonymous No.22813665]

>>22813652
>where do the axioms come from?
A PRIORI INTUITION

[Anonymous No.22813668]

>>22813655

euclid breaks down because we have a vastly different conception of space (if the greeks could even be said to have one); if you actually read spengler you would know this

[Anonymous No.22813670]

>>22813660
>you're retarded
ironic

[Anonymous No.22813676]

>>22813670
>what is the curvature of spacetime

[Anonymous No.22813678]

>>22813668
>we have a vastly different conception of space
>Kant thread
>anons didn't read Kant
many such cases

[Anonymous No.22813681]

>>22813678
but i did
if you actually read spengler you would know how he addresses this

[Anonymous No.22813682]

>>22813676
>what is the a priori form of externality

[Anonymous No.22813685]

>>22813682
spacetime isn't a genus because spatiality isn't a genus
you either deny that spacetime can be curved (retarded) or that there are types of spatiality (not kantian)

[Anonymous No.22813691]

>>22813681
>i did
Then read it again

>we can only represent to ourselves ONE space, and, when we talk of divers spaces, we mean only parts of ONE AND THE SAME space.

[Anonymous No.22813694]

>>22813691
yes and he was wrong since his conception of space isn't even the same one of infinitely dividable and breadthless space that's infinite (not in a merely boundless sense either)

[Anonymous No.22813696]

>>22813685
>spatiality isn't a genus
no shit brainlet because it's NOT A CONCEPT-- IT IS AN INTUITION.

>Space is no discursive, or as we say, general conception of the relations of things, but a pure intuition.
did everyone get filtered by the fucking transcendental aesthetic?

[Anonymous No.22813698]

>>22813696
reread my post
>you either deny that spacetime can be curved (retarded) or that there are types of spatiality (not kantian)
do you or do you not deny that spacetime is curved?

[Anonymous No.22813704]

>>22813659
>You have not read Kant and it shows.
No, I haven't but I never said I have. I am trying to have a mature conversation, I expect you (or anyone who wants to) to tell me why I am wrong. If no one cares enough to do it, that's okay with me.
Regarding Kant, I am stuying him but slowly because I have little time. Now, I am at the "explanation" of what synthesis is

[Anonymous No.22813706]

>>22813694
>isn't even the same one of infinitely dividable and breadthless space that's infinite (not in a merely boundless sense either)
*facepalm* YES IT IS? CAN YOU FAGGOTS NOT READ?

>Space is represented as an infinite given quantity.

>no conception, as such, can be so conceived, as if it contained within itself an infinite multitude of representations. Nevertheless, space is so conceived of, for all parts of space are equally capable of being produced to infinity.

[Anonymous No.22813712]

>>22813706
>>Space is represented as an infinite given quantity.
you're retarded if you remove the historical context of it and don't take infinite to mean just boundless in this sense

[Anonymous No.22813729]

>>22813698
your question presupposes a concept of space I already disagree with. Do you think space exists even if there were no humans to perceive it?

[Anonymous No.22813734]

>>22813729
>i disagree with reality
so you're retarded, got it

[Anonymous No.22813737]

>>22813734
>reality
lol ok

[Anonymous No.22813741]

>>22813729
>Do you think space exists even if there were no humans to perceive it?
Yes, maybe not as we perceive it but it definitely exists. Else, you wouldn't perceive it. There is the possibility that it isn't a thing but our way to interpret several things, but it doesn't make it not to exist, just not to be realized without humans

[Anonymous No.22813742]

>>22813737
>metaphysics
lole

[Anonymous No.22813756]

>>22813712
if you'd actually read Kant like you claim to have done you'd know for Kant space is both infinite in extension (breadth as you say) AND infinitely divisible.

[Anonymous No.22813758]

>>22813741
>Yes
and that's why you need to read Kant

[Anonymous No.22813764]

>>22813756
>space is both infinite in extension (breadth as you say)
you utter moron that's what i'm saying
for him infinite merely means that space is boundless, which is not true
he has no account for the expansion of space, obviously

[Anonymous No.22813779]

>>22813764
>merely means that space is boundless
no smoothbrain. as I said it's ALSO infinitely divisible.

[Anonymous No.22813782]

>>22813779
that doesn't entail expansion, midwit

[Anonymous No.22813792]

>>22813782
think faggot. if you can infinitely divide infinitely expansive space then that division will account for any "apparent" expansion.

[Anonymous No.22813816]

>>22813792
retard
>apparent
double retard

[Anonymous No.22813822]

>>22813758
Filtered by argumentation

[Anonymous No.22813826]

>>22813816
>>22813822
seethe more faggots.

[Anonymous No.22813827]

>>22813826
>seethe more at me being a retard!

[Anonymous No.22813842]

>>22813827
>can't win
>resorts to calling me retard
mfw

[Anonymous No.22813959]

>>22813842
>(You)

[Anonymous No.22814216]

>Plato
Math Chad and right about everything
>Descartes
Math Chad and right about everything
>Kant
Philosophy pleb, too low IQ for math, wrong about everything
>Russell
Philosophy pleb, too low IQ for math, wrong about everything
>Gödel
Math Chad and right about everything

I see a pattern here.

inb4 someone calls Russell a mathematician: He never contributed anything relevant to math and his understanding of math was infantile and poisoned by his own wordcel confusing tripping over his own language games as OP's quote shows.

[Anonymous No.22814242]

I never read kant or interacted with kant posters before this thread and I find them both obnoxious,

[Anonymous No.22814283]

>>22814242
Kant in general elicits strong tendencies for or against, this board generally doesn't care much for Russell although there are maybe 1 or 2 Russell anons here. I am pleasantly shocked how long this thread lasted before turning into a shit flinger.

[Anonymous No.22814429]

>>22810642
Depending on the definition of "belief" you can only believe in a priori truths, as for empirical science you can only accept experiments and theories as the closest iteration to the whole truth.

[Anonymous No.22814439]

>>22811671
The only post talking about apriori, does nobody else have their own observations

[Anonymous No.22814446]

Socrates even created an experiment in meno with the slave and the doubling of the square, these are things that can be reproduced right,

[Anonymous No.22814451]

Have we all been midwifed, have we all been brought to a conclusion without being told the conclusion

[Anonymous No.22815813]

>>22810579
What about deciding when the use of the axiom of choice is appropriate?

[Anonymous No.22816413]

>>22814216
>Gödel
>Math Chad and right about everything
He was wrong about his cause of death

[Anonymous No.22816795]

>>22813668
euclid doesn't 'break down', he deliberately stated that only very specific lines can be parallel, and this is the critical difference between euclidean and non-euclidean geometry.

[Anonymous No.22816814]

space is not a thing which exists, it is merely the law of communication and interaction in a certain (physical) sense. Space doesn't exist with objects placed inside of it, space is a byproduct of experience