Mathematics is the most beautiful language in the universe even French or English cannot compete with its elegance. Only individuals with a high IQ (> 130)can truly appreciate it. For those who cannot, worry not Brother Karabashov is not so bad
Mathematics is the most beautiful language in the universe even French or English cannot compete with its elegance.
Philosophy is higher than mathematics, but mathematics is the second highest discipline
Do Philosoturds really believe this?
mathematics is applied logic and logic is applied philosophy.
You literally needed a "greater than" concept to express that opinion. Mathematics wins again.
This point is as thin as air. "Greater than" can be used in a million different contexts, more of them philosophical than mathematical.
So a mathematical principle can be used in a million different contexts. Got it.
Also, cope moar.
It's not mathematical if "greater" doesn't mean numerically greater in context.
Cope more yourself Mr Cope, I'm not attached to this debate in any way.
>I'm not attached to this debate in any way.
Getting BTFO does that to you.
>BTFO
>Didn't even respond to my point.
If anything I'm probably more into mathematics than philosophy, but what you said was lazy and thoughtless and you don't get a free pass on it, Mr.
If you want to take the moral high ground, clean the shit off your shoes first.
Oh! A proverb now! Very good!
You've left my point unanswered, though.
What ye think of Kline’s books?
Wait, you said “you” as in second person pronoun? I need to tell you the concept of one is derived from a propri concept of substance. Sorry.
Proof, proof, proof! Yeah, that’s what a credulous religious sectarian will believe and demand, certainty and fear go hand in hand.
>Proof, proof, proof! Yeah, that’s what a credulous religious sectarian will believe and demand, certainty and fear go hand in hand.
We're talking about philosophy in comparison to math bro. You can very much prove things absolutely in math. Euclid is as valid and accepted now as he was prior to Plato and Aristotle. That's why it's comical to call math applied philosophy.
The point is that you’re giving mathematics preeminence due to its proving power. Absolute proofs in math means nothing in nature and likewise nothing for man.
Finally, none said it is applied philosophy, at most it may be applied platonism.
I'm giving math preeminence because philosophy is just a bunch of angry opinions being thrown at each other. Like I already said.
This is just as stupid (I think it is even more) as saying that math is nothing but ideal abstractions that have no real existence in nature and life and thus is totally meaningless. You lack subtlety.
>math is nothing but ideal abstractions that have no real existence in nature and life and thus is totally meaningless
Physics is applied math along with experiments. What has philosophy done that's even close? People frequently hold philosophical positions that actually contradict empirical reality
Physics is not math. The mathematicization of Physics, so to speak, is just a pattern revolution of its epistemological ground (you have read your Kuhn, right?), meaning, Physics progressed from epistemological and more purely philosophical inquiries on causality, movement, form-matter, etc. Why not mention Pythagorean and Platonic metaphysics when it comes to math, though? Many physicists later recognized their importance and everlasting perinence to their field.
>Why not mention Pythagorean and Platonic metaphysics
Because Aristotelian metaphysics is wholly fictional and held back physics for over a thousand years. Again many philosophical positions contradict empirical reality. See Galileo and the Tower of Pisa. Heavier objects do not fall faster than lighter ones no matter what your metaphysical daydreams are.
Pythagorean and Platonic metaphysics are not the same as Aristotelian metaphysics. But you must be a moron to ignore the advance in physics, optics, for instance, during the Middle Ages, which both christian and muslim philosophers/scientists (see there was not even a distinction until recently) developed based on some Aristotelian notions.
Many philosophical positions are literally the basis for the empirical epistemology on which you ground your moronic “rule of reality”. This is what happens when math and a utilitarian soul meet: the most destructive outcome possible.
>Pythagorean and Platonic metaphysics are not the same as Aristotelian metaphysic
Pythagorean and Platonic metaphysics make no empirical predictions and are totally superfluous for physics. They're superfluous for math as well since math can supply it's own logical foundation. That's pretty much the only thing math can do without experiments, give itself logically rigorous foundations along with the subsequent theorems implied by those foundations
>both christian and muslim philosophers/scientists (see there was not even a distinction until recently)
No kidding. And there has been more scientific development in the 200 years since the Enlightenment than the entirety of human history prior. Philosophy is worthless.
>Pythagorean and Platonic metaphysics make no empirical predictions and are totally superfluous for physics
I was referring to mathematics not physics when I mentioned them.
>math can supply it’s own logical foundation
It can’t and it hasn’t. It is not how it was developed. Law of contradiction, indentity of indiscernibles, etc. were logical-metaphysical laws that laid the foundations of formal and theoretical aspects of mathematics. Read someone like Kant and you’ll understand the metaphysical quality of a priori principles and how they serve for the foundation of geometry and mathematics and later physics. Space, whole-part, substance-monad will ground plane, point and geometrical notions. Time, movement synchronicity, then numerical progression etc.
>there has been more scientific development
Material development? For sure, but even here we have social and economic factors that contributed just as much as the change in epistemological pattern, for instance, the acceptance and normativity of slavery in the past, the industrial revolution, etc. and it is obvious that once the pattern is directed to material development, these will develop more rapidly than when the pattern was different.
Yes, philosophy is worthless in one sense, but so is physics, mathematics, material comfort as well. In the end evaluation comes all from one’s disposition, how surprising! Who could tell? Certainly not someone like you.
>Read someone like Kant and you’ll understand the metaphysical quality of a priori principles and how they serve for the foundation of geometry and mathematics and later physics.
Kant believed in a transcendental notion of space that served as the ground for human thought. Non-Euclidean geometry makes that laughable and after that general relativity showed it's not even physically true. Your philosophy is worthless and is not the basis for physics or math
The point was that his conception of space and time literally had metaphysical implications as said: whole-part, substance, monad, succession synchronicty, all of which math and physics cannot do without.
>The point was that his conception of space and time literally had metaphysical implications as said
And his conception of space and time were wrong and did not serve as the basis for math or physics since there are math and physics that actively contradict Kant's ideas.
Yes, physically they might be wrong, but that does not contradict the ideal preconditions it laid for the a priori possibility of math and geometry, just like the physics/math that contradict Kant’s are not devoid of metaphysical principles. But Kant was literally only one example of this ideality. If you think of social context, commerce, everyday activities which spurred mathematical and geometrical (land measuring after all) notions forward also implicated metaphysical principles. Kant again will attribute these principles merely to the form of experience we naturally take for granted. This inquiry did not start with him though. In sum, you cannot do math and physics without them.
>Yes, physically they might be wrong
Not just physically mathematically as well. There are several different notions of space covered by Euclidean and Non-Euclidean geometry and many more covered by Differential Geometry. The idea that the Kantian notion of space prefigures mathematics is clearly ridiculous since there are multiple types of math that contradict it. There are no metaphysical principles underlying math.
The problem is that you don’t understand Kantian notion of space. You understand it very partially, and taking it into account of what is not being discussed here, physical and mathematical theories, instead of their foundational principles.
>The problem is that you don’t understand Kantian notion of space
So the Kantian notion of space somehow prefigures math and you can't do math without it yet it contradicts whole areas of math(which has multiple contradicting notions of space depending on what axioms you use). You're trying to set up philosophy as something necessary for math without it having any effect on math at all so that math can't contradict it. Obvious bullshit. If something is foundational for a field and the field then contradicts that foundation it was never foundational to begin with.
>So the Kantian notion of space somehow prefigures math
Wrong.
> If something is foundational for a field and the field then contradicts that foundation it was never foundational to begin with.
How does math and geometry contradict the ideas of oneness, whole, part, sameness, identity, difference, sequence? How does physics contradict empirical epistemology?
>>So the Kantian notion of space somehow prefigures math
>Wrong.
This is just you taking things out of context and totally changing the meaning. The actual sentence
>So the Kantian notion of space somehow prefigures math and you can't do math without it yet it contradicts whole areas of math(which has multiple contradicting notions of space depending on what axioms you use).
is clearly sarcastic. I'm saying math is in no way prefigured by Kantian or any other type of metaphysics.
The rest of the sentence followed from your false premise. I didn’t say anywhere that the notion of space prefigures math, but what is implicated in his notion of space.
>no math has no relation to any metaphysics
It has though.
>I didn’t say anywhere that the notion of space prefigures math, but what is implicated in his notion of space.
Idiot level comment. If his notions of space imply whatever metaphysical gibberish you're claiming and that metaphysical gibberish implies math then Kant's notion of space implies math. Logical implication is transitive A implies B and B implies C means A implies C. You need a basic grasp of logic before you pretend to make a rigorous argument.
Idiot level reading. We talked about his idea of space being contradicted by other theories of space and by mathematical and physical theories, but this one side of his idea of space, not the whole, and it is precisely the other side that I’ve been pointing out to you for hours. The part is not the whole and the whole implicates more than the part.
You need a basic grasp of logic, anon.
Not him but seems like you are interpreting Kant's Euclidean spatial intuition as logical axioms about how all STATEMENTS regarding space (whether in physics or geometry) must conform to Euclid's parallel postulate. But this is mixing algebraic formalism (which can take effectively anything as a postulate) with epistemology.
Kant is doing epistemology. He simply says that our perception (intuition) is always Euclidean, and ordinary constructive geometry is based on Euclidean space. The whole reason it's called "Euclidean" in the first place is that Euclid set down a useful general description of our perception, i.e., of intuitive, constructible geometrical entities in three-dimensional space. He didn't invent it, he merely generalized about it in a way that still conforms to our experience.
This says nothing about the possibility of formalist algebraic mathematics that jettisons the requirement of constructibility and posits objects that still conform to several Euclidean axioms while NOT conforming to the parallel postulate and thus NOT to our mental or perceptual experience of geometrical objects (from which the parallel postulate was derived). Kant is not refuted by Riemann or Gauss. However, he would be very fascinated by the fact that the non-Euclidean algebraic geometries pioneered by these mathematicians are a cornerstone of modern physics which makes accurate predictions about the external physical world, and it would be fascinating to hear his response to this.
>Kant is doing epistemology. He simply says that our perception (intuition) is always Euclidean
And this is clearly false since we have Non-Euclidean geometry and relativity. Kant's intuition may have been limited to Euclidean geometry but people after him had new intuitions. Putting Kant on a pedestal is the worst type of if I can't imagine it, it must not exist.
Not that anon, I’m the one who brought Kant up to the table, and I did so only because I thought it would be clearer to show the epistemological/metaphysical relation to another ideal and abstract science that is math and geometry.
You are misunderstanding what intuition means in this context. You should read Kant at some point.
Spherical geometry doesn't contradict the Euclidean postulates unless its axioms are generalized to space in general. It's just a special case of Euclidean geometry, it still exists within an overall Euclidean space, that is, until you posit that it doesn't.
The issue with Riemannian etc. geometry is that it is completely un-intuitable (im-perceptible) and can only be thought. It's a noumenon (thought or thinkable), not a phenomenon (appearable, visible).
>Spherical geometry doesn't contradict the Euclidean postulates unless its axioms are generalized to space in general.
This is true but goofy since Euclidean geometry doesn't contradict the postulates of spherical geometry unless its axioms are generalized to space in general also. You can just as easily say that Euclidean geometry is a special case of spherical geometry which in fact happened historically since we draw flat maps of a spherical globe.
>The issue with Riemannian etc. geometry is that it is completely un-intuitable (im-perceptible) and can only be thought. It's a noumenon (thought or thinkable), not a phenomenon (appearable, visible).
Again the same response as above. How do you know that your intuition of Euclidean geometry isn't really taking place in spherical space? I can visualize spherical geometry just fine and since relativity shows reality is non-Euclidean what appearance can you point to as Euclidean?
I said in my original post that Kant would be the first person to be fascinated by the possibility that "reality" might be non-Euclidean, so I am not contradicting this possibility. I'm only saying that the Kantian explanation for spherical geometry existing as a subset of ordinary perceptual space (you're literally picturing a sphere IN a Euclidean space, unless your "background space" or negative space in your mind's eye is somehow inherently spherical and you're some sort of alien) is internally coherent and consistent.
You are not really arguing against Kant that our experienced intuition itself - again I'm not sure people in this discussion actually know what Kant means by this term - could be spherical with Euclidean space as a subset, you are arguing that LOGICALLY nothing contradicts this in terms of axioms (i.e., one can logically describe a space X whose rules are a modification of or addition to space Y with its rules). But Kant's theory of INTUITION is not a logical theory, it is not a set of postulates. Kant's view of Euclid's postulates is that they are a discursive description or logical generalization about something that is not itself discursive, i.e., actual perception, the actual space intuited by our actual mind's eye. This space is not spherical. If actual space, space as we can noumenally intend it, beyond the limits of our perception, is actually spherical (whatever that might mean), and were this empirically verifiable (a controversial claim) then even that wouldn't contradict Kant's point necessarily, although it would probably induce him to rethink things a lot.
>Kant's view of Euclid's postulates is that they are a discursive description or logical generalization about something that is not itself discursive, i.e., actual perception, the actual space intuited by our actual mind's eye.
And this is exactly what I called goofy above. Kant's intuitions aren't everyone's intuitions that should be obvious. The fact that non-Euclidean geometry was developed afterwards shows that. Einstein is known for his strong physical intuition that led him to a non-Euclidean form of physics. What you've reduced Kant here too is a theory in cognitive science that everyone visualizes space in a certain way which is clearly wrong.
Again, what you are saying stems from a misapprehension of what Kant means by "intuition." You are using it in a very general, English-language sense meaning "things he finds intuitive" (or something like that). Intuition in Kant jargon is a translation of Anschauung and simply means visual and mental-visual perception. I think Norman Kemp Smith is responsible for the weird translation as intuition, based on Kant also using the specialized scholastic term intueor as equivalent in his Latin writings. As I said in my first post, people ITT are mixing epistemology with vague notions of both intuition and axiomaticness. Kant does not mean DISCURSIVE DESCRIPTIONS of alternate ways of seeing or perceiving are logically or discursively impossible to give. We can both intend, noetically or noumenally, imperceptible entities, and (as a subset of these), entities imperceptible to us but perceptible to some other kind of mind.
But the reason Euclidean geometry held and was the foundation of Newtonian physics thousands of years later is simply that the mind's eye, as agreed upon by basically every philosopher except esoterics, psychonauts, or the geometer Coxeter claiming he once saw in n-dimensions, "sees in" "Euclidean geometry." Euclid merely wrote down what we all see.
The fact that non-Euclidean ALGEBRAIC geometry, which is specifically NON-CONSTRUCTIVE (all of its proponents explicitly say so, because they are ACKNOWLEDGING the impossibility of INTUITIVELY constructing the entities they are describing with, notwithstanding, ALGEBRAIC consistency), allows us to describe empirical realities is fascinating but has nothing to do with Kant's basic point that we see in three spatial dimensions and two temporal dimensions under normal conditions. It's like I said to the first guy, you are arguing with positions Kant didn't hold because you don't know what he meant by perception.
I am not even stating all this on my own authority. The very non-Euclidean geometers in question openly stated it as the most fascinating aspect of their discovery: "Isn't it cool that this geometry still works in algebra-land when it takes a vacation from constructibility-land?" Constructibility = visual/perceptual representation in normal Euclidean intuition.
>The fact that non-Euclidean ALGEBRAIC geometry, which is specifically NON-CONSTRUCTIVE (all of its proponents explicitly say so, because they are ACKNOWLEDGING the impossibility of INTUITIVELY constructing the entities they are describing with, notwithstanding, ALGEBRAIC consistency)
I already said above that a grade school level demonstration of spherical geometry can take place with a marker and balloon. Hyperbolic geometry was discovered first and is harder to represent but again just because you can't imagine something doesn't mean someone else can't.
>Intuition in Kant jargon is a translation of Anschauung and simply means visual and mental-visual perception.
Yeah imagination I fully understand.
>This says nothing about the possibility of formalist algebraic mathematics that jettisons the requirement of constructibility
You can do spherical geometry on a balloon with a marker. I saw a demonstration of it in middle school
>Yes, philosophy is worthless in one sense, but so is physics, mathematics, material comfort as well. In the end evaluation comes all from one’s disposition, how surprising! Who could tell? Certainly not someone like you.
I think you missed this big point right here. Philosophy and Math are useless at different things. You can be obsessed with all the quantitative relations in the world, but step too far and you get yourself Mengelean experiments or Unit-731. Ethics is just as much the limit of science and math as metaphysics is its ground. Obsessing over proofing and austere beauty in isolation is a naive dream.
>Non-Euclidean geometry makes that laughable and after that general relativity showed it's not even physically true.
moron, we are still observing those phenomena even if it’s through a telescope. His point is that space and time are necessary presuppositions if we are to make sense of the physical world. try to imagine a thing without space. Non-Euclidean geometry means nothing, you must only know that word through Lovecraft. One of Kant’s examples in the critique is literally non-Euclidean. Only Einstein matters, and if anything he only strengthen’s Kant’s position by putting an equation to it. Kant’s point is that the equation does not inhere in the thing-in-itself but only retains its validity when viewed through space and time. Not to mention that a posteriori sciences like physics take observation of the physical world as step one, meaning that all conclusions which come from it are rooted in our OBSERVATION of reality and not reality itself. Einstein even makes this point himself. Hell, you can even read his own thoughts on how his work fits perfectly into Kant’s system.
>One of Kant’s examples in the critique is literally non-Euclidean
Pretty impressive since Kant died in 1804 and Lobachevsky published his first paper in 1830. Kant could have been remembered for something real if he had drawn more attention to his "discoveries" in non-Euclidean geometry. moron.
And yet nothing about non-Euclidean geometry lol. No alternate to the parallel postulate in fact no mention of parallel lines at all. It's like you saw sphere and assumed spherical geometry like a mathematical moron. In no way or form imaginable did Kant know about non-Euclidean geometry since it outright contradicts his own ideas. Hey guys Aristotle knew about category theory since he wrote a whole book on the Categories.
What a fricking insane cope. This us what math does to you
You're seriously claiming Kant discovered non-Euclidean geometry 30+ years before everyone else? Forget philosophy or math just in terms of intellectual history you've made a huge discovery. IQfy can point to this shining example of new scholarship it has fostered.
Euclid himself had people point out to him that geometry is difficult to apply to our world which is not an entirely flat plane. Most of the first mathematicians were more absorbed in making sure that their ideas were constitutive of reality than actually doing math because of this. Sailors in the 1700s were aware that they traveled a globe. In fact, how do you explain the way they calculated latitude and longitude before 1830 then? Is there not an implicit understanding that you are abstracted as a line crossing the face of a sphere there? Is that not non-Euclidean geometry? As far as the postulates and actual formal creation of the discipline who cares. I would argue that those postulates rest on an abstracted understanding of normal geometry and thus still require space as a presupposition but whatever. The point is that non-Euclidean space still relies on SPACE to exist. All those postulates and jargon mean nothing if there is no intuition to apply it on. Not to mention that this is literally only a tangent to the main point that I made in my op to you.
>Sailors in the 1700s were aware that they traveled a globe. In fact, how do you explain the way they calculated latitude and longitude before 1830 then? Is there not an implicit understanding that you are abstracted as a line crossing the face of a sphere there?
Again showing how little clue you have of what we're talking about. Spherical geometry is not the description of a sphere in 3d Euclidean space.
>Is that not non-Euclidean geometry?
It's not which should be obvious since we wouldn't say non-Euclidean geometry was invented in the 1800s if it was discovered by sailors at some indeterminate time. Not to mention non-Euclidean geometry isn't just spherical geometry and spherical geometry wasn't even discovered before hyperbolic geometry.
>As far as the postulates and actual formal creation of the discipline who cares.
Lol. So you're losing the argument and you just throw up your hands and say who cares. Non-Euclidean geometry is all about different postulates from Eucldiean geometry.
>I would argue that those postulates rest on an abstracted understanding of normal geometry and thus still require space as a presupposition but whatever.
Not whatever. Non-Euclidean geometry explicitly contradicts the parallel postulate from Euclidean geometry. It can't rely on "normal" Euclidean space since it is not Euclidean.
>All those postulates and jargon mean nothing if there is no intuition to apply it on.
And again Kant lacked the intuitions of those that followed him. His visualization of space is not the only one people have. Obviously
Go back to IQfy and post about your homework
Kline’s Calculus or Kline’s Mathematics for the Nonmathematician?
both are 9/10
I was thinking about starting with his Math for the Nonmath. and after moving to his Math: the Loss of Certainty.
Nice that there’s approvation of his works, thanks!
>the concept of one
>literally mathematics
D'oh!
The concept of One transcends number. Mathematics arises from philosophy. Ever heard of Descartes? Ever heard of the foundational crisis of mathematics? This board's hatred of philosophy is just downstream from the greater positivist cultural fallacies of our time. I'm not into Guénon but "the reign of quantity" is really a great way to sum it up.
>Ever heard of the foundational crisis of mathematics
You mean the one that was solved by mathematical formalism?
>I'm not into Guénon but "the reign of quantity" is really a great way to sum it up.
Lol. Crank shit
>You mean the one that was solved by mathematical formalism?
Yes, the one that was solved by philosophy of mathematics.
>Lol. Crank shit
Dogmatist pseud needs a heckin approved source on the poetic description.
>Yes, the one that was solved by philosophy of mathematics.
If set theory counts as philosophy I guess you've got me beat. But if set theory is philosophy mathematicians are expert philosophers.
>Dogmatist pseud needs a heckin approved source on the poetic description.
I've read Reign of Quantity. Dude talks about the magic properties of gemstones and how magic worked in the past but not now because of the qualitative properties of time. New Age level bullshit.
>If set theory counts as philosophy
Mathematics has been inseparably philosophical since Cantor. In fact, any mathematics that relies on axiomatic statements, so anything beyond bare numeracy, is just applied philosophy. The mathematical rejection of philosophy is more accurately one of humanism.
>Dude talks about the magic properties of gemstones and how magic worked in the past but not now because of the qualitative properties of time.
Well, I did preamble my mention of him by clarifying it's just an apt descriptor, rather than an endorsement of his theosophical views.
>In fact, any mathematics that relies on axiomatic statements
If relying on axioms is philosophy then mathematicians are the best philosophers bar none. What you really mean is what justifies the axioms since you stupidly think the axioms need justification. The axioms are arbitrary you can make them whatever you want as long as it's logically consistent and you can interest someone in the resulting system. Non-Euclidean geometry arbitrarily replaces the parallel axiom with something more interesting that still leads to a logically consistent system. Let me repeat no philosophical justification of the axioms is needed or expected as much as you want it to be. Math is comparable to a game played with arbitrary rules.
Is not the interaction of those arbitrary rules postulated upon philosophical justification in order to reach a stable and consistent outcome? As I implied in my original post, any mathematics beyond counting on your fingers already has philosophical assumptions baked into it. Arguably, even natural numbers do. And if you want that logically consistent system to conform to reality accurately then philosophical justification is required. Even empirical measurement requires a pre-established philosophical basis in order to be carried out consistently. Then there's the question of logical consistency which in itself implies underlying philosophical justification.
Physics is also 'wholly fictional,' including the Copernican model, insofar as it is taken as anything more than pure mathematics. This might make you uncomfortable as an autismal, but fiction is how we understand reality. Like most stemgays, you confuse parsimony of description with reality itself. This, of course, isn't to say Aristotelian models work, but rather the confusion of map with territory leads to moronic hubristic notions like that of a mathematics divorced from philosophy.
>And there has been more scientific development in the 200 years since the Enlightenment than the entirety of human history prior. Philosophy is worthless.
An enlightenment entirely born from philosophy and propped upon the shoulders of giants.
>Is not the interaction of those arbitrary rules postulated upon philosophical justification in order to reach a stable and consistent outcome?
Logical consistency means you can't reach a contradiction by using logical rules on the axioms. No philosophy required
>And if you want that logically consistent system to conform to reality accurately then philosophical justification is required
Math doesn't care about reality. Physics does and you use experiments for that. No philosophy required and philosophy is frequently proven wrong, again refer to Galileo and the Tower of Pisa.
>Then there's the question of logical consistency which in itself implies underlying philosophical justification.
No it doesn't. The whole point of mathematical formalization is to reduce determining logical consistency to a mechanical operation. There is no philosophical justification involved only a mechanical application of the rules of natural deduction to the starting axioms and no one finding a contradiction.
>logical consistency
already implies the laws of identity and contradiction. Forgoing ontological commitment as in formalism (which in itself is a philosophical position btw) does not eschew philosophy from mathematics as a whole. That's terminally moronic and as the other anon said, go back to IQfy and post about your homework.
>already implies the laws of identity and contradiction
Again no justification of those laws is needed. You accept them the same way you do the axioms. It's going to blow your mind but their is constructive mathematics that doesn't use the the law of the excluded middle. The logic you use as well as the axioms you start from are arbitrary. No justification needed.
What is a contradiction?
>What is a contradiction?
When you apply your rules to your axioms and you get A and not A. This is bad in math since using natural deduction you can get from a contradiction to a proof of anything in several steps in what is called the principle of explosion. There are logics that are more resistant to contradictions but they never took off as more than novelties. The interest isn't there
Start with the contradiction A and not A
1. From A and not A you get A by conjunctive elimination
2. From A you get A and whatever by disjunctive introduction
3. From A and not A you get not A by conjunctive elimination.
4. From 2 and 3 you get whatever by law of the excluded middle.
Boom explosion. Trivializes math and makes it uninteresting.
>A and not A
What does it mean?
Means nothing that is the whole point of mathematical formalization. You apply arbitrarily chosen rules to the arbitrarily chosen axioms mechanically in such a rigorously defined way that no one can disagree on their application. That is what solved the foundational crisis at the turn of the 20th century. Not some goofy philosophical justification. If you really want the technical answer go to model and proof theory but again the "model" in model theory is a mechanically defined formal concept not some goofy philosophical BS.
You just gave a philosophical argument btw. He baited you so hard. Lmfao
>You just gave a philosophical argument btw
I've said as much here
. If set theory and mathematical formalism counts as philosophy then mathematicians are expert philosophers. No goofy Kant or metaphysics needed either.
Why are you not proving your point mathematically instead of recurring to historicist perspective, empirical epistemology, all of which are… philosophical operations?
>historicist perspective
Huh? Are you just coming up with random shit as a joke?
>empirical epistemology
Now I know you're kidding. I explicitly said several times that math has nothing to do with reality and does not use empirical proof.
1. You appealed to Enlightenment and modern science
2. You validated physics as applied math with empirical observations, you opposed philosophy to empirical observations several times
>You validated physics as applied math with empirical observations
Physics is applied math with empirical observations. But physics is not math. If you add empirical observations to math you get physics. But you don't so math has no empirical part to it. This is basic basic stuff. And besides you talked about reality in relation to philosophy several times. So that must mean you have an empirical epistemology. Checkmate
You’re justifying math and physics against philosophy philosophically
>You’re justifying math and physics against philosophy philosophically
More gibberish. You're just throwing random shit at the wall now like here
. You must be have a historicist perspective since you're referring to my previous posts.
See, you don’t know what is historicism, you don’t know what is philosophy and that’s why you don’t know the foundations of math, physics, geometry. But we told you. You want some books on this? Read thomas kuhn, jacob klein on greek mathematical thought.
>See, you don’t know what is historicism
I know what it is fine you accused me of it for totally nonsensical reasons. Look here is the post where I mention the enlightenment
. It's in response to you mentioning Middle Ages here
. So that means you must have a historicist perspective then right? Since you mentioned the Middle Ages. Of course that is fricking stupid but that seems to be what you think historicism is.
The issue is not whether I have a philosophical point of view, but that you have.
>The issue is not whether I have a philosophical point of view, but that you have.
Huh? Here is what you said
>Why are you not proving your point mathematically instead of recurring to historicist perspective, empirical epistemology
my response is that's gibberish since I have said nothing to indicate either of those positions. You then claimed I took a historicist perspective since in your words
>1. You appealed to Enlightenment and modern science
but the post where I mention the Enlightenment is a direct response to you mentioning the Middle Ages. So by the same fricking logic you must also have a historicist perspective.
But you have said and I have showed to you your own philosophical presuppositions for your validity of math and physics.
>historicist perspective
Yeah, I think historicism has some pertinence.
Again you're changing the subject. You stupidly accused me of having a historicist perspective and then even more stupidly of having an empirical epistemology in relation to math. Until you clarify what the frick you could have meant by that I'm safe in assuming that not only do you know nothing about math you know nothing about philosophy either. What have I said that would indicate I hold either position?
>philosophy is inferior because there is no application to the world, unlike math and physics, they are greater because we can observe they have empirical legitimacy
that is, you assume a correspondence between empirical observations and math, you are really a philosopher, anon!
>that is, you assume a correspondence between empirical observations and math
Where have I done this? Where? I have repeatedly said math has no connection to reality and that it doesn't do experiments. If you just make shit up sure I can prove you wrong. You said earlier philosophy was stupid and only gays like it.
When you said that philosophy might lead to what is contradicted by empirical reality. In this way, by opposing philosophy and physics/math thus, you either agree that philosophy and mathematics belong to a different realm (for both will have no empirical validity, or you class math with physics in having empirical validity. You said that philosophy has no relation to mathematics and that physics is applied math, so by coherence you affirm that math/physics have empirical correspondence with reality.
Again you're combining math and physics like a fricking moron. Physics is very fricking empirical and relies on experiments. Math is not empirical and has no experiments. Jesus fricking christ you are an idiot. MATH IS NOT PHYSICS.
>Physics is very fricking empirical and relies on experiments
Then this implies an empirical epistemology?
Do you know what is not empirical, as Mathematics? Metaphysics.
>Then this implies an empirical epistemology?
You're fricking post where you brought this idiot shit up
>Why are you not proving your point mathematically instead of recurring to historicist perspective, empirical epistemology, all of which are… philosophical operations?
Where the frick does it say anything about physics there. You are an actual fricking moron who can't even keep their own argument straight in their mind. This is the type of person philosophy appeals to. That and the dumb fricker who suggested reading Guenon above.
You said here
:
>Pythagorean and Platonic metaphysics make no empirical predictions and are totally superfluous for physics.
Then: ''philosophy is worthless and is not the basis for physics or math''
How is philosophy worthless for a field dependent on a philosophical stance that is empirical epistemology?
You said that mathematics can supply it's own logical foundation, but then you said that the foundation of mathematics is arbitrary. And that it is the only thing math can do without experiments.
What is this thing that is self-contained, arbitrary and divorced from reality?
Nah you're not getting away with ignoring your stupid shit you defended over multiple posts. Until you admit you were wrong, your arguments were dumb and nonsensical, and that you were just making shit up I'm not going to respond to anything else.
Yes, anon, that is why I need your answer to those questions. I'm very dumb, please help me, and answer:
You said:
>Pythagorean and Platonic metaphysics make no empirical predictions and are totally superfluous for physics.
Then: ''philosophy is worthless and is not the basis for physics or math''
How is philosophy worthless for a field dependent on a philosophical stance that is empirical epistemology?
Since you said that mathematics can supply it's own logical foundation, but then you said that the foundation of mathematics is arbitrary. And that it is the only thing math can do without experiments, what is this thing that is self-contained, arbitrary and divorced from reality?
>he literally can’t even understand it after it’s been pointed out to him 3 times
>Like most stemgays
I sense a chip on your shoulder
Perhaps even a sore on the ass
I am one myself so no, nice try though.
Nothing is ever proven or disproven in philosophy. It's just a bunch of angry opinions being thrown at each other. You still get people claiming Aquinas was the peak of philosophy on IQfy
>Philosophy is higher than mathematics
Nooooo. Mathematics is applied logic, that much is true, but mathematical logic is just a part of maths.
Philosophy is mostly just pseuds posturing, perhaps with some small fraction studying logic or neuroscience.
What a terrible way to start the thread.
I have the top left book and a Calculus textbook. Should I study Pre-calc on youtubve or go through these books? I took and passed half a pre-calc course in college but that was 8 years ago.
>go through these books
it's super friendly
>applied mathematics
No beauty there
Study group theory, ring theory, number theory, topology and analysis for the truest beauty
>No beauty there
Maxwell's equations?
Music is a better language. Arguably a dialect of math.
send some
true, to prove anons point:
Yes, mathematics is a primarily aesthetic experience. When you start looking at things, and seeing the beauty of it, is when it all starts to make sense.
Anyone know where to start with maths? Im in my 30s and havent touched maths since i left school at 15. I tried khan academy but got overwhelmed at where to start and all the options. Is there any book that does a condensed school course what to move onto after that.
Lang- Basic Mathematics
Just run with it and look up khan academy wherever you are stuck. It wouldn't hurt to just pick up school textbooks at your level. Once you're done with Basic Mathematics, you start with Calculus
top left of my chart
I've actually been wanting to learn math recently, I've been watching videos on Algebra and Geometry. What will physics help me with in my day to day life? Im an novice artist, a coder and a Mechanic so learning math is gonna help me some kind of way right?
Nope. Math will not help you in any of those. I have a master's in Physics and physics doesn't even help me day to day
Oh, I guess i'll just stick with Geometry and Algebra then.
yes your logic will be much better
Math is necessary to be a very good programmer
homosexuals who think mathematics and philosophy are mutually exclusive are capable of neither.
t. homosexual
>Mathematics
>language
Why do you keep repeating it? What does it mean? Can you say "Hello I'm anon and I like math" in mathematics?
What's the best book for a mathlet to get a grasp of mathetmatics?
>top left of my chart
What is Mathematics by Courant
mathematics is lierally gibberish and truns you into a schizo if you study it too much. Just look at Ted Kaczynski
Anyone studied math at uni? I am considering doing compsci + math. seems like a good combo.
If you major in CS at an American university you're only a few classes away from a math major. When I got my CS degree you automatically minored in math as part of it.
CS majors need Calculus I-III for Engineers, Linear Algebra for Engineers, maybe Discrete math and maybe a random Diff Eq. class. That's close to a math minor. Math major? Lol.
It was two discrete math courses but besides that you listed what I took. Maybe 4-5 more classes would have been a math major which seems pretty close.
Thats pretty much the first 2.5 years of a math major. It's about as far as you can go into a math major before encountering problems that have nothing to do with real scenarios (in abstract algebra, complex analysis, topology/abstract geometry, etc.). Many math major requirements include sophomore and junior level CS courses because CS is so fundamental to modern utilization of mathematics.
>even English
Ahahahaha.
>Mathematics is the most beautiful language
Glad to see someone else here isn’t a brain dead coping philosopseud or failed writer
But that’s what you’re assuming, that the whole is wrong when the whole comports two different branches of human cognition. If A contains B and C, and I’m relating C to X it follows that I’m not relating B to X.
In this order:
Birkhoff Mac Lane
Munkres
Atiyah Macdonald
Hatcher
CWM
EGA
SGA
STFU NERD
>Mathematics is the most beautiful language in the universe
I agree with this but only because one of my maths teachers in school was hot as frick
Oh my God I'm a midwit. I was always 2 ligma as a child but now I'm more like 1 according to Ravens Progressive Matrices. Thanks dude dudeweed and schizophrenia
>Only individuals with a high IQ (> 130)can truly appreciate it.
You post these words, but all the textbooks in picrel are mathematics for the disciplines. Not even applied mathematics as its own field, but mere mathematical shortcuts for non-mathematicians.
>Only individuals with a high IQ (> 130)can truly appreciate it
If im a standard deviation away will stimulents help me make up the gap?
Can anyone give me a roadmap of Category Theory? A step by step guide of all the books I'd need starting from level 0.
(I'm not actually at level 0 but still interested to know)
>Can anyone give me a roadmap of Category Theory?
If you legit have to ask here then, you probably have no reason to actually study it but just don't understand that yet and so have no reason to be given a roadmap. No, you don't need to understand it to use Haskel.
>he posts on IQfy and boasts about math and IQ
We can tell you have no friends, very sad, many such cases.
math feels manufactured to me for some reason it just rubs me the wrong way not because im bad at it or anything it just feels spiritually suspicious - any books on this?