What the fuck is this shit?
I was reading introduction to philosophy, and the "thinkers" aka """philosophers""" were just making shit up as they went, but this one is especially jarring.
What's the fucking point of this one and the similar ones?
>inb4 hurr durr 100 iq philistine
to filter out plebs like you
It is an argument against concerned with showing the problems that arise when you hold time and space to be divisibly. Even if you consider the 'mathematical solution' where you process to the limit to be valid, then take the next paradox: in order to cross 1 fixed distance you first have to cross half of that, then again first half of that half, and so on. Taking the limit of this sum, you will find it to be zero, hence proving that even in that case you would remain standing still. Aristotle tried to take on the paradox by making a distinction between possible divisibility (of e.g. a line) which is infinite, and actual divisibility which is not infinite but I'm myself not satisfied with this as he's basically admitting Zeno is right by saying that in an ideal, theoretical world the paradox would be correct and that it only is not correct in the sensible realm.
Also, those other thinkers (esp. Pythagoras) were making less 'shit' up than you might assume at first sight
>hence proving that even in that case you would remain standing still
Can you spoonfeed me, a brainlet, a little more, and expand on this thought? Thanks for your response regardless.
>unironically applying mathematics to zeno
>AND actually being this bad at math that you spout "in order to cross 1 fixed distance you first have to cross half of that, then again first half of that half, and so on. Taking the limit of this sum, you will find it to be zero"
so this is the finest Yea Forums has to offer, huh
Not him but that you cannot devise time because it would be infinite.
So?
Because it would be better viewed as a creature, as Augustine put it. But that our perceiving distance and set is the only thing effectually true. However ultimately the only thing that does not change is the pattern of the change itself, the thing however is constantly changing. That thing being what Hegel would call the Spirit of the Times. Hegelianism with the Augustinian view on time works together quite well.
>unironically applying mathematics to zeno
Here's what I said: Even if you consider the 'mathematical solution' where you process to the limit to be valid
My point is that 1. I don't think anyone should consider the mathematical 'solution' to be valid and 2. that even if you do, it only works for the turtle paradox, not for the other one
What?
Because you would be faced with time infinitely occurring between the two actions. And so time better viewed as a living animal, and definition our human perception - I suppose (about that latter part).
What do you not understand?
>Because you would be faced with time infinitely occurring between the two actions.
Why's that a problem?
I'm guessing I'm too retarded to understand the whole post. I've had the same problem with the introductory book, but there I could sit for an hour trying to understand a page of it, here I can just ask you.
>Why's that a problem?
If the time between two points is infinite (rather than time as a whole; as infinite) then in theory you would not be able to get to that second point. And so even though the Greeks new they *could* get to that second point they were perplexed by how and so that's what led them to say things as such.
>I'm guessing I'm too retarded to understand the whole post. I've had the same problem with the introductory book, but there I could sit for an hour trying to understand a page of it, here I can just ask you.
All good, if you don't understand just watch some youtube video. But I mean any particular points that confused you, I would be willing to answer.
>If the time between two points is infinite (rather than time as a whole; as infinite) then in theory you would not be able to get to that second point.
Yeah, but why wouldn't you be able to? Nothing about that resolution of the question seems to pop out for me as intuitive. Math shit aside, it feels like they are bruteforcing a certain view of the problem, like trying to fit in a screw with a hammer, which is what creates the paradox in the first place.
Alright, I'll check out something on what you said about Hegelianism and the Augustinian thing, then come back to this later.
Thanks user.
I want to add this because I dig on this, but when he "disproving" Zeno's paradox by potential infiniteness of Space, he means at "ideal, theoretical" model too. Even in the ideal, theoretical model Aristotle take Space as only commiting potential infinity.
So if you want to say anything such as "in ideal space model actual infinity is possible", then it must be outside of aristotelian realm whether it is sensible or not. That's how Bruno got burned.
There's no objective limit in nature.
Nothing that exclaims the boundaries of objects or events. Everything is object One and Infinitely many.
I won't recommend Hegel and Augustin when you are reading Zeno's paradox in introductory book
I would recommend Russell. That is what introductory philosopher is. I'll rather recommend whole Benacerraf&Putnam's philosophy of mathematics because not only they care about mathematics but also that is more easier than Hegel and Augustine
>when you are reading Zeno's paradox in introductory book
It was a cut through the entirety of philosophy, and I've read it whole already. I will take your advice though.
>Yeah, but why wouldn't you be able to? Nothing about that resolution of the question seems to pop out for me as intuitive. Math shit aside, it feels like they are bruteforcing a certain view of the problem, like trying to fit in a screw with a hammer, which is what creates the paradox in the first place.
The Paradox creates itself, they are as confused as we are. Although such abstract ideas are reserved for the "it doesn't matter except that we are curious" table of armchair philosophy. No one ever took it too seriously, but they found what they did and you can't deny it from the perspective that you can cut time. Though we do have answers just not in the same system.
Just know that it is literally true and it is your practical intuitive that denies it (as with everyone's) which is not wrong.
>Alright, I'll check out something on what you said about Hegelianism and the Augustinian thing, then come back to this later.
>Thanks user.
Hey wait a second there cowboy, it's going to take a little while to get a basic understanding of Hegel and maybe just a quick few flicks of Augustine on time but there is no specific conjunction of the two. I just found they worked quite well and found answers to certain philosophical ideas.
>Hey wait a second there cowboy
It does not matter, I need some direction in which to further study anyway, best to do it with a topic that interests me rather than some Yea Forums blanket "muh greeks" that others would provide. Again, thank you for your time.
Time is in creation; creation is not in time. Consider the mind to have access to a 'toolbox' that orders things 'in time' and 'in space' in our head. Plurality and multiplicity are only percieved but not real in and on themselves.
I did not know this, but at least it makes Aristotles refutation more coherent
Your welcome user, but seriously the Greeks are amazing specifically the Socratics. Read The Republic, then Plato Five Dialogues, then Symposium. And I think you will want to continue with Plato.
god you spliced together a lot of wrong shit in those several sentences
you've demonstrated you know jack shit about mathematics so just avoid using it in your arguments all together
The argument is important for Aristotle because it helps justify the act/potency distinction. The distinction between actuality and potentiality is necessary to do science as we know it. If Zeno is correct, then we couldn't trust the senses which tell us that change occurs and this would invalidate all observational and experimental evidence.
Zeno's paradox is not a mathematical problem, yet a lot of people attempt to solve it using infinite series converging to point B hence proving that it is mathematically possible to overtake the turtle/reach the point. What I am saying is that EVEN IF you want to take a mathematical aproach to a philosophical question regarding divisiblity of reality, you can still not solve pic related with convergent series, as you would arrive at 0 hence proving that the object will not move at all.
I don't see where I go in the wrong with my mathematics
>Zeno's paradox is not a mathematical problem
This. Its more about the idea of infinity we have
>what's the point of a thought experiment devised to make You think about the nature of space, movement and the faulty nature of any attempt to model them which forgets that It's only a model?
An infinitely small distance will be passed in an infinitely small amount of time. It's not that there's no movement, but rather that movement happens so quickly that to the unobserving, uncareful philosopher it could seem as if bodies were teleporting from spot to another.
Sum 1/(2^n) for n=1 to infinity equals 1, not 0.
How could it be zero if the very first term of the sum is 1/2 and all other terms are positive?
You're an idiot, kys.
It's an extremely subtle and mysterious set of paradoxes. One of the best writers on it is Russell but don't tell anyone I said that because Russell is a massive twat.
That series doesn't converge to zero you absolute fucking retard. This is high school math.
fpbp
>space in an abstract form is infinitely divisible
>yet we still move
this is the whole schtick
This, desu. It converges to the point B you're going towards.
He obviously means sequence you mongoloid
THe planck instant solved this.
SCIENCE 1, foolosophy 0
If you accept the identity as the first and universal
law of thought, you cannot explain or allow that thought could
conceptualise movement. Intrinsic dynamism is alien to the
constitution of our thought, for every time thought thinks of
movement, of an object moving, this precipitates in the identity of
being, necessary for thought to think of that object. Thought for the
impossibility to be nothing but self-identical, cannot mimic and so
really understand movement. Movement as a sort of hegelian
synthesis of two positions A and B in which thought thinks of an
object at different times is incompatible with the logic of the
identity. It is in fact this excluded middle, this no-man’s land
between two identities, the "space and time" where change and
movement must be placed. But, in fact, the logic of the identity
excludes this middle from what is rationally thinkable.
How does keep taking halves of halves not converge to zero?? 1/2 -> 1/4 -> 1/8 -> 1/16 -> ... -> 1/(2^inf) ~= 0
I probably do, my English is mediocre at best
Only in the paradox where one goes from point A (lets say 0) to point B (lets say 1) by going half of the distance to go at a time. This gives the sum 1/2 + 1/4 + 1/8 + ... which eventually converges to B (in this case 1)
However in the case explained here it does not for we are here trying to find 'how large' the first step we will take is, but it is infinitely small so we never would be able to take that first step at all ( the paradox were we try to find the last (infinitely small) step, which we can 'skip' because of convegence of infinite series)
Yeah there's a series associated to every sequence and it's usually thought of as the infinite sum of the sequence, but it's obvious you just mean the limit of the sequence. He's an autistic pedant
Yes, or using substraction since we're basically working from B to A in this case: 1 + SUM(-1/2^n n=1->inf)
Zeno’s paradox only makes any sense if you believe that mathematical constructs are constitutive of reality rather than epiphenomena. You can reach the turtle, but at no point do you “halve” the distance because “half” doesn’t exist outside of our minds. You never physically move half the distance, as there is no object which represents the value of “half” outside of mental invention, ergo Zeno’s paradox cannot apply to physical movement.
gay
I think people make it much more complicated than it needs to be. If the space between A and B can be divided an infinite amount of times then movement from A to B wouldn't be possible. Aristotle recognized that the infinite amount of division between A and B is only there virtually or potentially and not actually, and this makes actual movement from A to B possible.
Also: infinity doesn’t exist.
You have the ability to imagine infinity, but it is mere epiphenomenon. An objectively finite measure of space and matter exist. There is nothing — absolutely nothing — in reality which can be considered infinite. Those mathematics which rely on an infinite set or, worse, multiple infinite sets, are incorrect insofar as they can only possibly be applied to epiphenomena and any ontic application is doomed to be incorrect because no infinite sets of space or matter (things which exist) actually exists. As a result Zeno has given us an impossible task not of catching the turtle, but of physically engaging with epiphenomenal constructs.
>If the space between A and B can be divided an infinite amount of times then movement from A to B wouldn't be possible.
Pathetic post.
Its literally that Zeno was a brainlet pyrrhonist and he wasn't even aware of it.
>If the space between A and B can be divided an infinite amount of times then movement from A to B wouldn't be possible.
Bullshit.
There is infinitely many real numbers between 2 and 3, but the difference "3 minus 2" is still finite.
Windelband talks about the Achilles/tortoise paradox somewhere in his history to Greek philosophy as an example of the Eleatic tendency not to distinguish between reality and talk about reality, and consequently to derive metaphysical conclusions (specifically monism) from paradoxes in our language. He situates this analysis in a discussion of how the Eleatics and Heraclitus, respectively, are the two extremes of the central Greek problematic of the 5th century (though Heraclitus was born in the 6th): the problem of reconciling being and becoming. Both being and becoming are apparent or "given" in our experience. We want to say that both permanence or stability "is," and that impermanence, change, etc., "is." But the radical expression of one or the other precludes its opposite.
The upshot of Zeno's writings is that becoming is only apparent. Reality, revealed by irrefutable logical demonstrations, is being. There can be no change, no motion, no reversal, no novelty, etc. This is the Eleatic position.
A modern reading of the problem is trivial by comparison, and follows statements already explicit or implicit in Plato and Aristotle. Morris Kline casually references it in his history of mathematics. Essentially it's the problem of two different ways of conceiving motion that don't play nice together. Wittgenstein would say it's two different "language games" with incommensurable rules. One way of talking about motion depicts motion as continuous, which we can obviously easily envision. Picture someone pushing an object across the table. That's continuous motion. The other way of talking about motion is discrete leaps from fixed positions to other fixed positions. The problem comes in when you try to combine the two ways of visualising movement, in a single picture in your mind's eye. You simply can't do that.
The problem for the Eleatics is that they assumed language mirrored the world transparently and evenly. They wouldn't have understood the conception of different "language games" in conflict with one another, different ways of visualising a phenomenon that don't ultimately harmonise with each other in a single intuition. So they took the fact that continuous motion can be conceived as infinitely approaching but never reaching an end point by means of smaller and smaller discrete leaps as a metaphysical proof that motion of any kind can never be completed. Zeno's arguments weren't entirely serious or attempts at utterly rigorous proof. They were more like a series of reflections to lead you to the truth. It was common to collect all the "sorta-proofs" or semi-proofs or demonstrations that led to certain insights at the time, for example in mathematical treatises. Today we have different conceptions of what a proof is, but back then they had a kind of everything and the kitchen sink mentality, especially since these things would be discussed openly and written down more as guidebooks to further discussion than as the systematic final word on anything.
If you think the Eleatic confusing of thought and reality is naive, just think about how common it is to think that calculus solves Zeno's paradox. Calculus essentially gives infinitesimal slices of the area under a curve. It's basically a way of squaring the circle, a problem closely related to Zeno's paradox that the Greeks also obsessed over. But it's not ACTUALLY squaring the circle, not in the way in which that is meant (i.e., in the language game the original quest to square the circle originated from). Superadded notions of "logical equivalence" of an infinitesimal series of slices of a circle to a really squared circle don't negate the fundamental fact that it's impossible to intuit continuous and discrete motion in the same moment. Infinitesimally calculating the area under a curve is not the same as actually making any given rectilinear slice equal to that curve.
Just take a limit LMAO
Like just execute an infinite number of actions in finite time HAHAH
The point of that paradox is to prove that assuming space and time to be continuous leads to contradictions.
Zeno apparently wanted to prove the counterintuitive thesis that movement is not real, but the best way to solve the paradox is simply to assume that space and time are discrete rather than continuous. There is a smallest unit of time and a smallest unit of space, and movement simply means that after a unit of time has elapsed your position in space has shifted by a certain amount of units of space (how many units of space shift in a unit of time determines your speed). So movement is most likely a discrete process where matter just "jumps" from one position to the next; these jumps are small enough that they appear to us as a continuous process, just like a movie appears to us as a continuous process even though a movie is just made up of small "jumps" (the frames per second).
>Like just execute an infinite number of actions in finite time HAHAH
Ok, I will then. Loving every lel where philosotards assume something is impossible because... uh... well... it just doesn't feeeeeeeeeeeeeel right. Right? That's why you typed up that post.
None of what you just posted means that there can't be an infinite set of infinitesimal movements producing the same result.
do you understand that everything you say amounts to incoherent babble unless you try and back it up with reasoned argument?
What reasoned argument? You literally proposed that movement HAS to have discrete jumps to exist, and you can't have infinitesimal distances within infinitesimal times summing up to the macro movement. But nobody ever elaborates on why, except by shitfting the argument to some other bullshit.
I tried to get your points but I only got to 1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256+1/512+1/1024+1/2048 and then I gave up, sorry.
you need more RAM
limit is just a pseud "fuck this shit I will take the approximate value" thing mathematicians use
>Infinitesimally calculating the area under a curve is not the same as actually making any given rectilinear slice equal to that curve.
That's an interesting perspective. You can't actually produce a rectilinear figure equal to the circle even though you can calculate the circle's area with calculus because you can't find the exact position of Pi on your ruler. Calculus gives you an arithmetical solution to the problem of squaring the circle (the numerical value, which involves a trascendent irrational number), whereas the Greeks were looking for an actual geometric construction of the squared circle itself. They did find some solutions involving mechanical instruments, but they wished to find a solution which could carry out the desired construction with compass and straightedge alone (which apparently turned out to be impossible according to the results of modern algebra). The way in which modern people usually think of the problem of squaring the circle is very much anachronistic and is probably due to the paradigm shift caused by Descartes with the invention of analytic geometry, which made arithmetic the foremost branch of mathematics whereas for the Greeks it was synthetic geometry. Thus modern people think of "squaring the circle" as an arithmetic problem of finding the numerical value of the area, whereas for classical Greek geometry it was a problem of finding an effective construction.
the entire point of constructing the notion of a limit is to avoid having to deal with inifinesimal distances
it's an artificial concept standing solely on its rigorous definition to be used in math, you can't just plug it into your philosophical problem and claim something follows from it
I got more than enough to ram inside you, dear ;^)
based reply
everyone else is pants on head retarded
I rammed your mother's board last night
>Taking the limit of this sum, you will find it to be zero
The limit is 1
>pseud
Why do you use this word?
>one line is made of infinite dots
>one dot has zero length
>zero times infinite equals a line
???
Aristotle was kind of right though. You can infinitely divide numbers, there's no limit because they're just an abstraction. So in a theoretical "ideal" sense this is true, but in the material world, things can't be divided infinitely. There are limits (Planck length comes to mind), and at some point you can't divide the thing further.
Also, these ideas predate more theoretical math that gets nitty gritty about this shit by a long time. Its easy to be dismissive of some of them now, but try to think of it from the perspective of an ancient Greek citizen. What they knew and didn't know, their culture, etc.
>You literally proposed that movement HAS to have discrete jumps to exist
I never said that. I only said that assuming movement to be discrete is the best way to solve the paradox, in my opinion.
>and you can't have infinitesimal distances within infinitesimal times summing up to the macro movement
Assuming the continuity of space is just too problematic. When Cantor proved that there is a one-to-one correspondence between the interior of a square and one of its sides he allegedly said: "I proved this, but I do not believe it". As science moves forward, we come more and more to the conclusion that everything in physics is ultimately discrete. Think about atoms and molecules: some ancient thinkers believed that matter was infinitely divisible, so that you could take a stick of wood and divide in half, then halve it again, and again, ad infinitum. But we know nowadays that after a certain amount of divisions the stick would no longer be wood, because you would break down the molecules that make it wood. So a quantitative change (divison in half) can lead to a qualitative change (losing the propriety of being wood). So the hypothesis that any kind of matter has intrinsic properties and it can be infinitely divided without losing those properties is no longer tenable.
Yup exactly, great post. Ever watched Wildberger's lectures on Ancient Greek math? I'm not in his cult or anything, I just think he does some neat reconstructions of how the Greeks actually approached Euclid and conic sections. You'd really like Morris Kline's approach to the history of math - he also perceives this massive shift over to a mathematical-over-geometrical approach in the early modern period, just as you say, and he thinks in modern formal mathematics it leads to badly mistaken preconceptions and hypostatizations of mathematical entities (a bit like Wildberger hates set theory and shit). You'd like E.A. Burtt, he shows the mathematization of nature. Funkenstein too, Theology and Modern Science.
Some of this stuff dovetails with the crisis of foundations in the late 19th century too. What does it mean to "think" (intuit?) an irrational? What does it mean to think/intuit the truth of some logical/mathematical deduction at all, and how does that relate to our "certain" intuitions (if we even have any?) of fundamental arithmetical/geometrical ground-concepts.
>what is calculus
Sum of this series obviously equal to 1. It's geometric progression after all.
>Ever watched Wildberger's lectures on Ancient Greek math?
No, I don't know much about that guy, besides the memes on /sci/. I heard he started off by trying to rebuild trigonometry on a rational basis and the whole thing snowballed into a critique of modern mathematics. It might be philosophically interesting, but I doubt he will ever find a wide audience for his ideas. The working mathematician does not care about the ontological status of real numbers: the continuum is simply the best way to create models of many phenomena which might very well be discrete in nature, but their discrete structure is so small from our perspective that we might as well think of them as continuous. In other words real numbers are an useful approximation, and engineers will never accept to relearn mathematics on a more sound metaphysical basis if they can get reasonable accurate results with ordinary modern math.
>this massive shift over to a mathematical-over-geometrical approach in the early modern period
I think with the advent of digital computers we are witnessing a new paradigm shift towards numerical methods, which in some way tacitly undermines any assumption about continuity. The Greeks glorified the synthetic methods and regarded geometry as foremost; the early moderns made use od analytic methods and enshrined algebra and calculus as their fundamental sciences; nowadays numerical methods are all the rage and the computer algorithm is the holy grail of any practical application of mathematics. There is a sense of defeat in the willingness with which we accept any numerical methods so long as it "works"; we no longer care about reality. We gave up the concrete constructions of the Greeks when we embraced the equations of Descartes that did double duty as curves; and now we've given up the analysis of those euqations in favor of brute-force calculations carried out by ever faster machines.
The paradox has been explained and resolved by max planck, cantor and Russel 100 times over, most people just dont get the discreteness of space and time because it is not intuitive
ask /sci/ what the sum of series (1/n^2)-1 is
>There are limits (Planck length comes to mind)
Planck length only refers to the smallest possible MEASURABLE distance
>reality is strictly material
Because we successfully turned it into a synonym for stupid, retard
Well if we're gonna just be sitting around talking about how shit magically moves for math reasons we have yet to properly discover may as well just regress into jerking ourselves off to Kant's theory of cognition
cringe
and by magical I mean insanely unintuitive
dilate
>As science moves forward, we come more and more to the conclusion that everything in physics is ultimately discrete.
What the fuck are you talking about? That's the opposite of what is going on. Don't fucking tell me they haven't told you about fields in general in elementary school, or that you never investigated further. Did you seriously end at "quarks and other subatomic particles are indivisiable"? Here's some random result I get when typing in "quantum field of a particle" into google. I took this off the first page:
damtp.cam.ac.uk
"According to our best laws of physics, the fundamental building blocks of Nature are not discrete particles at all. Instead they are continuous fluid-like substances, spread throughout all of space. We call these objects fields."
This is really the problem here. Philosophy makes arguments with its feet on the floor of natural sciences, and tries to explain the empirical with non-empirical. The meaning of that is far from "I get to make shit up". Like you did right there. You fucking bellend.
>I would recommend Russell
Opinion discarded
Neither Achilles or the Turtle are ever in one place, but superpositioned, we always vibrate a few planck lengths constantly, therefore we transition to the next section while stil partially being in the previous one. Everything flows.
Whoops meant to post this picture
youtu.be
