Zeno's Paradoxes (is motion possible?)

I'm confused.

Can you help me understand, why is motion impossible?

@twincams

division is proportionate to the infinite inversly, therefore, your proposition is inverse, asuming the aforementioned is correct, then 1/infinity = infinity/1, infinately.

where 1 = n

ps. i think i agree with you

Looks like this would only be true if you were only allowed to cross half the distance at a time.

If Zeno were here...I guess I could deal with his supposed paradox by offering a challenge.

A bet of a sort.

Let him stand 10 paces from me...and I will shoot an arrow at him.

If his paradox is correct...he'll be fine...and I'll pay him an agreed upon sum.

If my arrow gets to him...and in fact goes through him. despite his paradox...I get a like sum from his estate.


Think he'd take the bet?

because to achieve just 1 step, you have to travel a finite distance, which is infinitely divisible, which means it cannot be traversed in a finite time!

infinitely divisible distance, infinitely many intervals in a finite time duration.. No contradiction here.

I haven't given an opinion yet, merely asking for input :wink:

There are obvious flaws in Zeno's first paradox... can anybody point them out??

As the distance covered with each step gets smaller, so, too, does the duration of time that it takes to cover it. These are proportionate to each other and cancel out.

There are many traps in the concepts of "infinity." Zeno has noticed hints of the difficulty in the concepts of infinity.
In moder mathematics, there are no contradictions in the form of Zeno's paradox. (Russels paradox talks about totally different problems.) But in modern physics infinite divisibility of timespace or other quantities is put into a question (as theories are "quantumized").

Correct! the sum of all these infinite parts is always = 1 x the finite given distance and the sum of the relative infinite periods of time, must also = 1 x the finite given time... BUT, our defence of logical thinking can be turned around using simple physics...

Aristotle reports the first paradox, known as the Dichotomy in one brief line:

[It is] . . . the one about a thing's not moving because what is traveling must arrive at the half-way point before the end (Physics 239 b 9-14).

The paradox is reconstructed as follows.

The Dichotomized Line

Suppose an object, A, is required to move from S to F. In order to get to F, A must first arrive at the halfway point M. Having reached M, A has now to travel from M to F. Before it can get to F from M, it must first arrive at M', which is halfway between M and F. This continues indefinitely, since the distance between S and F is infinitely divisible. In order to reach F from S, A must pass through the infinite sequence of points M, M', M", . . . etc. Passing through an infinite sequence of points, however, involves completing an infinite number of tasks (i.e., first A arrives at M, then A arrives at M', then

. . .). But, an infinite number of tasks cannot be completed. Therefore, A cannot move from S to F.

Zeno's basic argument can be formalized as follows:

(1) If anything moves from one place to another, then it

performs infinitely many tasks.

(2) Nothing can perform infinitely many tasks.

Therefore,

(3) Nothing moves. (adapted from Barnes, 1979 I, 263)

The argument, as it stands, is valid, i.e., the conclusion must be true, if both premises are true. Given that we are unpersuaded by Parmenidean monism, we reject the conclusion as false. It follows that at least one of the two premises must be false.

One might want to reject the first premise on the grounds that moving from S to F over a distance L is one task, not many, let alone infinitely many. There is some justice to this. However, the fact is that the interval can be divided as many times as one wishes. A could, in fact, stop anywhere along the route. Thus, it seems arbitrary to deny that infinitely many tasks are performed (cf. Barnes, 1979 I, 263f.).

Given that we are prepared to accept (1), we must reject (2), if we are to deny the conclusion. Aristotle's initial remarks on the Dichotomy are, in effect, an attack on the second premise. Aristotle says

Zeno's argument assumes a falsehood--that one cannot pass through an unlimited number of things or touch an unlimited number of things individually in a finite time. For both length and time--and, in general, whatever is continuous--are called unlimited in two ways: either by division or as to their extremes. Now one cannot touch things unlimited in respect of quantity in a limited time, but one can touch things unlimited by division--for the time itself is unlimited in this way. (Physics 233a, 21-31; from Barnes 261-2).

Any rebuttal??

This premise can be "assumed" away from the beginning. Until any further (think backward) contradiction is found, infinite procedures are "assumed" to be performed in principle..

They solved this already. Eventually the infinite decimal numbers will end up when added together to 1.

As we say in the real world... assumption is the mother of all f*ck ups
Let us deal with facts and laws of physics

As I have said earlier in this thread, physics already has thrown away the infinite divisibility. Mathematics does not necessarily deal with the actual world.

Ok, so we've established that Zeno was a blithering idiot, so... what conclusions did Albert Einstein and Mileva Maric draw from Zeno's 'paradoxes', how did their findings relate to the theory of special relativity and why did this theory conflict with Newton't laws?

Good day to ya all,

Zeno eh?Part of the Eleatic bunch of losers.Which was a pagan equivalent of our modern day philosophy schools and as such specialised in sitting on it's collective backside discussing unanswerable conundrums being waited on hand and foot by slaves and other low caste manual workers such as myself.It is a well known principle that manual work is low caste precisely because it was associated with slaves.Waste is therefore closely linked with superiority.It will all be corrected due to the exigencies of global shiteheaps
when the problem of inferiority complexes is addressed.It will have to be.Otherwise our lovely grandchildren will be exclusively engaged in a mass clean up operation.
The Eleatics (Zeno of Elea,Parmenides and Melissus) rejected sense experience as a way of finding truth.They would have been in their element on this thread.The usual method was the
"reductio ad absurdum" principle which is in modern day use in the member profile of Spendius.
Their positive contribution was to improve methods of reasoning.A barmy idea can often result in fruitful research as Euclid showed.
In Classical times,pagan times,it was proscribed to discuss publicly the difference between the "become" and the "becoming".The former being static and the latter in motion.Also proscribed were considerations of the infinite and the infinitesimal and the exposure of the details of the Eleusian mysteries which I will leave for Lola to explain.
The paradoxes concerning the nature of motion were therefore unsolvable.cf-Ency.Brit.,X1ed.,Article Zeno of Elea.
Nature to us is in constant motion in every respect.
It is past becoming future and is only static as a time period tends to zero.Or is zero.
This is the reason why the Greek culture was unable to discover the infinitesimal calculus and as a consequence it's mathematics came to an end and with it the culture.Oswald Spengler,so far as I understand him,considered our mathematics to have reached a similar state and from that he predicts the Decline of the West.Mahler's Song of the Earth is the most famous funeral march accompanying this decline which many artists feel to be unstoppable.Mathematics may find new areas of progress in space which might explain why we devote time and effort to it.
It boils down to the question of whether you are "Greek" or "Faustian".The Faustian project is the Christian project and every aspect of our daily existence is derived from it and conditioned by it.
Non Christians,I'm afraid,are excess baggage and are exceedingly fortunate that we can afford to indulge their narcissistic naivety.Non Christians reach for the simplest and most selfish satisfactions and Faustians reach for the sky.It is possible to be neither and be a well evolved microbe instead and just spectate it all with a glaze of disinterested indifference from inside the niche provided.To be Born In Time.(cue song).

spendius.

The words "pot", "kettle", and "black" all come to mind.

Re: Zeno's Paradoxes (is motion possible?)


Sounds like Zeno needs to stop confusing the English language with his own confused use of language.