I'm saying no more than that your description does not work. — Banno
Sounds odd. It's a bit like saying that since there is no highest number to count to, I can't ride a bike. How does one have any effect on the other? — Luke
But there is a first position to pass through, regardless of whether you can calculate it. — Luke
You (and Zeno) derive the impossibility of motion via the infinite divisibility of space, but space is not motion; position is not momentum. — Luke
Thinking about this leads me to what I think is a fairly precise mathematical statement of the controversial assumption that Zeno's argument makes. It is this:If I want to count in order the 1/(2n) numbers between 0 and 1, which is the first number I count? If I want to move from 0m to 1m which is the first 1/(2n)m distance I pass through? There isn't one, and if there isn't a first step the task cannot start. — Michael
Does this part of the article answer your objection? — Walter Pound
I agree with the first point. For the second point, we need to be careful about what we mean by 'sequentially'. If we mean that we pass through x before y iff x<y then there's no problem. If we take a different meaning of 'sequentially' I suspect we are going to get another dubious, controversial assumption.Because if space is infinitely divisible then there exists such a subset and if motion is continuous then it must pass through each member sequentially — Michael
Proving that there is no smallest will do it. Like this: Assume there is a smallest, call it x. Then x must equal 2^-M for some M. But 2^-(M+1) is less than that and is also in S, which contradicts our assumption that x was the smallest. Hence there can be no smallest.How exactly could one show that one can’t start counting each rational number between 0 and 1 from smallest to largest? — Michael
The single act of passing all members of S is the single act of traversing track Y from A to B. In doing so, object O will pass each member, in order. The act starts at time 0 with object O at location A.if there is no smallest then the act of passing each member cannot start — Michael
When I imagine zeno's paradox, I tend to imagine an arrow travelling for a bit and then I stop it momentarily in my imagination and say to myself "This is now the arrow's position. Now how did it get here?". But of course I am not allowed to mentally stop the arrow from moving, for I would no longer thinking of a moving arrow.
Is it even possible to imagine a moving object that has a precise velocity and/or position? Personally I don't think so. I always find myself either fantasising that I have mentally stopped the arrow in order to measure it's position, or that I am entirely ignoring it's position when thinking about it's motion. — sime
But there is a first position to pass through, regardless of whether you can calculate it. — Luke
The single act of passing all members of S is the single act of traversing track Y from A to B. In doing so, object O will pass each member, in order. — andrewk
I chose to use the word 'passing' rather than 'counting', with intent. There is a critical difference between 'counting' and 'passing'.But this is just like saying that the single act of counting all members of S is the single act of counting the rationals from 0 to 1. — Michael
It is the insistence that the points must not only be Passed In Order, but also Counted In Order — andrewk
'Sequential' is the problem word here. I would say that passing in order is not sequential, because the events are not sequential if we use the usual meaning of being in order-preserving bijection with the natural numbers.I’m saying that passing in order is a sequential series of events with no start and so cannot be started. — Michael
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