So in reaching B from A the object has completed occupying infinitely many locations in succession. — Michael
Yes... however the time it needed to travel between those infinitesimally small distances is infinitesimally short as well. — Svizec
Since I find this patently absurd — aletheist
In the end, objects actually move finite distances in finite times, and that is what we can and do observe and measure.
The problem is that the logic of discrete motion is incoherent, hence motion isn't discrete. — aletheist
Motion is logically impossible but physically actual. And so the first of MadFool's suggestions seems correct; our logic is faulty. — Michael
I have, with my example of a machine that counts each coordinate as it passes through them in order. — Michael
As I said, as long as you persist in conflating ordering with counting, your argument won't get off the ground. It's simply not logical, because there is no logical requirement for counting here. — SophistiCat
Either space is infinitely divisible or it is not. Whether anyone can actually divide space into infinitely many parts is completely irrelevant - only whether it could potentially be divided into infinitely many parts. — aletheist
Only the motion from one actual location (i.e., arbitrarily defined coordinate) to the next is a discrete event. We can only define a finite number of distance coordinates, so we can only measure motion in discrete units. — aletheist
Well, it's only that something like this must happen if motion is to be possible.
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There are a finite number of coordinates for the object to pass through, "jumping" from one point to the next without passing through the space in between. — Michael
How can something "jump" from one discrete location to another without ever occupying the space in between? This is pure nonsense to me. — aletheist
I don't know why you're comparing counting to ordering. — Michael
The comparison is between counting and moving. And as explained here, there's no reason to suggest that they're fundamentally different. — Michael
Because I was responding to your own line of argument, e.g. here. — SophistiCat
You haven't argued that moving is somehow related to counting, you just imagined some impossible contraption and asserted without any argument that continuous motion necessarily involves something of the sort.
You seem to just be misunderstanding. What I'm trying to say there is that you can't answer the question "if we want to count every rational number between 1 and 2, what number do we count first?" with "pick any at random, and then pick the next one at random, and so on" (as Banno suggested). Each number must be greater than the previous, and we can't count a number if we haven't counted a smaller number.
And so by the same token, each coordinate an object passes through must be closer to the target than the previous, and it can't pass through a coordinate if it hasn't passed through one that's further away. — Michael
each coordinate an object passes through must be closer to the target than the previous, and it can't pass through a coordinate if it hasn't passed through one that's further away.
I'm saying that the act of moving from one location to another can be considered an act of counting, like a clock counting the hours as the hand performs a rotation. — Michael
Counting is just a physical act like any other. I don't know what you think it is. — Michael
Yes, this nicely illustrates the very confusion that I've been talking about.
True enough, but this has nothing to do with counting. — SophistiCat
You are saying this, but you are not proving this. — SophistiCat
True, but that doesn't imply that all physical acts involve counting.
You're still making the same mistake. It is false to say that space is potentially infinitely divisible unless it actually is. — Metaphysician Undercover
This indicates that you have a deep misunderstanding of the concept of "potential". — Metaphysician Undercover
You're still making the same mistake. It is false to say that space is potentially infinitely divisible only if it actually is. — aletheist
While it is the fundamental nature of a continuum to be undivided, it is nevertheless generally (although not invariably) held that any continuum admits of repeated or successive division without limit. This means that the process of dividing it into ever smaller parts will never terminate in an indivisible or an atom—that is, a part which, lacking proper parts itself, cannot be further divided. In a word, continua are divisible without limit or infinitely divisible.
The point is that, as with the example of a clock hand, the very act of moving from one point to another can be considered to be an act of counting. — Michael
You're still making the same mistake. It is false to say that space is potentially infinitely divisible only if it actually is. — aletheist
Space is actually infinitely divisible and potentially infinitely divided. — Michael
This is exactly the question brought up by the op. Is space actually infinitely divisible, or is this just a false assumption, a mistaken theory? — Metaphysician Undercover
You seem to be confusing "infinite divisibility" and "infinitely divided". — Michael
Space is actually infinitely divisible and potentially infinitely divided. — Michael
You believe that something is possible (potentially doable) though it is actually impossible to do it. — Metaphysician Undercover
I'm saying that the act of moving from one location to another can be considered an act of counting, like a clock counting the hours as the hand performs a rotation. Counting is just a physical act like any other. I don't know what you think it is. — Michael
You can move "through" any number of uncountable points — Svizec
This is the assumption that I'm showing to be false. — Michael
Each movement from one point to the next is a tick. — Michael
No one is talking about doing anything. To say that something is infinitely divisible does not mean that a human being is actually capable of infinitely dividing it. It means that it is possible in principle to divide it infinitely. — aletheist
No this is a misunderstanding; the moving object does not have to 'account for and check off' every point it moves through, not least because it does not actually move through any points. — John
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