Re: infinity

Stephen wrote:

> Gordon Collins <poste...@xxxxxxxxxxx> wrote:
>> Stephen wrote:
>>> What explanation would you accept?
>> One that /shows/ the completion of an infinite iterated (i.e.,
>> discrete) procedure would do.
>
> I do not know what that means.

An infinite iterated procedure is the same thing as an algorithm, with
one exception: an algorithm terminates after a finite number of steps.
An infinite iterated procedure does not terminate. It is not to be
confused with a sequence as commonly understood - that is a static
object.


> That is a mathematically sensible way to model the problem.
> There is no last step, so any attempt to talk about what
> happens at the last step is mathematically absurd.

There are no steps /at all/ in this model of the problem. Look, I KNOW
there's no last step - I'm the one who insists that that has
implications! But I'm not talking about steps here, and I'm not
talking about vases or balls in the rest of the post - I'm talking
about a different idea.


> Just because you define a sequence of times that all occur
> before noon it does not mean noon ceases to exist. Just
> as the sequence 1/2, 3/4, 7/8, etc. does not cause 1 to cease
> to exist. Claiming that you cannot reach noon sounds like
> you are claiming that noon somehow no longer exists.

I haven't said anything about whether or not noon exists. There is a
difference between /existence/ along the number line and smooth
/movement/ along that line. There is apparently no mathematical way to
deal with the latter.

As I tried to say, just defining a sequence is not what keeps you from
reaching a particular moment in time. I had said that that results
from following a certain kind of timed infinite iterated procedure, but
on second thought, it's not the infinitude of the tasks that bogs
things down, it's the infinitude of the precision demanded of time. A
process with 3 steps that are to be done at times 1, Pi, and 4 will
require infinite degree of precision, requiring time to be continuous,
not discrete, and thus creating the same morass if its continuum is of
the same type as that of the reals.


> I do not see how you can claim that you do not pass an infinite
> number of points when travelling from 0 to 10 and also
> claim that space and motion are continuous.

It is easy when the continuum is not composed of points!


> I said nothing about moving from point to point in succession.

If space is composed of points and nothing else, that is what movement
/is/.


> If space is continuous, there are no consecutive points. However
> you still have to pass an infinite number of points to move
> from one location to another,

I don't see how I am to do that without moving from point to point in
succession. I don't think you mean that I pass all of them
simultaneously.

Gordon

.

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