Please define your terms and assumptions. What is "time"? What is a "moment"? Why do you think that "infinite time between any two moments" is impossible?

Probably the best model for time is that it is quantised.

The shortest unit of time perhaps being the 'Planck time' .. some 10**-43 seconds if I recall correctly.

Is it not equally impossible for every two points on a line to have distance between them, because it would result in infinite distance between any two points?

Yes, it is equally impossible, which is to say it's not impossible, because that doesn't happen. Any two points on a line have distance between them, because if they didn't they would just be the same point. But those distances can get arbitrarily small, so you can add a point any two points on a line and still have only finite distance between all of the points, then add more points in between those and still have only finite distance between them all, because the distances in question just get smaller and smaller the more you do that. There are infinitely many points on the real number line between 0 and 1, but not an infinite distance between 0 and 1. The same applies to points in time as to points in space.

That's assuming an abstract idealized continuous space and time, of course. Real space and time are probably quantized, as Seagull says, though the details of that are still up in the air awaiting a theory of quantum gravity.

The shortest unit of time perhaps being the 'Planck time' .. some 10**-43 seconds if I recall correctly.

Time is a moment. There is no such a thing as a fraction of a moment. Suppose someone claims that there is. Suppose they say, that there is a moment, then half a moment, then a full moment. He is saying, we have one moment + half a moment + half a moment = two moments. But in actuality, we have a moment, then this moment we call half a moment, then this moment he called a full moment. So that means, there were three moments. So, a fraction of a moment cannot exist. The smallest number of moments is one.

What is "time"? What is a "moment"?

It is very hard to define time or moment.

"infinite time between any two moments" is impossible?

Suppose we have moment called A and a moment called B. There are infinite moments between them. For moment A to become non-existent and a different moment called B to become existent, infinite moments have to become existent and non-existent one after another.

The best definition of time that I know of..and I think it is Einstein's is:
Time is what a clock measures.

Hello everyone,

This discussion is about the time in between moments. It is impossible for every two moment to have time between it because It would result in infinite time between any two moments. — elucid

Maybe it's helpful to point out that you are assuming the time is like space. It's the usual metaphor, but philosophers have questioned it.

It belongs to the essence of perception not only that it has in view a punctual now and not only that it releases from its view something that has just been, while ‘still intending’ it in the original mode of ‘just-having-been’, but also that it passes over from now to now and, in anticipation, goes to meet the new now. The waking consciousness, the waking life, is a living-towards, a living that goes from the now towards the new now. — Husserl

https://plato.stanford.edu/entries/consciousness-temporal/#BerHusRusBro

Consider as you read this sentence that each new word shapes your interpretation of the previous words and your expectation of the words that will follow. The interpretation of this sentence too is a function of the one you just read and your general sense of what I'm getting at.

If what your OP is getting at is the continuity of time (not breakable into discrete nows), then perhaps my response will support your OP.

This discussion is about the time in between moments. — elucid

The error in your assumption is the fact that you forgot that "Time" is just a collection of "Moments", thinking as scales, Time is greater than the Moment, and can't be lessened as to put it between moments. In conclusion, "Time" is composed of infinite amounts of moments, but "Moment" is not and cannot be composed of Time.

i agree.

I have a problem. It begins with the way numbers are presented to us in school. The usual methods:

1. Set method: A given collection of items are used to convey what numbers mean. A set of three apples are counted beginning with 1 and ending in 3. This pattern is then applied to other sets and we get an understanding of what numbers mean.

2. Line number method: Here a line is used and distances from 0 are used to teach children what numbers mean.

Which of the two methods above maps on to time? It isn't the set method but rather the line number that's used to represent time. Before I venture further with my analysis or perhaps just a sorry attempt at analysis I'd like to say that a possible explanation may be found here.

My analysis:


Sets aren't used for time and a line number is preferred because time is believed to be a continuum and sets are inconvenient to work with when you want to talk of such things. A line number not only has a form that is continuous in appearance, it also represents distance which is a continuum.

However, the number 3 in a time measurement, say seconds, means nothing more than that 3 seconds have passed. People are in the habit of talking about moments/instances and this can only be understood in terms of saying something like the third second. A moment understood in this sense is more like a signpost on a road telling us how much time has elapsed. Just as a signpost isn't an actual distance any moment in time is NOT time at all.

My argument depends on the difference between ordinal and cardinal numbers. Just to add, I think this is one of the reasons why a line number is used to represent time since it's more amenable to showing ordinals, allowing us to depict an nth second/minute/hour/ etc, which is not as easy to convey with a set model.

If one wants to discuss moments in time we'd need to use ordinals and talk of the 1st, 16th, 23rd, nth, unit of time. However we must remember that the moment itself is NOT time which is by definition a, for lack of a better word, "gap" between moments. To think that a moment is time would be like saying that the location 3 cm on a scale is the distance 3 cm which is actually the spatial "gap" between 0 cm and 3 cm.

I agree that if time really is infinitely divisible then it does contain an infinite number of moments. This is exactly what a line number captures. However, as moments are only positions in time (ordinals) this doesn't matter. Time is actually the finite "gap" between moments. Why is the "gap" finite? Divide any given duration of time by any number of your choosing except zero and you'll always get a finite result. Ergo time is not infinite even though there are an infinite moments between any two positions of time.

Basically what I am saying is that Zeno has made a mistake when concluding that time does not exist and motion is impossible. Suppose, you have three apples. You take one, throw it in the basket, then the second one, then the third one. Now, suppose Zeno comes up and says that it is impossible for three apples to be in that basket, because for there to be three apples in the basket, first there must be one and a half, then 0.75, then 0.375, then 0.1875, and so on and so on. It's true, if you divide three apples in half, you would get one and a half, if you divide that, you would get 0.75, and so and so on. But, that is not the way the apples went into the basket. It went in one at a time.

Time being the quantity of moments, and a fraction of moments cannot be possible, means that the increase amount of time is one moment at a time.