The arrow can move because time is not made up of zero-sized instances/moments; instead time is essentially an interval and so, the arrow can move. — TheMadFool
Bergson already solved this paradox adequately in my view. — emancipate
Continuous motion is a more fundamental reality that discrete positions in space and discrete instants in time. — aletheist
The arrow indeed will pass all the Ms that we actually mark, but that will be a finite number. — aletheist
Quantification represents space and time accurately enough for most mathematical and practical purposes, but the mistake is thinking that this entails that space and time are really discrete, rather than continuous.With the paradox addressed in mind, this stance in turn implies that our conceptual quantification of space and time, as a mapping of the terrain, does not accurately represent that which is being mapped. — javra
No, this is a mistake in the other direction; the theory of relativity assumes that space and time are continuous, rather than discrete.Of note, with its possible philosophical interpretations here placed aside, the theory of relativity clearly indicates that space and time are not discrete but a continuum. — javra
I agree, and personally prefer the "growing block" theory of time in which the past and present exist, but not the future. For more on that, see my recent thread on "The Reality of Time."All the same, the quoted mindset with which I agree will also stand in opposition to the block-universe model of the world, wherein there can be no real motion (due to there being no real change). — javra
Yes, in my view a discrete position (or instant) is an abstraction that we impose when we mark it for some purpose, not a real constituent of space (or time). It certainly does not exist, since it does not react with anything.If we don’t mark a location, or else don’t think of a location, does that then mean that the location does not exist – this in contrast to those locations we do mark or think about which would thereby exist? — javra
Theoretically viewing a frozen instant of the arrow in flight does not destroy the momentum the arrow possesses at that instant. — jgill
I'm certain that Zeno's Arrow Paradox has been dealt with effectively i.e. a solution has been found; nevertheless, I'd like your views on my take of the paradox.
Zeno's arrow paradox basically states that, IF time can be considered as composed of instants, an arrow, being unable to move at any one instant since no time has elapsed for any motion to occur, too wouldn't be able to move. No motion at any instant; ergo, no motion at all.
It seems Zeno agrees that, if, for the arrow, one takes an non-zero interval of time, there can be motion; after all, that's why the great Zeno speaks of instants/moments. His argument would fail if we use time intervals because motion is possible if non-zero time is allowed.
The first problem Zeno faces is with the definition of the unit of time. Take the second for instance; whatever physical phenomenon is used to define the second, it is essentialy an interval and not an instant. This is probably the one big clue to what I'm about to say.
To illustrate my point, I would like you to take length for example, say in the units centimetere (cm). A ruler that measures length has length markings on it - begins at 0 cm and goes on to, suppose, 30 cm. The length markings on the ruler read off lengths which are intervals in space. Consider now, what a point on this ruler means? A point, by definition, has no size; being thus, a point can't be a length. Being zero cm in length is the same thing as not being length: zero apples are not apples :smile:
Now consider the notion of instants in time. Just as zero cm in length is not length and zero apples are not apples, zero seconds, instants/moments, isn't time at all. It seems, therefore, that time can't be considered as composed of size-zero instants for it's like saying zero cm is a length and we know that to say something has a length of zero cm is exactly the same as saying that thing has no length. Likewise when we speak of zero units of time, we're not talking about time anymore.
So, Zeno, by thinking zero-sized instants/moments as time is making the same mistake as someone who thinks zero apples are apples. The arrow can move because time is not made up of zero-sized instances/moments; instead time is essentially an interval and so, the arrow can move. — TheMadFool
Gotta love a great paradox!
But...
In a frozen universe where there was no movement, would time exist?
In this frozen timeless universe, should the archer release the arrow, then time would begin. It isn't 'time' which prevents the arrow from moving -- it is the motionless arrow that prevents time from passing.
There was no time before the Big Bang, and there will be no time again when (and if) the universe cools to absolute zero. — Bitter Crank
Those who say space is discrete or that the continuous doesn't apply to the real world are morons and I refuse to debate them anymore. — Gregory
I can imagine the arrow has its momentum during any duration of time however short, but at the point where no time passes? — tim wood
I agree. If for people who like to find this paradoxical in this modern age (and i have met some) find the idea of instant confusing, instead say "an interval so small that it has similarities to an instant". So we might say a 1/10,000th of a second. Then explain that with some stipulations we can make this very tiny interval the same effectiveness as the normal age old instant of time.
We can even attach wierd symbols to this very tiny interval and give it a latin name. And when people go to look up this latin name they'll see a detailed explanation that this very tiny time interval is really just a substitute for a instant in time for people in this modern age who like to make a mountain out of a mole hill.
Well thats what we philosophers do, we make a mountain out of a mole hill. — christian2017
I wouldn't say that the arrow paradox is something philosophers are making a mountain out of a molehill of. If Zeno is right, motion would be impossible and all that we see around us would be an illusion. Isn't that something to worry about?
As for infinitesimal calculus, I think it's a clever way around the problem of instantaneous velocity. — TheMadFool
Where would the heat have come from in a (presumably) empty universe, prior to the BB? — Bitter Crank
I agree. If for people who like to find this paradoxical in this modern age (and i have met some) find the idea of instant confusing, instead say "an interval so small that it has similarities to an instant". So we might say a 1/10,000th of a second. Then explain that with some stipulations we can make this very tiny interval the same effectiveness as the normal age old instant of time.
We can even attach wierd symbols to this very tiny interval and give it a latin name. And when people go to look up this latin name they'll see a detailed explanation that this very tiny time interval is really just a substitute for a instant in time for people in this modern age who like to make a mountain out of a mole hill.
Well thats what we philosophers do, we make a mountain out of a mole hill.
— christian2017
I wouldn't say that the arrow paradox is something philosophers are making a mountain out of a molehill of. If Zeno is right, motion would be impossible and all that we see around us would be an illusion. Isn't that something to worry about?
As for infinitesimal calculus, I think it's a clever way around the problem of instantaneous velocity. — TheMadFool
Time is not composed of instances. Time is relative change. Movement is relative.
An interval is simply a string of instances - each a particular snapshot of time in the mind. Instances and intervals only exist in minds. Time exists everywhere there is relative change. The mind breaks up time into instances, just like it breaks processes into objects. The mind is converting the analog signal of the world into binary bits - objects of thought (instances in time and objects in space). — Harry Hindu
Looks like movement is relative, whether relative to another object, or a point in space (a point in space seems to qualify as an object in space). The mind has this habit of quantifying (or objectifying) space/change.What do you mean by movement is relative? Time is relative in that is really an iteration of events, and is hard to accurately measure unless it is a small subset of the universe (special relativity). But two objects can pass through and gauge their velocity based on the same point in 3d space. Next thing you are going to tell me is two objects can't pass through the same "point" in 3d space. — christian2017
What do you mean by movement is relative? Time is relative in that is really an iteration of events, and is hard to accurately measure unless it is a small subset of the universe (special relativity). But two objects can pass through and gauge their velocity based on the same point in 3d space. Next thing you are going to tell me is two objects can't pass through the same "point" in 3d space.
— christian2017
Looks like movement is relative, whether relative to another object, or a point in space (a point in space seems to qualify as an object in space). The mind has this habit of quantifying (or objectifying) space/change. — Harry Hindu
Of note, with its possible philosophical interpretations here placed aside, the theory of relativity clearly indicates that space and time are not discrete but a continuum. — javra
No, this is a mistake in the other direction; the theory of relativity assumes that space and time are continuous, rather than discrete. — aletheist
seems contradictory with what you say here:Continuous motion is a more fundamental reality that discrete positions in space and discrete instants in time. — aletheist
Yes, in my view a discrete position (or instant) is an abstraction that we impose when we mark it for some purpose, not a real constituent of space (or time). It certainly does not exist, since it does not react with anything. — aletheist
Prove an object moves without referring to its change in position relative to something else, like a point in space. — Harry Hindu
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.