## "Infinity" poses a ton of problems for both science and philosophy, I'm sure,

"Infinity" poses a ton of problems for both science and philosophy, I'm sure, but I would like to ask about a very particular aspect of this problem. What ideas are out there right now about infinitely divisible time and human death? If hours, minutes, seconds, half-seconds, can be cut down perpetually, what does this mean for my "time of death"?

### One might mean either of two

One might mean either of two things by "infinitely divisible time." One might mean merely that (1) any nonzero interval of time can in principle be divided into smaller and smaller units indefinitely: what's sometimes called a "potentially infinite" collection of units of time each of which has nonzero duration. Or one might mean that (2) any nonzero interval of time actually consists of infinitely many -- indeed, continuum many -- instants of time each of which has literally zero duration: what's sometimes called an "actually infinite" collection of instants. I myself favor (2), and I see no good reason not to favor (2) over (1).

Both views of time are controversial among philosophers, and some physicists conjecture that both views are false (they conjecture that an indivisible but nonzero unit of time exists: the "chronon"). But let's apply (2) to the time of a person's death. Classical logic implies that if anyone goes from being alive to no longer being alive, then there's either (L) a last time at which the person is alive or a (F) first time at which the person is no longer alive. If (2) is true, then there can't be both L and F, because according to (2) no two instants of time are adjacent to each other. In other words, if L exists, then there's no earliest instant at which the person is no longer alive; and if F exists, then there's no latest instant at which the person is still alive. According to (2), there are instants other than L that are arbitrarily close to L but no instants right next to L. Ditto for F.

To put it another way: (2) implies that no transition is literally from one instant to the next, because there's no such thing as the next instant. This includes the transition from being alive to no longer being alive. Nevertheless, exactly one of L or F exists. Which one is it? I don't know the answer to that question, but I'm not sure it's a well-posed question anyway.

### One might mean either of two

One might mean either of two things by "infinitely divisible time." One might mean merely that (1) any nonzero interval of time can in principle be divided into smaller and smaller units indefinitely: what's sometimes called a "potentially infinite" collection of units of time each of which has nonzero duration. Or one might mean that (2) any nonzero interval of time actually consists of infinitely many -- indeed, continuum many -- instants of time each of which has literally zero duration: what's sometimes called an "actually infinite" collection of instants. I myself favor (2), and I see no good reason not to favor (2) over (1). Both views of time are controversial among philosophers, and some physicists conjecture that both views are false (they conjecture that an indivisible but nonzero unit of time exists: the "chronon"). But let's apply (2) to the time of a person's death. Classical logic implies that if anyone goes from being alive to no longer being alive, then there's either (L) a last time at...

What makes Xeno's paradox paradoxical? It sounds more like a trick question than a bona fide paradox. Achilles and the tortoise are going to have a half-mile race, and Achilles gives the tortoise a 1/4 mile head start. Suppose Achilles runs as fast as a decent male high school track athlete, and he can cover 1/2 mile in 2-1/2 minutes. He gives the tortoise a head start of 1/4 mile. According to a quick internet search, the average turtle moves at 3 to 4 mph. Let's say our tortoise is particularly fast, and moves at 5 mph. It thereby takes the tortoise 3 minutes to cover 1/4 mile. Achilles finishes 30 seconds ahead of the tortoise. Where's the paradox?

### The reasoning you gave

The reasoning you gave illustrates why Zeno's example has a chance of counting as a paradox at all. As you show, of course Achilles will overtake the tortoise. But Zeno claimed to have equally good reasoning showing that Achilles never overtakes the tortoise. That's the paradox: apparently good reasoning in favor of each of two incompatible claims.

For Zeno's reasoning and a critique thereof, see sections 3.1 and 3.2 of this SEP entry.

### The reasoning you gave

The reasoning you gave illustrates why Zeno's example has a chance of counting as a paradox at all. As you show, of course Achilles will overtake the tortoise. But Zeno claimed to have equally good reasoning showing that Achilles never overtakes the tortoise. That's the paradox: apparently good reasoning in favor of each of two incompatible claims. For Zeno's reasoning and a critique thereof, see sections 3.1 and 3.2 of this SEP entry .

## Is time traveling to the past a logical contradiction? I mean because if I were

Is time traveling to the past a logical contradiction? I mean because if I were to go into a time machine tomorrow then the "past" I travel to would actually be the future relative to today.

### Defenders of the possibility

Defenders of the possibility of time-travel usually address this potential contradiction by distinguishing between your personal time (the time kept by your biological clock) and external time (the time kept by the world's calendars). Your departure on a time-travel voyage can be future in your personal time (as well as in external time) even though your destination is past in external time (and future in your personal time).

This distinction is already required by Einstein’s special theory of relativity. If you travel in a rocket so fast that your personal time passes much more slowly than external time passes for residents of Earth, you may return after one year of your personal time to find that your generation has died off: think of it as time-travel into the future. Stories about time-travel into the past also require distinguishing between these two kinds of time.

## Have Zeno's paradoxes of motion actually been satisfactorily solved? Physicists

Have Zeno's paradoxes of motion actually been satisfactorily solved? Physicists and mathematicians I've read on the matter seem to regard them as no longer important, but never explain convincingly (for my money) why they're not still important. Have philosophers said anything interesting about them recently? Could you either succinctly explain how they've been solved or point me in the direction of good recent discussions?

I recommend starting with the SEP entry on the topic, available here.

There's an article not cited by the entry that may be relevant because it takes a skeptical view of the standardly accepted solution to one of the paradoxes: "Zeno's Metrical Paradox Revisited," by David M. Sherry, Philosophy of Science 55 (1988), 58-73. Sherry argues that the standardly accepted solution "defuses" the paradox but is too ad hoc to count as a "refutation" of Zeno's reasoning.

I recommend starting with the SEP entry on the topic, available here . There's an article not cited by the entry that may be relevant because it takes a skeptical view of the standardly accepted solution to one of the paradoxes: "Zeno's Metrical Paradox Revisited," by David M. Sherry, Philosophy of Science 55 (1988), 58-73. Sherry argues that the standardly accepted solution "defuses" the paradox but is too ad hoc to count as a "refutation" of Zeno's reasoning.

## I don't think time exists. I think we have existence and being, we have

I don't think time exists. I think we have existence and being, we have contingent beings that are mutable and contingent items such as rocks that wear down but time has no impact on either. Time is just a concept that man invented. If there were no movement we would still have existence and hence for sake of phenomenological talk - time would still exist. My hair turns gray and my skin wrinkles because of the change in my hormones - not time. Often time is used as though it has causative powers. Can someone give me an argument that would refute this statement that time is not real but merely a concept?

Let's be careful about wording. You say that (1) time doesn't exist. You also say that (2) time is a concept that was invented by humans. If time is a concept, then I don't know which concept it could be except the concept of time. But if time is the concept of time, then each of them is the concept of a concept of a concept (and so on without end), which is an unintelligible regress.

Even if time isn't the concept of time, your assertions (1) and (2) are inconsistent with each other. If time is a concept that we succeeded in inventing, then our invention must exist (or have existed), in which case (1) is false. You asked for a refutation of the statement that time is not real but merely a concept. Unless concepts aren't real, there's your refutation.

So I take it that you mean, instead, that (3) the concept of time is an unfulfilled concept, like the concept of a unicorn: nothing answers to the concept, even if the concept itself exists. In that case, I haven't answered the question you meant to ask: Why think that time exists, i.e., that something does indeed answer to our concept of time? I don't have a good philosophical answer to that question, but I'd point out that the equations in our best physical theories require time as a parameter. In any case, I hope that what I've said is helpful in at least sorting out the question.

Let's be careful about wording. You say that (1) time doesn't exist. You also say that (2) time is a concept that was invented by humans. If time is a concept, then I don't know which concept it could be except the concept of time . But if time is the concept of time, then each of them is the concept of a concept of a concept (and so on without end), which is an unintelligible regress. Even if time isn't the concept of time , your assertions (1) and (2) are inconsistent with each other. If time is a concept that we succeeded in inventing, then our invention must exist (or have existed), in which case (1) is false. You asked for a refutation of the statement that time is not real but merely a concept. Unless concepts aren't real, there's your refutation. So I take it that you mean, instead, that (3) the concept of time is an unfulfilled concept, like the concept of a unicorn: nothing answers to the concept, even if the concept itself exists. In that case, I haven't answered the question...

## Since nothing could change without some kind of movement, and time would not be

Since nothing could change without some kind of movement, and time would not be perceivable without some kind of change, why isn't time fundamentally motion. Likewise, since space would not be perceivable without some sort of motion, why isn't space fundamentally motion as well? In other words, what part of space or time is conceivable without bringing motion into the explanation?

The reasons you gave for thinking that time is fundamentally motion and that space is fundamentally motion seem to depend on this principle: If A isn't perceivable (or isn't explicable) without some kind of B, then A is fundamentally B. But that principle looks false. Motion isn't perceivable without some kind of perceptual apparatus, but that doesn't imply that motion is fundamentally perceptual apparatus. Motion isn't explicable without some kind of explanation, but that doesn't imply that motion is fundamentally explanation. Furthermore, if time and space are both fundamentally motion, are time and space identical to each other? Even physicists who talk in terms of "spacetime" nevertheless talk about time as a separate dimension of spacetime; I don't think they regard time and space as one and the same.

One might also question whether space, or the perception of space, requires motion. When I stare at my index fingers held one inch apart, I perceive them as occupying different spaces, and I judge there to be "empty space" between them, but I don't think I'm relying on the perception of motion in that case.

For an argument that time can pass without any change, have a look at Sydney Shoemaker's classic article "Time Without Change" (1969). I also found some lecture notes about the article at this link.

The reasons you gave for thinking that time is fundamentally motion and that space is fundamentally motion seem to depend on this principle: If A isn't perceivable (or isn't explicable ) without some kind of B, then A is fundamentally B. But that principle looks false. Motion isn't perceivable without some kind of perceptual apparatus, but that doesn't imply that motion is fundamentally perceptual apparatus. Motion isn't explicable without some kind of explanation, but that doesn't imply that motion is fundamentally explanation. Furthermore, if time and space are both fundamentally motion, are time and space identical to each other? Even physicists who talk in terms of "spacetime" nevertheless talk about time as a separate dimension of spacetime; I don't think they regard time and space as one and the same. One might also question whether space, or the perception of space, requires motion. When I stare at my index fingers held one inch apart, I perceive them as...