## "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.

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.

## 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.

## Does the future exist? In theory, is the future a 'place' that I can go to in a

Does the future exist? In theory, is the future a 'place' that I can go to in a time-machine or does the universe alter in such a way that my desired era appears before me?

A timely topic, if you'll pardon the pun. It's very much a live issue in contemporary philosophy and as you'd guess, there is more than one camp.

Very roughly, we can carve the territory up this way:

Presentists say that only the present is real. The future does not exist, and will only come into being after the present has slipped away. One reason why some people defend presentism is that they believe it does more justice to our sense of the passage of time. On this view, things "become."

Eternalists think that all events are equally real. There is no special moment that counts as "the present." Rather, for any given moment, there are earlier and later moments. One reason (though not the only one) why some people defend eternalism is that it seems to fit better with the understanding of space and time that we get from the theory of relativity. Think of it this way. Suppose an event happens outside my window as I'm writing this—say, a car backfires. And suppose that on a planet far away in another galaxy, there's a certain event—an explosion, say—that happens, but as it works out no light signal, no matter how powerful, could get from here to that explosion, not could any other signal. To put it in the language of relativity, suppose the explosion on the other planet is outside the lightcone of the the backfire of the car. In that case, relativity says there's simply no answer to the question of which event happened first: backfire or explosion. In fact, if we say that only the present is real, we have no good way of saying what's part of the supposed present of any event.

That's a bit quick and dirty, but it may help give you the bigger picture. There's a big literature on this topic. One reader-friendly place to start is with Craig Callender's little book Introducing Time . Don't be put off by the fact that it has lots of cartoon pictures. It's very good. And you can even download it as an ebook.

## 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've read that as we go faster time dilates and so time slows down. So my

I've read that as we go faster time dilates and so time slows down. So my question is that If suppose a person in a spacecraft accelerates to the speed of light. After sometime (in his prospective) he decides to decelerate finally to much much lower than the speed of light. Then during all of this how much time will have passed for everything outside? Will he be able to decelerate at all? I mean for an outside observer, who by some means, is able to see everything that is happening in the spaceship, will the person be frozen (in time) and therefore not able to push the button that decelerates the ship and ultimately travel infinitely in time and space? (again another assumption that the fuel does not run out). And (in the prospective of the space traveler) after pushing the button where will he be in time with respect to the observer? I hope I am able to convey my problem. Thanks in advance.

A good question. The nub of the matter is this: if something is moving literally at light speed, then the amount of time between two points along its trajectory, measured in its frame, is 0. So your hunch is right in one way: at light speed (along the edge of a light cone), time doesn't pass.

However, if we try to accelerate a massive body (for example, a spaceship) to light speed, we'll fail. Close enough for present purposes, the reason is that as the body accelerates, it takes on mass, and that mass approaches infinity as the speed approaches c. So your space traveler will never arrive at "frozen" time.

## Causation has (has it?) an essential relation to time. If some event caused some

Causation has (has it?) an essential relation to time. If some event caused some other event, then the former was previous. But we hear from scientists that time is just one dimension of space-time and indeed that there may be (or might have been) some more dimensions, other than space and time. Should there be analogues of causation related to the other dimensions? Should there be a wider category than causation encompassing all those analogues? Isn't this all a bit perplexing?

Really, it's not perplexing. The connection between causation and time is that causation implies time. A cause has to precede its effect. Now why is that? Some philosophers have thought that the proposition 'A cause precedes its effect' is synthetic a priori. Others have thought, more plausibly, that it tells us part of what a cause is, so it's analytic. (A cause might be a certain juxtaposition of conditions, for example. In that case the cause and the effect could be almost simultaneous.) Still others have thought that a cause can occur after its effect. Even then, though, causation has a relationship to time. And there is the so-called "bilking" argument. If a cause can occur after its effect, all we have to do is wait for the effect to occur, and then prevent its cause from occurring. The fact that this is possible shows that there cannot be reverse causation, i.e. causation in which the effect comes before the cause. As to other dimensions - is there an analogue to causation in them? (1) Are there beagles in these other dimensions? I have just discovered that the most popular dog in Rome is the beagle, but it was a discovery, not something I could have produced an argument for. (Also the plural of "beagles" in Italian is "beagles". I thought it would have to be "beagli" - no such luck.) (2) What is our definition or understanding of causation according to which it has analogues in other dimensions?

## 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.

## 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.

## What is time? My friend and I are having an argument about the nature of time.

What is time? My friend and I are having an argument about the nature of time. If I understand her position correctly my friend believes that time is simply an artefact of changes in the universe, or that change is itself synonymous with time. This seems to be a commonly accepted position, however I replied that if two spheres were moving in space in parallel to one another but one sphere was moving faster than the other then that would mean that that sphere would traverse a greater distance in less time but with an equal degree of change in the universe. Thus time and change are two separate things. I guess the physics of that claim are debatable but I suspect that it demonstrates something true in a way that is a priori irrespective of the physics because even if there were a physical difference in the amount of forces which change it would be hard to see how those imperceptible forces would contribute to a difference in how we perceive the time effect of those different objects. What do you...

Some good questions.

One view is that if there is change, there is time. However, it doesn't follow from that that time has a "metric" -- that there is an answer to questions of the sort "how much time?" If all that existed were two solid spheres in relative motion, then someone might say that there's no answer to the question "What's the relative velocity?" (hence how much time has passed between varying degrees of separation) even though there is change going on, and hence there's time.

More generally we can at least imagine a universe where time _order_ among events -- what happens before, after or simultaneously with what -- is definite, but without there being any correct answers to questions such as "How much time passed between event x and event y?" Insofar as that's right, it provides a way around your objection.

Whether time requires change is yet another question. Not everyone agrees that it does. Sidney Shoemaker, in a paper from some years ago, argues that there could be definite periods of time with no change. The reference is: “Time Without Change,” Journal of Philosophy 66 (1969), pp. 363-381. You might also look at the article on time in the Stanford Encyclopedia of Philosophy:

http://plato.stanford.edu/entries/time/