## I understand points as entities with zero extension. (Is this correct?) Yet

I understand points as entities with zero extension. (Is this correct?) Yet infinitely many points are said to compose space. It seems like even infinitely many zeros could never add up to a finite non-zero value. So, what's up with points? If they don't have any extension, what are they? As a follow up, does it make sense to think about points in space in a different way from how we think about points in time?

Yes, a point has length, depth, and height zero. So do two points, three points, and even as many points as there are natural numbers. But if you have as many points as there are real numbers (of which there are more than there are natural numbers), then that set of points may have some positive length, depth, or height, though it may not. (In that case, they will not have zero length, depth, and height but may have no assignable length, depth, or height.) The branch of mathematics in which such things are studied is called "measure theory".

Exactly what a point is is another question. In mathematics, points may be regarded in a wide variety of ways, as is convenient. Are there any points in space itself? That's a disputed question, and an empirical one, not one on which philosophers can pronounce.

## What was before the beginning of time? Or perhaps I am asking the wrong question

What was before the beginning of time? Or perhaps I am asking the wrong question because "before" is a measurement of time, and what I want to know is what was there when there was no time. So I should be asking: What is time? Right?

Can't do much better here than to quote from St. Augustine:

My answer to those who ask 'What was God doing before he made heaven and earth?' is not 'He was preparing Hell for people who pry into mysteries.' This frivolous retort has been made before now, so we are told in order to evade the point of the question. But it is one thing to make fun of the questioner and another to find the answer.* So I shall refrain from giving this reply. For in matters of which I am ignorant I would rather admit the fact than gain credit by giving the wrong answer and making a laughing-stock of a man who asks a serious question.

... A fickle-minded man, whose thoughts were all astray because of his conception of time past, might wonder why you, who are God almighty, Creator of all, Sustainer of all, and Maker of heaven and earth, should have been idle and allowed countless ages to elapse before you finally undertook the vast work of creation. My advice to such people is to shake off their dreams and think carefully, because their wonder is based on a misconception.

How could those countless ages have elapsed when you, the Creator, in whom all ages have their origin, had not yet created them? What time could there have been that was not created by you? How could time elapse if it never was?

You are the Maker of all time. If, then, there was any time before you made heaven and earth, how can anyone say that you were idle? You must have made that time, for time could not elapse before you made it.

But if there was no time before heaven and earth were created, how can anyone ask what you were doing 'then'? If there was no time, there was no 'then'.

(Sections 12, 13, Book XI of The Confessions, translated by R. S. Pine-Coffin.)

So, to paraphrase Gertrude Stein, there was no then then.

I have always been struck by two things here: (1) how, if you were to substitute "Big Bang" for "God" in the above, what you'd get would not be far from what a contemporary physicist would tell you; and (2) that there's something in the very situation Augustine is trying to describe that makes it impossible for him to describe it (there was no time before [!?] God brought heaven and earth into being).

___________________

*In this connection, the reader might also look at Question 227.

## Is it possible to travel back into time?

Is it possible to travel back into time?

I don't think that we know the answer to this one yet.

Leaving aside the question of whether travel back in time violates any physical laws, there are some reasons to think that it is conceptually incoherent. For one thing, there is the well-known "Grandfather Paradox." Suppose you were to travel back in time and kill your own grandfather before the time your mother was conceived, thus preventing her conception and obviously your own as well. This leads to a logical puzzle, since you would cause something to happen that would make it the case that you had never existed.

It is very hard to tell a coherent time travel story. Science fiction representations of time travel often involve some kind of paradox. Very often, they fall victim to the "second time around" fallacy -- they depict events in some year, say 2005; our hero travels back in time and makes some crucial change; when he then returns to 2005 things are different. But this suggests that we have 2005-the-first-time-around and 2005-the-second-time-around, and that doesn't seem to make sense. How could 2005 occur twice? (Back to the Future depicts time travel this way.) One interesting recent depiction of time travel that avoids this mistake is the novel The Time Traveler's Wife.

There might be various ways to get around these puzzles. A good introduction to the philosophical puzzles of time travel is David Lewis's paper, "The paradoxes of time travel."

One last thought. A common objection to time travel that you often hear is that if time travel to the past were possible, then we should be surrounded now by time travelers. Some students at MIT recently tried to test this hypothesis by holding The Time Travelers Convention. There were not as many attendees as they had hoped.

## If the future doesn't exist until it happens, then does it exist? Wouldn't that

If the future doesn't exist until it happens, then does it exist? Wouldn't that make it the present and not the future?

Some philosophers think that time is a lot like space: just as all places are equally real even though I am only in one place, so all times are equally real even though I am only in one time. On this view, the fact that the future exists now no more makes it present than the existence of a place over-there makes that place exist here.

## Hello. I wonder what you think about the following: About 13.7 billion years ago

Hello. I wonder what you think about the following: About 13.7 billion years ago, there probably was a Big Bang. The astronomers start their counting of time from that. What do the philosophers think of what happened before the Big Bang? JB from Sweden

Well, I've answered other similar questions despite my not being terribly well-informed about science, so I'll take a stab at this one, too.

The answer to this question depends partly upon whether the universe is "open" or "closed", that is, upon whether the expansion of matter will eventually cease, the universe will start contracting, and everything will end in a "Big Crunch". If so, then it is my understanding that the energy so generated would lead to another Big Bang, and the whole process would start again. If that's how things are, then, before the Big Bang, that may have been how things were.

So suppose things weren't like that. Then I believe current physical theory implies that there wasn't any "before the Big Bang". Astronomers start counting time with the beginning of the Big Bang because time itself began with the Big Bang. If that seems bizarre, well, the theory of relativity does have a way of upsetting one's everyday assumptions about time.

Someone who knows more about this than I do care to confirm or deny?

## Does the future exist in any knowable fashion? If so, can it be known in any

Does the future exist in any knowable fashion? If so, can it be known in any absolute way? If not, why do so many of us believe it can?

On one view of time, the future is as real now as the present or the past, much as other places are as real as the place you happen to be; on another view the future is not yet real but will be. Either way, many philosophers would say that we can know some things about it, though Hume's great sceptical argument against induction attacks this idea. But Hume's argument is not especially about the future: it applies to any inference from what we have observed to what we have not observed, whether what we have not observed is in the future, present or past. In any event, it's not very surprising that we believe we can know something about the future, since we have so often formed expectations that we have subsequently found to be satisfied.

## Is it true that time has no end?

Is it true that time has no end?

This is an open question, and one that will be decided in the branch of physics known as cosmology. Since time is best conceived as a dimension of the universe, and as we do not now know the long-term future of the universe, this cannot be answered at present.

## We are often told time is like a river. Are there other useful analogies for

We are often told time is like a river. Are there other useful analogies for time? For example: Time is like a bowl of jello with fruit: time is the jello and events are the fruit stuck in it. I guess what I'm really asking is does time have to flow? Is there another way of thinking about time?

Thinking of time as flowing obscures far more than it clarifies, on my view, and I think that the river analogy is dangerous. Anything that flows flows at some rate. How fast does time flow? Sixty minutes per hour? The image raises the prospect of a supertime against which the flow of time occurs, and that raises a nasty regress. Better to think of time as a dimension of the universe, but one that is anisotropic,t hat is, one in which going in one direction is different from going in another, unlike, say, East-West travel.

## Is it true today what I will do tomorrow?

Is it true today what I will do tomorrow?

If on Tuesday you play chess, then if you had said on Monday "Tomorrow I will play chess" you would have said something true. It's easy to think that the truth of that future tense statement as uttered on Monday constrains what you can do on Tuesday; that is, it's easy to think that the claim's truth on Monday restricts your freedom. It seemed as if you had a choice about whether to play chess on Tuesday — but really you didn't, since it was already true the day before that you will play chess! Most philosophers reject this threat to our freedom. To many, it seems like a piece of verbal trickery. Yet there are disagreements amongst them about what precisely the trick is.