Any "change" in the past is inherently paradoxical (to say the least). In fact, I think it is actually worse than that: Such changes would involve making it both true and false in the history of our world that the changed event did (or did not) take place. That's a contradiction, not a paradox.

On the other hand, one could go back in time and do what one actually did in some time long past (or do what one actually will do, some time long in the future). If it is actually possible to go back in time, for example, and be one's own father, then one would live in a universe in which that is (and always was) precisely what happened. What are called "looping" universes, in which time did not flow linearly, but in a closed loop, would make such apparently strange events possible. And though we have good reasons for supposing that we do not live in a looping universe, it does not seem that logic makes such an idea impossible.

To find out more about this topic, have a look at an article by David Lewis entitled "The Paradoxes of Time Travel" which was published in the American Philosophical Quarterly, vol. 13 (1976), 145-152. Lewis also cites two stories by Robert Heinlein in which the picture of time travel that he develops appear to be assumed.

I already addressed your second concern in response to a previous question on this site. I'd invite you to take a look at my answer there.

As to the first concern, when we speculate about a possible beginning to time, we are doing so from a frame in time. We start at the present, and we conceptually project ourselves backwards through the period that intervened between the present and that supposed first moment. Was there a time one year ago? Yes. Was there a time two years ago? Yes. Was there a time thirteen billion years ago? Yes. Was there a time fourteen billion years ago? No! The supposition of a beginning to time means that there exists a number n, such that there was a moment of time n years back from the present but no moment n+1 years back. The supposition of an infinite past simply means that there is no such number.

Not a silly question at all, absolutely not! But the answer is no.

Suppose you built a time machine last year, 2008. Then it is true now that you built a time machine in 2008, and it always will be true that you built a time machine in 2008. Suppose now that, next year, you decide that it would be amusing to create a paradox by using your machine to go back in time and prevent yourself from building the machine in the first place. But it's still going to be true that you did in fact build it in 2008. Which means that, no matter how determined you might be, it will still be a fact that you didn't succeed in your plan of preventing this. Logic alone can show that something or other must have scuppered your plan: because success would indeed generate a paradox, whereby you both did and did not build the machine, which is a logical impossibility. Now, what logic won't show us is what scuppered your plan. Maybe you had a last-minute fit of conscience and just decided not to go through with it. Maybe you did make an attempt, but your 2008 self managed to overpower your intruding 2010 self. Or maybe something else intervened. If you had CCTV cameras set up around your laboratory last year, you might actually be able to find out what prevented your scheme. Now in 2009, you could go back and watch the images of your 2008 self as you were still tinkering with the machine, and maybe you'll spot your 2010 self, tiptoeing up out of the shadows, about to conk the other one on the head with a spanner... and then slipping on a banana peel, knocking themselves out instead, while the younger one, quite oblivious to what's going on behind them, successfully completes the machine. There will be some perfectly ordinary explanation for why you failed to prevent the building of the machine, and this will be a proper subject for historical research -- because, even if it was initiated by events in 2010, that failure already happened in 2008. But something will have thwarted your plan, because the fact is that you did build the machine.

My own thinking on matters like this has probably been most influenced by the late, great American philosopher, David Lewis, particularly his article 'The Paradoxes of Time Travel'. It first appeared in the American Philosophical Quarterly, 13 (1976) 418-46, and is reprinted in his own Philosophical Papers, vol. II. I recommend it.

'We can only live in this "here and now" moment . . . in fact , there is no way we can ever live out of it . . . is it not?'

I am not sure what is supposed to meant by living in the present instant ("moment" I think has more to do with action). Living at an instant seems as impossible as living at some other time, because there isn't even time to draw breath in an instant. In any case I do not believe that there is something called "the present instant", so I don't see how we could live in it (at it?)

It (the present instant) is an abstraction, and it is not, in reality! I do believe there are present times, though, such as the present day or hour. The trouble with the instant is that it is not a time.

If the alternatives are living in the past and living in the future, we can only live in the present. If the alternatives are thinking about the past and thinking about the future and thinking about the present, we have choices. "Living in the present" is a cognitive psychological technique used, often successfully, by those who brood about the past or fret about the future. Concerns with the past or future may be appropriate (e.g. someone regrets a romantic choice or gets a worrisome medical diagnosis) or inappropriate (due to anxiety, excessive guilt etc); the technique works for all of them. Many people report that it helps them live a fuller and calmer life. For those who suffer from poor impulse control or psychopathy, however, it might be better to focus more on the future and the past and less on the present.

Why does there have to be a reason? Maybe some events occur when they do just by chance. There seems to be nothing incoherent about that idea. Indeed, that's how we think that the world actually works. For example, the law governing the radioactive decay of an unstable atomic nucleus seems to be merely chancy. An atom of polonium-214 has a fifty/fifty chance of decaying in the next 3 minutes or thereabouts. But nothing determines when it actually decays. There is, according to our best scientific theory of the matter, no answer to the question of why the decay happens at the moment that it does rather than a little while before or a little while after. Why should there be?

Our knowledge of the past derives from perception, memory and inference, in the sense that these are answers to the question, 'How or by what means do you know?' (There are other ways, for example report or testimony). But our knowledge of the future has in it no elements of memory or perception. So as one might therefore expect it is harder to come by knowledge of the future, and we have less of it per hour, if you want. We typically can know more about a past hour than about a future hour, though by no means all of the past hours, for example those in past centuries. If I know p, and p is a proposition about the future, I cannot know it by memory, special cases apart. (A special case would be that I come to know that I am going to Africa next summer - a piece of knowledge about the future - by remembering that I am going to Africa next summer. 'How do you know?' 'I just remembered it . . .' makes sense as a conversation.)

It seems to me, in spite of the assumption you make, however, that in some cases there may not be an element of uncertainty in either knowledge of the past or the future. There is no uncertainty that the cat will be roughly where it is on the sofa in one attosecond - cats don't move that fast - and there is no uncertainty that the cat has been sitting there for the last five minutes, as I have been watching it for the whole time. There is an interesting mistake (I myself think it's a mistake, anyway) to be avoided in this area. Why are there asymmetries in time with respect to knowledge? I am not sure the question put just like that makes sense. Why can we remember the past but not the future, for example? The simple answer is that if I remember something, then it must already have happened, so memory of the future is a contradiction. My own view is that even the alleged logical asymmetries between past and future are much more slippery than they seem at first glance, and we must be careful to get our tenses right. It is certainly true, for example, that the past exists, in the sense that past events have occurred - and what other sense are we considering? But then so does the future exist, in just the same sense: future events will occur.

As a warm-up exercise, consider the following two infinite ordered sets of numbers. Firstly, take the negative and positive integers in their 'natural' ordering

... -4, -3, -2, -1, 0, 1, 2, 3, 4, ...

trailing off unendingly to the left and to the right. Second, take all the negative numbers, in increasing size, followed by zero and all the positive numbers:

-1, -2, -3, -4, ... o, 1, 2, 3, ...

Now, in both orderings, any positive number is preceded by an infinity of numbers (including all the negative numbers). But there is a very important difference between the two cases -- they have, as mathematicians say, different 'order types'. One big difference is this: there is no first member of the first ordering (i.e. for any given element of the ordered series, there's an earlier one); but there is a first member of the second ordering (namely, -1). To bring out another difference, suppose in each ordering we take one of the negative numbers, and we ask: can we start with that predecessor of 0 and by taking finite number of steps to the right, to successors in the ordering, eventually get to 0 and on to the positive numbrs? In the first case the answer is 'yes'. Pick any predecessor, e.g. -43. Then after a finite number of steps (43 of them!), we'll reach o, and we can keep on marching throuugh the positive numbers. In the second case the answer is 'no'. Pick any predecessor, e.g. -43 again. Then after a finite number of steps, we'll just reach another, bigger, negative number.

OK, now let's turn to the case of time. Suppose (to keep the argument simple, but without losing anything essential to the present issue) we take time to be discrete, with moments ordered by the 'before/after' relation. We could tag the moments with numbers, and suppose we use some positive number like 2009 to mark the present moment, NOW. And let's ask: is the 'order type' of the temporal sequence like our first ordered sequence of numbers or like the second?

If time were whackily ordered like the second number series, there would be a first moment in the ordering (the one tagged -1), though the present moment 2009 would still have an infinite number of predecessors. But in that case, we couldn't have got to NOW by a finite number of steps from any given moment, wherever in the past. But of course, if we do suppose that 'time stretches back to infinity', then the natural view, still assuming discreteness, is that time is ordered like the first number series. So NOW is again preceded by an infinity of earlier moments, but there is no first moment, and from any past moment, a finite number of steps from one moment to the next reaches NOW.

Of course, it is another question whether we do have to accept that time does stretch back to infinity: but the point I'm making is that there is no paradox in supposing that it does, if you give time a sensible order-type.

One answer to your question is that there may be multiple "orders of time" and, in particular, there may exist an order of time that is separate from the one we normally experience and within which events can occur.

Thus, for example, in Western Europe around and in the centuries before 1500 certain religious rituals, ecstatic experiences, moments in liturgical calendars, may have been experienced as occurring in a special "sacred time" that constitutes a different temporal order from commonplace "secular time." In his A Secular Age (and a book I've mentioned before on this site),Charles Taylor argues that our ancestors in Western Europe possessed this bifurcated experience of two orders of time and he provides a rich account of why it is that almost everyone alive today in Western Europe and North America experiences secular time only.

The idea that we move through time is at best odd, but at worst very confused - no offense at all intended to the author of this fine question, though, as this species of confusion is the motor of philosophy and it is the job of philosophy to describe it and then put it right, among other jobs. The picture is of time around us - and what does this mean? - and us trundling along through it. If indeed this is our conception, the idea of movement has come off its bearings and becomes what lawyers and students call "wordage", as in "we need some wordage to cover this point here". Equally bad, as I see it, is the idea that time moves through us or past us or whatever. You might wonder where it is going, but this question has its own kind of nonsense too. The difficulties here are all due to the A-series conception of time. I agree that the idea of change outside of time is a very interesting one, but I don't see the connection with your first question clearly. What does the question whether we move through time have to do with whether there is change without time? Are you thinking that the idea of moving through time is so strange that perhaps it will give us a clue to understanding change outside time? But things are not this difficult. You can think of the change of direction of a line. That strictly is a change. "Change" comes from cambiare, after all, as in changing money, but all it means, Aristotelian-style, is the substitution of one condition for another. The direction of the road changes in an utterly literal and non-temporal sense, turning sharp left, say, but no time is involved.