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...

I'd go along with Peter Smith's answer, but I figured I'd just take the occasion to point you in the direction of a couple of classic discussions in this area, which you might be interested in following up. First, your question is startlingly close to a problem raised by Saint Augustine at the end of the fourth century AD -- you're in good company! If you're not already familiar with Augustine's discussion, it's in his Confessions , book 11, paragraphs 17 to 38, pages 168 to 174 in this edition . I don't know how much his own solution to the problem would actually appeal to you, which is effectively to say that time only really exists in the mind, the past in memory, the present in sight or consideration, and the future in expectation. But another way around the problem is suggested by J.E. McTaggart's article, 'The Unreality of Time', first published in the journal Mind in 1908 and available online here . McTaggart lays out various alternative ways of thinking about time, and it's up to you...

I shall begin with a 'philosophical' kind of answer, the kind of answer that philosophers ever since Aristotle's time might have given. (Indeed, it is closely related to the answers that Aristotle himself gave to Zeno's paradoxes of motion. Perhaps you're already familiar with those paradoxes: but, if not, then I'd invite you to look them up, for you might enjoy pondering them). I think the flaw in your question lies in that phrase "the next moment". In the case of space, you seem to be treating it as continuous in the sense that, between any two points, no matter how close they might be, there will still be further spatial points between them -- so that to jump straight from one to the other would have to involve some sort of teleportation, bypassing all those intervening points. And yet (as a philosopher might tell you) time itself is equally continuous, and in exactly the same way. At any given moment of time, there is simply no such thing as the next moment. The continuous nature of time...

Time is a sequence of distinct moments, one after another, such that the universe has (or at least could have) a different state at each one. We understand time from the perspective of the present moment, the one at which our thoughts are occuring. On the basis of our memory, we know that there were other moments before this one, because we remember that things used to be different from how they now are, and any such change must have involved a passage of time. Our expectations lead us to believe that there will be moments of time after the present. Such a belief is not utterly indefeasible -- everything could just suddenly stop -- but it seems a pretty safe bet. Looking at things from the perspective of the present moment, it's not so very hard to conceive that either the past or the future could be infinite (though it's for the physicists, or perhaps the theologians, to decide whether either actually is). We can easily think about a time one year ago, and a time two years ago, and a time...

Short answer : You say: "That is, if an infinite amount of time was necessary to get to the present time?" But to get to the present time from when ? The natural impulse is to say: to get here from the first moment. But, of course, the hypothesis of an infinite past means precisely that there was no first moment. So, again, where are we going to start counting? To get here from a time ten years ago will take ten years. To get here from a time twenty years ago will take twenty years. So, given an infinite past, we can pick a time infinitely long ago, and it will take infinitely many years to get to here from there, right? Wrong. The hypothesis of an infinite past does not mean that there was a time infinitely distant from the present. What it means is that there are infinitely many past moments of time, each one of which is some finite distance from the present. Now, this hypothesis may well be false (I take it that both the physicists and the theologians would agree that it is, albeit for...