If the universe has existed forever, i.e. if the universe did not have a beginning, would the present time be possible? That is, if an infinite amount of time was necessary to get to the present time? And if this is so, does this mean the universe necessarily had a beginning?

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 very different reasons): but I'm not persuaded that it's logically incoherent.

Longer answer: Philosophers will often draw a distinction between two different ways of thinking about time, which they call the 'A-series' and the 'B-series'. (This distinction has its origins in work done by John McTaggart about a hundred years ago). The two series differ in the way they pick out different moments of time: both are equally common in ordinary discourse, but philosophers will disagree over which gets more to the heart of what is really going on at a metaphysical level. The A-series specifies moments of time through their relation to the present; while the B-series specifies them according to the order they have amongst themselves, without giving any privileged status to any one moment in particular. Thus, "now", "yesterday", "ten years in the future", "soon", "a long time ago" and the like would all be A-series expressions; while dates such as "15 May" or "the ides of March, 44 BC", together with comparative terms like "earlier than" or "ten years after" all belong to the B-series. Note that, in the A-series, the same expressions are continually changing their reference from one moment to another. Tomorrow, the word "today" will refer to a different day than the one to which it currently refers. "It is not raining" is true now, but it was false a few hours ago, and the chances are that it will be false again pretty soon. In the B-series, by contrast, there is no such change: thus, the B-series sentence "The date of Julius Caesar's death is the ides of March, 44 BC" is just as true today as it was when it happened. Indeed, as the seer saw, it was already true that he would die on that day, even before the fateful day arrived.

Now, with this distinction in mind, let's think about your question again. Suppose, first, that we decide that the right way to think about time is with the A-series. But, with the A-series, we have no need to "get to" the present, because we're already here. The present is our starting point: not in a physical sense, but rather in the sense that all other times, past as well as future, are defined in relation to the present. And so, if we begin defining the following sequence of times: "one year ago", "two years ago", "three years ago", we will notice that there is no finite point at which we are logically required to draw this sequence to a close. This should not be thought to imply that an infinite past is physically possible, just that it is logically possible. No matter how large a number n one opts to insert into the specification "n years ago", one can always replace it with n+1. It's up to the physicists (or, if this should be more to anyone's taste, the theologians) to decide whether there actually is any number n such that "n+1 years ago" doesn't refer to any genuine moment of time. But at least the question makes sense, and that's enough to settle the philosophical issue.

But then, what if the B-series is a better way of specifying different moments of time? Well, then it should be even more readily apparent that there will be no logical impediment to an infinite past, because the B-series doesn't recognise the notion of "past" at all. In the terms of the B-series, take any date d you like: there is no number n such that another date n+1 years earlier than d cannot be defined. (Though, again, it's for others to decide whether or not all such specifications will actually refer to really existing moments of time).

It's also worth just noting that all of the same points can be made about future time as about past time.

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