While I was attending college, a new professor appeared on campus. Although it was, and still is so far as I know, a small liberal arts college, that in itself wasn't extraordinary or significant. Professors would appear now and then and some would leave after a time; some would not. What was unusual in the case I recall here was that this particular professor was said to be a sociologist. He was the first of his kind at my college. At least, he was the first to be called a sociologist.
As a professor of philosophy I admired and respected thought him to be worthy, I signed up for one of his classes. The class in question addressed Time. If I remember correctly, the first thing we students were asked to do was submit a paper describing what we felt Time to be. I think I wrote something to the effect that time was a concept by which we determined when certain events took place or should take place (planting crops, for example). I thought, in other words, that we came to keep time because it was useful to do so for various purposes, especially as our societies became larger and more complex. This I suppose was a kind of anthropological view. Time was a method used in determining and defining what takes place or should take place. Such was, and is, my guess, in any case. But in all honesty I'm not sure just what I thought. That was a long time ago.
I confess I thought my view of Time to be superior to the views of others in the class who relied on Simon and Garfunkel (Hazy Shade of Winter) and others to arrive at a definition. The professor, though, treated our views as equally deficient and dismissed them all in a rather cursory manner. To this day I have no idea what he thought was the correct definition of "Time." I know only he was almost contemptuous of what we thought ("Ah yes, this is the so-and-so. view of Time"). He may have declined to give us a definition. He was one of those professors who thought that teaching consists of asking, not answering, questions. I encountered a few like-minded professors in law school. It may be there is or was a widespread belief that this style of teaching is the fabled Socratic Method. I find it hard to believe that anyone who actually reads Plato can come to such a conclusion, as I think he carefully prepared his dialogues so that they would inevitably result in a position he thought appropriate through the device of questions; much as a lawyer prepares questions to put to a witness.
It happens that Time is a subject of philosophical analysis. There are philosophers of Time and so must be a Philosophy of Time. The ontological status of time is studied and debated. Philosophers discuss the difference between the past, the present and the future. They consider why Time seems to us to be an arrow. They wonder whether there truly is anything but the present. They wonder about fatalism. They ask why Time seems to move swiftly in some cases or to certain people.
For my part, I wonder as I do in most cases whether these wonderings make any difference to how we live our lives, and am inclined to say they make no difference whatsoever. Also for my part, I feel that if they make no such difference, debating them is futile. This may well be a fault of mine. There may be something lacking in me.
Perhaps the professor of sociology I encountered (or did I? It was in the past!) would have though that C.S. Peirce's pragmatic maxim would be of some assistance in defining Time; more assistance, even, than Paul Simon's lyrics. It's hard to say. The maxim has appeared in different forms, but I'll make reference to the form in which it appeared in Peirce's essay entitled How to Make Our Ideas Clear:
"Consider what effects, that might conceivably have practical bearings, we conceive the object of our conception to have. Then, our conception of these effects is the whole of our conception of the object."
I can't remember whether I knew of this maxim when I studied under the eminent sociologist, but would have recourse to it now if recourse was required. Happily, it isn't. But I think the maxim would indicate that our conception of Time would be one which is made up of the uses to which we put that concept in doing things we do, e.g. eating, sleeping, working, taking vacations, parking cars, etc.
I find myself baffled if I seek to define Time or even think of it in any other way. Baffled, I say, in finding any reason to do so. Clearly, we say there is a difference between what has happened and what is happening, and in identifying such things the concept of Time can be useful. Should we say that there is such a difference? Why not? How do we err if we do? Should we say there is no past? Why?
Won't we keep on living as we do, using Time, making Time, regardless of the ontological status of Time? Won't we continue to distinguish past, present and future regardless of the differences there may be between them? It seems we understand the differences between them well enough, and those differences hardly seem surprising or worthy of analysis. Will we ever, seriously, claim that nothing happened in the past, that there will be no future? Do we ever make the distinctions philosophers make or reach the conclusions they do as to Time while living our lives? If we don't, doesn't that tell us something significant about the Philosophy of Time?
Perhaps another maxim along the lines of the pragmatic maxim would be useful. Something like this: "Consider what effects, that might conceivably have practical bearings, which may result from our study of the subject in question. If there are no such effects, then our study serves no purpose." Let's call it "the pertinence maxim." [Copyright Ciceronianus, 2017.]
It may be that there are aspects of Time that may usefully be subject to scientific study, e.g. the reasons why we perceive times' passage in different ways in different circumstances. Of course, Time has also been a subject of study in physics. It seems to me, though, that this kind of study is one best pursued by scientists, not by philosophers.