Of course an integer exists; it's a mathematical zero-dimensional point. Time is not a pure mathematical construct like that; it's continuous (at non-quantum scales, at least). Characters are integral, non-continuous values too... there's nothing between "a" and "b".
If you define the total order of a set of time ranges as an ordering on their beginnings, then you have the ordering you're talking about. If you compare time ranges that have different granularities the results might not make a ton of sense depending on what you're trying to do, but they'll be consistent. Eg: 2012 < 2012-05 < 2012-05-03 < 2012-05-03T15:00:00. Is the year 2012 "less than" May 3, 2012? Interpreted as a point in time, yes, but interpreted as time periods no, not really, because they overlap. But 2012 might be a perfectly valid value for when a customer bought some widget; if you ask them they may not remember the date any more specifically than that, and if you're deciding whether or not to process a warranty claim just knowing the year might be sufficient.