A calendar is not an scheme for "giving names to days and years". What a year is is
defined by the calendar...for example, in a lunar calendar a year is something different than in a solar one.
- I didn't write that that line, but actually I can't fault it. The primary purpose of most calendars is indeed to provide names for periods of time. Calendars generally do also define terms of common usage like "month", "week", and "year", and usually give alternate definitions for them that correspond in greater or lesser degree to other usages of those words which are not calendar-based (things like "mean sidereal year" exist independently of any calendar). But the purpose of those definitions is to provide a convenient way to label moments and/or periods of time in the past and future, to make it easier to record history and make long-range plans.
"Provide names to periods of time" that's a bit closer to it...my problem is, a year did not exist until a calendar that defined it did, so a calendar doesn't give a name to a year, creates it. But how do you measure those periods of time? A day is a pretty obvious thing, based on the movement of an astronomical object, the sun. The year is a bit more problematic, and you can only define it observing the constelations in the sky at sunset or sunrise. Thus my attempted definition. If you can do better, please be my guest, but I'm not going to leave that line as it is.
- You could always look at it from the units-of-measurement point of view. Things like "hour", "second", "week", etc. are somewhat arbitrary products of definition, but just as we chose units like "pounds" to be useful for everyday life and commerce (imagine buying food from a grocer if your only units of weight were milligrams or tons), our choice of units for time was not entirely arbitrary. The day was such an obvious thing that it made sense for smaller units to evenly divide it. Likewise the cycle of seasons pre-dated any calendar, so it made sense for calendars to define the "year" unit of time measure in a way that made it convenient for knowing when to plant crops. So I wouldn't call calendars totally "arbitary", but I would say that they defined measurements of time that served the purposes of the prople that created them.
The various astronomical days, months and years really do exist; but the calendrical day and month and year do not. They are creations of the calendar, which approximate the astronomical periods in some ways. But they aren't just inaccurate measurements; to use the astronomical units would be wrong by the calendar. So these units have no existence without the calendar. -- SJK