Can a society exist without a concept of time? If a society was forced underground, cut off from cycles like day and night, without any time-keeping technology, would one be invented at some point or would people simply dictate everything by the "now," eating when they are hungry and sleeping when they are sleepy etc.

What an inventive thought experiment, though a bit scary (it is hard to imagine that a society would undergo this transition due to creative, peace-time reasons). I take it that you are suggesting that we often measure time in terms of the sun, moon, and other above-ground factors (tides, stars...), tempered by various forms of technology. Without daylight and machines (no clocks of any kind or devices that would offer us a reliable metric system), "telling time" might be difficult indeed, but it is difficult to imagine any society without a grasp of the past, present, and future. None of us can live in the (or an) instant --that infinitesimally small "knife-edge" present in which there is no past or future. One may put the point technically as the claim that we live in intervals or events, not instants. I actually think that "instants" (like points in space) are more theoretical entities as opposed to concrete individual objects. So, I would say that an instant is the end or beginning of an event. In any case, so long as there is thought, language, action (etc) one implicitly must function with some sense of temporal endurance (that is, one must have some "concept of time." So, in your examples of hunger and eating one would (presumably), if one engages in eating, need some understanding that you have to have one spoonful of food before you have a second spoonful and, just as basically, you would need some temporal understanding that eating (in the future) can satisfy your (current, present) appetite.

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