Free construction of time from events

Conclusions and conjectures

Some may be of the opinion that one event can begin before another only by virtue of the existence of some event (a “witness”) which wholly precedes the other and does not wholly precede the one (and similarly for “ends before” and “does not abut”). Those would prefer $\mathbb{F}$ ₀ to $\mathbb{F}$ as a model for observers' apprehensions of events. Since G is a functor from $\mathbb{M}$ to $\mathbb{F}$ ₀, the current construction (restricted to $\mathbb{F}$ ₀) remains applicable.

This work supports a claim that the psychologically fundamental temporal relationships are “wholly precedes”, “begins before”, “ends before” and “abuts”. But only in a very weak sense. Any other set of relationships which is interdefinable with this one, using only quantifier-free formulas in the definitions, could be used to define a category $\mathbb{F}$ ^′ which is indistinguishable from $\mathbb{F}$ (because the same functions preserve and reflect the new relationships). This work equally supports the claim that those relationships are the psychologically fundamental ones, or the claim that it is just “wholly precedes” which is fundamental, and that we perceive “begins before” just by virtue of witnesses. But it refutes the claim that only “wholly precedes” is fundamental, and that we understand “begins before” only because we understand time as a linear ordering.