Temporal Predication with Temporal Parts and Temporal Counterparts

If ordinary objects have temporal parts, then temporal predications have the following truth conditions: necessarily, (a is F) at t iff a has a temporal part that is located at t and that is F. If ordinary objects have temporal counterparts, then, necessarily, (a is F) at t iff a has a temporal counterpart that is located at t and that is F. The temporal-parts account allows temporal predication to be closed under the parthood relation: since all that is required to be F at t is to have a temporal part, a t, that is located at t and that is F, every object that has a t as a temporal part is F at t. Similarly for the temporal-counterparts account. Both closure under parthood and closure under counterparthood are shown to have unacceptable consequences. Then strategies for avoiding closure are considered and rejected.