Philosophy Research Archives

Volume 3, 1977

Is Every Possibility Actualized in an Infinite Period of Time?

It has often been thought that the existence of an infinite amount of time implies the realization of all possibilities. However, it can be proved that it is not true that for any T, if T is an infinite period of time, then every possibility is actualized in T. The proof works for any sense of 'possibility' in which there are possibilities that cannot be actualized simultaneously. It still might be argued that if there is an infinite amount of time, then each possibility is actualized sometime (during some infinite period of time, though not all). In particular it might be claimed that if there is an infinite amount of time, then there is an uninterrupted infinite period of time; and (P*) for any T, if T is an uninterrupted infinite period of time, then every possibility is actualized in T. However, it can also be shown that (P*) is not necessarily true. For it to be actually true, some very strong Principle of Universal Random Change must be true.