The problematic
character of infinite past time is revealed by a seemingly inescapable analytical
contradiction in the very expression “infinite past time.”
If one splits the
expression into its two component parts: (1) “past time”
and (2) “infinite,” and attempts to find a
common conceptual base which can apply to both terms (much like a lowest common
denominator can apply to two different denominators in two fractions), one can
immediately detect contradictory features. One such
common conceptual base is the idea of “occurrence,”
another, the idea of “achievement,” and still another, the
idea of “actualizability.” Let us begin with the
expression “past time.”
Past time can only be
viewed as having occurred, or having been achieved, or having been actualized;
otherwise, it would be analytically indistinguishable from present time and
future time.
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