Infinity of past and future time

1. There's no conclusive cosmological evidence that time began with the big bang about 15 billion years ago, and it is a matter of some debate whether we live in an oscillating universe (big bang/big crunch/big bang, etc).  However, the issue of the temporal infinity of the world is far from new.  Aristotle believed that the world is eternal, and the eternity of the world was a hot topic in the 13th century between St. Thomas and St. Bonaventure.  Of course, both believed that the world began (the scriptures tell us that); but while for the latter thought he could prove that the world cannot be eternal, the former thought reason was unable to determine the issue and that one has to recur to revelation.

2. The past is infinite iff (if and only if) there is an infinite number of same length intervals,  e.g., years, before the present one, e.g.: 0 (present year), -1, -2, -3 (year),....
NOTE: in order to avoid confusion, it's important to keep in mind the following points:

3. Criticisms of the possibility that the past is infinite. 4. Can there be an infinite future?
The cosmology is unclear:


Aquinas on the eternity of the world

The XIII century saw a big controversy on whether it could be proved, and not merely accepted by faith, that the world began.  Saint Bonaventure held that it can be proved that the world began, while Saint Thomas Aquinas held that it cannot. Here we look at some of the arguments of Saint Thomas.
1. Since Aquinas adopted the Aristotelean theory of demonstration, according to which science deals with what is necessary, he held that it's impossible to prove that the world began because:

2. Aquinas considers eight objections to his view and answers them.  Here we'll consider only three:
  1. Nothing can be equal to God in any respect.  But if the world had no beginning, it would be equal to God with respect to infinite duration.  Hence, the world has a beginning.

  2. Reply: Divine duration is not successive.
  3. If an infinity of days had to pass before today, then today would never had arrived because it's impossible to traverse the infinite.

  4. Reply: this presupposes a starting day by adding to which we get to today. But there is no such starting day, and from any day in the past one can get to the present one in a finite number of steps.
  5. If the world were eternal, then any man would have been begotten of a previous one in an infinite series.  But the father is the efficient cause of the son, and an infinity of efficient causes is impossible.

  6. Reply: Aquinas draws a distinction between two types of series of efficient causes: