A Potentially Infinite Past

A few days ago, whilst discussing with a friend the second premise of the Kalam cosmological argument (that the universe began to exist), he proposed an idea that I had not before come across. Instead of the universe having a beginning, or an actually infinite past, he claimed that it was perhaps the case that the universe has a potentially infinite past. Depicted below shows this theorem along side a universe with a beginning, and a universe with no beginning.

Fig 1. Three theories for a past, where O indicates the present; an arrow indicates a potential infinite; a | indicates a beginning; and a vertical ~ indicates an actual infinite. Top: An absolute beginning. Middle: An actually infinite past. Bottom: A potentially infinite past.

My friend claimed that he could imagine a possible world in which time played in rewind. The laws of physics would be such that the second law of thermodynamics would have broken plates jump onto tables and form themselves anew. Taking this further, he brought this idea into the actual world. Under this theory he imagined, time must be progressing both forwards and backwards, at two different positions in time. I present two arguments against this position in order to provide evidence that it is implausible for the universe to have a potentially infinite past. Not dissimilar to how we experience the future becoming the present, this theory would result in the idea that the past must also be changing, and therefore new past events are actualizing. This leads into the first argument:

1. The past alters or affects the present.
2. If the past is changing, then the present is changing.
3. The present is not changing.
4. Therefore, the past is not changing.
5. Therefore, the past is not potentially infinite.

First objection: Premise 3 is unsound. If the past is changing, our memories are also changing, therefore we cannot know if the present is changing or not. Therefore it is possible that the past is changing.

Refutation: We hold a properly basic belief that the past exists unchanging.

Second objection: Premise 1 is unsound. For an oscillating universe model, and past occurrences before the big bang would not affect out past and present, therefore our immediate past and present are not changing.

Refutation: Oscillating universe models predict that after each cycle, the universe expands to a slightly larger size. If we extrapolate into the past, each prior universe must be slightly smaller. Therefore, there is a point at which the universe has no size, therefore cannot have a previous cycle. This means that the model does not avoid a beginning.

My second argument is in regards more directly to the flow of time. By tracing time - contrary to a popular David Bowie song - we may conclude that even if a potentially infinite past exists, it does not avoid a beginning:

1. For a potentially infinite time into the future, time can be traced back to the present. This is equally valid for tracing the past forwards to the present.
2. If the past is potentially infinite, it is not finite.
3. A finite amount of time must have passed between now and the potential past.
4. From the contradiction of premises 2 and 3, it must be the case that the past can be traced back to it's starting point.
5. This starting point is equivalent to a beginning of time.

This argument may be better represented with the use of a further diagram. The past must have begun emanating from some point in time. Whenever this time is, it is a beginning.

Fig 2. A universe with a potentially infinite past. Dashed red arrows show that the past and future can be traced back to a specific time. In this case, O indicates an arbitrary point in time.