Potential Versus Actual Infinites

Taken from: http://carm.org/debate-matt-slick-eddie-tabash-does-god-exist

1. Two Types of Infinity: Actual and Potential
   
   1. Actual Infinite – A timeless totality that does not increase or decrease with the number of members it contains.
      1. Example: The number of points on a line is an actual infinite; there is no exact number.
      2. Problems with actual infinites:
         1. If an actual infinite exist, there are problems that arise. Following are some examples.
            1. Consider an infinitely long line of dominos in the universe. If we take half of them, we still have an infinite number. But, 1/2 of the original infinite contains the same number of dominos as the original infinite. This would mean that one half of the whole is equal to the whole. This cannot be.
            2. An infinitely old clock. The hour hand makes its circuit around the face of the clock 2 times a day. The minute hand 24 times a day. But, an infinite amount of time results in both the minute hand and the hour hand having an equal number of rotations even though the minute has 12 times as many rotations as the hour hand. This cannot be.
            3. Therefore actual infinities do not exist.
   2. Potential Infinite – A Potential Infinite is comprised of a finite set that increases its number through time by adding members to its set. Each addition results in a larger finite set.
      1. Example: Dividing line in half, and then in half, and half again, results in a finite set of divisions. It is possible to continue to do this, but with each division, a finite number of divisions still exists.
2. Cannot Cross an Actual Infinite
   1. Imagine a timeless, infinitely long line of dominoes
   2. By traveling along the line of successive dominos, in order to arrive at any particular domino you would have to traverse an infinite number of them in order to arrive at that particular domino. But an infinite number of dominos cannot be traversed—otherwise it isn’t infinite. So, we cannot have an actual infinite number of dominos.
   3. Likewise, if each domino represents one second of time and each domino were falling one after another, representing successive moments in time, the line of dominos could not be infinite in length in the past because…
      1. There would never have been a first domino that fell. If there is no first, there can be no second, no third, no fourth, and so on.
   4. Therefore, an actual infinite (timeless infinite number) of successive events in the past is logically impossible.
3. Summary: an actual infinite of successive events in the past is logically impossible because
   1. It would require traversing an infinite number of events which cannot be done.
   2. There would be no first event. If there is no first event, there cannot be a second, or a third, and no following series of events. Therefore, there must be a beginning of events.

Cosmological Argument

1. The universe exists
2. There are only two options available to account for the Universe
   1. The universe either had a beginning or it had no beginning
      1. “Beginning” and “no beginning” is an antonymic pair.
      2. Antonyms are opposites. i.e., beginning/no beginning; personal/non personal. There can be no third option in these antonymic pairs. Therefore, these pairs are not false dichotomies since no other options are possible.
3. If the universe had no beginning, then it is either Eternally Static or Eternally non-Static (Oscillating)
   1. Eternally Static Universe: The universe has always existed.
      1. This does not agree with Cosmic Microwave Background Radiation (CMBR) which shows the universe had a beginning.
      2. The universe always existing would be impossible since it would mean the universe had an infinite number of successive events (atoms moving, stars forming, etc.), before we got to now. But this is impossible as we have seen above.
      3. Conclusion: The universe is not infinitely old. It had a beginning.
   2. Eternally non Static, or Oscillating Universe: The universe has come in and out of existence as it expands and contracts, forms, collapses, forms, collapses, for an infinite amount of time.
      1. This does not agree with the 2nd law of thermodynamics. The universe, as a whole, is a closed system. There is no known mechanism for a 100% efficient exchange of energy in formation and reformation.
      2. An eternally oscillating universe would require an infinite number of oscillations but this is impossible since it would mean the universe had an infinite number of successive events.
      3. Conclusion: The universe had a beginning and could not have been eternally oscillating.
4. If the universe had a beginning, then something brought the universe into existence.
5. There are only two options to account for the cause of the existence of the universe:
   1. First Option: Impersonal Cause
   2. Second Option: Personal Cause
6. First Option: Impersonal Cause of the universe
   1. Only two possible options
      1. First Option: The universe brought itself into existence
      2. Second Option: The universe was caused to exist
   2. Impersonal Cause, First option: the universe brought itself into existence.
      1. This is not possible because in order for an action to occur, something has to cause the action. A cause is itself an action. An action results from something that exists prior to it. But if something has no existence (nothing), then it has no prior existence, no properties, no abilities, and cannot perform any actions. Therefore, nothing comes from nothing and the universe did not bring itself into existence.
   3. Impersonal Cause, Second option: The universe was caused to exist by an impersonal means.
      1. Whatever caused the universe to exist, existed prior to the universe.
      2. This existence was ontologically prior (essence/existence), not temporally prior to the universe.
         1. In Mr. Tabash’s debate with Phil Fernandez he said at 54:44, “We can’t even speak of a cause [of the universe] because there was no time and space for sequential causation to play out before the big bang occurred.”
         2. Two things to note here:
            1. Mr. Tabash denies temporality before the universe.
            2. Mr. Tabash, by his own admission, cannot offer us a cause of the universe.
      3. An impersonal, ontologically prior cause either existed in a timeless and changeless state or it did not.
         1. Quentin Smith (an atheist), Professor of Philosophy who is listed under Suggested Links on Eddie Tabash’s site (tabash.com) said, “…that the cause of space-time exists timelessly.”
         2. Timeless, Changeless state: An impersonal, ontologically prior cause existing in a timeless and changeless state cannot do anything since it can’t suddenly decide to do anything. It just is.
            1. Conclusion: an impersonal, ontological prior cause could not have brought the universe into existence.
         3. Non-Timeless, Changing state: If the impersonal, ontologically prior cause existed in a non-timeless, changing state then whatever caused it to change is a prior cause which would be a cause external to itself.
            1. We then must ask what caused that prior cause, and the cause before that, etc. This would mean that no matter how far back we go, we would never find the first event. With no first event, there can be no second, third, etc., and nothing would ever happen.
            2. Remember: an infinite regression of prior causes would mean there is an infinite regression of uncaused causes which would have to be traversed before we found the cause of the universe, but this is impossible per Point 3 above (Summary: an actual infinite of successive events in the past is logically impossible.
         4. Conclusion regarding an Impersonal Cause of the Universe:
            1. Neither the Impersonal Timeless, Changeless State or the Non-Timeless, Changing State can account for the beginning of the universe.
         5. Two Options: When we have only two options to account for something (impersonal and personal) and one of them is negated, then by default the other is validated. Since the impersonal cause cannot account for the beginning of the universe, the only option left is the personal cause.
         6. The universe was caused to exist by a Personal Cause.
         7. That Personal Cause is God.
7. Second Option: Personal Cause of the Universe.
   1. There are only two options to account for a Personal Being to Act to create the universe: External and Internal Cause.
      1. An External Cause which only brings the issue of causation back to its prior causes, for infinity, which cannot happen since we cannot have an infinite regression of causes.
      2. An Internal Cause in a Personal Being which would be self determined, a Decision to Act.
   2.  Therefore, the personal Cause of the Universe made a decision to act and created the universe.

I have wrestled with this idea for some time mostly in it's application to cosmology. I had a friend present me with a Mobius strip as some sort of demonstration as to how the universe or time might work. I don't think that the two are in any way analogous. It's as if we had traced our finger along the strip to reach a certain point. Consider our fingertip is the current frame of reference. We must start tracing to reach any point. We were not tracing for an infinite duration of time. In that same manner, I see that we are currently at a frame of reference in the universe and to reach this frame it must have traversed a finite number of frames before it. i don't think this is in any way attributed to a failure of human understanding. It's just the way things are. I'm not seeking to confuse my reasoning to imagine something that is just not so...