Reply to William Lawhead:

A keen and thought-provoking analysis of the purported implications of the  kalam cosmological argument:  BUT I reject both the neo-kalam  argument and the neo-kalam  supplement (since my writings on the cosmological argument--and Craig's--are well-known to you, I will make no attempt to remformulate the argument itself).

  1. I claim that:

    1. both:

      1. an actually infinite number of entities cannot exist (since the concept of such a series is self-contradictory);

      2. the series of actual events is finite (since each member is a determinate number of events after the first member), so that this series is not actually infinite, but rather indefintely extended or (if you like) potentially infinite;

    2. the symmetry thesis therefore does not hold;

    3. the concept of a potentially infinite or indefinitely extended series of future events is not self-contradictory;

      1. but of course it is merely a contingent truth (contra a necessary truth) that there will be an indefinitely extended future;

      2. if god created the space-time universe  ex nihilo, He also possesses the power to resolve it into nothing (though my belief is that He does not possess the will to do so);

  2. the main difficulty is with the neo-kalam supplement, and especially with the claim that God's perfect knowledge of the future consitutes, if God is a timelessly necessary being, an actually infinite series of temporally ordered events in the divine Mind;

    1. while there are no actual events (past, present, or future) that God cannot or does not know so far as they are logically possible objects of knowledge, there are many things that God cannot know because they are not logically possible objects of knowledge;

      1. God cannot know the truth or falsity of contra-factual propositions (if it is the case or is determined that the Hacketts are not going to have a fourth child, God cannot know what that child will be like, because there is no object to be known;

      2. if any given mathematically (potentially) infinite series has by definition no last member, then, in the case of the series of whole numbers (for example), God cannot know what the last or highest numjber of the series is, since there is no such object to be known;

      3. if the series of actual events is a determinate and numberable series which extends indefinitely (so that, in your words, the series of future events is unending), then God cannot know the last event in this series, since, by definition, there is no such object to be known;

        1. it follows that, even in the Divine knowledge the series of actual (or therefore future) events is therefore not a completed series, since, again by definition, there is no such object to be known (the concept of a completed series of indefinitely extended events is a self-contradictory concept);

        2. but if the series of actual events has no beginning, then every actual event is  both the completion of an actually infinite series  and also an extension of it by increase--and that is self-contradictory;

      4. I therefore conclude that the so-called symmetry thesis does not hold, and that:

        1. an 'actually infinite series of events'  is self-contradictory;

        2. but an 'unending series of future events' is not self-contradictory;

    2. Put this whole thing a different (but logically equivalent) way: is the concept of 'all actual events' (past, present, and future), a logically possible object of knowledge for God?

      1. No--if it is construed as a completed set (which by definition it is not, if the series of future events is unending), since that would be self-contradictory--hence, God does not know 'all actual events' collectively as a completed set (since He cannot know a logically contradictory object);

      2. Yes--if the concept of all actual events is construed distributively as individually distinguishable and successivley identifiable or numerable so that any given event is locatable for God in its temporal vicinity.

        [P.S. remember that precisely because God transcends time and space, He is present and operative at every space-time location, as otherwise He could not be.]

  3. On the last page of your article (pg. 111):

    1. you claim that it is not your purpose here to affirm any of the following:

      1. an actual infinite is possible;

      2. divine foreknowledge is impossible;

      3. the future is finite;

      4. the past is infinite;

    2. but your neo-kalam argument and supplement are successful only if at least one of these four propositions (correctly interpreted) is true and its contradictory false; are you prepared to accept that consequence and its implications for classical theism?