Saturday, August 28, 2010

An Inductive Argument Against an Infinite Regress of Non-temporal Causes

1. For any non-temporal causal regress, that regress is either finite or infinite. (Definition)

2. The causal regress of X is an attribute of X. (Premise)

3. If every observable attribute of X is finite, then the causal regress of X is most likely finite. (Premise)

4. Every observable attribute of X is finite. (Premise)

5. Therefore, the causal regress of X is most likely finite. (From 1 – 4)

Take, for example, my favorite illustration of a watch. The causal regress of one gear turning to cause another gear's turning is an attribute of the watch - in support of our second premise. (3) introduces induction to the argument. If attributes A, B, C, and D of X are all observed to be finite, the likelihood that E of X is also finite is increased significantly. Moreover, if all of the known attributes of X are finite, and none of them are infinite, it follows that all of X's attributes - both known and unknown - are most likely finite.

For any non-temporal causal regress, then, it follows that the regress itself is most likely finite, given the finitude of every other attribute. In arguing for a metaphysically necessary non-temporal First Cause, the inductive argument against an infinite regress may be combined with the following argument:

1*. Every existing entity is either contingent or necessary. (Premise)

In this context, an entity is contingent if it has its existence in another; and it is necessary if it is self-existent, and exists simply by virtue of the fact that it cannot not-be.

2*. If a non-temporal regress of causes is finite, then a metaphysically necessary First Cause exists. (Premise)

3*. The non-temporal regress of causes is most likely finite. (Premise)

4*. Therefore, a metaphysically necessary First Cause most likely exists. (From 2 and 3)

I tend to think that this argument is also applicable to strictly temporal causal events. So long as time is an attribute of a thing, the inductive argument may be modified to fit this change of focus.

1. You could just as easily reason the whole thing backward:

1. Every existing entity is either contingent or metaphysically necessary.

2. If no observable entity is metaphysically necessary, metaphysically necessary entities likely do not exist.

3. Every observable entity is contingent.

4. Therefore, metaphysically necessary entities likely do not exist.

5. If the causal regress of X is finite, then a metaphysically necessary First Cause exists.

6. Therefore, the causal regress of X is most likely infinite.