Another failed alternative to the Principle of Sufficient Reason
November 30, 2011 — 12:43

Author: Alexander Pruss  Category: Existence of God  Tags: , , , ,   Comments: 3

We presuppose something like the Principle of Sufficient Reason (PSR) in daily life and science. So there is very good reason to accept something like PSR. But suppose you don’t want to accept PSR, maybe because you think it implies the existence of God or maybe because you just think it has counterexamples. What can you do? Here is an option:

  1. The probability that a particular ordinary event, like the coming into existence of a brick or the death of a person, occurs without an explanation is non-zero but very low.

Here are some problems for this. Consider an infinite series of possible events: a brick of weight 2.5kg coming into existence in front of me now, a brick of weight 2.25kg coming into existence in front of me now, a brick of weight 2.125kg coming into existence in front of me now, …. By (1), each of these is very unlikely to happen without an explanation, but there is a non-zero probability for each. Moreover, plausibly, these non-zero probabilities are approximately the same.[note 1] So, we have an infinite number of possible events, each of which has approximately the same non-zero probability. Barring some further dependence story, we should conclude that very likely at least one of these events will happen. But none of these events in fact happened. Repeat the argument with mugs, rocks, etc. None of the analogues there happened. The theory, thus, stands refuted.

If we grant that two bricks can’t come into existence in the same place at the same time, the argument can be made stronger. Specify in each event the same location L for the brick. Then we have an infinite number of mutually exclusive events, each of which has approximately the same non-zero probability. And that not only is contrary to observation, but violates the conjunction of the total probability axiom and the finite additivity of probabilities (at least on the right understanding of “approximately the same” that ensures that if an infinite sequence of positive numbers is “approximately the same”, their mutual ratios are all moderately close to 1, say between 0.5 and 2).

Comments:
  • Jeremy Gwiazda

    My initial reaction is along the following lines. For any ’empty’ area of space over some time frame, some sort of basic particle has a very small chance of coming into existence. Then, essentially heavier bricks are less likely than lighter ones, and so it isn’t the case that ‘these non-zero probabilities are approximately the same’.

    December 6, 2011 — 11:26
  • 1. There are, plausibly, infinitely many kinds of fundamental particles. So we can run the argument on the basis of the particles, and get an extremely high probability that any given spot will get occupied by at least one of them.
    2. I think your suggestion still satisfies the definition in the definition of “approximately the same”. Let p1 be the probability of the 2.5 kg brick popping in and let p2 be the probability of the 2 kg brick. Let b = p1/p2 and c = p2/p1. I think your size-based intuitions, which I share, show that the definition is satisfied.

    December 9, 2011 — 11:24
  • Jeremy Gwiazda

    Regarding 2, I don’t follow. Wouldn’t p1 and p2 differ greatly, so that the ratios would not be near 1?

    December 12, 2011 — 16:02