## Wednesday, November 30, 2011

### A failed alternative to the Principle of Sufficient Reason

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").

#### 6 comments:

James Bejon said...

Here are some fairly random questions that vaguely have to do with this post (or at least have occurred to me as I've thought about this post):

1. If God exists, then why don't the same issues exist? That is, why can't we consider the probability of God's creating a brick of 2.5 kg, etc., and arrive at similar conclusions?

2. Suppose I ask God to pick a natural number. What are the odds that it's even? (I can buy that, in practice, when a human chooses a natural number, he's only choosing from a finite range, but I can't see this in God's case).

3. What do you think about the following argument?

(1) Any proposition that's true must be possibly knowable
(2) If God doesn't exist, then the proposition that the PSR is false isn't possibly knowable
(3) Therefore, either God exists or the PSR is true

some kant said...

Barring some further dependence story

Is it even possible to suggest that? If brick i is statistically dependent on brick i-1 all the way down to the first brick, is this the same as saying that each brick is "explained" by its predecessor(s)?

Alexander R Pruss said...

James:

1. I think the probability that God would create any particular such brick is zero. It's possible, but the probability is zero, just as the probability that you will get heads each time if you toss a coin infinitely often is zero, even though the outcome is possible.

2. I don't know. It depends on what sorts of reasons God might have for choosing different numbers.

3. This reminds me of Rutten's argument.

James Bejon said...

Good answers! Regarding 2, though, let's suppose God doesn't have any particular reasons for choosing any particular number, as we would in the case of someone other than God unless we had any reason not to do so. Or alternatively--since this may not be too plausible an assumption--let's just consider the question in epistemic terms.

Sam Harper said...

This is just brilliant. It's eloquent in its simplicity. (Yeah, that's a line from The Middleman, but I mean it.)

I have a question about the principle of sufficient reason that isn't directly related to your blog except that it presents a possible counter-example to the PSR. So if you don't want to answer it, that's fine, but if you do, I'll really appreciate it.

On page 466 of Philosophical Foundations for a Christian Worldview by Bill Craig and J.P. Moreland, they quoted Gottfried Leibniz as saying, "no fact can be real or existent, no statement true, unless there be a sufficient reason why it is so and not otherwise." This is what they called "the principle of sufficient reason."

But earlier in the book, while explaining libertarian free will, they said that "if Smith freely does (or wills to do) A, he could have refrained from doing (or willing to do) A or he could have done (or willed to have done) B without any conditions whatever being different. No description of Smith's desires, beliefs, character or other things in his make-up and no description of the universe prior to and at the moment of his choice to do A is sufficient to entail that he did A" (p. 271).

How can libertarian free will be reconciled with the principle of sufficient reason? There seems to be a contradiction in saying, on the one hand, that there is a sufficient reason for everything that happens, and saying, on the other hand, that there is no sufficient condition, inside or outside a person, to entail a particular choice.

Alexander R Pruss said...

The short answer is you either reject the "and not otherwise" part of Leibniz's answer (see this post), or you do a lot of hard work on the explanation of free choices. Part of the work is done here in Section 2.3.2 and its subsections.

I will also say something about it in a few minutes in a post.