To quickly recap, Swinburne argues that the probability of God's existence (h), given certain empirical evidence (e) and background tautological evidence (k) is high. This is stated in Bayesian form as:

- Pr(h|e&k) = Pr(e|h&k) Pr(h|k) / Pr(e|k)

Obviously, this equation is meaningless without actual numerical values. We saw in part two that problems arise when we combine some of Swinburne's proposed values and with his assumptions about probability. In particular, we saw that if he wants

*h*to confer a high probability on

*e,*he may have to abandon his commitment to God's simplicity.

In this part we will look at another mathematical difficulty. One that arises when Swinburne considers alternatives to theism.

Swinburne is trying to offer an explanation for the evidence we observe in this universe. He thinks theism is the most probable explanation. But he identifies three alternatives:

**1. What are the Alternatives?**Swinburne is trying to offer an explanation for the evidence we observe in this universe. He thinks theism is the most probable explanation. But he identifies three alternatives:

*h1*= "There are many Gods responsible for the creation of the universe"*h2*= "There is an eternal physical universe (or multiverse)"*h3*= "There is no explanation; the universe is just a brute fact"

So we end up with four possible explanations for the observed universe:

**2. Putting Figures on the Alternatives**

For the purposes of analysing the argument, we can assume that these four possibilities are mutually exclusive and jointly exhaustive. In other words, they amount to a complete carving-up of the available probability space. And since all probabilities have a value between 0 and 1, we must accept the following equation:

- Pr(h|k) + Pr(h1|k) + Pr(h2|k) + Pr(h3|k) = 1

Now we need some estimate of the different probabilities. Interestingly, as Gwiazda points out, Swinburne thinks that the Pr(h|k) could be very small indeed. His reason being that the existence of something rather than nothing is highly improbable. This leads Gwiaza to put a figure of 0.001 on it.

You may think this figure is slightly suspicious (I did) but I think Gwiazda is only using it to make a point about the combination of Swinburne's reluctance to put precise figures into his equation with his philosophical assumptions about what makes something probable or not.

Anyway, if we accept the figure of 0.001 for Pr(h|k) we must also accept that:

- Pr(h1|k) + Pr(h2|k) + Pr(h3|k) = 0.999

**3. Muddled Reasoning**

Now let's go through Swinburne's thoughts on each of these alternative explanations. He starts off by saying that the probability of there being many gods (h1) must be much lower than the probability of a single God. This would seem to make sense.

He goes on to say that the probability of no explanation (h3) must be "infinitesimally low". I'm not sure how defensible that is. I guess it depends on how we understand probability. If we are working from a subjective or epistemic understanding, then I guess the thought that the universe had no explanation would be pretty surprising. This would then lead to an infinitesimally low figure for Pr(h3|k). Still, I have my doubts.

Nonetheless, if we accept Swinburne's reasoning we must ask: Where does that leave the probability of the eternal physical universe (h2)? In pretty good shape actually. For if Swinburne is correct, h1 and h3 must be less intrinsically probable than h. This means that they must be less than 0.001.

That can mean only one thing: h2 must have a high intrinsic probability. Indeed, it could have a probability of up to 0.998. This would make h2 the most attractive explanation by a mile.

Obviously, Swinburne does not agree. He thinks the physical universe is highly complex and so highly improbable. Now we saw how this assumption was problematic in the previous post, but if its going to work here Swinburne will need to raise his estimate for the intrinsic probability of theism, or consider more alternative explanations.

Either way, he has work to do.

**4. Summing up and Moving On**

The first two entries in this series have dealt with some technical problems that arise from Swinburne's use of Bayes' theorem. Gwiazda's main argument has been that Swinburne's philosophical assumptions about probability have placed him somewhere between a rock and a hard place when it comes to proving his central thesis that God is a better explanation of complex universe than anything else.

In future entries in this series we will move on from these technical problems to consider Swinburne's understanding of God's simplicity.

This is a nice series.

ReplyDeleteYou might want to clean up a few slight errors:

h1 = "There are many God's responsible for the creation of the universe"

change God's to Gods.

Pr(h|k) + Pr(h1|k) + Pr(h2|k) + Pr(h2|k) + Pr(h3|k) = 1

Pr(h2|k) is repeated twice

Thanks for pointing those out.

ReplyDelete