Swinburne’s case for God (in The Existence of God, 2nd ed.) can be summed up this way:

1. Based on evidence other than religious experience, the existence of God is not very improbable.
2. If based on evidence other than religious experience, the existence of God is not very improbable, then the evidence from religious experience (in combination with other relevant evidence) makes the existence of God more probable than not.
Therefore:
3. The evidence from religious experience (in combination with other relevant evidence) makes the existence of God more probable than not.



The expression ‘not very improbable’ in premise (1) is a bit vague, making it difficult to determine whether or not Swinburne has succeeded in establishing this claim, so we should try to clarify this expression.

Let’s say that h is the hypothesis that God exists. Clearly Swinburne means that the probability of h (given the evidence he considers and given our background knowledge) is greater than some low probability at the upper border of a range of probabilities that we would consider to be ‘very improbable’.

One chance in a million or a probability of .000001 is obviously in the ‘very improbable’ range, but is presumably not at the upper border of that range. What we need to clarify is where (approximately) that upper border falls.

I think it makes sense to first clarify the notion ‘very probable’ and then use that as the basis for clarifying the notion of something being ‘very improbable’. My linguistic intuitions seem firmer when dealing with the positive concept of probability, as opposed to the negative concept of improbability.

Six chances in ten or a probability of .60 would qualify an hypothesis as being ‘probable’ in the sense of being more probable than not. But a probability of .60 would not ordinarily count as being ‘very probable’. So, the lower border of the range of probabilities categorized as ‘very probable’ must be some number above .60. I would say the same of seven chances in ten or a probability of .70.

Would eight chances in ten or a probability of .80 count as being ‘very probable’ ? Perhaps, but my linguistic intuition is that .90 is closer to being at the lower edge of the range of probabilities that we would ordinarily consider to be ‘very probable’. If this is correct, then the claim that ‘hypothesis h is very probable’ means something like this:

P (h I e & k) ≥ .90

If this clarification of ‘very probable’ is correct, then it is reasonable to infer that the upper border of ‘very improbable’ would be one chance in ten or a probability of .10. In that case, the claim that ‘hypothesis h is very improbable’ means something like this:

P (h I e & k) ≤ .10

If this is a proper way to understand the expression ‘very improbable’, then Swinburne’s premise (1) which speaks of God’s existence as being “not very improbable” can be restated with a bit more precision:

1a. Where e is the specific evidence (considered by Swinburne in EOG) for and against the existence of God, excluding the evidence of religious experience, and where h is the hypothesis that God exists, and where k is our background knowledge:
P (h I e & k) > .10

However, Swinburne probably intends something slightly stronger than this.
Suppose that Swinburne agrees that a probability of .10 is at the upper boundary of the range of probabilities in the category ‘very improbable’. Suppose that Swinburne’s case for this first premise only proved this:

P (h I e & k) = .11

This would be enough to prove that (1a) was true, but the probability in this case is so close to the border between what is considered ‘very improbable’ and what is considered ‘not very improbable’ that the truth of Swinburne’s original claim would still be in doubt. So, I think a slightly higher number needs to be used as the cutoff in order to ensure that the probability indicated by the evidence is clearly beyond what could reasonably be considered ‘very improbable’. Thus, I would suggest that the cutoff be bumped up from .10 to .20, to remove any doubts introduced by the fuzzy boundary here:
1b. Where e is the specific evidence (considered by Swinburne in EOG) for and against the existence of God, excluding the evidence of religious experience, and where h is the hypothesis that God exists, and where k is our background knowledge:
P (h I e & k) > .20

Therefore, if Swinburne can show that the evidence relevant to the hypothesis that God exists (specifically, the evidence that he considers in EOG), excluding the evidence of religious experience, and given our background knowledge, makes the probability of this hypothesis greater than .20, then I think we should accept the first premise of his argument, namely the claim that this evidence makes the existence of God “not very improbable”.

Most of the arguments presented in EOG are part of a cumulative case to establish premise (1). For this part of his case, Swinburne is making a fairly modest claim. He claims to have shown that the evidence for and against the existence of God taken together, and setting aside the evidence of religious experience, provides some degree of confirmation of the hypothesis that God exists, making this hypothesis “not very improbable”.