Let’s take a brief break from conditional probabilities and probability calculations involving Bayes’ theorem.

Much of Chapter 7 of The Existence of God (EOG) consists of general points, objections, and replies to objections, along the lines that one would expect in a more traditional philosophical discussion about cosmological arguments. I’m not clear on how some of these points connect with the conditional probabilities and probability equations for the cosmological argument. An important question, therefore, to keep in mind is, “How does this point relate back to the cosmological argument presented in terms of Bayes’ theorem?”

The Nature of Cosmological Arguments (p. 133-137)
1. Cosmological arguments are based on “…the existence of some finite object or, more specifically, a complex physical universe.” (EOG, p.135)
2. We can reach justifiable conclusions about the origin or development of the universe, despite the fact that we have information about only one universe. (EOG, p.134-135)
3. The “…two most persuasive and interesting versions of the cosmological argument are that given by Leibniz in his paper ‘On the Ultimate Origination of Things’, and that given by his contemporary Samuel Clarke in his Boyle Lectures for 1704 and published under the title A Demonstration of the Being and Attributes to God. The former seems to be the argument criticized by Kant in The Critique of Pure Reason and the latter the argument criticized by Hume in the Dialogues.” (EOG, p.136)
4. “…no argument from any such [clearly true] starting points to the existence of God is deductively valid. For, if an argument from, for example, the existence of a complex physical universe to the existence of God were deductively valid, then it would be incoherent to assert that a complex physical universe exists and God does not exist. There would be a hidden contradiction buried in such co-assertions.” (EOG, p.136)
A. Attempts to derive an obviously incoherent proposition from these two assertions have failed. (EOG, p.136)
B. One can spell out an obviously coherent scenario in which both assertions would be true (e.g. matter has always rearranged itself in various combinations, and the only persons have been embodied persons.) (EOG, p.136-137)
5. “Our primary concern is however to investigate whether it [the cosmological argument] is a good C-inductive or P-inductive argument, and just how much force it has.” (p.137)
At the end of Chapter 7, Swinburne concludes that his cosmological argument “is a good C-inductive argument.” (EOG, p.152) I agree with J.L. Mackie’s comment that this conclusion is insignificant, because it is so weak:
…all that is being said is that the existence of a complex physical universe raises the likelihood of a god, makes it more probable than it would have been otherwise, that is, if there had been no such universe. (The Miracle of Theism, p.98)
The following could be evaluated as a good C-inductive argument, by use of Swinburne’s criterion:
1. I purchased one state lottery ticket today.
Therefore:
2. I will win millions of dollars from the state lottery this week.
Obviously, my purchasing one state lottery ticket raises the probability that I will win millions of dollars from the state lottery. As the advertising slogan states, “You can’t win if you don’t play”. However, the increase in probability is extremely small in this case (e.g. about one in 100 million). Although this argument could qualify as a good C-inductive argument, it is clearly a bad argument. That is, it gives us only an extremely weak reason in support of the conclusion.
So, the real issue is the one mentioned last by Swinburne: We need to determine “just how much force it [the cosmological argument] has.” (EOG, p.137)