C vs P-Inductive Arguments

Borrowing from Richard Swinburne, an argument is C-inductive if some evidence (call that E) raises the likelihood of some hypothesis (call that H). An argument is P-inductive if E makes H probable (more than 50%).

More precisely, an argument is C-inductive IFF P(h/e&K) > P(h/K), which means some evidence (e) increases the probability of a particular hypothesis to a higher level than it would otherwise be given our background knowledge. Whereas an argument is P-inductive IFF P(h/e&K) > ½, which means some evidence (e) increase the probability of a particular hypothesis to at least 50%. 

Here are some things to note about C-inductive arguments. First, by themselves, they may support more than one hypothesis. Second, their raising the likelihood of some hypothesis may not be very substantial. It may increase the likelihood just a small amount; nevertheless, it still counts as evidence in favor of that hypothesis.

If I notice that my driveway is wet, this evidence helps various hypotheses, including the hypothesis that it rained AND the hypothesis that my sprinkler activated. Just noting that some evidence may favor more than one hypothesis is not a good objection to using C-inductive arguments. At most, it only shows they are of limited value in certain situations. However, when considered alongside other evidence, C-inductive arguments can become extremely powerful for establishing a particular hypothesis, as Richard Swinburne has persuasively argued in his The Existence of God, where he cords together a series of C-inductive arguments (cosmological argument, teleological argument, argument from consciousness, etc.) to construct a P-inductive argument, which he claims makes the existence of God far more probable than not.

Of course, some hypotheses are exclusive in ways that rainy weather and sprinkler system’s activating are not. Either God exists or God does not exist – it is either one or the other, not neither, not both. Hence in these cases might be easier to sort evidence in favor of one hypothesis over another. (Notice I said easier but not necessarily easy.)

Physical fine-tuning is an example. That our universe displays such an intricate, delicately-balanced physical set up – namely, one that allows for the emergence of interactive, intelligent life – is a feature that strikes people as expected if God exists but very surprising if God does not exist.

Some say fine-tuning is C-inductive. Others, like Michael Rota, when dumping the entire thing into Bayes, argue fine-tuning should make us virtually certain of God’s existence. Hence, it’s P-inductive.