The Existence of God (book)
The Existence of God is a 1979 book by British philosopher of religion Richard Swinburne, Swinburne discusses the intrinsic probability of theism, with an everlastingly omnipotent, omniscient and perfectly free God. He states various reasons for the existence of God, such as cosmological and teleological arguments, arguments from the consciousness of the higher vertebrates including humans, morality, providence, history, miracles and religious experience. Swinburne claims that the occurrence of evil does not diminish the probability of God, and that the hiddenness of God can be explained by his allowing free choice to humans. He concludes  that on balance it is more probable than not that God exists, with a probability larger than 0.5, on a scale of 0.0 (impossible) to 1.0 (absolutely sure). Swinburne summarised the same argument in his later and shorter book "Is There a God?", omitting the use of Bayes' theorem and inductive logic, but including a discussion of multiple universes and cosmological inflation in the 2010 edition. Arguments in inductive logic. Central to the argument of Swinburne is the use of inductive logic. He defines a "correct C-inductive argument" as an argument where the premisses merely add to the probability  of the conclusion, and a stronger "correct P-inductive argument" when the premisses make the conclusion probable with a probability larger than 1/2. Probability of God according to theism using Bayes' theorem. Swinburne applies mathematical conditional probability logic to various hypotheses related to the existence of God and defines The notation formula_4 is used for the conditional probability of an event formula_1 occurring given that another event formula_3 occurred previously. This is also termed the posterior probability of formula_1 given formula_3. The probability of the present evidence formula_1 given background knowledge formula_3 can be written as the sum of the  evidence with God existing (formula_11, e and h) and the evidence without God (formula_12, e and not h): Application of Bayes' theorem to formula_16, the probability of the God hypothesis formula_2 given evidence formula_1 and background knowledge formula_3, results in The probability of a universe of our kind, as evidenced by formula_1 without a single omnipotent god (formula_22) formula_23 can written as the sum of the probabilities of several optional hypotheses formula_24 without a god, i = 1, 2, 3: The sum of probabilities becomes formula_28 Swinburne then claims to refute these three hypotheses: Admittedly this hypothesis formula_27 can explain  the present state of affairs in the universe - the evidence formula_1 - without the need of a God, that means the probability is 1.0: formula_37. However, Swinburne estimates that the probability formula_38 given the background knowledge is infinitesimally low. Then the sum of probabilities of the various hypotheses without God So formula_41, the posterior probability of theism or God formula_2 on the evidence formula_1 considered with background knowledge formula_3, will be 1/2 or more, by a "correct P-inductive argument". Swinburne states that it is impossible to give exact numerical values for the probabilities used. Swinburne concludes that deductive proofs of  God fail, but claims that on the basis of the above P-inductive argument theism is probably true. He notes that in his calculation the evidence from religious experience and historical evidence of life, death and resurrection of Jesus were ignored: its addition would be sufficient to make theism overall probable with a probability larger than 1/2.