RS evaluates theism using Bayes's Theorem (BT). Here, we'll review:

- BT as RS presents it and
- reasons to use BT to evaluate theism.

__The Theorem__

Where:

- h = the hypothesis in questions
- e = evidence for h
- k = general background knowledge (GBK; tautological knowledge)
- P = the probability of h

then:

- P(h/e&k) = the probability of h, given e & k
- P(e/h&k) = the probability of e, given h & k
- P(h/k) = the probability of h, given k, i.e., the prior probability of h
- P(e/k) = the probability of e, given k, i.e., the prior probability of e
- P(h/e&k) = [P(e/h&k) P(h/k)] / P(e/k) all of which =
- the probability of h, given e & k = [(the probability of e, given h & k) * (the probability of h, given k)] divided by the probability of e, given k

Plug in the variables for theism and you get:

the probability that God exists, given evidence wrt God's existence & general background knowledge =

[(the probability of the evidence wrt God's existence, given God's existence and GBK) * (the probability of God exists, GBK)] all divided by (the probability of the evidence wrt God's existence, GBK)

*Why Use BT Wrt Theism*

RS will consider the following arguments:

- cosmological
- teleological
- from consciousness and morality
- from providence
- from evil
- from history and miracles
- from religious experience

RS will combine the arguments by considering them in the above order and assessing their probability according to Bayes’s theorem. E.g., he first considers the cosmological argument. When he gets to considering a second (or later) argument, whatever assessment he’s made of the prior argument(s) will be included in the evidence [(e)] of the second (or later) argument. I.e., the results of an argument’s assessment is included in the evidence [(e)] of subsequent assessments, so adding them one at a time combines the arguments.

RS's assessments of the arguments will be imprecise bco the difficulties in calculating exact probability values for theistic and non-theistic propositions, claims, arguments, etc.. He maintains that BT can be useful with broad probability estimates, e.g., giving such-and-such theory a probability >0.5 but less than 1. He will use such broad estimates here.

The SEP entry notes that BT is handy when there is disagreement wrt calculation of unconditional and conditional probabilities. If certain info is known and agreed upon, the inverse probability may be more easily calculated and may be more readily agreed upon.

Though a mathematical triviality, Bayes's Theorem is of great value in calculating conditional probabilities because inverse probabilities are typically both easier to ascertain and less subjective than direct probabilities. People with different views about the unconditional probabilities of

EandHoften disagree aboutE's value as an indicator ofH. Even so, they can agree about the degree to which the hypothesis predicts the data if they know any of the following intersubjectively available facts: (a)E'sobjectiveprobability givenH, (b) the frequency with which events likeEwill occur ifHis true, or (c) the fact thatHlogically entailsE. Scientists often design experiments so that likelihoods can be known in one of these "objective" ways. Bayes's Theorem then ensures that any dispute about the significance of the experimental results can be traced to "subjective" disagreements about the unconditional probabilities ofHandE.

This particular feature hasn't any important role in RS's calculations. He maintains that BT does not imply that the predictive success of theories must be known. BT can be used to calculate a theory's probability without proof of predictability. The probability that we observe certain evidence can confirm a certain hypothesis even if we have not observed said evidence. Given what they would argue is relevant evidence, a person could use BT to calculate the probability of a future event, e.g., if and when an asteroid will hit Earth, and this calculated probability is important in itself, regardless of whether ot not actual events are ever observed in accordance or in opposition to the calculated probability.

Theism argues from the existence and nature of the universe to the existence of a non-embodied omnibeing. Some folks argue from the existence of certain evidence, e.g., personal experiences, to the existence of non-embodied beings, i.e., ghosts. We should use BT wrt theism bc we should use it when assessing other arguments that are similar in nature to theism, such as arguments about ghosts. It sounds like RS is saying here that we should use the same methods of evaluating theism as we use wrt other theories. As an aside, it might be interesting to think about other features of theory evaluation, e.g., parallels wrt the nature of evidence, proof, etc. in theistic v. non-theistic arguments. It reminds me of intelligent design proponents' attempts to change the method by which we typically evaluate theories. This change in method would result in propositions being accepted as knowledge which, under the current method, may have been discredited as knowledge and vv. Another time for that, perhaps.

Next up: The scientifically inexplicable and different breadths of explanation.

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