Professor Michael Sudduth

Readings in Religious Epistemology

Handout #12 (11/23/99)

How can we construct a good argument for God's existence via inference to best explanation?

The likelihood of some proposition h given some evidence e can be determined by inference to best explanation.

Let P = the probability of

h = the target proposition (taken as a hypothesis)

e = the relevant evidence

k = background knowledge.

Note: e and k represent the way in which one's total evidence can be divided. It is useful to divide one's total evidence into the background information you bring to determinations of whether some new or specific evidence supports a particular hypothesis. For instance, if you are investigating a murder scene and trying to determine who committed the murder, k would include forensics, etc. and e would be what you uncover at the scene of the crime or thereafter in the investigation. K may generally thought of as "what we know in relevant or neighboring fields," in relation to the proposition or hypothesis in question. But the division between k and e is sometimes arbitrary.

So the probability of some proposition h given one's evidence e is expressed as: P(h/e&k)

The P(h/e&k) is a function of the explanatory power of h and the prior probability of h.

• The explanatory power of h is determined by

h's predictive power, P(e/h&k) (does h lead us to expect e?)

e's prior probability, P(e/k) (how likely is e whether or not h is true?)

• The prior probability of h, P(h/k) is a function of

h's simplicity

h's fit with background knowledge.

Explanatory power is increased in relation to the h's predictive power being high and e's prior probability being low. Hence, the probability of some proposition h is increased just if

P(e/h&k) > P(e/k), and P(e/h&k) > P(e/k) just if either P(e/h&k) is high or P(e/k) is low. How high the probability is increased will depend on how high P(e/h&k) is and how low P(e/k) is.

The significance of h's prior probability enters in when trying to determine how likely h is given one's total evidence base. It will often turn out that there is some alternate hypothesis h* such that P(e/h*&k) > P(e/k).

How do we determine which hypothesis has the higher probability on evidence e, when both h and h* have equal explanatory power?

The following formula can be used to determine this:

If P(e/h&k) = P(e/h*&k), then P(h/e&k) > P(h*/e&k) just if P(h/k) > P(h*/k).

In other words, prior probability enables us to choose between rival hypotheses that have equal explanatory power. Fit with background knowledge has already been explained. A simple hypothesis is one that postulates the fewest number of entities and component laws describing their interaction. Simplicity is especially important when there is no background knowledge, perhaps because there is no relevant close field from which we can draw information with which to assess h. If h is very general or unique, this problem arises. In such cases, simplicity is the only factor that determines prior probability.

*The sort of probabalistic reasoning developed (above) is studied in confirmation theory and involves so-called Bayesian probability (after the mathematician Rev. Thomas Bayes).

(e1) There exists a complex physical system U (the Universe).

(e2) U exhibits significant temporal regularities.

(e3) U is fine-tuned for the emergence of life in U.

God (g) = df. a being with unlimited power, knowledge, and freedom.

(Properties such as immateriality, eternity, and omnibenevolence can be logically deduced from this definition)

There are three questions that must be asked in trying to determine whether {e1, e2, e3} provide good support for theism (g).

For the sake of simplicity I will let e = {e1, e2, e3}

Is P(e/g&k) high?

Is P(e/k) low?

Are there any evidentially relevant alternate hypotheses which (i) have equal or greater explanatory power than g and (ii) have an equal or greater prior probability than g?

In Handout #11 (available on-line), I develop answers to these questions that support the contention that there is a significant probability of God's existence given e.