The Justification of Scientific Explanation
– The prior probability of a theory is its probability before we consider the detailed evidence of observation cited in its support.
– The prior probability of a theory depends on the degree of its fit with background knowledge (an a posteriori matter), and on its simplicity and scope (features internal to the theory and so an a priori matter).
– A theory fits with our general background knowledge of how the world works in so far as the kinds of entities and laws that it postulates are similar to those that probably (on our evidence) exist and operate in other fields.
– Its degree of simplicity and its scope determine the intrinsic probability of a theory, which is its probability independent of its relation to any evidence.
– The simplicity of a theory is a matter of it postulating few (logically independent) entities, few properties of entitites, few kinds of entitites, few kinds of properties, properties more readily observable, few separate laws with few terms relating few variables, the simplest formulation of each law being mathematically simple.
– Yet, a theory’s intrinsic probability is diminished in so far as its scope is great. Clearly, the more you assert, the more likely you are to make a mistake. But typically, when a theory loses scope, it loses simplicity as well. Therefore, the criterion of small scope is not very important.
Justification of Personal Explanation
– The same criteria of prior probability (determined by simplicity, scope, and fit with background knowledge, if any) and explanatory power are at work in assessing the probability of a hypothesis of personal explanation (which is a hypothesis that a certain agent produced some effect in virtue of certain beliefs, intentions, and powers).
– Principle of charity and principle of simplicity in personal explanations.
– In case of human personal agents, we assume (all things being equal) approximately similar set of beliefs, powers, etc. as those with which we are directly acquainted by our own firsthand experience.
– Extensions of the account to the way that animals act.
– The similarities and dissimilarities that result from applying personal explanation to non-embodied agents that might exist.
– Simplicity in the case of hypotheses of personal explanation is a matter of postulating few persons, few properties, few constant intentions, and continuing basic powers, and simple laws.
– The explanatory power of a hypothesis of personal explanation is a matter of its ability to predict the phenomena that we in fact observe. Also, it should be the case that the phenomena that is taken as evidence is not an expected consequence on other hypotheses.
– The hypothesis of theism that seeks to explain the existence of the universe and its various features is a hypothesis of personal explanation, and so it is to be assessed by these criteria.
– Just as with the physical “theory of everything”, theism is a hypothesis of enormous scope, and consequently, there will not be background knowledge with which it has to fit. Therefore, it is not a disadvantage to it if it postulates a person that is in many ways rather unlike the embodied human persons that we are familiar with — as long as the existence of human persons, etc. is explained by the hypothesis of theism. (Analogy from the situation with regard to fundamental particles vs. our empirical observations.)
– Restatement of the previous points in terms of Bayes’ theorem.
– It is a matter of indifference as regars the theorem, whether evidence is observed before or after the formulation of the hypothesis. What matters is the relations of probability that hold between evidence and hypothesis. (To claim otherwise would be to make probability highly subjective.)
– Newton’s theory of motion was judged to be highly probable on the evidence available in the late 17th century, even though it made no new immediately testable predictions, other than the predictions that were already made by laws that were already known and that it explained (Kepler’s laws of planetary motion, Galileo’s law of fall, etc.) Its high probability arose solely from its being a very simple fundamental theory from which those diverse laws are deducible.
– The practice of scientists, historians, etc. shows that they judge a very simple theory to be bery much more probable than less simple theories. However, when we come to not quite so simple theories (which we may need to do when very simple theories have low explanatory power), the intrinsic probability of the simplest remaining theory is not much greater than that of the next less simple theory.
– The probability, on the evidence, of God’s existence will depend on how well the hypothesis of God’s existence is able to explain the occurrence of phenomena that would otherwise be highly unlikely; and on its prior probability, which (since there will be no background knowledge) means its intrinsic probability, which in turn is dependent on its simplicity and scope.
– The hypotheses that compete with theism (such as physicalism) are of equally vast scope, so the discussion can focus on the issue of simplicity (and scope was seen to be the less important of these two criteria anyway).