You seem to use phrases like “prior probability”, “final probability”, “explanatory power”, and “inductive correctness” as terms of art. What do those terms mean?
I do indeed use those and other phrases as terms of art consistent with how they are used within formal inductive logic. Allow me to explain. Given that historical arguments are shot through with appeals to probability, it is useful to introduce Bayes’s Theorem as a way of clarifying the role of probability in historical argumentation. Let E be the evidence to be explained, H be our explanatory hypothesis for E, and let B represent our relevant background knowledge. B includes all of our information relevant to H other than evidence E. B includes facts that determine the intrinsic probability of rival explanatory theories and facts that partially determine their explanatory power. E includes unusual facts within the context of this background that need to be explained. We are now in a position to introduce Bayes’s Theorem, a mathematical formula for representing the effect of new information upon our degree of belief in a hypothesis. In one form, Bayes’s Theorem may be expressed as fol
I do indeed use those and other phrases as terms of art consistent with how they are used within formal inductive logic. Allow me to explain. Given that historical arguments are shot through with appeals to probability, it is useful to introduce Bayes’s Theorem as a way of clarifying the role of probability in historical argumentation. Let E be the evidence to be explained, H be our explanatory hypothesis for E, and let B represent our relevant background knowledge. B includes all of our information relevant to H other than evidence E. B includes facts that determine the intrinsic probability of rival explanatory theories and facts that partially determine their explanatory power. E includes unusual facts within the context of this background that need to be explained. We are now in a position to introduce Bayes’s Theorem, a mathematical formula for representing the effect of new information upon our degree of belief in a hypothesis. In one form, Bayes’s Theorem may be expressed as fol
