Note: this is the second installment of our review of the paper “Bayesian reasoning in science” by Colin Howson and Peter Urbach.

Following their short introduction on gambling odds (see post below for a summary), Howson and Urbach present the basic laws or “axioms” of probability theory. (You can read more about the laws of probability here. See also the formal paper by Russian mathematician S. S. Vallander below.) More importantly, they note the relation between probability and truth: “Suppose h is some scientific hypothesis,” they write. “Experimental data can never conclusively prove that h is true, even if it is true. [A reference to Karl Popper would have been nice here.] So you are never absolutely certain of h’s truth, only more or less. The inductive inference [therefore] consists in assessing the degree of certainty warranted by the evidence.” [Emphasis added by us.]

We quote Mssrs Howson and Urbach at length here because we believe that these three crisp sentences not only reveal an important insight about the underlying nature of hypothesis testing in science; the Bayesian approach to truth also tells us a lot about litigation and the legal process generally (of which we shall have much more to say in future blog posts). In short, ultimate truth is not an “all or nothing” affair like religion or politics. Truth is more like a horse race or the World Cup (or “Copa do Mundo” for those of you in Brazil and Portugal) — for she is subject to the same vagaries of uncertainty as the outcome of a horse race or a football tournament.

For now, however, notice how this Bayesian view of truth poses a potential paradox. Again, in the words of Howson and Urbach, “if the probability of a hypothesis merely reflects our own personal degree of belief in h, how can an objective logic of inductive inference be based on such probabilities?” A good portion of Howson & Urbach’s paper is devoted to this fundamental question, so “stay tuned” … we shall continue our review in future posts …