 In cases where a hypothesis is deductively related to an outcome \(e\) of an observational or experimental condition \(c\) (via background and auxiliaries \(b\)), we will have either \(h_i\cdot b\cdot c \vDash e\) or \(h_i\cdot b\cdot c \vDash{\nsim}e\). For example, \(h_i\) might be the Newtonian Theory of Gravitation. A test of the theory might involve a condition statement \(c\) that describes the results of some earlier measurements of Jupiter’s position, and that describes the means by which the next position measurement will be made; the outcome description \(e\) states the result of this additional position measurement; and the background information (and auxiliary hypotheses) \(b\) might state some already well confirmed theory about the workings and accuracy of the devices used to make the position measurements. Then, from \(h_i\cdot b\cdot c\) we may calculate the specific outcome \(e\) we expect to find; thus, the following logical entailment holds: \(h_i\cdot b\cdot c \vDash e\). Then, provided that the experimental and observational conditions stated by \(c\) are in fact true, if the evidential outcome described by \(e\) actually occurs, the resulting conjoint evidential claim \((c\cdot e)\) may be considered good evidence for \(h_i\), given \(b\). (This method of theory evaluation is called the hypothetical-deductive approach to evidential support.) On the other hand, when from \(h_i\cdot b\cdot c\) we calculate some outcome incompatible with the observed evidential outcome \(e\), then the following logical entailment holds: \(h_i\cdot b\cdot c \vDash{\nsim}e\). In that case, from deductive logic alone we must also have that \(b\cdot c\cdot e \vDash{\nsim}h_i\); thus, \(h_i\) is said to be falsified by \(b\cdot c\cdot e\). The Bayesian account of evidential support we will be describing below extends this deductivist approach to include cases where the hypothesis \(h_i\) (and its alternatives) may not be deductive related to the evidence, but may instead imply that the evidential outcome is likely or unlikely to some specific degree r. That is, the Bayesian approach applies to cases where we may have neither \(h_i\cdot b\cdot c \vDash e\) nor \(h_i\cdot b\cdot c \vDash{\nsim}e\), but may instead only have \(P[e \pmid h_i\cdot b\cdot c] = r\), where r is some “entailment strength” between 0 and 1. 