The Bayesian definition of evidence favoring a hypothesis is evidence which we are more likely to see if the hypothesis is true than if it is false. Observing that a syllogism is logically valid can never be evidence favoring any empirical proposition, because the syllogism will be logically valid whether that proposition is true or false. Syllogisms are valid in all possible worlds, and therefore, observing their validity never tells us anything about which possible world we actually live in.
