Jaynes references Polya's books on the role of plausible reasoning in mathematical investigations. The three volumes are How to Solve it, and two volumes of Mathematics and Plausible Reasoning. They are all really fun and interesting books which kind of give a glimpse of the cognitive processes of a successful mathematician.

Particularly relevant to Jaynes' discussion of weak syllogisms and plausibility is a section of Vol. 2 of Mathematics and Plausible Reasoning which gives many other kinds of weak syllogisms. Things like: "A is analogous to B, B true, so A is more credible."

Just a heads up in case anyone wants to see more of this sort of thing (as at least one person on IRC #lesswrong did).

There are also fun exercises -- for example: cryptic crossword clues as an exercise in plausible reasoning.