[2] His research areas include the philosophy of mathematics and the 'formal sciences', the history of probability, Australian Catholic history, the parallel between ethics and mathematics, restraint, the quantification of rights in applied ethics, and the analysis of extreme risk.
Its central theme was ancient and medieval work on the law of evidence, which developed concepts like half-proof, similar to modern proof beyond reasonable doubt, as well as analyses of aleatory contracts like insurance and gambling.
[9][10][11] Over the years, the School has hosted emerging Australasian researchers and philosophers such as Anne Newstead, Lisa Dive, and Jeremiah Joven Joaquin.
Paul Thagard writes that "the current philosophy of mathematics that fits best with what is known about minds and science is James Franklin's Aristotelian realism.
"[12] In the philosophy of probability, he argues for an objective Bayesian view according to which the relation of evidence to conclusion is strictly a matter of logic.
[21] Franklin has defended Pascal's Wager[22] and Leibniz's Best of all possible worlds theory,[23] and has discussed emergentism as an alternative to materialist atheism and theism.