“One Man’s Modus Ponens § Jaynes on ESP”, 2012-05-01 (; similar):
One man’s modus ponens is another man’s modus tollens is a saying in Western philosophy encapsulating a common response to a logical proof which generalizes the reductio ad absurdum and consists of rejecting a premise based on an implied conclusion. I explain it in more detail, provide examples, and a Bayesian gloss.
Bayesian E.T. Jaynes, in “Chapter 5: Queer uses for probability theory”, discusses the probabilistic generalization of the reasoning we are engaged in when we choose whether to modus ponens or modus tollens, with early ESP experiments as an example, pointing out that from a Bayesian perspective, all claims are being evaluated in a larger Bayesian-model-comparison context where issues like experimenter error or bias are always possibilities: