Inferring from Negated Conditionals Connexively; an experimental investigation of a Boethian inference

In his sixth century commentary on Cicero’s Topics Boethius presents four examples of what he takes to be valid inferences involving a negated conditional, the form of which we generalise informally as “if ~(A→ B) and A , then ~B ”. We argue that Boethius’ endorsement of these inferences provides evidence of his likely endorsement of reversed variants of Boethius’ Thesis, e.g., ~(A→ B)→(A→~B), a principle which is validated by some connexive logics. It has furthermore been claimed that connexively valid principles are not only highly intuitive, but that human reasoning can plausibly be characterised as connexive in virtue of this. We investigate the first part of this claim via an experiment in which participants infer outcomes of a simulated game. We conclude that there is good evidence for the intuitiveness of inferences along the lines of reversed variants of Boethius’ Thesis.