RUME 27
2025
Alexandria, Virginia
How do Introduction-to-Proof Textbooks Explain Conditionals? Mathematical, Natural-Language and Hybrid Examples
Page: 165
Mathematics defines the propositional conditional ‘if P then Q’ as the truth-functional material conditional: it is false if P is true and Q is false, and true otherwise. This is counterintuitive with respect to natural language in that ‘missing-link’ conditionals (with true but unconnected P and Q) are considered true, as are conditionals with false antecedents. How is this reflected in the examples used by introduction-to-proof textbooks? Do these use natural-language conditionals in their explanations, or avoid them in favour of mathematical conditionals? What characteristics do their chosen examples share, and where do they diverge? We address these questions using a theoretically informed qualitative analysis of content on conditionals in 17 commonly recommended introduction-to-proof textbooks. We consider advantages and disadvantages of different approaches in relation to research in philosophy and psychology as well as in undergraduate mathematics education.