Proceedings of the Annual Meeting of the Cognitive Science Society

A proof by mathematical induction demonstrates that ageneral theorem is necessarily true for all natural numbers. Ithas been suggested that some theorems may also be provenby a ‘visual proof by induction’ (Brown, 2010), despite thefact that the image only displays particular cases of thegeneral theorem. In this study we examine the nature of theconclusions drawn from a visual proof by induction. We findthat, while most university-educated viewers demonstrate awillingness to generalize the statement to nearby cases notdepicted in the image, only viewers who have been trained informal proof strategies show significantly higher resistance tothe suggestion of large-magnitude counterexamples to thetheorem. We conclude that for most university-educatedadults without proof-training the image serves as the basis ofa standard inductive generalization and does not provide thedegree of certainty required for mathematical proof.