On the sophistication of naïve empirical reasoning: Factors influencing mathematicians' persuasion ratings of empirical arguments

This paper presents the results of an experiment in which mathematicians were asked to rate how persuasive they found two empirical arguments. There were three key results from this study: (a) Participants judged an empirical argument as more persuasive if it verified that integers possessed an infrequent property than if it verified that integers lacked such a property. (b) Participants judged an empirical argument about modular congruence as more persuasive than an empirical argument about generating primes, suggesting that empirical arguments might be more convincing in some domains than others. (c) There was a marginally statistical effect between mathematical field of study and level of persuasion, with applied mathematicians finding empirical arguments more persuasive than pure mathematicians.