For many scientists, statistics and mathematics have become the ultimate authorities on the significance and universality of scientific statements. Most scientific journals, therefore, demand that authors adhere to strict rules of data treatment in satisfying the requirements of statistical significance. Yet both mathematics and statistics are changing disciplines. Of late, some basic views in the world of mathematics and statistics have changed, leading to some new and rather innovative techniques that might be useful for behavior analysts. In mathematics, several fundamental principles have been questioned. The controversy is whether logical and mathematical principles describe firm and readily apparent empirical tendencies (mathematical empiricism) or reflect purely rational tendencies, independent of empirical verification (mathematical apriorism) (e.g., Kitcher, 1983; Kline, 1980). The recent trend toward mathematical empiricism stresses that elementary truths are acquired through ordinary perception and through learning about practical experiences with objects and events over many generations. Indeed, the new approach makes contact with Gibson's perception theory of ecological realism (Kitcher, 1983; cf. Costall, 1984). The implication for the practicing scientist may be that mathematics could be used as a way to effectively communicate how the scientist interacts with the subject matter. This view contrasts with