Pragmatic Rationalism and Pragmatic Nominalism in the Lvov-Warsaw School

Abstract

Rationalism is the ontological and epistemological view to the effect that there exist abstract entities—as classes, numbers, points, etc.—being cognitively available to our minds. Thus, the axiom of abstraction can be interpreted as the most concise statement of the rationalist position in its ontological facet. The acknowledging of abstracts may be motivated either with their direct intellectual vision, as claimed by Plato, or with their ‘indispensability’ for scientific progress, as claimed by Quine and a host of other famous thinkers. For such a practical approach the term ‘Pragmatic Rationalism’ should be in order (more frequently one speaks of ‘pragmatic platonism’ but in the present context this term would be misleading). Among its followers there are some eminent members of the Lvov-Warsaw School. Predominantly, Kazimierz Ajdukiewicz for his program of empirical methodology of sciences, and Alfred Tarski for the abundant use of highly abstract concepts in his mathematical research. Radical nominalism pioneered by Stanisław Leśniewski and Tadeusz Kotarbiński, denying the existence of classes, did not comply with methods and results of sciences. However, there is a moderate version of nominalism which pragmatically does admit classes, for the sake of scientific progress. This version has been suggested by Andrzej Grzegorczyk under the name of ‘liberal reism’. In such a pragmatic form, nominalism can comply with pragmatic rationalism, and the other way around. The latter is not bound to deny what nominalism says about ontological and epistemological priority of physical individuals. Even such a convinced rationalist as Gödel shared with nominalists (unlike Plato) that observational statements concerning physical individuals are most basic in the structure of our knowledge. A nice example of such reconciliation is found in Tarski’s work ‘Foundations of the geometry of solids’. He recedes from Euclid’s idea of point as a primitive concept, in accordance with the claim of reistic nominalism that only solids can play such a role. Instead, he starts from the concept of sphere, defining ‘the point as the class of all spheres which are concentric with a given sphere’. Thus, the typically abstract concept of class (attacked by radical nominalism) proves indispensable to do justice to the ontological priority of physical individuals—a hallmark of nominalism. In such a way, Tarski, when doing justice to nominalism, at the same time gains considerable scores for pragmatic rationalism as well. Such a constructive collaboration of the two opposing camps within the School sheds a new light on the School’s ability to solve hard problems with a vigorous and ‘penetrative discussion’ between opposite standpoints.