Abstract

Maziarz proposes to offer "a solution that meets the requirements of recent developments in mathematics" as well as to chart "the course of its historical development." The leitmotiv of his entire treatment is the doctrine of abstraction. Says he: "...mathematics...in common with all sciences...arises through the mental action of abstraction from sense data," and again, "pure mathematics is a speculative science which originates from the mental action of formal abstraction from things." More specifically, we are told that "the laws of mathematical thinking are imposed on the mind from the very nature of quantified substance as given to the mind as it abstracts from the phantasms given by the sense from extramental reality." The implications of this claim for the status of mathematical entities are then asserted to be the following: "The mathematical natures, though not capable of extramental existence as such, are not purely fictitious; it is the natural state of mathematical natures to be so abstracted and abstractly considered and mathematical natures are still ens naturæ and not merely ens rationis." By virtue of the abstractive pedigree which is claimed for it, mathematics is held to give us knowledge concerning ens naturæ and is therefore accorded essentially the same logical status as empirical knowledge. Maziarz maintains that both types of knowledge derive their truth from what he calls "the identification of the intellect with the thing known" and the mind's "conformableness" to "real, extra-mental being." The knower is said to become "the object in the order of intention... while remaining what he is--man--in the order of nature."