THE CHALLENGE TO THE TRADITIONAL IDEAL OF SCIENCE 457 



Cantor on the foundations of mathematics, tended to show that 

 mathematics could no longer be regarded as the ideal type of 

 absolute knowledge, but was based upon axioms and theorems 

 freely chosen and adopted by convention. Such studies led 

 naturally to an investigation of logical processes, and the sub- 

 sequent renovation of logic stressed the dominance of hypo- 

 thetical over categorical judgments, that is, of the relative 

 over the absolute. In mathematical physics, the theories of 

 relativity, and the formulation of the principle of indeter- 

 minacy, emphasized the part played by the scientist in building 

 up his theories, which were thus seen to be more subjectivist 

 than was formerly imagined. Relativism, already widely dif- 

 fused by Historicism and Evolutionism, seemed now to gather 

 new force from such studies on the nature of the sciences that 

 had hitherto been generally accepted as prototypes of universal 

 and absolute knowledge. In the new climate of such far-reach- 

 ing changes in the mental outlook of modern science, the Greek 

 notion of science, if at all retained, could at best be viewed as 

 an unattainable ideal, or, more usually, as a technique or 

 clarification rather than of discovery. 



The Contemporary Scene 



Among the main currents, outside of Catholic circles, which 

 are significant in philosophy to-day, and pertinent to our prob- 

 lem, we may mention, first of all, Physicalism, which is usually 

 associated with some form of Naturalism, and carries on the 

 tradition of Positivism and Scientism. The only form of knowl- 

 edge admitted as scientific by Physicalists is that delivered by 

 the natural sciences, which seek to formulate laws " based ex- 

 clusively on spatio-temporal coincidence and counting," ^ and 

 deal only with the local movement of bodies. Various theories 

 of intelligence have been proposed in line with this tendency, 

 such as P. W. Bridgman's Operationalism, which states that 

 the concept of any physical quantity must be defined by the 



■^ J. Russell, S. J., Science and Metaphysics (London & New York: Sheed & Ward, 

 Newman Philosophy of Science series, n. 1, 1958), p. 21. 



