88 THE ANATOMY OF SCIENCE 



tions. The use and usefulness of these empirical devices I consider 

 in Chapter Vl. 



An imentory of the contents of the conceptual lobe is difficult. 

 Prominent here is a considerable group of methodological and sub- 

 stantive principles, examined in Chapter VII. Here too appear col- 

 ligative relations in a variety of other guises, as well as a great array 

 of concepts furnishing terms for the expression of theories and rela- 

 tions. Here also is found a heterogeneous stock ( 1 ) for the framing of 

 analogies and the construction of models, and an enormous stock 

 (2) of formal relations furnished by logic and mathematics. 



Modern science arose after, and profited from, the development of 

 mathematical tools the Greeks wholly lacked: e.g., the concepts of 

 zero, probability, and functional relationship. The profits are enor- 

 mous because advances in mathematics oflFer more than convenient 

 new symbols and devices for the expression of colligative relations. 

 They provide also immensely powerful new machinery for the con- 

 struction of postulational systems. As alternative to the restricted 

 possibilities of deduction in the syllogistic and Euclidean modes, we 

 acquire a variety of others the importance of which first becomes 

 manifest in the magnificent achievement of the Newtonian synthesis. 



Much accelerated by growth of the formal stock ( 2 ) , due to prog- 

 ress in logic and mathematics, the advance of science is probably 

 even more profoundly accelerated by growth of the analogic stock 

 ( 1 ) . Once science achieves a competent development, and becomes 

 capable of generating its own analogic stock, its further progress may 

 thus be rendered auto-accelerative. That is, with more ample ana- 

 logic stock scientific advance becomes more rapid, and more rapidly 

 generates new analogic stock, as a result of which . . . and on and 

 on. We find this eflPect even in die formation of laws. Ohm, for exam- 

 ple, arrives at his well known law by treating the "flow" of electricity 

 as analogous to the "flow" of heat previously treated by Fourier. 

 Success thus feeds on success, as is even more apparent when we 

 turn from laws to theories. The astronomers' conception of the solar 

 system furnishes the analogy on which Bohr founds his conception 

 of the nuclear atom with circumambient electrons; and that theory 

 of the atom, completed in quantum mechanics, furnishes in its turn 

 the analogy by which we conceive a "shell structure" of the nucleus. 



However we appraise their relative importance, both the formal 

 stock and the analogic stock clearly belong to the heuristic apparatus. 



