viii CONCEPTUAL RECONSTRUCTION 125 



was not purely deductive. Systematic observation was 

 practised in astronomy, and by Aristotle himself in biology 

 and sociology, while in the hands of Archimedes experi- 

 ment guided by mathematical genius of the first order 

 laid the foundations of mechanics. But the ancients 

 had neither the mathematical methods nor the physical 

 instruments which have given to experimental science the 

 range which it has obtained in the modern world. Thus 

 it comes about that when Greek thinkers move outside 

 the region accessible to common observation, they give us 

 conjectures rather than true hypotheses. These conjec- 

 tures are often singularly brilliant and happy. The atomic 

 theory of Democritus, the evolutionist suggestions from 

 Empedocles onward, bear an interesting analogy to modern 

 ideas. But it is easy to overrate their significance. 

 Modern science, as will be remarked later, often obtains 

 fruitful results by assuming positions which it cannot 

 directly prove because it has worked out methods of 

 reasoning from such assumptions and comparing its results 

 with those of observation. An assumption so treated is a 

 hypothesis. One which cannot be so treated remains a 

 conjecture, and Greek theories of that which lay beyond 

 the domain of direct observation remained for the most 

 part conjectures. It needs no lengthy argument to show 

 that it was in the construction of the conceptual order itself 

 that the main work of the Greek enquirers lay. Thus 

 we have on the one side the fundamental metaphysical 

 enquiries, the analysis of the elementary categories, the 

 statement of the philosophical problem, the elaboration of 

 a deductive logic, the exposition of the ideal of knowledge 

 and truth. On the other hand, we have the positive 

 development of mathematics beginning along with the first 

 philosophic impulse, but continuing long after philosophy 

 had reached and passed its first culmination. We have the 

 first completely systematic exposition of a body of truth 

 in Euclid, the development of theoretical arithmetic, and, 

 growing in importance at the close of Greek activity, the 

 beginnings of algebra. Then we have mathematics 

 applied to mechanics by Archimedes, and to astronomy 

 by the long series of investigators whose work was ulti- 



