$ i34] Estimate of Galilei's Work 177 



astronomy he was building on foundations laid by pre- 

 vious generations, in dynamics it was no question of im- 

 proving or developing an existing science, but of creating 

 a new one. From his predecessors he inherited nothing 

 but erroneous traditions and obscure ideas ; and when these 

 had been discarded, he had to arrive at clear fundamental 

 notions, to devise experiments and make observations, to 

 interpret his experimental results, and to follow out the 

 mathematical consequences of the simple laws first arrived 

 a\ The positive results obtained may not appear numerous, 

 if viewed from the standpoint of our modern knowledge, 

 but they sufficed to constitute a secure basis for the super- 

 structure which later investigators added. 



It is customary to associate with our countryman Francis 

 Bacon (1561-1627) the reform in methods of scientific 

 discover)' which took place during the seventeenth century, 

 and to which much of the rapid progress in the natural 

 sciences made since that time must be attributed. The 

 value of Bacon's theory of scientific discovery is very 

 differently estimated by different critics, but there can be 

 no question of the singular ill-success which attended his 

 attempts to apply it in particular cases, and it may fairly 

 be questioned whether the scientific methods constantly 

 referred to incidentally by Galilei, and brilliantly exemplified 

 by his practice, do not really contain a large part of what 

 is valuable in the Baconian philosophy of science, while at 

 the same time avoiding some of its errors. Reference has 

 already been made on several occasions to Galilei's protests 

 against the current method of dealing with scientific 

 questions by the interpretation of passages in Aristotle, 

 Ptolemy, or other writers ; and to his constant insistence 

 on the necessity of appealing directly to actual observation 

 of facts. But while thus agreeing with Bacon in these 

 essential points, he differed from him in the recognition 

 of the importance, both of deducing new results from 

 established ones by mathematical or other processes of 

 exact reasoning, and of using such deductions, when 

 compared with fresh experimental results, as a means of 

 verifying hypotheses provisionally adopted. This method 

 of proof, which lies at the base of nearly all important 

 scientific discovery, can hardly be described better than by 



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