192 INTRODUCTION TO PHILOSOPHY OF SCIENCE 



anticipations as these are possible only through the use of 

 the hypothetical method. 



TECHNIQUES OF HYPOTHESIS-FORMATION 



Since the remaining techniques of discovery are less highly 

 determinate in character, they may be conveniently dis- 

 cussed under the present heading. As was pointed out, the 

 techniques of hypothesis-formation are simply those methods 

 which permit only a very limited ascertainment of the con- 

 tent of the explanatory entity, hence leave room for the 

 activity of the imagination. It should be remembered, 

 therefore, that the following techniques are also methods 

 of construction. Three types will be discussed: (a) serial 

 operations, (b) cause and effect inferences, and (c) opera- 

 tions of analysis and synthesis. 



(a) Serial operations. These are of two kinds, depending 

 upon whether the operation is from a given segment of a 

 series to an element beyond the segment, or between two 

 supposedly adjacent members. The former may be called 

 the method of serial extension, or of extrapolation, and has 

 been aptly characterized by Eddington as the method of 

 "just like this only more so." * It permits extension beyond 

 any given range of data when they are capable of serial 

 arrangement; the property of gradual increase or decrease 

 exhibited by the known segment of the series is taken as a 

 defining principle by which the character of the elements 

 beyond the limits of observation may be ascertained. The 

 latter is the method of interpolation, and involves the in- 

 sertion of an element between two apparently contiguous 

 members. Serial operations are employed in all of the sciences 

 for the purpose of defining "ideal" entities, such as perfect 

 levers, frictionless motion, ideal gases, Utopias, and per- 

 fectly isolated individuals; they are the characteristic meth- 

 ods of mathematics and are used in the definition of infinity, 

 irrationals, fractions, zero, and the negatives. More specific 

 illustrations of their employment will be given in Part Two. 



1 Nature of the Physical World, p. 247. 



