37 THE SCIENCE OF LOGIC 



the preceding step is called a REGRESSIVE, or ANALYTIC, or 

 PROSYLLOGISTIC, chain of reasoning. 



The former, or Progressive Polysyllogism^ is commonly met 

 with in the Synthetic or Deductive sciences, such as Geometry 

 and Mathematics, constituting what is known as the Synthetic or 

 Deductive Method. When such a polysyllogism is condensed 

 by the omission of some of its constituent propositions it is called 

 a SORITES. 



The latter, or Regressive Polysyllogism, is met with in the 

 Analytic or Inductive sciences, such as Physics, constituting what 

 is known as the Analytic or Inductive method. When it is 

 similarly condensed it is sometimes called an EPICHEIREMA. 1 



With these two abridged chains of reasoning, the progressive 

 and the regressive, we shall now briefly deal. 



1 88. THE SORITES. A sorites is a progressive polysyllogism 

 in which all the conclusions are omitted except the final one, and all 

 the major or minor premisses are omitted except the initial one. 

 Every sorites is a progressive polysyllogism, i.e. it proceeds from 

 prosyllogism to episyllogism. In such a process, each syllogism 

 may prove either the major or the minor premiss of the succeed 

 ing syllogism. Hence, there are two possible kinds or forms of 

 sorites : one in which each constituent syllogism proves the major 

 premiss of the subsequent one (the minors being assumed as true 

 or otherwise proved) : the other in which each constituent syllogism 

 proves the minor premiss of the subsequent one (the majors being 

 assumed as true, or otherwise proved). The following are ex 

 amples of each sort : 



Major . 

 Minor . ( i ) 

 [Conclusion 

 and Major] 



Every Z is P ( Every S is X . . Minor. 



Every Y is Z f . I Every X is Y . .Major. 



[. : Every Y is P\\ \ T \ [. -. Every S is Y\\ . {Conclusion 



and Minor]. 



1\.-. Every Sis Y\\ 

 \ ! 



Minor . . Every X is Y \^ Every Y is Z p 2 Major. 



[Conclusion ( [.. Every X is P]) f [.*. Every S is Z]] . [Conclusion 



and Major] I . I and Minor]. 



Minor . (3) | Every S is X \of\ Every Z is P . . Major. 

 Conclusion \ . . Every S is P \ . . Every S is P . .Conclusion. 



In these examples the propositions that are usually omitted 

 are supplied in square brackets. 



In the first form, (a), it will be noted that all the majors are 



1 Aristotle used this title to designate the syllogism by which a disputant 

 attacked the thesis defended by the respondent in a dialectical discussion. Cf. 

 JOSEPH, op. cit., p. 325, n. 3. 



