382 THE SCIENCE OF LOGIC 



(2) Only one premiss, and that the first, caw be particular. 

 Precisely similar reasoning reveals two corresponding rules 

 for the Goclenian sorites in the first figure : 



(1) Only one premiss, and that the first, can be negative. 



(2) Only one premiss, and that the last, can be particular. 



The student should try to reason out both pairs of rules from those of 

 the first figure, rather than rely on memory for the distinction between each 

 pair. Remembering that the Aristotelean sorites comes naturally before the 

 Goclenian (both historically and alphabetically), and that &quot; p &quot; commences 

 the words &quot; prima &quot; and &quot; particularism he may get some assistance from 

 the mnemonic : 



[Sola] Prima [Praemissa potest esse] -^^^ z? Particularis. 



[Sola] Ultima [Praemissa potest esse] ^-&quot;&quot;&quot;&quot;^ ^-^ Negans. 



These lines, read horizontally, give the rules for the Aristotelean sorites. 

 Read in the direction of the arrow-heads, they give the rules for the 

 Goclenian sorites. 



We have next to inquire whether it is possible to have a 

 sorites in any other figure than the first, i.e. all the constituent 

 syllogisms of which are in some figure other than the first. This 

 question was not satisfactorily answered until Dr. Keynes con 

 structed examples of sorites in the second and third figures, 1 

 the constituent syllogisms being in the moods Baroco and 

 Bocardo respectively. 



The following is an example of Baroco in the second figure 

 (with the suppressed propositions supplied) : 



Minor Some S is not X. 



Major Every Y is X, 



[Conclusion and Minor]. . [. . Some S is not Y]. 



Major Every Z is Y. 



[Conclusion and Minor] . [. . Some S is not Z] 



Major Every P is Z 



Conclusion . Some S is not P . 



We may have a sorites in Camestres, as well as in Baroco, of 

 the second figure. Only the first syllogism of a sorites in this 

 figure can be in Cesare or Festino. 



It will be observed, from the example given, that the sorites 



in the second figure is analogous to the Aristotelean sorites in the 



first figure : a minor premiss comes first ; the other expressed 



propositions are majors ; the suppressed conclusions are minors. 



Logicians have not expressly formulated rules for the present 



1 op. /., pp. 373 sqq. 



