56 THE PIimCIPLES OF SCIENCE. j;ohap. 



If we put A for Neptune, B for planet, and C for " having 

 retrograde motion," then by the corresponding negative 

 term c, we denote " not having retrograde motion." The 

 premises now fall into the forms 



A = AB (i) 



B = Be, (2) 



and by substitution for B, exactly as before, we obtain 



A = ABc. _ (3) 



What is called in the old logic a particular conclusion 

 may be deduced without any real variation in the symbols. 

 Particular quantity is indicated, as before mentioned 

 (p. 41), by joining to the term an indefinite adjective of 

 quantity, such as some, a part of, certain, &c., meaning that 

 an unknown part of the term enters into the proposition 

 as subject. Considerable doubt and ambiguity arise out of 

 the question whether the part may not in some cases be 

 the whole, and in the syllogism at least it must be under- 

 stood in this sense.^ Now, if we take a letter to represent 

 this indefinite part, we need make no change in our 

 formulae to express the syllogisms Darii and Ferio. Con- 

 sider the example — 



Some metals are of less density than water, (i) 

 All bodies of less density than water will float 



upon the surface of water; hence (2) 



Some metals will float upon the surface of 



water. (3) 



Let A = some metals, 



B = body of less density than water, 

 C = floating on tlie surface of water 

 then the propositions are evidently as before, 



A = AB, (I) 



J^> - BC ; (2) 



hence A = ABC, (3) 



Thus the syllogism Darii does not really differ from r)ar- 

 bara. If tlie reader prefer it, we can readily employ a 

 distinct symbol for the indefinite sign of quantity. 

 Let P = some, 



Q = metal, 

 B and C having the same meanings as before. Then the 

 premises become 



* -iLUiutiiUary ijessoTm in Logic, pp. 67, 79. 



