190 



Mr DE morgan ON THE SYLLOGISM, No. Ill, 



thought conducted in a limited universe, but this so palpably that express mention is seldom 

 needed. A person strikes into a conversation to deny the first he has heard of it, and is in- 

 stantly put down by, We were talking of . A proposition, false in the whole universe 



of thought, is true in the universe of the speaker's argument. The first sentence in Euclid is 

 a marked instance : a point is that which has no part. My firm conviction that Euclid was 

 a man and not a myth has no part : I cannot dichotomize it ; is it then a point .-' Any one 

 can answer that Euclid was talking of space, not of historical beliefs and convictions : space 

 and its laws are the universe of his book. The definite universe, the duality of every classifi- 

 cation, exclusion as definite as inclusion, shou'd be of the logica docens because it is possible, 

 and of the logica utens because it is actual : and fundamental in both. 



X. We think by class, or by attribute, under relations. The relation which must take 

 precedence of all others, because it must be present in the mere idea of nomenclature, is that 

 of whole and part, of containing and contained. This relation, and its concomitants, I call 

 onymatic relations : and it appears to me that, onymatic being absent, formal* has supplied 

 its place. There is a fourfold mode of thought, which logicians confound into one by a four- 

 fold use of the word ' is.' I denote and symbolise the four modes as follows, proceeding only 

 by an instance, and leaving the full description of the relations for the summary in the second 

 part. 



i. Logico-mathematical ; class aggregant of class. The class moTi included in the class 

 animal. Always intended where symbols are both common parentheses, as )) ( ) &c. • 



2. Logico-physical ; attribute predicated of class. Animal a quality of every man, an 

 attribute of the class. Symbols )] (] &c. 



3. Logico-metaphysical ; attribute component of attribute. The notion animal a compo- 

 nent part of the notion human. Symbols ]] [] &c. 



4. Logico-contraphysical, attribute-]- subjected to class. Human, an attribute to be 

 looked for within the class animal. Symbols ]) [) &c. 



1. Mathematical. The logicians excluded — or rather tried to exclude — all predication 

 except reference of class to class : accordingly, genus as an aggregate of species they called the 

 logical whole. The name is good so long as the exclusion lasts, and no longer. Aggregation 

 of individuals into species, they called the mathematical whole : I call it the arithmetical. And 

 aggregation of species into genus I call the mathematical whole: mathematical, because sum- 

 mation of parts is a mathematical process ; but not necessarily arithmetical, or proceeding by 

 enumeration of similars. The difference between species and individual is, in some points, 

 extralogical. The logician, as such, never knows whether he has or has not specified down to 

 an individual, or even down to nonexistence, at each or any step of the process. His stoppage 

 at an infima species, composed of many individuals, was his own fiction. Begin from animal, 

 and compound successively the differentice, human, Roman, ancient, general, conqueror of 



• The more I read of the common statements about form 

 and matter, with the word onymatic in my mind, the more 

 does the conviction grow upon me that logicians have taken 

 the distinction between forms which are and which are not 

 onymatic to be the distinction between formal and material, 

 t Nee quarta loquiperaona laboret. It seems to be a rule 



that every quaternion of logic shall contain one member who 

 is to be considered a disgrace to the family, if not entirely 

 disowned. Of the four universal propositions, one, marked by 

 me (-), is unknown to the logicians ; the same of one parti- 

 cular, ) (. We all know what a bad character the fourth figure 

 has had, ever since it got a footing as a poor relation. 



