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uses are objective. It is also the name of a class, or of an attribute 

 by which the mind thinks of a class : these two uses are subjective. 

 The subjective uses are reductions of plurality to unity, a description 

 for the truth and reality of which the author contends. 



It is affirmed that the logicians have not only confined themselves 

 within the mathematical side of logic, but that even the recent 

 attempts to introduce the metaphysical appear like attempts to 

 create a second mathematical branch. This is evidenced by the 

 manner in which unity of attribution has been discarded in favour of 

 plurality of qualification. Thus it has been said, in obedience to 

 the theory of quantification of the predicate, that the humanity of 

 Newton is a different thing from the humanity of Leibnitz. That 

 this view, though true, belongs to the mathematical side of logic, is 

 contended for and enforced at length. 



Aristotle made the distinction which the logicians now recognize 

 as that of extension and comprehension, and which Mr. De Morgan 

 distinguishes as that of mathematical and metaphysical reading, as 

 follows : — In one sense the species is in the genus : in another the 

 genus is in the species. That is, all the species are aggregants of the 

 genus : the whole genus is a component of the notion of the species. 



Recent English logicians of high name have misconceived this 

 distinction to the extent of imagining that by changing ' Every A is 

 some B ' into ' Some B is every A,' they make the change alluded to 

 by Aristotle. Mr. De Morgan restores the old distinction, and 

 completely incorporates what was only partially introduced, the 

 change of quantity which takes place in passing from the mathe- 

 matical to the metaphysical reading. Thus ' Every A is B ' is in 

 the first reading ' The whole class A is one aggregant of the class 

 B ' ; and in the second, ' The whole attribute B is one component of 

 the attribute A.' 



The limitation of the universe of a proposition, made throughout 

 the author's preceding writings, is again contended for. 



A proposition is the assertion or denial of a relation between two 

 notions. Relations which are of necessity involved in nomenclature, 

 are called onymatic ; and these must be first studied. Mr. De 

 Morgan believes that the logicians have described, under the di- 

 stinction of formal and material, no more than the distinction of 

 onymatic and non- onymatic. The mathematical notion of class, and 

 the metaphysical notion of attribute, give four different readings of 

 a proposition: — 1. Logico -mathematical, class aggregate of class; 

 man contained in animal. 2. Logico-physical, attribute predicated 

 of class; animality attribute of the class man. 3. Logico-meta- 

 physical, attribute component of attribute ; animality a component 

 of humanity. 4. Logico- contraphysical, attribute subjected to class ; 

 humanity only predicable within the class animal. 



The logicians confined logical predication to the idea of class 

 contained in class, species in genus. The genus in species, attribute 

 component of attribute, they relegated to metaphysics. Hence 

 their distinction of the logical and metaphysical whole. The class 

 composed of individuals they called the mathematical whole : Mr, 



