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Mr DE morgan, ON THE SYLLOGISM, No. Ill, 



There is no use* in the arithmetically definite syllogism : to this there is almost unani- 

 mous agreement. But the study of it would have prevented such mistakes as that on which 

 I am now writing. For it is an exercise in the study of the relations of quantity as part, and 

 pari only, of the study of the coalescence and non-coalescence of notions. It shows that 

 quantification of the predicate is a superfluity, an excrescence which disappears in the elabora- 

 tion of rules of inference : and that the only entrance of comparison of quantity into negatives 

 is through the limitation of the universe by which those negatives are but other affirmatives. 



I now proceed to the second part of this paper, the first elements of the system on which 

 the preceding remarks are made. Some part of the groundwork of its higher developments is 

 contained in my second paper. 



Section 2. First Elements of a System of Login. 



XXII. A name is a sign by which we distinguish one object, process, or product of 

 thought from another. 



A name has four applications : two objective, signs of what the mind can (be it right or 

 wrong in so doing) conceive to exist though thought were annihilated ; two subjective, signs of 

 what the mind cannot but conceive to be annihilated with thought. (§ VI.) 



The objective applications are: — first, to individual objects external to the mind; secondly, 

 to individual notions attaching to or connected with objects, called qualities, which are said 

 and thought to inhere in the objects. The object itself is but a compound of qualities. The 

 quality is, in logic, any appurtenance whatever : thus to to be called Caesar is a quality. 



The subjective applications are : — to designate class, collection of objects having similar 

 qualities, or put into one notion by some similar class-mark; and a class may consist of one 

 individual only, if only one have the mark : secondly, to designate attribute, the class-name of 

 quality, the notion of quality in the mind. 



Class and attribute are two modes of thinking many in the manner of one ; two reduc- 

 tions of plurality to unity. The class man is one notion in the mind, the receptacle of many 

 individuals : the attribute human is also one in thought, being the notion derived from similar 

 qualities possessed by many individuals. Class is a noun of multitude, but not a multitude 

 of nouns, nor even one noun selected from a multitude. 



Quality, as a class name, may be distributed over any number of individuals. But it has 

 a division peculiar to itself. As merely an appurtenant notion, it may be the compound of 

 several notions. And similarly, attribute may be the compound of several attributes. 



In grammar, class is often a substantive capable of designating the individual also, and 

 used in both ways, as man, the man Plato. Quality is often an adjective, as human; attri- 

 bute is often an abstract substantive, as humanity, which cannot designate an individual. 



* It is, I find, at the utmost, worth doing once or more as a 

 school-exercise. This is exactly the view I take, and have 

 always taken, of all that I now call the arithmetical whole of 

 logic, including the common form of syllogism. Nineteen 

 years ago I wrote my First notions of Logic, intended, as 

 the preface states, ultimately to become an appendix to my 



Arithmetic, I had not then any glimpse, so far as my memory 

 serves, of the numerical syllogism ; and I doubt if I could have 

 given any very distinct account of my reason for appending 

 the common syllogism to a book of numbers. But it may be 

 that my now confirmed notion of the usual form of syllogism 

 being arithmetical was germinating. 



