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Between the opinion of Kant that logic cannot be improved, and 

 that of some recent writers, who hold it perverted, and not always 

 correct, the truth is held to lie in this, — that existing logic, in its 

 quod semper, quod ubique, quod ab omnibus, is true and accurate ; but 

 that it is only a beginning, and that the low estimation in which it 

 has been held is a consequence of its incompleteness. 



The modern definition of logic, the form of thought, relates to 

 a distinction which is more familiar to mathematicians than to 

 logicians, but is rather in the common use of the mathematician 

 than in his clear apprehension. Aristotle, who first implicitly made 

 the distinction of form and matter, was a mathematician ; and so 

 also was Kant, who first explicitly introduced this distinction into 

 the definition of logic. The only two nations who had a logic 

 taking character from the distinction, the Greeks and Hindus, are 

 precisely the two nations to whom we owe the rudiments of our 

 mathematics. It is affirmed by the author, that, in our time, the 

 distinction is more in the theory of the logician than in his practice, 

 more in the practice of the mathematician than in his theory. 



Various illustrations are given of the manner in which recent 

 logical writers have, according to Mr. De Morgan, misconceived 

 the distinction of formal and material. In another part of the 

 paper he suggests that this distinction has been confounded with 

 the distinction which he designates as onymatic and non-onymatic. 

 By onymatic he means what arises out of the use and meaning of 

 nomenclature : thus the relation of containing and contained is an 

 important relation of names to each other as names, or an onymatic 

 relation. 



The modern logic, by the simplicity of its final examples, is pre- 

 vented from being of much use as a mental gymnastic. Instances 

 are given of a proposition and a syllogism which are more worthy 

 of being propounded as exercises than the instances which are found 

 in works on logic. 



The objections to symbols are discussed. Every science which 

 has thriven has organized symbols of its own : and logic, the only 

 science which confessedly has made no progress for many centuries, 

 is also the only science which has grown no symbols. 



The logicians have confined themselves hitherto within what Mr. 

 De Morgan calls the logico-mathematical field : they now begin to 

 contend for the inclusion of what he calls the logico-metaphysical. 

 This distinction they take as that of extension and comprehension. 

 The author contends for a distinction of extension and intension in both 

 the sides of logic, the mathematical and the metaphysical ; though 

 undoubtedly extension predominates in the mathematical side, and 

 intension in the metaphysical. These distinctions are onymatic. 

 If the name C contain all that is in A or in B, or in both, symbolized 

 by C = (A, B), then A and B are in the extension of C. But if C 

 be contained both in A and in B, symbolized by C = A-B, or AB, 

 then A and B are in the intension of C. 



A name is used in four senses. It is the name of an object, or of 

 a quality inhering in an object, and distinguishing a class : these two 



