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Logic or the Analytic of Explicit Reasoning
Logic or the Analytic of Explicit Reasoning Author:George H. Smith Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free. This is an OCR edition with typos. Excerpt from book: CHAPTER III DOCTRINE OF THE PROPOSITION I RUDIMENTS OF THE DOCTRINE § 50. Proposition Defined.—A proposition may be denned as the expression of a re... more »lation of signification between two terms; which, of course, implies the expression of the corresponding relation between the notions expressed in the terms. § 51. The Grammatical Proposition.— But here there is a difference between Logic and Grammar, or, we may say, between the logical and the grammatical proposition. In the latter, any of the innumerable relations existing between terms, or, what is the same thing, between the things denoted by them, whether past, present, or future, may be expressed as existing between the terms; and the relation may be expressed by any copula or connecting word, or the same word may be used to express both copula and predicate, as, e. g.," John struck William " ; " The sun will rise at six o'clock to-morrow"; " It rains"; " The Carthaginians did not conquer Rome," etc. But in Logic the only copula used is the present tense of the verb "to be," with or without the negative particle; and the only in- terterminal relation considered is that of species and genus; which may be either affirmed or denied. § 52. The Logical Proposition.— Accordingly the logical proposition is of two forms, the affirmative and the negative. In the former the relation of species and genus between the terms is affirmed,—as, e.g.," Man is mortal," " Y is X," etc.; in the latter it is denied,—as, e. g., " Man is not perfect," " Y is not X," etc. The affirmative proposition may be read, either, " Y is X," or " Every Y is X," or " All Y's are X's " ; or, to take the concrete example, " Man is mortal," or " Every man is mortal," or " All men are mortal,"—these expressions being all equivalent, and signifying equ...« less