# First notions of logic, preparatory to the study of geometry

Taylor & Walton, 1840 - Arithmetic - 32 pages

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Page 3 - The logic of the schools has nothing to do with the truth of the facts, opinions, or presumptions, from which an inference is derived; but simply takes care that the inference shall certainly be true if the premises be true.
Page 17 - ... must be affirmative, and, being particular, neither of its terms is universal. Consequently both the terms as to which the conclusion is to be drawn enter partially, and the conclusion (Rule 2) can only be a particular affirmative proposition. But if one of the premises be negative, the conclusion must be negative (as we shall immediately see).
Page 6 - In common conversation the affirmation of a part is meant to IMPLY the denial of the remainder. Thus, by 'some of the apples are ripe', it is always [sic!] INTENDED TO SIGNIFY that some are not ripe.
Page 5 - No," most frequently means that he is the contrary of tall, or considerably under the average. But it must be remembered, that, in all logical reasoning, the negation is simply negation, and nothing more, never implying affirmation of the contrary.
Page 8 - These may be thus summed up : The affirmation of a universal proposition, and the denial of a particular one, enable us to affirm or deny all the other three ; but the denial of a universal proposition, and the affirmation of a particular one, leave us unable to affirm or deny two of the others. In such propositions as ' Every A is B,' ' Some A is not B,' &c., A is called the subject, and B the predicate, while the verb 'is' or ' is not,
Page 5 - Moreover, the negative words not, no, &c., have two kinds of meaning which must be carefully distinguished. Sometimes they deny, and nothing more : sometimes they are used to affirm the direct contrary. In cases which offer but two alternatives, one of which is necessary, these amount to the same thing, since the denial of one, and the affirmation of the other, are obviously equivalent propositions. In many idioms of conversation, the negative implies affirmation of the contrary in cases which offer...
Page 17 - But it is not immediately obvious when the middle term enters one of the premises universally. The following reasoning will serve for exercise in the preceding results. Since both premises are particular in form, the middle term can only enter one of them universally by being the predicate of a negative proposition ; consequently (Rule 3) the other premise must be affirmative, and, being particular, neither of its terms is universal. Consequently both the terms as to which the conclusion is to be...
Page 23 - It is also in such propositions that men convey opinions which they would not willingly express. Thus, the honest witness who said, ' I always thought him a respectable man — he kept his gig,' would probably not have admitted in direct terms, ' Every man who keeps a gig must be respectable.
Page 2 - This tract contains no more than the author has found, from experience, to be much wanted by students who are commencing with Euclid.
Page 3 - Logic is... the examination of that part of reasoning which depends upon the manner in which inferences are formed... It has so far nothing to do with the truth of the facts, opinions or presumptions, from which an inference is derived : but simply takes care that the inference shall certainly be true, if the premises be true1.