Logic: Designed as an Introduction to the Study of Reasoning

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W. Allen, 1864 - Logic - 209 pages

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Page 37 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Page 147 - When we say, All men are mortal Socrates is a man therefore -•'Socrates is mortal; it is unanswerably urged by the adversaries of the syllogistic f.
Page 154 - All inference is from particulars to particulars : General propositions are merely registers of such inferences already made, and short formulae for making more : The major premise of a syllogism, consequently, is a formula of this description : and the conclusion is not an inference drawn from the formula, but an inference drawn according to the formula: the real logical antecedent, or...
Page 108 - Achilles run ten times as fast as the tortoise, yet if the tortoise has the start, Achilles will never overtake him. For suppose them to be at first separated by an interval of a thousand feet: when Achilles has run these thousand feet, the tortoise will have got on a hundred; when Achilles has run those hundred, the tortoise will have run ten, and so on for ever: therefore Achilles may run for ever without overtaking the tortoise.
Page 152 - When, therefore, we conclude from the death of John and Thomas, and every other person we ever heard of in whose case the experiment had been fairly tried, that the Duke of Wellington is mortal like the rest ; we may, indeed, pass through the generalization, All men are mortal...
Page 143 - ... again. He believes this in every case which happens to arise; but without looking, in each instance, beyond the present case. He is not generalizing; he is inferring a particular from particulars. In the same way, also, brutes reason.
Page 108 - ... does not mean any length of time ; it means any number of subdivisions of time. It means that we may divide a thousand feet by ten, and that quotient again by ten, and so on as often as we please ; that there never...
Page 144 - Logic is not the science of Belief, but the science of Proof, or Evidence. In so far as belief professes to be founded on proof, the office of logic is to supply a test for ascertaining whether or not the belief is well grounded.
Page 151 - If a man is asked a question, and is at the moment unable to answer it, he may refresh his memory by turning to a memorandum which he carries about with him. But if he were asked, how the fact came to his knowledge, he would scarcely answer, because it was set down in his note-book : unless the book was written, like the Koran, with a quill 1rom the wing of the angel Gabriel.

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