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a v b affirmative Algebra of Logic ampliative inference apagogical argument atomic weight Boole Boole's C. S. Peirce character class terms clusion coefficient combinations compound event conclusion contains contraposition copula denotes eliminated Epicurean Epicurus equal equation equivalent example exclusives expression formula gism given Hence hypothetic inference included inconsistency induction or hypothesis Jevons Logic of Relatives lover McColl means method middle term modus tollens Morgan multiplication negative non-existent notation number of instances number of objects obtained occurrence pairs particular propositions Peirce Philodemus polynomial possible predesignation predicate probable deduction propo proportion ratio reasoning rela relation of identity relative number result rule rules of inference sample Schroder sition sP Sp sp specific gravities statistical deduction statistical syllogism suffices supposed syllogism symbol taken theory things tion true universal propositions universe of class valid
Page 130 - But another man, who never took the pains to observe the demonstration, hearing a mathematician, a man of credit, affirm the three angles of a triangle to be equal to two right ones, assents to it, ie, receives it for true : in which case the foundation of his assent is the probability of the thing; the proof being such as for the most part carries truth with it : the man on whose testimony he receives it, not being wont to affirm anything contrary to or besides his knowledge, especially in matters...
Page 152 - The rule requires that the sample should be drawn at random and independently from the whole lot sampled. That is to say, the sample must be taken according to a precept or method which, being applied over and over again indefinitely, would in the long run result in the drawing of any one set of instances as often as any other set of the same number.
Page 181 - ... all human knowledge, up to the highest flights of science, is but the development of our inborn animal instincts.
Page 180 - Nature is a far vaster and less clearly arranged repertory of facts than a census report; and if men had not come to it with special aptitudes for guessing right, it may well be doubted whether in the ten or twenty thousand years that they may have existed their greatest mind would have attained the amount of knowledge which is actually possessed by the lowest idiot.
Page 177 - ... refrain therefrom, the observed ratio in the cases upon which I had bet might be quite different from the observed ratio in those cases upon which I had not bet. I grant, then, that even upon my theory some fact has to be supposed to make induction and hypothesis valid processes; namely, it is supposed that the supernal powers withhold their hands and let me alone, and that no mysterious uniformity or adaptation interferes with the action of chance.
Page 146 - We conceive that Cases arise under these laws ; these cases consist in the predication, or occurrence, of causes, which are the middle terms of the syllogisms. And, finally, we conceive that the occurrence of these causes, by virtue of the laws of Nature, result in effects which are the conclusions of the syllogisms.
Page 145 - In point of fact, a syllogism in Barbara virtually takes place when we irritate the foot of a decapitated frog. The connection between the afferent and efferent nerve, whatever it may be, constitutes a nervous habit, a rule of action, which is the physiological analogue of the major premiss. The disturbance of the ganglionic equilibrium, owing to the irritation, is the physiological form of that which, psychologically considered, is a sensation; and, logically considered, is the occurrence of a case....
Page 127 - no very large nor very small proportion," etc. In short, p is subject to every kind of indeterminacy; it simply excludes some ratios and admits...
Page 144 - Result of that rule in that case. For example: Rule. All men are mortal, Case. Enoch was a man; Result. :. Enoch was mortal. The cognition of a rule is not necessarily conscious, but is of the nature of a habit, acquired or congenital. The cognition of a case is of the general nature of a sensation; that is to say, it is something which comes up into present consciousness. The cognition of a result is of the nature of a decision to act in a particular way on a given occasion.