Pure Logic: Or, The Logic of Quality Apart from Quantity; with Remarks on Boole's System and on the Relation of Logic and Mathematics

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E. Stanford, 1864 - 87 páginas
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Página 63 - IfAisB.EisF; and if C is D, E is F ; but Either A is B or G is D ; therefore, E is F.
Página 76 - and," "or," interposed between the terms descriptive of two or more classes of objects, imply that those classes are quite distinct, so that no member of one is found in another. In this and in all other respects the words "and" "or" are analogous with the sign + in algebra, and their laws are identical.
Página 6 - Amongst other evils of such a plan it leads up to the catastrophe of having to maintain "that the old distinction of connotative and non-connotative names is wholly erroneous and unfounded," and that "singular, proper, or socalled non-connotative terms, are more full of connotation or meaning in intent or quality than others, instead of being devoid of such meaning.
Página 86 - ... an indefinite class term. But his critic understands this to mean that wherever - appears "we must have another distinct system by which to get that meaning". Two sections before the conclusion of his book he adds: "Supposing it prove true that Prof. Boole's Calculus of 1 and 0 has no real logical force and meaning, it cannot be denied that there is still something highly remarkable, something highly mysterious in the fact, that logical forms can be turned into numeral forms, and while treated...
Página 77 - Twas not their infirmity, It was married chastity. Truth may seem, but cannot be; Beauty brag, but 'tis not she; Truth and beauty buried be. To this urn let those repair That are either true...
Página 81 - ... removed from one side of an equation to the other by changing its sign. This is in accordance with the algebraic rule of transposition. But instead of dwelling upon particular cases, we may at once affirm the general axioms : — 1st. If equal things are added to equal things, the wholes are equal. 2nd. If equal things are taken from equal things, the remainders are equal.
Página 85 - ... such an expression), the more does it depart from the condition of satisfying the fundamental law above referred to. The symbol -, whose interpretation was previously discussed, does not necessarily disobey the law we are here considering, for it admits of the numerical values 0 and 1 indifferently. Its actual interpretation, however, as an indefinite class symbol, cannot, I conceive, except upon the ground of analogy, be deduced from its arithmetical properties, but must be established experimentally.
Página 76 - A peer is either a duke, or a marquis, or an earl, or a viscount, or a baron.' If expressed in Professor Boole's symbols, it would be implied that a peer cannot be at once a duke and marquis, or marquis and earl. Yet many peers do possess two or more titles, and the Prince of Wales is Duke of Cornwall, Earl of Chester, Baron Renfrew, etc.
Página 78 - Either productive of pleasure or preventive of pain," in the above definition, is meant to be equivalent to " Either productive of pleasure; or, if not productive of pleasure, preventive of pain." Thus the class of things which the above expression, taken alone, would define, would consist of all things productive of pleasure, together with all things not productive of pleasure, but preventive of pain, and its symbolical expression would be p+(lp)r.

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