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A Boole Anthology: Recent and Classical Studies in the Logic - download pdf or read online

By Samuel Neil (auth.), James Gasser (eds.)

ISBN-10: 904815491X

ISBN-13: 9789048154913

ISBN-10: 940159385X

ISBN-13: 9789401593854

Modern mathematical common sense wouldn't exist with no the analytical instruments first built through George Boole in The Mathematical research of Logic and The legislation of Thought. The impression of the Boolean institution at the improvement of good judgment, continuously known yet lengthy underestimated, has lately turn into a tremendous learn subject. This assortment is the 1st anthology of works on Boole. It comprises works released in 1865, the yr of Boole's dying, yet by no means reprinted, in addition to numerous vintage reviews of contemporary a long time and ten unique contributions showing right here for the 1st time. From the programme of the English Algebraic university to Boole's use of operator equipment, from the matter of interpretability to that of psychologism, an entire variety of concerns is roofed. The Boole Anthology is necessary to Boole reports and should stay so for years to come.

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Extra info for A Boole Anthology: Recent and Classical Studies in the Logic of George Boole

Example text

In general, vx =somex (1) It can easily be shown, that, as in Algebra, so in the logical system which we are describing, the literat symbols, x. , are commutative; that is, xy =yx ; 27 J. ), ABooie Anthology, 27-43. © 2000 Kluwer Academic Publishers. P. YOUNG and that they are also distributive; that is, z(x ± y) =zx ± zy (3) Another relation between Algebra and the Logical System under consideration is, that, in the latter as weil as in the former, a Iiteral symbol may be transposed from one side of an equation to the other by changing the sign of operation, + or - .

We commonly reason by the aid of words, and in the forms of a well-constructed language. This is both an actual condition of and an important safeguard in the reasonings and discourses of common life; for thus not only every step of the connected train of thought, and every mediate result estabIished in the course of thought, is thus brought forward to show its correspondency with experience and intelligible expression; but in doing so we seldom attend to the ulterior grounds upon which the forms alike of language and of thought have been established; and we often remain quite unconscious that any (or at least what) law underlies the processes by which premiss and conclusion are knit together.

Take, for instance, the proposition-'Men who do not possess courage and practise self-denial are not heroes'. Here, on Professor Boole's method, a variety of concepts are supposed to be before the mind, as, men, those who practiseself-denial, those who possess courage, REMARKS ON BOOLE'S MATHEMATICAL THEORY 33 and heroes. But in reality, when we form the judgment expressed in the proposition given, the separate concepts, men, those who practise self-denial, those who possess courage, are not before the mind; but simply the two concepts, men who do not possess courage and practise self-denial, and heroes.

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A Boole Anthology: Recent and Classical Studies in the Logic of George Boole by Samuel Neil (auth.), James Gasser (eds.)

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