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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 by means of George Boole in The Mathematical research of Logic and The legislation of Thought. The impact of the Boolean tuition at the improvement of common sense, continuously known yet lengthy underestimated, has lately develop into an important examine subject. This assortment is the 1st anthology of works on Boole. It includes works released in 1865, the 12 months of Boole's demise, yet by no means reprinted, in addition to numerous vintage reviews of modern many years and ten unique contributions showing the following for the 1st time. From the programme of the English Algebraic university to Boole's use of operator tools, from the matter of interpretability to that of psychologism, a whole diversity of concerns is roofed. The Boole Anthology is integral to Boole reviews and should stay so for years to come.

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Additional resources for A Boole Anthology: Recent and Classical Studies in the Logic of George Boole

Example text

By assuring them that Dr. Boole has no desire to introduce this x-y-z-ity into speech or writing. 'The perfection of the method of logic' , he says, ' may be chietly valuable as an evidence of the speculative truth of its principles. To supersede the employment of common reason ing, or to subject it to the rigour of technical forms, would be the last desire of one who knows the value of that intellectual toil and warfare which imparts to the mind an athletic vigour, and teaches it to contend with difficulties and to rely upon itself in emergencies' .

Signs of operation, as +, - , x; and 3rd, the sign of identity, =. The sign + is used to express the mental operation by which parts (of extensive quantity) are collected into a whole. For instance, if x represent animals, and y vegetables, x + y will represent the dass made up of animals and vegetables together. On the other hand, the sign - is used to express the mental operation of separating a whole (of extensive quantity) into its parts . Thus , x representing human beings, and y representing negroes, x - y will represent all human beings except negroes.

This hardly seems to us a very significant fact in the philosophy of the intel1ectual powers. If indeed the formula in question could be shown to represent some law of thought of wider application than the law of contradiction, that would be a very significant fact. But such is not the case. The equation x(l - x) = 0 is just the law of contradiction symbolical1y expressed: neither more nor less. The Aristotelian logic is charged with being incomplete , as wel1 as with being not sufficiently fundamental.

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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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