The algebra of logic
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The algebra of logic
The Project Gutenberg EBook of The Algebra of Logic, by Louis CouturatThis eBook is for the use of anyone anywhere at no cost and with almost no restr The algebra of logic rictions whatsoever. You say copy it, give it away or re-use it under the terns of the Project Gutenberg License included with this eBook or online at www.gulenberg.netTitle: The Algebra of LogicAuthor: Louis CouturatRelease Date: January 26, 2004 [EBook <10836]Language: EnglishCharacter set encodin The algebra of logic g: TeXSTART OF THIS PROJECT GUTENBERG EBOOK THE ALGEBRA OF LOGICProduced by David Starner, Arno Peters, Susan Skinner and the Online Distributed ProofThe algebra of logic
reading Teas.THE ALGEBRA OF LOGICBYLOUIS COVTƯRATAUTHORIZED ENGLISH TRANSLATIONBYLYDIA GILLINGHAM ROBINSON, B. A.With a Phkface hy PHILIP E. B. JOURDAThe Project Gutenberg EBook of The Algebra of Logic, by Louis CouturatThis eBook is for the use of anyone anywhere at no cost and with almost no restr The algebra of logic by Peano to what is also known (after Venn ) as “Symbolic Logic'; ami Symbolic Logic is, in essentials, the Logic of Aristotle, given new life and power by being dressed lip in the wonderful— almost magical armour and accoutrements of Algebra. In less than seventy years, logic, to use an expression The algebra of logic of De Morgan’s, has so thriven upon symbols and, in consequence, so grown and altered that the ancient logicians would not recognize it, ami many old-The algebra of logic
fashioned logicians will not recognize it. The metaphor is not quite correct: Logie has neither grown nor altered, hut we now see more of it and more The Project Gutenberg EBook of The Algebra of Logic, by Louis CouturatThis eBook is for the use of anyone anywhere at no cost and with almost no restr The algebra of logic racteristic power and rapid development of mathematical knowledge. Attempts to treat the operations of formal logic in an analogous way had been made not infrequently by some of the more philosophical mathematicians, such as Leibniz and Lambert ; but their labors remained little known, and it was BO The algebra of logic OLE and De Morgan, about the middle of the nineteenth century, to whom a mathematical—though of course non-quantitative—way of regarding logic was dueThe algebra of logic
. By this, not. only was the traditional or Aristotelian doctrine of logic reformed and completed, but out of it. has developed, in course of time, anThe Project Gutenberg EBook of The Algebra of Logic, by Louis CouturatThis eBook is for the use of anyone anywhere at no cost and with almost no restr The algebra of logic dly taken in hand, arid in which they have as repeatedly failed.First of all, it is necessary to glance at the growth of symbolism ill mathematics: where alone it first reached perfection. There have been three stages in the development of mathematical doctrines: first came propositions with particu The algebra of logic lar numbers, like the one expressed, with signs subsequently invented, by “2 + 3 = 5”; t hen came more general laws holding for all numbers and expresThe algebra of logic
sed by letters, such as“(a + b)c = ac. + ftc”;lastly came the knowledge of more general laws of functions and the formation of the conception ami exprThe Project Gutenberg EBook of The Algebra of Logic, by Louis CouturatThis eBook is for the use of anyone anywhere at no cost and with almost no restr The algebra of logic ons of arithmetic mostly date from the sixteenth and seventeenth centuries; ami these “constant” symbols together with the letters first used systematically by ViỀTE (1040-1603) and Descartes (1596-1650), serve, by themselves, to express many propositions. It is not, then, surprising that Descartes, The algebra of logic who was both a mathematician and a philosopher, should have had the idea of keeping the method of algebra while going beyond the material of traditioThe algebra of logic
nal mathematics and embracing the general science of what thought finds, so that philosophy should become a kind of Universal Mathematics. This sort oThe Project Gutenberg EBook of The Algebra of Logic, by Louis CouturatThis eBook is for the use of anyone anywhere at no cost and with almost no restr The algebra of logic .pdfgrip.comerroneous idea, arising from a simple confusion of thought, that algebraical symbols necessarily imply something quantitative, for the antagonism there used to be and is on the part of those logicians who were not and are not mathematicians, to symbolic logic. This idea of a universal ma The algebra of logic thematics was cultivated especially by Gottfried Wilhelm Leibniz (16-16 1716).Though modern logic is really due to Boole and De Morgan, Leibniz was thThe algebra of logic
e first to have a really distinct plan of a system of mathematical logic. That this is so appears from research much of which is quite recent into LeiThe Project Gutenberg EBook of The Algebra of Logic, by Louis CouturatThis eBook is for the use of anyone anywhere at no cost and with almost no restr The algebra of logic unded of a very small number of simple ideas which form the “alphabet of human thoughts”; (2) Complex ideas proceed from these simple ideas by a uniform and symmetrical combination which is analogous to arithmetical multiplication. With regard to the first principle. the number of simple ideas is mu The algebra of logic ch greater than Leibniz thought; and, with regard to the second principle, logic considers three operations—which we shall meet with in the followingThe algebra of logic
hook under the names of logical multiplication, logical addition and negation instead of only one.“Characters” were, with Leibniz, any written signs, The Project Gutenberg EBook of The Algebra of Logic, by Louis CouturatThis eBook is for the use of anyone anywhere at no cost and with almost no restr The algebra of logic simply serve to represent ideas, and some serve for reasoning. Egyptian ami Chinese hieroglyphics and the symbols of astronomers and chemists belong to the first category, but Leibniz declaretl them to be imperfect, ami desired the second catttgory of characters for what he called his “universal cha The algebra of logic racteristic".2 It was not in the form of an algebra that Leibniz first conceived his characteristic, probably because he was then a novice in mathematThe algebra of logic
ics, but ill the form of a universal language or script.3 4 It was in 1676 that he first dreamed of a kind of algebra of thought.* and it was the algeThe Project Gutenberg EBook of The Algebra of Logic, by Louis CouturatThis eBook is for the use of anyone anywhere at no cost and with almost no restr The algebra of logic ributed to this alone the whole of his discoveries in mathematics.*1 Ami, in fact, his infinitesimal calculus affords a most brilliant example of the importance of, and Leibniz’ s skill in devising, a suitable notation.7Now, it must be remembered that what is usually understood by the name “symbolic The algebra of logic logic", and which though not its name—is chiefly due to Boole, is what Leibniz called a Calf ulus ratiocinatin', and is only a part of the UniversalThe algebra of logic
Characteristic. In symbolic logic Leibniz enunciated the principal properties of what we now call logical multiplication, addition, negation, identityThe Project Gutenberg EBook of The Algebra of Logic, by Louis CouturatThis eBook is for the use of anyone anywhere at no cost and with almost no restr The algebra of logic s, Paris, 1901, pp. 431-432, IB.1 Ibid.. p. 81.3Ibid , pp. fil, 784Ibid., p. 151.The Project Gutenberg EBook of The Algebra of Logic, by Louis CouturatThis eBook is for the use of anyone anywhere at no cost and with almost no restrGọi ngay
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