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The Laws of Thought
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{{Short description|Book by George Boole}}{{About|Boole's book on logic|overview on the axiomatic rules due to various logicians and philosophers|Law of thought}}{{italic title}}An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities by George Boole, published in 1854, is the second of Boole's two monographs on algebraic logic. Boole was a professor of mathematics at what was then Queen's College, Cork (now University College Cork), in Ireland.- the content below is remote from Wikipedia
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Review of the contents
The historian of logic John Corcoran wrote an accessible introduction to Laws of ThoughtGeorge Boole. 1854/2003. The Laws of Thought, facsimile of 1854 edition, with an introduction by J. Corcoran. Buffalo: Prometheus Books (2003). Reviewed by James van Evra in Philosophy in Review.24 (2004) 167â169. and a point by point comparison of Prior Analytics and Laws of Thought.John Corcoran, Aristotle's Prior Analytics and Boole's Laws of Thought, History and Philosophy of Logic, 24 (2003), pp. 261â288. According to Corcoran, Boole fully accepted and endorsed Aristotle's logic. Boole's goals were âto go under, over, and beyondâ Aristotle's logic by:- Providing it with mathematical foundations involving equations;
- Extending the class of problems it could treat from assessing validity to solving equations, and;
- Expanding the range of applications it could handle â e.g. from propositions having only two terms to those having arbitrarily many.
Uninterpretable terms
In Boole's account of his algebra, terms are reasoned about equationally, without a systematic interpretation being assigned to them. In places, Boole talks of terms being interpreted by sets, but he also recognises terms that cannot always be so interpreted, such as the term 2AB, which arises in equational manipulations. Such terms he classes uninterpretable terms; although elsewhere he has some instances of such terms being interpreted by integers.The coherences of the whole enterprise is justified by Boole in what Stanley Burris has later called the "rule of 0s and 1s", which justifies the claim that uninterpretable terms cannot be the ultimate result of equational manipulations from meaningful starting formulae (Burris 2000). Boole provided no proof of this rule, but the coherence of his system was proved by Theodore Hailperin, who provided an interpretation based on a fairly simple construction of rings from the integers to provide an interpretation of Boole's theory (Hailperin 1976).Booleâs 1854 definition of the universe of discourse
{{Blockquote|text=In every discourse, whether of the mind conversing with its own thoughts, or of the individual in his intercourse with others, there is an assumed or expressed limit within which the subjects of its operation are confined. The most unfettered discourse is that in which the words we use are understood in the widest possible application, and for them the limits of discourse are co-extensive with those of the universe itself. But more usually we confine ourselves to a less spacious field. Sometimes, in discoursing of men we imply (without expressing the limitation) that it is of men only under certain circumstances and conditions that we speak, as of civilized men, or of men in the vigour of life, or of men under some other condition or relation. Now, whatever may be the extent of the field within which all the objects of our discourse are found, that field may properly be termed the universe of discourse. Furthermore, this universe of discourse is in the strictest sense the ultimate subject of the discourse. |author=George Boole|source=Page 42: George Boole. 1854/2003. The Laws of Thought. Facsimile of 1854 edition, with an introduction by J. Corcoran. Buffalo: Prometheus Books (2003). Reviewed by James van Evra in Philosophy in Review 24 (2004): 167â169.}}Editions
- Boole (1854). An Investigation of the Laws of Thought. Walton & Maberly.
- Boole, George (1958[1854]). An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities. Macmillan. Reprinted with corrections, Dover Publications, New York, NY (reissued by Cambridge University Press, 2009, {{ISBN|978-1-108-00153-3}}).
See also
References
Citations
{{reflist}}Bibliography
- Burris, S. (2000). The Laws of Boole's Thought. Manuscript.
- Hailperin, T. (1976/1986). Boole's Logic and Probability. North Holland.
- Hailperin, T, (1981). Boole's algebra isn't Boolean algebra. Mathematics Magazine 54(4): 172â184. Reprinted in A Boole Anthology (2000), ed. James Gasser. Synthese Library volume 291, Spring-Verlag.
- Huntington, E.V. (1904). Sets of independent postulates for the algebra of logic. Transactions of the American Mathematical Society 5:288â309.
- Jevons, W.S. (1869). The Substitution of Similars. Macmillan and Co.
- Jevons, W.S. (1990). Pure Logic and Other Minor Works. Ed. by Robert Adamson and Harriet A. Jevons. Lennox Hill Pub. & Dist. Co.
- Peirce, C.S. (1880). On the algebra of logic. In American Journal of Mathematics 3 (1880).
- Schröder, E. (1890-1905). Algebra der Logik. Three volumes, B.G. Teubner.
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