Abstract
An association of algebraic symbols and their properties with those of logic would hardly have been conceivable before the 16th century. Systematic use of letters for numbers in general, and symbols for operations on them, were a development of the 16th and 17th centuries. Although Aristotle’s theory of the syllogism used letters of the alphabet for arbitrary general terms, i.e., used variables, there was no formal notion of the composition of terms nor of a negative term, hence no notion of an operation on terms. An early, perhaps the earliest, mention of such an algebraic-like operation occurs in Jacques Bernoulli’s Parallelismus ratiocinii logici et algebraici... 1
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Bernoulli, Jacques. 1969. Die Werke von Jakob Bernoulli, Band 1. Basel: Birkhäuser.
Bernoulli, Jacques and Jean Bernoulli. 1685. Parallelismus ratiocinii logici et algebraici,... Reprinted in Jacobi Bernoulli, Basileensis, opera vol. 1 (Geneva 1744) 211–24 and in Bernoulli 1969, 263–74.
Boole, George. 1847. The mathematical analysis of logic, being an essay towards a calculus of deductive reasoning. Cambridge: Barclay & Macmillan; London: George Bell.
Boole, George. 1854. The laws of thought. London: Walton and Maberley. Reprinted 1916, 1951.
Couturat, Louis, ed. 1903. Opuscules et fragments inédits de Leibniz. Extraits des manuscrits de la Bibliothèque royale de Hanovre. Paris: Presses Universitaires de France. Reprinted 1961, Hildesheim: Olms.
Gerhardt, C.I., ed. 1890. Die philosophischen Schriften von Gottfried Wilhelm Leibniz, Band 7. Berlin (English translation of XIX and XX in Parkinson 1966, 122–44).
Gregory, D.F. 1840. On the real nature of symbolical algebra. Transactions of the Royal Society of Edinburgh 14: 208–16.
Hailperin, Theodore. 1976. Boole’s logic and probability. Amsterdam: North-Holland.
Hailperin, Theodore. 1986. Revised and enlarged second edition of Hailperin 1976.
Leibniz, Gottfried Wilhelm. 1768. G.G. Leibnitii opera omnia. Edited by L. Dutens. Geneva.
Leibniz, Gottfried Wilhelm. 1890. Die philosophischen Schriften von Gottfried Wilhelm Leibniz, Band 7. Berlin. Reprinted 1961, Hildesheim: Olms.
Leibniz, Gottfried Wilhelm. 1971. Sämtliche Schriften und Briefe. Sechste Reihe, Erster Band. Berlin: Akademie-Verlag.
Lenzen, Wolfgang. 1984. Leibniz und die Boolesche Algebra, Studia Leibnitiana 16 (2). Wiesbaden: Franz Steiner.
Parkinson, G.H.R., ed. 1966. Leibniz logical papers. A selection translated and edited with an introduction. Oxford: Clarendon Press.
Peacock, George. 1830. A treatise on algebra. Cambridge: J. & J.J. Deighton.
Peacock, George. 1834. Report on recent progress and present state of certain branches of analysis. Report on the third meeting of the British Association for the Advancement of Science held at Cambridge in 1833. London: John Murray.
Peckhaus, Volker. 1997. Logik, Mathesis universalis und allgemeine Wissenschaft. Berlin: Akademie-Verlag.
Schröder, Ernst. 1877. Der Operationskreis des Logikkalküls. Leipzig: Teubner.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Hailperin, T. (2000). Algebraical Logic: Leibniz and Boole. In: Gasser, J. (eds) A Boole Anthology. Synthese Library, vol 291. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9385-4_8
Download citation
DOI: https://doi.org/10.1007/978-94-015-9385-4_8
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5491-3
Online ISBN: 978-94-015-9385-4
eBook Packages: Springer Book Archive