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Logic of relatives
The logic of relatives, more precisely, the logic of relative terms, is the study of relations as represented in symbolic forms known as rhemes, rhemata, or relative terms. The treatment of relations by way of their corresponding relative terms affords a distinctive perspective on the subject, even though all angles of approach must ultimately converge on the same formal subject matter.
The consideration of relative terms has its roots in antiquity, but it entered a radically new phase of development with the work of Charles Sanders Peirce, beginning with his 1870 paper “Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the Conceptions of Boole's Calculus of Logic”.
- Peirce, C.S., “Description of a Notation for the Logic of Relatives, Resulting from an Amplification of the Conceptions of Boole's Calculus of Logic”, Memoirs of the American Academy of Arts and Sciences 9, 317–378, 1870. Reprinted, Collected Papers CP 3.45–149, Chronological Edition CE 2, 359–429.
- Aristotle, “The Categories”, Harold P. Cooke (trans.), pp. 1–109 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.
- Aristotle, “On Interpretation”, Harold P. Cooke (trans.), pp. 111–179 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.
- Aristotle, “Prior Analytics”, Hugh Tredennick (trans.), pp. 181–531 in Aristotle, Volume 1, Loeb Classical Library, William Heinemann, London, UK, 1938.
- Boole, George, An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities, Macmillan Publishers, 1854. Reprinted with corrections, Dover Publications, New York, NY, 1958.
- Maddux, Roger D., Relation Algebras, vol. 150 in ‘Studies in Logic and the Foundations of Mathematics’, Elsevier Science, 2006.
- Peirce, C.S., Collected Papers of Charles Sanders Peirce, vols. 1–6, Charles Hartshorne and Paul Weiss (eds.), vols. 7–8, Arthur W. Burks (ed.), Harvard University Press, Cambridge, MA, 1931–1935, 1958. Cited as CP volume.paragraph.
- Peirce, C.S., Writings of Charles S. Peirce : A Chronological Edition, Volume 2, 1867–1871, Peirce Edition Project (eds.), Indiana University Press, Bloomington, IN, 1984. Cited as CE 2.
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