Abstract
During the period from 1846 to 1850, De Morgan’s thinking about relations developed in two ways which were essential for motivating a formal logic of relations. The first was the recognition that relations are a subject for logical study in their own right. The form which this recognition took in De Morgan’s work was unusual, and it gave rise to philosophical problems; but it was important in shaping his entire approach to the logic of relations.
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Notes
De Morgan often referred to the fact that FL appeared on the same day as George Boole’s The Mathematical Analysis of Logic (Cambridge: Macmillan, Barclay, & Macmillan, 1847). His first reference to this seems to be in his review of Boole, where he says, “On the very day in which Mr. De Morgan’s work was published in London, the one at the head of our article appeared at Cambridge.” (Athenaeum, 29 January 1848, 107.) This claim is essentially correct, though De Morgan may have stretched the truth by a day or two. He wrote in his own copy of Boole’s work (University of London Library) that he received it on 27 November 1847. He wrote Boole on 28 November that he had read Boole’s work “with great admiration,” which suggests either that De Morgan read the work very quickly, or that he received it before the 27th, or that he was being overly polite. FL was published on 24 November.
See G.C. Smith, The Boole-De Morgan Correspondence 1842–1864 (Oxford: Clarendon Press, 1982), 24.
De Morgan correctly adds the qualification that in the general case, we have “y = -x as one at least of certain alternatives.” Thus, suppose that y = - x and z = x2 yield z = (- y)2. From this it follows only that z = (- y)2 and z = (x)2 yield either y = - x or y = x. Thus, y = - x is only one of two alternatives. But not even this condition is satisfied in the relational case (3.14). (A comment by John Corcoran pointed out to me the need for this clarification.)
Unsigned review of FL, Athenaeum (11 December 1847), 1264. De Morgan does not identify the critic, but his phrasing is exactly the same as that of the review, except that there is a misprint which has replaced “marking” by “making.”
It must be confessed that De Morgan does not have a clearly stated distinction between premises and rules; but some such distinction seems required in this context. For an interesting discussion of this distinction in Boole, see John Corcoran and Susan Wood, “Boole’s Criteria for Validity and Invalidity,” Notre Dame Journal of Formal Logic 21 (1980): 609–38.
C.S. Peirce, “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, n.s. Vol. 9, pt. 2 (1870): 317–78. On the relation between De Morgan and Peirce see my article, “De Morgan, Peirce and the Logic of Relations,” Transactions of the Charles S. Peirce Society 14 (1978): 247–84.
On earlier treatments of oblique inferences see Paul Thorn, “Termini Obliqui and the Logic of Relations,” Archiv für Geschichte der Philosophie 59 (1977): 143–55
E.J. Ashworth, “Joachim Jungius (1587–1657) and the Logic of Relations,” Archiv für Geschichte der Philosophie 49 (1967): 72–85
G.H.R. Parkinson, Logic and Reality in Leibniz’s Metaphysics (Oxford: Oxford University Press, 1965), 37–50. Oblique inferences contain oblique terms-that is, terms in some grammatical case other than the nominative.
Thus Alfred North Whitehead and Bertrand Russell appear to be incorrect in their treatment of the argument. Principia Mathematica, Vol. I, 2d ed. (1925; reprinted, Cambridge: Cambridge University Press, 1950), 291. For more on the formulation of this argument, see R.G. Wengert, “Schematizing De Morgan’s Argument,” Notre Dame Journal of Formal Logic 15 (1974): 165–66; and in response, my “On De Morgan’s Argument,” Notre Dame Journal of Formal Logic 18 (1977): 133–39.
Logic, 50.
S2, 28–29. Leibniz seems to have used a similar principle in dealing with oblique inferences. See Leibniz’s 1687 letter to Vegetius, in G.H.R. Parkinson, ed., Leibniz Logical Papers (Oxford: Clarendon Press, 1966), 88.
C.S. Peirce, “Description of a Notation for the Logic of Relatives,” passim.
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© 1990 Kluwer Academic Publishers
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Merrill, D.D. (1990). Generalizing the Copula. In: Augustus De Morgan and the Logic of Relations. The New Synthese Historical Library, vol 38. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2047-7_3
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