Augustus De Morgan and the Logic of Relations

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Springer Netherlands, Nov 30, 1990 - Philosophy - 262 pages
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The middle years of the nineteenth century saw two crucial develop ments in the history of modern logic: George Boole's algebraic treat ment of logic and Augustus De Morgan's formulation of the logic of relations. The former episode has been studied extensively; the latter, hardly at all. This is a pity, for the most central feature of modern logic may well be its ability to handle relational inferences. De Morgan was the first person to work out an extensive logic of relations, and the purpose of this book is to study this attempt in detail. Augustus De Morgan (1806-1871) was a British mathematician and logician who was Professor of Mathematics at the University of London (now, University College) from 1828 to 1866. A prolific but not highly original mathematician, De Morgan devoted much of his energies to the rather different field of logic. In his Formal Logic (1847) and a series of papers "On the Syllogism" (1846-1862), he attempted with great ingenuity to reformulate and extend the tradi tional syllogism and to systematize modes of reasoning that lie outside its boundaries. Chief among these is the logic of relations. De Mor gan's interest in relations culminated in his important memoir, "On the Syllogism: IV and on the Logic of Relations," read in 1860.

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Contents

The Traditional Syllogism
1
Whately and the Revival of Formal Logic 2 Euclid and the Syllogism
2
Reid Hamilton and Mansel on Relational Inferences
3
Logic and Mathematics
6
First Thoughts on the Copula 1 The Two Copulas
26
First Notions of Logic
35
A Rigorous Formulation
37
Relations and Identity
43
Properties of Relations
124
NOTES
127
Singular Relational Syllogisms Unit Syllogisms
129
Quantified Relational Syllogisms
142
The Limited Unit Syllogism
143
The Ordinary Syllogism and the Relational Syllogism
145
D9? WW7 vii
170
INDEX
174

Generalizing the Copula
48
The Abstract Copula
56
The Bicopular Syllogism and the Composition of Relations
60
Oblique Inferences and De Morgans Dictum
79
The Problem of Form and Matter
89
Sundry Perversions of the Syllogistic Form
90
The Material Copula
95
De Morgans Response
99
The Issues
103
Heads and Tails
110
The Logic of Relations
113
ww Philosophical Preliminaries
114
General Logic of Relations
117
ll
181
U1t tI
186
Properties of Inclusion and Identity
202
26
208
Additional Inclusion Laws
217
De Morgans Conjectures
240
35
246
43
250
95
255
103
256
145
258
Copyright

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About the author (1990)

Daniel D. Merrill is professor emeritus of philosophy at Oberlin College.

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