Augustus De Morgan and the Logic of Relations
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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The Traditional Syllogism
First Thoughts on the Copula
Generalizing the Copula
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abstract copula affirmative analysis animal applied argument arithmetic assertion Assumption Augustus De Morgan axioms basic bicopular syllogism Boole categorical propositions categorical syllogism Chapter claim complex composition of relations conclusion condition consider contain convertible and transitive convertible relation discussion distinction equivalent Euclid example expressed fact figure formal logic fortiori geometry gives greater Hamilton identity relation inherent quantity instance interpretation involve joined judgment laws logic of relations logical form logician Mansel material mathematics means Morgan Morgan's logic negative notation notion object oblique inferences onymatic Penny Cyclopaedia predicate principle problem proof propositional forms quantification theory reasoning reduced reflexive relation term relational inferences requires result rule of inference rules second premise sentential logic species syllogistic form symbolical algebra theorems thing thought tion traditional syllogism transitive and convertible transitive relations transitivity of equality transitivity of identity unit syllogisms University Whately Whately's