AMS Chelsea Publishing 1971; 540 pp; hardcover Volume: 251 ISBN10: 0821841998 ISBN13: 9780821841990 List Price: US$62 Member Price: US$55.80 Order Code: CHEL/251.H
 Venn's style is to take his readers very much into his confidence: as he builds the theory, he carefully points out the alternative paths he might have taken, the alternative definitions he might have used, he shows what the implications of these alternatives are, and justifies his choice on the broadest possible grounds. What is distinctive about this work may be given in part in Venn's own words: "The thorough examination of symbolic logic as a whole, that is, in its relation to ordinary logic and ordinary thought and language; the establishment of every general symbolic expression and rule on purely logical principles, instead of looking mainly to its formal justification; and the invention and employment of a scheme of diagrammatic notation which shall be in true harmony with our generalizations." Table of Contents  Objections to the introduction of mathematical symbols into logic. Mutual relation of these symbols. The generalizations of the symbolic logic, and their relation to the common system. Anticipations of Boole; especially by Lambert. Biographical notes on Lambert and Boole
 On the forms of propositions: (1) The traditional logical forms; (2) The exclusion and inclusion, or Hamiltonian forms; (3) The compartmental, or symbolic, forms
 Symbols of classes. Symbols of operations: (1) Aggregation of classes together; (2) Exception of one class from another; (3) Restriction of one class by another. Symbolic representation of these operations. Use of the equation symbol
 The inverse operation to logical class restriction. Its symbolization by the sign of division. Process of logical abstraction
 On the choice of symbolic language. Reasons for selecting that of mathematics for logical purposes
 Diagrammatic representation. Defects of the familiar Eulerian scheme; and proposal of a new scheme, better fitted to represent the complicated propositions of the symbolic logic. Its application to terms and to propositions. Logical machines
 The import of propositions, as regards the actual or conventional existence of their subjects and predicates. Such existence doubtful in the common logic, but certainly not implied in the symbolic. Application of this principle to (1) the incompatibility of propositions, (2) their independence
 Symbolic expression of the four common forms of propositions: (1) Universal, (2) Particular. Existential explanation of these latter. Quantification of the predicate. Disjunctives
 Hypothetical propositions; their real significance and their symbolic expression. Degrees of complexity in them. What our symbols actually represent here. Discussion of some extreme cases
 The universe of discourse. Its interpretation and symbolic representation
 On development or expansion; (1) by empirical processes, (2) by a generalized symbolic process. The symbol \(\frac{0}{0}\) and its explanation. Formulæ for contradiction. Certain extreme cases of expansion
 Logical statements or equations; (1) when explicit, (2) when implicit, (3) when involving indefinite class factors
 Logical statements or equations (continued). Groups of equations (1) affirmatively, (2) negatively translated. Abbreviated formulæ. The interpretation of equations, in general. The socalled inductive problem: Jevons' solution: other solutions
 Miscellaneous examples, symbolically and diagrammatically treated, in illustration of the foregoing chapters
 Elimination in logic, empirically treated; (1) from propositions in their affirmative, (2) in their negative, form. Extension to the case of particular propositions. Diagrammatic illustration
 Elimination by a general symbolic rule. The meaning and use of the expressions \(f(1)\) and \(f(0)\) in logic. The indefinite expression \(\frac{0}{0}\)
 Completion of the logical problem, by the determination of any function of our class terms from any given group of statements or equations; (1) empirically, (2) by a general symbolic rule. The syllogism and its symbolic treatment
 Generalizations of the common logic; Classes, contradictory and contrary. Propositions, their conversion and opposition, and the schedule of their various forms. Elimination. Reasonings
 Class symbols as denoting propositions. The modifications of interpretation demanded on this view
 Intensive interpretation in general. Attempts to carry this out rigidly
 Historic notes; (1) On the various schemes of symbolic notation, as exhibited in the expression of the universal negative proposition; (2) On the various schemes of geometrical or diagrammatical representation of propositions
 Index of subjectmatter, and of bibliographical references
