Synopses & Reviews
The two works reprinted in this volume are a unique fusion of logical thought and inimitable whimsy. Written by the 19th-century mathematician who also gave us "Alive in Wonderland", they are among the most entertaining logical works ever written, and contain some of the most thought-provoking puzzles ever devised.
Synopsis
Over 350 ingenious problems involving classical logic: logic expressed in symbols; syllogisms and the sorites diagrammed; logic as a game played with 2 diagrams and a set of counters.
Synopsis
In this unique fusion of logical thought and inimitable whimsy, Over 350 ingenious problems involve classical logic: logic is expressed in terms of symbols; syllogisms and the sorites are diagrammed; logic becomes a game played with 2 diagrams and a set of counters. Two books bound as one.
About the Author
Lewis Carroll (1832-98) was the pseudonym of Charles Lutwidge Dodgson, a Professor of Mathematics at Cambridge University. Alice's Adventures in Wonderland and its sequel, Through the Looking Glass, are rich repositories of his sparkling gifts for wordplay, logic, and fantasy.
Table of Contents
Book I. Things and Their Attributes
I. Introductory
II. Classification
III. Division
§1. Introductory
§2. Dichotomy
IV. Names
V. Definitions
Book II. Propositions
I. Propositions Generally
§1. Introductory
§2. Normal form of a Proposition
§3. Various kinds of Propositions
II. Propositions of Existence
III. Propositions of Relation
§1. Introductory
§2. Reduction of a Proposition of Relation to Normal form
§3. "A Proposition of Relation, beginning with "All," is a Double Proposition"
§4. "What is implied, in a Proposition of Relation, as to the Reality of its Terms?"
§5. Translation of a Proposition of Relation into one or more Propositions of Existence
Book III. The Biliteral Diagram
I. Symbols and Cells
II. Counters
III. Representation of Propositions
§1. Introductory
§2. Representation of Propositions of Existence
§3. Representation of Propositions of Relation
IV. "Interpretation of Biliteral Diagram, when Marked with Counters"
Book IV. The Triliteral Diagram
I. Symbols and Cells
II. "Representation of Propositionsin Terms of X and M, or of Y and M"
§1. "Representation of Propositions of Existence in terms of x and m, or of y and m"
§2. "Representation of Propositions of Relation in terms of x and m, or of y and m"
III. "Representation of two propositions of relation, one in terms of x and m, and the other in terms of y and m, on the same diagram"
IV. "Interpretation, in terms of x and y, of triliteral diagram, when marked with counters or digits"
Book V. Syllogisms
I. Introductory
II. Problems in Syllogisms
§1. Introductory
§2. Given a Pair of Propositions of Relation
§3. Given a Trio of Propositions of Relation
Book VI. The Method of Subscripts
I. Introductory
II. Representation of propositions of relation
III. Syllogisms
§1. Representation of Syllogisms
§2. Formula for Syllogisms
§3. Fallacies
§4. Method of proceeding with a given Pair of Propositions
Book VII. Soriteses
I. Introductory
II. Problems in Soriteses
§1. Introductory
§2. Solution by Method of Separate Syllogisms
§3. Solution by Method of Underscoring
Book VIII. "Examples, with answers and solutions"
I. Examples
§1. Propositions of Relation
§2. Pairs of Abstract Propositions
§3. Marked Triliteral Diagrams
§4. Pairs of Abstract Propositions
§5. Pairs of Concrete Propositions
§6. Trios of Abstract Propositions
§7. Trios of Concrete Propositions
§8. Sets of Abstract Propositions
§9. Sets of Concrete Propositions
II. Answers
III. Solutions
§1. Propositions of Relation reduced to normal form
§2. Method of Diagrams
§3. Method of Subscripts
Notes
"Appendix, addressed to teachers"
Notes to Appendix
Index