Book:William Warren Bartley, III/Lewis Carroll's Symbolic Logic

Subject Matter

 * Symbolic Logic

Contents

 * Note to the Reader From the Editor and Publisher


 * Editor's Introduction (W.W.B.)
 * Editor's Acknowledgements (W.W.B.)
 * Editor's Bibliography (W.W.B.)

Part One: Elementary

 * Introduction to Learners
 * Preface to Fourth Edition


 * BOOK I THINGS AND THEIR ATTRIBUTES


 * Chapter I Introductory
 * Things
 * Attributes
 * Adjuncts


 * Chapter II Classification
 * Classificaion
 * Class
 * Peculiar Attributes
 * Genus
 * Species
 * Differentia
 * Real and Unreal, or Imaginary, Classes
 * Individual
 * A Class regarded as a single Thing


 * Chapter III Division
 * $$[\S 1]$$ Introductory
 * Division
 * Codivisional Classes
 * $$[\S 2]$$ Dichotomy
 * Dichotomy
 * Arbitrary limits of Classes
 * Subdivision of Classes


 * Chapter IV Names
 * Name
 * Real and Unreal Names
 * Three ways of expressing a Name
 * Two senses in which a plural Name may be used


 * Chapter V Definitions
 * Definition
 * Examples worked as models


 * BOOK II PROPOSITIONS


 * Chapter I Propositions Generally
 * $$[\S 1]$$ Introductory
 * Technical meaning of "some"
 * Proposition
 * Normal form of a Proposition
 * Subject, Predicate, and Terms
 * $$[\S 2]$$ Normal form of a Proposition
 * Its four parts :
 * (1) Sign of Quantity
 * (2) Name of Subject
 * (3) Copula
 * (4) Name of Predicate
 * $$[\S 3]$$ Various kinds of Propositions
 * Three kinds of Propositions :
 * (1) Begins with "Some." Called a Particular Proposition: also a Proposition in I
 * (2) Begins with "No." Called a Universal Negative Proposition: also a Proposition in E
 * (3) Begins with "All." Called a Universal Affirmative Proposition: also a Proposition in A
 * A Proposition, whose Subject is an Individual, is to be regarded as Universal
 * Two kinds of Propositions: Propositions of Existence, and Propositions of Relation


 * Chapter II Propositions of Existence
 * Proposition of Existence


 * Chapter III Propositions of Relation
 * $$[\S 1]$$ Introductory
 * Proposition of Relation
 * Universe of Discourse, or Univ.
 * $$[\S 2]$$ Reduction of a Proposition of Relation to Normal form
 * Rules
 * Examples worked
 * $$[\S 3]$$ A Proposition of Relation, beginning with "All" is a Double Proposition
 * Its equivalence to two Propositions
 * $$[\S 4]$$ What is implied, in a Proposition of Relation, as to the Reality of its Terms?
 * Propositions beginning with "Some"
 * Propositions beginning with "No"
 * Propositions beginning with "All"
 * $$[\S 5]$$ Translation of a Proposition of Relation into one or more Propositions of Existence
 * Rules
 * Examples worked


 * BOOK III THE BILITERAL DIAGRAM


 * Chapter I Symbols and Cells
 * The Diagram assigned to a certain Set of Things, viz. our Univ.
 * Univ. divided into the $$x$$-Class and the $$x'$$-Class
 * The North and South Halves assigned to these two Classes
 * The $$x$$-Class subdivided into the $$xy$$-Class and the $$xy'$$-Class
 * The North-West and North-East Cells assigned to these two Classes
 * The $$x'$$-Class similarly divided
 * The South-West and South-East Cells similarly assigned
 * The West and East Halves have thus been assigned to the $$y$$-Class and the $$y'$$-Class
 * Table I. Adjuncts of Classes, and Compartments, or Cells, assigned to them


 * Chapter II Counters
 * Meaning of a Red Counter placed in a Cell
 * Meaning of a Red Counter placed on a Partition
 * American phrase sitting on the fence
 * Meaning of a Grey Counter placed in a Cell


 * Chapter III Representation of Propositions
 * $$[\S 1]$$ Introductory
 * The word "Things" to be henceforward omitted
 * Uniliteral Proposition
 * Biliteral Proposition
 * Proposition in terms of certain Letters
 * $$[\S 2]$$ Representation of Propositions of Existence
 * The Proposition "Some x exist"
 * Three other similar Propositions
 * The Proposition "No x exist"
 * Three other similar Propositions
 * The Proposition "Some $$xy$$ exist"
 * Three other similar Propositions
 * The Proposition "No $$xy$$ exist"
 * Three other similar Propositions
 * The Proposition "No $$x$$ exist" is Double, and is equivalent to the two Propositions "No $$xy$$ exist" and "No $$xy'$$ exist"
 * $$[\S 3]$$ Representation of Propositions of Relation
 * The Proposition "Some $$x$$ are $$y$$"
 * Three other similar Propositions
 * The Proposition "Some $$y$$ are $$x$$"
 * Three other similar Propositions
 * Trio of equivalent Propositions, viz.
 * Some $$xy$$ exist $$=$$ Some $$x$$ are $$y$$ $$=$$ Some $$y$$ are $$x$$
 * Converse Propositions, and Conversion
 * Three other similar Trios
 * The Proposition "No $$x$$ are $$y$$"
 * Three other similar Propositions
 * The Proposition "No $$y$$ are $$x$$"
 * Three other similar Propositions
 * Trio of equivalent Propositions, viz.
 * No $$xy$$ exist $$=$$ No $$x$$ are $$y$$ $$=$$ No $$y$$ are $$x$$
 * Three other similar Trios
 * The Proposition "All $$x$$ are $$y$$"
 * The Proposition "All $$x$$ are $$y$$" is Double, and is equivalent to the two :::: Propositions "Some $$x$$ are $$y$$" and "No $$x$$ are $$y'$$"
 * Tables II, III. Representation of Propositions of Existence and Relation
 * Seven other similar Propositions


 * Chapter IV Interpretation of Biliteral Diagram, When Marked with Counters
 * Interpretation of $$\begin{array}{|c|c|} \hline \bigodot & \quad \\ \hline \quad & \quad \\ \hline \end{array}$$
 * And of three other similar arrangements
 * Interpretation of $$\begin{array}{|c|c|} \hline \bigcirc & \quad \\ \hline \quad & \quad \\ \hline \end{array}$$
 * And of three other similar arrangements
 * Interpretation of WIP: Insert table
 * And of three other similar arrangements
 * Interpretation of $$\begin{array}{|c|c|} \hline \bigodot & \bigodot \\ \hline \quad & \quad \\ \hline \end{array}$$
 * And of three other similar arrangements
 * Interpretation of $$\begin{array}{|c|c|} \hline \bigcirc & \bigcirc \\ \hline \quad & \quad \\ \hline \end{array}$$
 * And of three other similar arrangements
 * Interpretation of $$\begin{array}{|c|c|} \hline \bigodot & \bigcirc \\ \hline \quad & \quad \\ \hline \end{array}$$
 * And of seven other similar arrangements


 * BOOK IV THE TRILITERAL DIAGRAM


 * Chapter I Symbols and Cells
 * Change of Biliteral into Triliteral Diagram
 * The $$xy$$-Class subdivided into the $$xym$$-Class and the $$xym'$$-Class
 * The Inner and Outer Cells of the North-West Quarter assigned to these Classes
 * The $$xy'$$-Class, the $$x'y$$-Class, and the $$x'y'$$-Class similarly subdivided
 * The Inner and Outer Cells of the North-East, the South-West, and the South-East Quarters similarly assigned
 * The Inner Square and the Outer Border have thus been assigned to the $$m$$-Class and the $$m'$$-Class
 * Rules for anding readily the Compartment, or Cell, assigned to any given Attribute or Attributes
 * Table IV. Attributes of Classes, and Compartments, or Cells, assigned to them


 * Chapter II Representation of Propositions in Terms of $$x$$ and $$m$$, or of $$y$$ and $$m$$
 * $$[\S 1]$$ Representation of Propositions of Existence in terms of $$x$$ and $$m$$, or of $$y$$ and $$m$$
 * The Proposition "Some $$xm$$ exist"
 * Seven other similar Propositions
 * The Proposition "No $$xm$$ exist"
 * Seven other similar Propositions
 * $$[\S 2]$$ Representation of Propositions of Relation in terms of $$x$$ and $$m$$, or of $$y$$ and $$m$$
 * The Pair of Converse Propositions
 * Some $$x$$ are $$m$$ $$=$$ Some $$mn$$ are $$x$$
 * Seven other similar Pairs
 * The Pair of Converse Propositions
 * No $$x$$ are $$m$$ $$=$$ No $$m$$ are $$x$$
 * Seven other similar Pairs
 * The Proposition "All $$x$$ are $$m$$"
 * Fifteen other similar Propositions
 * Tables V, VI, VII, VIII. Representation of Propositions in terms of $$x$$ and $$m$$, or of $$y$$ and $$m$$''


 * Chapter 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
 * The Digits I and O to be used instead of Red and Grey Counters
 * Rules
 * Examples worked


 * Chapter IV Interpretation, in Terms of $$x$$ and $$y$$, of Triliteral Diagram, When Marked with Counters or Digits
 * Rules
 * Examples worked


 * BOOK V SYLLOGISMS


 * Chapter I Introductory
 * Syllogism
 * Premisses
 * Conclusion
 * Eliminands
 * Retinends
 * Consequent
 * The Symbol $$\therefore$$
 * Specimen-Syllogisms


 * Chapter II Problems in Syllogisms
 * $$[\S 1]$$ Introductory
 * Concrete and Abstract Propositions
 * Method of translating a Proposition from concrete into abstract form
 * Two forms of Problems
 * $$[\S 2]$$ Given a Pair of Propositions of Relation, which contain between them a pair of codivisional Classes, and which are proposed as Premisses: to ascertain what Conclusion, if any, is consequent from them
 * Rules
 * Examples worked fully
 * The same worked briefly, as models
 * $$[\S 3]$$ Given a Trio of Propositions of Relation, of which every two contain a Pair of codivisional Classes, and which are proposed as a Syllogism: to ascertain whether the proposed Conclusion is consequent from the proposed Premisses, and, if so, whether it is complete
 * Rules
 * Examples worked briefly, as models


 * BOOK VI THE METHOD OF SUBSCRIPTS


 * Chapter 1 Introductory
 * Meaning of $$x_1$$, $$xy_1$$, &c.
 * Entity
 * Meaning of $$x_0$$, $$xy_0$$, &c.
 * Nullity
 * The Symbols $$\dagger$$ and $$\P$$
 * Like and Unlike Signs


 * Chapter II Representation of Propositions of Relation
 * The Pair of Converse Propositions
 * Some $$x$$ are $$y$$ $$=$$ Some $$y$$ are $$x$$
 * Three other similar Pairs
 * The Pair of Converse Propositions
 * No $$x$$ are $$y$$ $$=$$ No $$y$$ are $$x$$
 * Three other similar Pairs
 * The Proposition "All $$x$$ are $$y$$"
 * The Proposition "All $$x$$ are $$y$$" is Double, and is equivalent to the two Propositions "Some $$x$$ exist" and "No $$x$$ are $$y'$$"
 * Seven other similar Propositions
 * Rule for translating: "All $$x$$ are $$y$$ from abstract into subscript form, and vice versa


 * Chapter III Syllogisms
 * $$[\S 1]$$ Representation Syllogisms
 * Rules
 * $$[\S 2]$$ Formulae for solving Problems in Syllogisms
 * Three Formulae worked out:
 * Fig. I. $$xm_0 \dagger ym'_0 \P xy_0$$, its two Variants ($$\alpha$$) and ($$\beta$$)
 * Fig. II. $$xm_0 \dagger ym_1 \P x'y_1$$
 * Fig. III. $$xm_0 \dagger ym_0 \dagger m_1 \P x'y'_1$$
 * Table IX. Formulae and Rules
 * Examples worked briefly, as models
 * Notes
 * $$[\S 3]$$ Fallacies
 * Fallacy
 * Method of finding Forms of Fallacies
 * Forms best stated in words
 * Three Forms of Fallacies:
 * (1) Fallacy of Like Eliminands not asserted to exist
 * (2) Fallacy of Unlike Eliminands with an Entity-Premiss
 * (3) Fallacy of two Entity-Premisses
 * $$[\S 4]$$ Method of proceeding with a given Pair of Propositions
 * Rules


 * BOOK VII SORITESES


 * Chapter I Introductory
 * Sorites
 * Premisses
 * Partial Conclusion
 * Complete Conclusion (or Conclusion)
 * Eliminands
 * Retinends
 * Consequent
 * The Symbol $$\therefore$$
 * Specimen-Soriteses


 * Chapter II Problems in Soriteses
 * $$[\S 1]$$ Introductory
 * Form of Problem
 * Two Methods of Solution
 * $$[\S 2]$$ Solution by Method of Separate Syllogisms
 * Rules
 * Example worked
 * $$[\S 3]$$ Solution by Method of Underscoring
 * Underscoring
 * Subscripts to be omitted
 * Example worked fully
 * Example worked briefly, as model
 * Seventeen Examination-papers


 * BOOK VII EXAMPLES, ANSWERS AND SOLUTIONS
 * Chapter I Examples
 * $$[\S 1]$$ Propositions of Relation, to be reduced to normal form
 * $$[\S 2]$$ Pairs of Abstract Propositions, one in terms of $$x$$ and $$m$$, and the other in terms of $$y$$ and $$m$$, to be represented on the same Triliteral Diagram
 * $$[\S 3]$$ Marked Triliteral Diagrams, to be interpreted in terms of $$x$$ and $$y$$
 * $$[\S 4]$$ Pairs of Abstract Propositions, proposed as Premisses.. Conclusions to be found
 * $$[\S 5]$$ Pairs of Concrete Propositions, proposed as Premisses: Conclusions to be found
 * $$[\S 6]$$ Trios of Abstract Propositions, proposed as Syllogisms: to be examined
 * $$[\S 7]$$ Trios of Concrete Propositions, proposed as Syllogisms: to be examined
 * $$[\S 8]$$ Sets of Abstract Propositions, proposed as Premisses for Soriteses: Conclusions to be found
 * $$[\S 9]$$ Sets of Concrete Propositions, proposed as Premisses for Soriteses: Conclusions to be found


 * Chapter II Answers
 * Answers to
 * $$[\S 1]$$
 * $$[\S 2]$$
 * $$[\S 3]$$
 * $$[\S 4]$$
 * $$[\S 5]$$
 * $$[\S\S 6, 7]$$
 * $$[\S\S 8, 9]$$


 * Chapter III Solutions
 * $$[\S 1]$$ Propositions of Relation reduced to normal form
 * Solutions for $$[\S 1]$$
 * $$[\S 2]$$ Method of Diagrams
 * Solutions for
 * $$[\S 4]$$ Nos. 1-12
 * $$[\S 5]$$ Nos. 1-12
 * $$[\S 6]$$ Nos. 1-10
 * $$[\S 7]$$ Nos. 1-6
 * $$[\S 3]$$ Method of Subscripts
 * Solutions for
 * $$[\S 4]$$
 * $$[\S 5]$$ Nos. 13-24
 * $$[\S 5]$$ Nos. 1-12 and 25-101
 * $$[\S 6]$$
 * $$[\S 7]$$
 * $$[\S 8]$$
 * $$[\S 9]$$

Part Two: Advanced

 * BOOK IX SOME ACCOUNT OF PARTS II AND III


 * BOOK X INTRODUCTORY


 * Chapter 1 Introductory


 * Chapter II The Existential Import of Propositions
 * Letter from Lewis Carroll to T. Fowler, November 13, 1885


 * Chapter III The Use of "Is-not" (or "Are-not") as a Copula


 * Chapter IV The Theory that Two Negative Premisses Prove Nothing


 * Chapter V Euler's Method of Diagrams


 * Chapter VI Venn's Method of Diagrams


 * Chapter VII My Method of Diagrams


 * Chapter VIII Solution of a Syllogism by Various Methods
 * (1) Solution by ordinary Method
 * (2) Symbolic Representation
 * (3) Solution by Euler's Method of Diagrams
 * (4) Solution by Venn's Method of Diagrams
 * (5) Solution by my Method of Diagrams
 * (6) Solution by my Method of Subscripts


 * Chapter IX My Method of Treating Syllogisms and Sorites


 * Notes to Book X


 * BOOK XI SYMBOLS, LOGICAL CHARTS


 * Chapter I Logical Symbols
 * Chapter II Figures or Forms
 * Fig. I
 * Fig. I$$\alpha$$
 * Fig. I$$\beta$$
 * Fig. II
 * Fig. III
 * Fig. IV
 * Fig. V
 * Fig. VI


 * Chapter III Fallacies


 * Chapter IV Logical Charts
 * Logical Chart I
 * Logical Chart 11
 * Logical Chart 111
 * Logical Chart IV
 * Logical Chart V
 * Interpretation of Charts I-V
 * Interpretation of Chart VI
 * Logical Chart VI
 * Logical Chart VI*
 * Logical Chart VI**
 * Interpretation of Chart VII
 * Logical Chart VII
 * Illustrations from Carroll's Workbook of Logical Charts


 * BOOK XII THE METHOD OF TREES


 * Chapter I Introductory


 * Chapter II Sorites-Problems with Biliteral Premisses


 * Chapter III Sorites-Problems with Triliteral and Multiliteral Premisses
 * Tree I
 * Tree 2
 * Tree 3
 * Tree 4
 * Letter from Carroll to John Cook Wilson, November 6, 1896
 * Tree 5


 * The Method of Trees: Appendix


 * BOOK XIII SOME PROBLEMS TO BE SOLVED BY THE METHODS OF PART II


 * Chapter I Introductory


 * Chapter II Problems in Sequences
 * Tree for Problem One
 * Commentary on the Tree for Problem One
 * Tree for Problem Three
 * Addendum: Excerpts from the Eighth and Ninth Papers on Logic


 * Chapter III The Problem of the School-Boys
 * Some answers to the Problem of the Schoolboys
 * Tree I
 * Tree II
 * Tree III


 * Chapter IV The Pork-Chop Problem
 * Version I
 * Version 11
 * Solution to the Pork-Chop Problem
 * Pork-Chop Problem Dictionary
 * Pork-Chop Problem in Subscript Form
 * Pork-Chop Problem Register
 * Carroll's Letters kowloon Cook Wilson on the Pork-Chop Problem
 * 1. November 12, 1896
 * 11. November 1, 1698
 * 111. November 12, 1896


 * Chapter V Froggy's Problem
 * Dictionary for Froggy's Problem


 * Chapter VI The Members of Parliament Problem
 * The Solution to the Members of Parliament Problem
 * The Problem in Abstract Form
 * Carroll's Letters to John Cook Wilson concerning the Members of Parliament Problem
 * I. October 29, 1896
 * II. Undated, probably October 30, 1896
 * III. November 3, 1896
 * Carroll's Letters to his sister Miss Louisa Dodgson concerning the Members of Parliament Problem
 * I. November 16, 1896
 * II. November 18, 1896
 * Louisa Dodgson's Attempt to Solve the M.P. Problem


 * Chapter VII The Problem of Six Friends and their Wives
 * Version I
 * Version II


 * Chapter VIII The Problem of the Five Liars
 * The Salt and Mustard Problem
 * The Problem of the Five Liars
 * Version I
 * Version II
 * Carroll's Letters to John Cook Wilson concerning the Five Liars and Salt and Mustard Problems
 * I. October 25, 1896
 * II. October 28, 1896
 * III. November 2, 1896
 * IV. November 16, 1896
 * V. December 18, 1896


 * Chapter IX The Great-Grandson Problem
 * Solution to the Great-Grandson Problem
 * Carroll's Letters to John Cook Wilson about this Problem
 * I. February 16, 1897
 * II. May 17, 1897


 * Chapter X The Jack Sprat Problem
 * Carroll's letter to his sister, Miss Louisa Dodgson, of September 28, 1896, on the Jack Sprat Problem
 * An Answer to the Jack Sprat Problem


 * Chapter XI The Library Problem
 * Carroll's Letters to John Cook Wilson relevant to the Library Problem
 * I. November 4, 1896
 * II. November 11, 1896
 * III. November 18, 1896
 * IV. December 26, 1896


 * Chapter XII The Pigs and Balloons Problem


 * Chapter XIII The Problem of Grocers on Bicycles


 * Chapter XIV The Pets Problem


 * Chapter XV The Winds and Windows Problem


 * BOOK XIV SOME FURTHER PROBLEMS TO BE SOLVED BY THE METHODS OF PART II


 * Problems and Exercises 1-83


 * BOOK XXI LOGICAL PUZZLES


 * Chapter I Introductory


 * Chapter II Classical Puzzles
 * 1. Introductory
 * 2. Pseudomenos
 * 3. Crocodilus
 * 4. Antistrephon
 * 5. Achilles
 * 6. Raw Meat


 * Chapter III Other Puzzles
 * 1. About Less
 * 2. Men Tall and Numerous
 * 3. The Socialist Orator and the Irish Mob
 * 4. Death at Any Moment
 * 5. The Small Girl and Her Sympathetic Friend
 * 6. A Notice at the Seaside
 * 7. On the Way to the Barber-shop
 * 8. What the Tortoise Said to Achilles


 * Chapter IV Solutions of Classical Puzzles
 * 1. Introductory
 * 2. Pseudomenos
 * 3. Crocodiles
 * 4. Antistrephon
 * 5. Achilles
 * 6. Raw Meat


 * Chapter V Solutions of Other Puzzles
 * 1 . About Less
 * 2. Men Tall and Numerous
 * 3. The Socialist Orator and the Irish Mob
 * 4. Death at Any Moment
 * 5. On the Way to the Barber-Shop
 * Letter to J. Welton on the Barber-Shop


 * Appendix A [to Book XXI]
 * Editor's Note on Carroll's Barber-Shop Paradox


 * Appendix B [to Book XXI]. Versions of the Barber-Shop Paradox
 * I. A Disputed Point in Logic. April 1894
 * II. A Disputed Point in Logic: A Concrete Example. April 11, 1894
 * III. A Disputed Point in Logic: A Concrete Example. April 16, 1894
 * IV. A Disputed Point in Logic. May 1, 1894
 * V. A Theorem in Logic. June 1894
 * VI. A Logical Paradox. July 1894
 * Note
 * VII. A Logical Puzzle. September 1894


 * Appendix C [to Book XXI]
 * Editor's Note on Carroll's "What the Tortoise Said to Achilles"
 * Exchange of Correspondence between Carroll and G. F. Stout
 * Letter from Carroll to John Cook Wilson, December 14, 1896


 * BOOK XXII SOLUTIONS TO PROBLEMS SET BY OTHER WRITERS
 * Chapter I Problems
 * Taken from the works of George Boole, Augustus DeMorgan, W. B. Grove, W. Stanley Jevons, John Neville Keynes, John Venn, and the Members of the Johns Hopkins University
 * Illustration from Carroll's Workbook, showing how he worked out some of the problems given