Book:William Warren Bartley, III/Lewis Carroll's Symbolic Logic
Contents
William Warren Bartley, III: Lewis Carroll's Symbolic Logic
Published $1977$, Harvester Press
- ISBN 0-85527-984-2.
Subject Matter
Contents
- Note to the Reader From the Editor and Publisher
Part One: Elementary
- Introduction to Learners
- Preface to Fourth Edition
- BOOK I THINGS AND THEIR ATTRIBUTES
- Chapter I Introductory
- Things
- Attributes
- Adjuncts
- Chapter I Introductory
- 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 II Classification
- Chapter III Division
- $[\S 1]$ Introductory
- Division
- Codivisional Classes
- $[\S 2]$ Dichotomy
- Dichotomy
- Arbitrary limits of Classes
- Subdivision of Classes
- $[\S 1]$ Introductory
- Chapter III Division
- 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 IV Names
- Chapter V Definitions
- Definition
- Examples worked as models
- Chapter V Definitions
- 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
- Its four parts :
- $[\S 3]$ 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
- Three kinds of Propositions :
- $[\S 1]$ Introductory
- Chapter I Propositions Generally
- Chapter II Propositions of Existence
- Proposition of Existence
- Chapter II Propositions 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
- $[\S 1]$ Introductory
- Chapter III Propositions of Relation
- 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 I Symbols and Cells
- 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 II Counters
- 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
- $[\S 1]$ Introductory
- Chapter III Representation of 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
- Chapter IV Interpretation of Biliteral Diagram, When Marked with Counters
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- 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 I Symbols and Cells
- 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 $x$
- The Pair of Converse Propositions
- 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 $m$
- The Pair of Converse Propositions
- $[\S 1]$ Representation of Propositions of Existence in terms of $x$ and $m$, or of $y$ and $m$
- Chapter II 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 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
- Chapter IV Interpretation, in Terms of $x$ and $y$, of Triliteral Diagram, When Marked with Counters or Digits
- Rules
- Examples worked
- Chapter IV Interpretation, in Terms of $x$ and $y$, of Triliteral Diagram, When Marked with Counters or Digits
- BOOK V SYLLOGISMS
- Chapter I Introductory
- Syllogism
- Premisses
- Conclusion
- Eliminands
- Retinends
- Consequent
- The Symbol $\therefore$
- Specimen-Syllogisms
- Chapter I Introductory
- 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
- $[\S 1]$ Introductory
- Chapter II Problems in Syllogisms
- 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 1 Introductory
- 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
- The Pair of Converse Propositions
- Chapter II Representation of Propositions of Relation
- 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
- Three Formulae worked out:
- $[\S 3]$ 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
- $[\S 1]$ Representation Syllogisms
- Chapter III Syllogisms
- BOOK VII SORITESES
- Chapter I Introductory
- Sorites
- Premisses
- Partial Conclusion
- Complete Conclusion (or Conclusion)
- Eliminands
- Retinends
- Consequent
- The Symbol $\therefore$
- Specimen-Soriteses
- Chapter I Introductory
- 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
- $[\S 1]$ Introductory
- Chapter II Problems in Soriteses
- 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 I Examples
- Chapter II Answers
- Answers to
- $[\S 1]$
- $[\S 2]$
- $[\S 3]$
- $[\S 4]$
- $[\S 5]$
- $[\S\S 6, 7]$
- $[\S\S 8, 9]$
- Answers to
- Chapter II Answers
- 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
- Solutions for
- $[\S 3]$ Method of Subscripts
- Solutions for
- $[\S 4]$
- $[\S 5]$ Nos. 13-24
- $[\S 5]$ Nos. 1-12 and 25-101
- $[\S 6]$
- $[\S 7]$
- $[\S 8]$
- $[\S 9]$
- Solutions for
- $[\S 1]$ Propositions of Relation reduced to normal form
- Chapter III Solutions
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 II The Existential Import of Propositions
- 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 VIII Solution of a Syllogism by Various Methods
- 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
- Chapter IV 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
- Chapter III Sorites-Problems with Triliteral and Multiliteral Premisses
- 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 II Problems in Sequences
- Chapter III The Problem of the School-Boys
- Some answers to the Problem of the Schoolboys
- Tree I
- Tree II
- Tree III
- Some answers to the Problem of the Schoolboys
- Chapter III The Problem of the School-Boys
- 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 IV The Pork-Chop Problem
- Chapter V Froggy's Problem
- Dictionary for Froggy's Problem
- Chapter V 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
- The Solution to the Members of Parliament Problem
- Chapter VI The Members of Parliament Problem
- Chapter VII The Problem of Six Friends and their Wives
- Version I
- Version II
- Chapter VII The Problem of Six Friends and their Wives
- 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
- The Problem of the Five Liars
- 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 IX The Great-Grandson Problem
- 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 X 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
- Carroll's Letters to John Cook Wilson relevant to the Library Problem
- Chapter XI The Library Problem
- 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 II Classical Puzzles
- 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 III Other Puzzles
- Chapter IV Solutions of Classical Puzzles
- 1. Introductory
- 2. Pseudomenos
- 3. Crocodiles
- 4. Antistrephon
- 5. Achilles
- 6. Raw Meat
- Chapter IV Solutions of Classical Puzzles
- 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
- Chapter V Solutions of Other Puzzles
- Appendix A [to Book XXI]
- Editor's Note on Carroll's Barber-Shop Paradox
- Appendix A [to Book XXI]
- 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 B [to Book XXI]. Versions of the Barber-Shop Paradox
- 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
- Appendix C [to Book XXI]
- 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
- Chapter I Problems