George Englebretsen - Figuring It Out: Logic Diagrams

George Englebretsen

Figuring It Out

Philosophical Analysis

Edited by

Volume

George Englebretsen

Logic Diagrams

ISBN 9783110621631

e-ISBN (PDF) 9783110624458

e-ISBN (EPUB) 9783110621846

Bibliographic information published by the Deutsche Nationalbibliothek

The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at http://dnb.dnb.de.

2019 Walter de Gruyter GmbH, Berlin/Boston

For:

Libbey, who draws the lines

Russell, who keeps the lines straight

Suzanne, who minds the intersections

Morgan, who directs the arrows

and Gal, who still draws the conclusion

(Emma, Carlee, Sam, Nathan, and Aaron continue to run in circles)

Figure 2.1:

The Pythagorean Theorem

Figure 2.2:

The Pentacle and the Golden Ratio

Figure 2.3: Figure 2.4:

The Diagonal of a Unit Square

Figure 2.5:

Aristotles First Square

Figure 2.6:

Aristotles Second Square

Figure 2.7:

Possible Line Diagrams for Barbara and Celarent

Figure 2.8:

Diagram of AB

Figure 2.9:

Diagrams for the Three Aristotelian Figures

Figure 2.10:

Diagram for Cesare

Figure 2.11:

Barbara and Baroco

Figure 2.12:

Leibnizs Linear Diagrams of the Categoricals (extensional)

Figure 2.13:

Leibnizian Diagram of Barbara

Figure 2.14:

Leibnizs Linear Diagrams of the Categoricals (intensional)

Figure 2.15:

Lambert Diagrams

Figure 2.16:

Euler Diagrams of the Categoricals

Figure 2.17:

Eulers Asterisk for Some S is P

Figure 2.18:

Euler Diagram for Cesare

Figure 2.19:

Euler Diagrams for Some A is not B and Some B is not A

Figure 2.20:

Euler Diagrams for Contradictory Pairs

Figure 2.21:

Euler Diagrams for All A are B and Some A are C

Figure 2.22:

Euler Diagrams for Contrary Pairs

Figure 2.23:

Venn Diagrams of Celarent and Festino

Figure 2.24:

Square Diagram for 4 Terms

Figure 2.25:

Peirces Diagram for Festino

Figure 2.26:

Pierce Diagram of Propositional Disjunction

Figure 2.27:

Alpha Graphs

Figure 2.28:

Beta Graphs for the Four Categoricals

Figure 2.29:

Beta Graphs with Relationals

Figure 2.30:

Beta Graphs of Identity

Figure 2.31:

Beta Graphs for Quantification

Figure 2.32:

Beta Graphs Illustrating Quantifier Scope

Figure 2.33:

A Single Beta Graph Illustrating a Logical Equivalence

Figure 2.34:

Fregean Diagrams for Propositional Logic

Figure 2.35:

Fregean Diagrams for Predicate Logic

Figure 2.36:

Fregean Diagram

Figure 2.37:

Fregean Modus Ponens

Figure 2.38:

Fregean Universal Instantiation

Figure 2.39:

A Fregean Proof

Figure 3.1:

Directed Graphs of A, E, I, and O

Figure 3.2:

Directed Graph of an Argument

Figure 3.3:

Directed Graph of Barbara

Figure 3.4:

Directed Graph of Celarent

Figure 3.5:

Directed Graph of Darii

Figure 3.6:

Directed Graph of Ferio

Figure 3.7:

SYLL Diagrams of the Four Perfect Syllogisms

Figure 3.8:

SYLL Diagram of Baramtip

Figure 3.9:

SYLL Proof that E and I are Contradictory

Figure 3.10:

A Term Line

Figure 3.11:

A Singular Term Point

Figure 3.12:

A Negative Term Line

Figure 3.13:

Universal Affirmative Line Diagram

Figure 3.14:

Line Diagram for Two Co-extensive Terms

Figure 3.15:

Universal Negative Line Diagram

Figure 3.16:

Particular Affirmative Line Diagram

Figure 3.17:

Diagrams for Predicate Denial and Term Negation

Figure 3.18:

Line Diagrams for Obverted Categoricals

Figure 3.19:

Line Diagrams for Affirmative and Negative Singulars

Figure 3.20:

An Attempted Diagram for a Contradictory Pair

Figure 3.21:

Diagrams for Tautologies

Figure 3.22:

Full Diagram of A

Figure 3.23:

Full Diagram of E

Figure 3.24:

Full Diagram of I

Figure 3.25:

Full Diagram of O

Figure 3.26:

Contrapictions of A/E Contrariety

Figure 3.27:

Diagram of Subcontrariety

Figure 3.28:

Two Versions of Subalternation

Figure 3.29:

Line Diagrams for the Perfect Syllogisms

Figure 3.30:

Line Diagrams for Universal and Particular Syllogisms

Figure 3.31:

Every M is P

Figure 3.32:

Barbara

Figure 3.33:

Cesare 1

Figure 3.34:

Cesare 2

Figure 3.35:

Datisi

Figure 3.36:

Bocardo

Figure 3.37:

Ferison

Figure 3.38:

Fresison

Figure 3.39:

Barbarip

Figure 3.40:

A Five-term Diagram

Figure 3.41:

An Inconsistent Set

Figure 3.42:

A Contrapiction of Baroco

Figure 3.43:

Wild Quantity

Figure 3.44:

Diagrams for Singular and Negative Singular Subjects

Figure 3.45:

Leibnizs Syllogism with a Singular Predicate Term

Figure 3.46:

Diagrammed Syllogism with Two Singular Terms

Figure 3.47:

Reflexivity, Symmetry, and Transitivity in TFL

Figure 3.48:

Diagrams With Terms of Explicit Denotation

Figure 3.49:

Diagrams With a Team Name and With an Explicit Team Name

Figure 3.50:

Romeo loves Juliet

Figure 3.51:

Juliet loves Romeo

Figure 3.52:

Unanalyzed Complex Relational

Figure 3.53:

Partially Analyzed Complex Relational

Figure 3.54:

Fully Analyzed Complex Relational

Figure 3.55:

The Principle of Relational Analysis

Figure 3.56:

A Corollary

Figure 3.57:

Unsimplified Relational

Figure 3.58:

Simplified Relational

Figure 3.59:

Valid Relational Inference

Figure 3.60:

De Morgans Inference

Figure 3.61:

Four Special Inferences

Figure 3.62:

The Principle of Relational Extension

Figure 3.63:

Specific vs Non-Specific Reference

Figure 3.64:

The Principle of Relational Reduction

Figure 3.65:

Attempted Singular Reflexive Diagram

Figure 3.66:

Singular Reflexive Diagram

Figure 3.67:

Attempted General Diagram

Figure 3.68:

Proper Diagram

Figure 3.69:

Argument With a Reflexive

Figure 3.70:

A Simple Pronominalization

Figure 3.71:

A Full Pronominalization

Figure 3.72:

An Example of Interlocking Pronominalizations

Figure 3.73:

A Diagrammed Inference with Pronouns

Figure 3.74:

Negative Relationals

Figure 3.75:

Inference with Negative and Positive Relationals

Figure 3.76:

How to Diagram a Singular

Figure 3.77:

Diagrams for Sentential Logic

Figure 3.78:

The Domain of Domains for Conditionals

Figure 3.79:

Alternative Diagrams for a Conjunctive Statement

Figure 3.80:

Diagrams for Contraposition

Figure 3.81:

Some Elementary Rules of Propositional Logic

Figure 3.82:

Unanalyzed and Analyzed Complex Terms

Figure 3.83:

A Diagrammed Deduction

Figure 3.84:

Diagram of a Consistent Set of Statements

Figure 3.85:

Proof of an Inconsistent Set of Statements

Figure 3.86:

Diagrammatic Resolutions of the Two Disanalogies

Figure 4.1:

Lemon and Pratt Counter-example

Figure 4.2:

Illustration of the Principle of Compound Term Analysis

Figure 4.3:

First Response to Lemon and Pratt

Figure 4.4:

Line Diagrams for a is a

Figure 4.5:

Beta Graphs for Something is a

Figure 4.6:

Second Response to Lemon and Pratt

Figure 4.7:

Beta Graph for A is greater than something greater than B

Figure 4.8:

ED Diagram for A is greater than something greater than B

Figure 4.9:

Beta Graph for A man gave a bribe to a senator