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9780754613664

An Invitation to Formal Reasoning: The Logic of Terms

by
  • ISBN13:

    9780754613664

  • ISBN10:

    0754613666

  • Format: Hardcover
  • Copyright: 2016-07-15
  • Publisher: Routledge

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Summary

An Invitation to Formal Reasoning introduces the discipline of formal logic by means of a powerful new system formulated by Fred Sommers. This system, term logic, is different in a number of ways from the standard system employed in modern logic; most striking is its greater simplicity and naturalness. Borrowing insights from Aristotle's syllogistic, Scholastic logicians, Leibniz, and the 19th century British algebraists, term logic takes its syntax directly from natural language. Its naturalness is the result of its ability to stay close to the forms of sentences usually found in every day discourse. Written by the founders of the term logic approach, An Invitation to Formal Reasoning is a unique introduction and exploration of this new system, offering numerous exercises and examples throughout the text. Summarizing the standard system of mathematical logic to set term logic in context, and showing how the two systems compare, this book presents an alternative approach to standard modern logic for those studying formal logic, philosophy of language or computer theory.

Table of Contents

Preface x
Reasoning
Introduction
1(3)
The Form of an Argument
4(1)
A Word About the Form of Statements
4(1)
The Form of Singular Statements
5(2)
Terms and Statements
7(2)
Symbolizing Compound Statements
9(2)
A Word About Validity
11(2)
How Material Expressions are Meaningful
13(1)
Terms
13(1)
Some Terms are `Vacuous'
14(3)
Statement Meaning
17(2)
Truth and Correspondence to Facts
19(1)
Propositions
20(1)
`States of Affairs'
21(1)
The facts and the FACTS
22(1)
What Statements Denote
22(1)
Summary and Discussion on the Meaning of Statements
23(2)
Picturing Propositions
State Diagrams
25(3)
Representing Singular Propositions
28(2)
Entailments
30(3)
Negative Entailments
33(2)
STATES and states
35(1)
Positive and Negative `Valence'
36(1)
The Limitations of State Diagrams
36(2)
The Statement Use of Sentences
38(1)
Truth Relations
39(1)
Logical Syntax
40(3)
Term Way vs. Predicate Way
43(2)
Some Useful Terminology
45(1)
Subjects and Predicates
46(3)
The Language of Logic (I)
Introduction
49(1)
Writing `Y some X' as an Algebraic Expression
50(1)
Affirmation (+) and Denial (-)
50(1)
Binary and Unary Uses of a Sign
51(1)
Positive and Negative Valence
51(1)
Contrary Terms and Sentences
52(1)
`Every'
53(1)
Why Some Equal Sentences are not Logically Equivalent
54(1)
E-forms and A-forms
55(1)
Transcribing Affirmative Statements
56(1)
How to Tell the Valence of E-form Statements
57(1)
Negative Valence = Universal Quantity
57(1)
The Law of Commutation in E-form
58(1)
`Every' in E-form Transcriptions
59(2)
`Isn't'
61(1)
The General Conditions of Equivalence
61(3)
The General Form of Statements
64(3)
The Logical Law of Commutation Applied to Compound Terms
67(1)
The Logical Law of Association
68(1)
Derivations
69(2)
More on Regimenting Sentences
71(2)
Uniquely Denoting Terms and Singular Statements
73(3)
Identities
76(1)
The Language of Logic (II)
Compound Statements
77(1)
`If...then'
78(2)
More on Transcription
80(1)
`Or'
81(2)
Representing Internal Structures
83(2)
The General Form of Compound Statements
85(1)
Direct Transcriptions
86(2)
Relational Statements
88(1)
A Word About Pairing
89(2)
Subject/Predicate; Predicate/Subject
91(1)
`Dyadic Normal Forms'
92(1)
Commuting Relational Terms
93(2)
Immediate Inferences from Relational Statements
95(1)
Obversion
96(1)
The Passive Transformation
97(1)
Simplification
98(1)
Pronouns and Proterms
99(3)
Appendix to Chapter 4
Bounded Denotation
102(1)
Terms in their Contexts
103(3)
Rules for Using Markers
106(3)
Syllogistic
Validity
109(5)
Inference
114(4)
Enthymemes
118(4)
Why Regal Works
122(2)
Inconsistent Conjunctions: The Tell-tale Characteristics
124(3)
Equivalent Conjunctions
127(1)
How This is Related to Regal
128(1)
Syllogisms with Singular Statements
129(1)
The Laws of Identity
130(1)
Proofs of These Laws
131(2)
The Matrix Method for Drawing Conclusions
133(2)
Venn Diagrams
135(4)
Relational Syllogisms
Introduction
139(1)
Applying the Dictum to Relational Arguments
140(1)
Distributed Terms
141(2)
Applying DDO
143(4)
Indirect Proofs for Relational Arguments
147(1)
Transforming Arguments
148(2)
Annotating a Proof of Validity
150(1)
Arguing with Pronominal Sentences
151(7)
Distributed Proterms
158(5)
Statement Logic
Introduction
163(2)
Contradictions
165(1)
Tautology
166(1)
Inconsistent Statements
167(1)
Contingent Statements
167(1)
Direct Proofs
168(1)
Rules of Statement Logic Used in Proofs
169(6)
Disjunctive Normal Forms (DNF)
175(1)
Inconsistency and Validity
176(2)
Graphic Representation of Compound Statements
178(5)
Regimenting Statements for Treeing
183(2)
Large Trees
185(7)
Drawing Conclusions
192(1)
Partial Disjunctions
193(6)
Using the Tree Method for Annotated Proofs
199(2)
Statement Logic as a Special Branch of Syllogistic Logic
201(8)
Venn Diagrams for the Singleton Universe of Propositional Logic
209(4)
Modern Predicate Logic
Syntax
213(1)
MPL: The Predicate Way
214(1)
General Sentences in MPL
215(1)
The Logical Language of MPL
216(4)
Singular Sentences in MPL
220(2)
How the Logical Syntax of MPL is `Ontologically Explicit'
222(2)
Dyadic Normal Forms
224(3)
Translating Pronominalizations
227(2)
Preparing the TFL Bridge
229(1)
Identity in MPL
230(2)
Logical Reckoning in MPL
232(1)
Transformation Rules
233(2)
Rules of Inference
235(2)
Literal Formulas
237(3)
Reckoning in MPL
240(1)
Canonical Normal Forms (CNF)
241(1)
Indirect Proofs in MPL
242(2)
Relational MPL Arguments
244(5)
Identity Arguments in MPL
249(4)
Rules, Laws and Principles 253(6)
A Note on Further Reading 259

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