Basic Concepts and Symbolization in Propositional Logic: Workbook 1 (Logic Self-Taught Workbooks)

Book Synopsis: Like personal trainers, the Workbooks offer a practical and empathic approach to introductory logic. They are designed for beginners and for anyone who wants to build confidence by doing more exercises. Workbook 1 helps you learn how to: identify five propositional connectives (of negation, conjunction, disjunction, material biconditional, and material conditional) in English sentences, determine the main connective of a proposition, symbolize simple and complex English sentences, symbolize "neither-nor," "not-both," "only-if," and "unless," read necessary and sufficient conditions from conditionals. There are numerous exercises whose difficulty increases gradually. The point is to train your "logic muscles" until they become strong enough to carry "heavy-weight" content. The study is aided by many examples worked out step by step, warnings of common errors, as well as complete solutions to all exercises.

Logic Self-Taught Workbooks are based on the insight that understanding logic is not sufficient for learning logic, just as understanding how to swim is not sufficient for learning to swim and understanding the grammar of a foreign language is not sufficient for learning the language. You need to practice and take an active part in self-teaching. Through systematic work with the Workbooks, you will build self-confidence. You can learn logic, even its hardest parts.

Contents

Unit 1.1 Basic Concepts
A. Sentences and Propositions (Statements)
B. Arguments
C. Validity, Invalidity, and Logical Form
D. Validity of Arguments and Truth of Premises and Conclusion
E. Soundness of Arguments
F. Enthymematic Arguments
G. Fallacies

Unit 1.2 The Basics of Propositional Logic
A. Propositional Logic as a Logical Theory
B. Simple and Complex Propositions
C. The Symbolization Key (Legend)
D. Negation
E. Conjunction
F. Disjunction
G. Material Biconditional
H. Material Conditional

Unit 1.3 The Basics of Symbolization
A. Main Connective
B. Finding the Main Connective: Stage 1 (Two-Place Connectives)
C. Finding the Main Connective: Stage 2 (Including Negations)
D. Symbolization as an Art and as a Skill

Unit 1.4 “Neither … Nor …” and “Not … Both …” in Symbolizations
A. Multiple Conjunctions and Disjunctions
B. “Neither … Nor …”, “Not Both … and …” (Take 1)
C. The Exclusive Disjunction “Either … or … but Not Both”
D. De Morgan Laws
E. “Neither … Nor …”, “Not Both … and …” (Take 2)
F. “All”, “Some”, “Not All”, “None”
G. Complicated Symbolizations

Unit 1.5 “… Only If …” in Symbolizations
A. Your worst nightmare: “Only if”
B. Complicated Symbolizations
C. Necessary and Sufficient Conditions (optional)

Unit 1.6 “… Unless …” in Symbolizations
A. “Unless”
B. Complicated Symbolizations

Solutions to Exercises