# Logic

Introduces formal and informal reasoning, traditional logic, validation techniques, fallacies, and symbolic logic

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A Concise Introduction to Logic is an introduction to formal logic suitable for undergraduates taking a general education course in logic or critical thinking, and is accessible and useful to any interested in gaining a basic understanding of logic. This text takes the unique approach of teaching logic through intellectual history; the author uses examples from important and celebrated arguments in philosophy to illustrate logical principles. The text also includes a basic introduction to findings of advanced logic. As indicators of where the student could go next with logic, the book closes with an overview of advanced topics, such as the axiomatic method, set theory, Peano arithmetic, and modal logic. Throughout, the text uses brief, concise chapters that readers will find easy to read and to review.

Reviews available here: https://open.umn.edu/opentextbooks/textbooks/a-concise-introduction-to-logic

Subject:
Philosophy
Material Type:
Textbook
Provider:
State University of New York
Provider Set:
OpenSUNY Textbooks
Author:
Craig DeLancey
03/27/2017
Only Sharing Permitted
CC BY-NC-ND
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Derek Turner, Professor of Philosophy, has written an introductory logic textbook that students at Connecticut College, or anywhere, can access for free. The book differs from other standard logic textbooks in its reliance on fun, low-stakes examples involving dinosaurs, a dog and his friends, etc.

Outline
The Logic Sheet
Getting Rid of Content
§1. Modus ponens
§2. Abstraction and Form
§3. Use and Mention
§4. Statements, Statement Forms, and Bivalence
§5. Statements, Propositions, and Truth
§6. Modus ponens arguments in Langerese: Syntax
§7. Modus ponens arguments in Langerese: Semantics
§8. The Bed of Procrustes
Logical Operators
§9. The Counter-intuitiveness of the Arrow
§10. Conjunction and Material Equivalence
§11. Translating Conjunctions
§12. Non-Truth Functional Operators
§13. Negation and Disjunction
§14. Unless
§15. Necessary vs. Sufficient Conditions
§16. Translating Conditional and Biconditional Statements
§17. Fun with Longer Statements
Truth Tables
§18. Calculating Truth Values for Statements
§19. Tautologies
§20. Two Ways of Constructing Truth Tables
§21. Human Limitations
§22. Short Truth Tables for Tautologies
§23. The Anti-Laws of Logic
§24. Analyticity
§25. Testing for Logical Equivalence
§26. Quirks of Logical Equivalence
§28. Logical Consistency
§29. How Many Logical Operators Do We Need?
Validity and Soundness
§30. Validity
§31. Validity’s Quirks
§32. Deductive Arguments
§33. Soundness
§34. Abbreviated Truth Tables for Validity
§35. Inductive Arguments
§36. Translation and Testing for Validity
§37. Logic, Rhetoric, and the Principle of Charity
How to Prove Stuff
§38. Natural Deduction
§39. Introduction Rules
§40. Other Inference Rules: HS and CD
§41. Conditional Proof
§42. Using Conditional Proof to Prove Tautologies
§43. Logical Equivalence and Replacement Rules
§44. Formalizing Philosophical Arguments
§45. Reductio Ad Absurdum
§46. Other Valid Arguments
Predicates and Quantifiers
§47. Chrysippus’s dog
§48. Subjects and Predicates
§49. Relations
§50. Individual Constants and Variables
§51. Interpreting the Quantifiers
§52. Modus ponens with the Universal Quantifier
§53. Modus ponens with the Existential Quantifier
§54. Putting Langerese to Work
§55. Quantifiers and Negation
§56. Translation Holism
§57. Some Technicalities
§58. Identity
§59. Form and Content: The Value of Formal Logic
Technical Definitions

Subject:
Philosophy
Material Type:
Textbook
Author:
Derek D. Turner
02/11/2020
Unrestricted Use
CC BY
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Fundamental Methods of Logic is suitable for a one-semester introduction to logic/critical reasoning course. It covers a variety of topics at an introductory level. Chapter One introduces basic notions, such as arguments and explanations, validity and soundness, deductive and inductive reasoning; it also covers basic analytical techniques, such as distinguishing premises from conclusions and diagramming arguments. Chapter Two discusses informal logical fallacies. Chapters Three and Four concern deductive logic, introducing the basics of Aristotelian and Sentential Logic, respectively. Chapter Five deals with analogical and causal reasoning, including a discussion of Mill's Methods. Chapter Six covers basic probability calculations, Bayesian inference, fundamental statistical concepts and techniques, and common statistical fallacies.

Reviews available here: https://open.umn.edu/opentextbooks/textbooks/fundamental-methods-of-logic

Subject:
Philosophy
Material Type:
Textbook
Provider:
University of Wisconsin-Milwaukee
Author:
Matthew Knachel
09/08/2017
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forall x is an introduction to sentential logic and first-order predicate logic with identity, logical systems that significantly influenced twentieth-century analytic philosophy. After working through the material in this book, a student should be able to understand most quantified expressions that arise in their philosophical reading.

This books treats symbolization, formal semantics, and proof theory for each language. The discussion of formal semantics is more direct than in many introductory texts. Although forall x does not contain proofs of soundness and completeness, it lays the groundwork for understanding why these are things that need to be proven.

Throughout the book, I have tried to highlight the choices involved in developing sentential and predicate logic. Students should realize that these two are not the only possible formal languages. In translating to a formal language, we simplify and profit in clarity. The simplification comes at a cost, and different formal languages are suited to translating different parts of natural language.

The book is designed to provide a semester's worth of material for an introductory college course. It would be possible to use the book only for sentential logic, by skipping chapters 4-5 and parts of chapter 6.

Chapter 1: What is logic?
Chapter 2: Sentential logic
Chapter 3: Truth tables
Chapter 4: Quantified logic
Chapter 5: Formal semantics
Chapter 6: Proofs

Subject:
Philosophy
Material Type:
Textbook
Author:
P.D. Magnus
06/12/2020
Unrestricted Use
CC BY
Rating

This is an introductory textbook in logic and critical thinking. The goal of the textbook is to provide the reader with a set of tools and skills that will enable them to identify and evaluate arguments. The book is intended for an introductory course that covers both formal and informal logic. As such, it is not a formal logic textbook, but is closer to what one would find marketed as a critical thinking textbook. Downloadable as a pdf file.

Subject:
Philosophy
Material Type:
Textbook
Provider:
Lansing Community College
Author:
Matthew J. Van Cleave
01/04/2016
Unrestricted Use
CC BY
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Introduction to Philosophy: Logic provides students with the concepts and skills necessary to identify and evaluate arguments effectively. The chapters, all written by experts in the field, provide an overview of what arguments are, the different types of arguments one can expect to encounter in both philosophy and everyday life, and how to recognise common argumentative mistakes.

1. What is Logic?
2. Evaluating Arguments
3. Formal Logic in Philosophy
4. Informal Fallacies
5. Necessary and Sufficient Conditions

Access also available here: https://press.rebus.community/intro-to-phil-logic/

Subject:
Philosophy
Material Type:
Textbook
Author:
Benjamin Martin
Cassiano Terra Rodrigues
Christina Hendricks
Matthew Knachel
Michael Shaffer
Nathan Smith
11/24/2020
Unrestricted Use
CC BY
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This course provides an introduction to critical thinking, informal logic, and a small amount of formal logic; its purpose is to provide students with the basic tools of analytical reasoning. Upon successful completion of this course, students will be able to: Understand what critical thinking is and why it is valuable; Distinguish between good and bad definitions, Recognize the differences between explicit and implicit meaning, and remove ambiguities of meaning from unclearly worded statements; Recognize arguments in writing, pick out good and bad arguments by their form, and construct sound arguments of their own; Diagnose the most common reasoning errors and fallacies, as well as identify ways of improving them; Understand the basics of sentential and predicate logic and gain practice manipulating meaning symbolically; Understand the rudiments of scientific methodology and reasoning; Evaluate arguments that rely on specific types of visual representation; Understand the basics of strategic reasoning and problem solving; Understand the particular challenges involved in reasoning about values and morality; Diagnose fallacies and evaluate arguments about values and morality. (Philosophy 102)

Subject:
Arts and Humanities
Philosophy
Material Type:
Assessment
Full Course
Homework/Assignment
Lecture
Syllabus
Provider:
The Saylor Foundation
04/29/2019
Unrestricted Use
CC BY
Rating

The Open Logic Text is an open-source, collaborative textbook of formal meta-logic and formal methods, starting at an intermediate level (i.e., after an introductory formal logic course). Though aimed at a non-mathematical audience (in particular, students of philosophy and computer science), it is rigorous.

The Open Logic Text is a collaborative project and is under active development. Coverage of some topics currently included may not yet be complete, and many sections still require substantial revision. We plan to expand the text to cover more topics in the future. We also plan to add features to the text, such as a glossary, a list of further reading, historical notes, pictures, better explanations, sections explaining the relevance of results to philosophy, computer science, and mathematics, and more problems and examples. If you find an error, or have a suggestion, please let the project team know.

The project operates in the spirit of open source. Not only is the text freely available, we provide the LaTeX source under the Creative Commons Attribution license, which gives anyone the right to download, use, modify, re-arrange, convert, and re-distribute our work, as long as they give appropriate credit.

I Sets, Relations, Functions
II Propositional Logic
III First-order Logic
IV Model Theory
V Computability
VI Turing Machines
VII Incompleteness
VIII Second-order Logic
IX Normal Modal Logics
X Instuitionistic Logic
XII Methods
XIII History

Subject:
Computer Science
Philosophy
Material Type:
Textbook
Author:
Andrew Arana
Audrey Yap
Gillian Russell
Nicole Wyatt
Richard Zach
Walter Dean
06/12/2020
Unrestricted Use
CC BY
Rating

Textbook for Calgary's Logic II course based on the Open Logic Project. Covers naive set theory, first-order logic, sequent calculus and natural deduction, the completeness, compactness, and Löwenheim-Skolem theorems, Turing machines, and the undecidability of the halting problem and of first-order logic.

Subject:
Philosophy
Material Type:
Textbook
Provider:
Open Logic Project
Author:
Richard Zach
01/01/2017
Unrestricted Use
CC BY
Rating

This course provides an introduction to symbolic logic with an emphasis on formal logical languages and natural deduction systems of logical proof. Students learn how to translate reasoning into a symbolic logical language and how to prove arguments valid with the precision of mathematics using formal systems of proof.

Subject:
Philosophy
Material Type:
Assessment
Full Course