Symbolic Logic and Other Forms of Deductive Reasoning

Symbolic Logic and Other Forms of Deductive Reasoning PDF Author: Richard L. Trammell
Publisher: Createspace Independent Publishing Platform
ISBN: 9781535230773
Category :
Languages : en
Pages : 506

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Book Description
This text does not presuppose any technical background in math or logic. The first seven chapters cover all the basic components of a first course in symbolic logic, including truth tables, rules for devising formal proofs of validity, multiple quantifiers, properties of relations, enthymemes, and identity. (One exception is that truth trees are not discussed.) The five operator symbols used are: (.) and, (v) or, ( ) not, and also if-then, represented by the sideways U and material equivalence represented by the triple line. There are also four chapters which can be studied without symbolic logic background. Chapter 8 is a study of 7 immediate inferences in Aristotelian logic using A, E, I, O type statements with a detailed proof concerning what existential assumptions are involved. Chapter 9 is a study of classic Boolean syllogism using Venn diagrams to show the validity or invalidity of syllogisms. Chapter 10 is a study of the type of probability problems that are deductive (example: having 2 aces in 5 cards drawn from a randomized deck of cards). Chapter 11 is a study of the types of problems that are often found on standardized tests where certain data are given, and then multiple-choice questions are given where the single correct answer is determined by the data. In the symbolic logic chapters, it is shown many times how putting English statements into symbolic notation reveals the complexity (and sometimes ambiguity) of natural language. Many examples are given of the usage of logic in everyday life, with statements to translate taken from musicals, legal documents, federal tax instructions, etc. Several sections involve arguments given in English, which must be translated into symbolic notation before proof of validity is given. Chapter 7 ends with a careful presentation of Richard's Paradox, challenging those who dismiss the problem because it is not strictly mathematical. The conclusion of this chapter is the most controversial part of the text. Richard's paradox is used to construct a valid symbolic logic proof that Cantor's procedure does not prove there are nondenumerable sets, with a challenge to the reader to identify and prove which premise of the argument is false. There are several uncommon features of the text. For example, there is a section where it is shown how the rules of logic are used in solving Sudoku puzzles. Another section challenges students to devise arguments (premises and conclusion) that can be solved in a certain number of steps (say 3) only by using a certain 3 rules, one time each (for example, Modus Ponens, Simplification, and Conjunction). In proofs of invalidity, if there are 10 simple statements (for example), there are 1024 possible combinations of truth values that the 10 statements can have. But the premises and conclusions are set up so that only 1 of these combinations will make all the premises true and the conclusion false - and this 1 way can be found by forced truth-value assignments, with no need to take options. Another unusual section of the text defines the five operator symbols as relations (for example, Cxy = x conjuncted with y is true), and then statements about the operators are given to determine whether the statements are true or false. To aid in deciding what sections to cover in a given course or time frame, certain sections are labeled "optional" as an indication that understanding these sections is not presupposed by later sections in the text. Although there are a ton of problems with answers in the text, any teacher using this text for a course can receive free of charge an answer book giving answers to all the problems not answered in the text, plus a few cases of additional problems not given in the text, also with answers. Send your request to [email protected], and you will be sent an answer key using your address at the school where you teach.

Symbolic Logic and Other Forms of Deductive Reasoning

Symbolic Logic and Other Forms of Deductive Reasoning PDF Author: Richard L. Trammell
Publisher: Createspace Independent Publishing Platform
ISBN: 9781535230773
Category :
Languages : en
Pages : 506

Get Book Here

Book Description
This text does not presuppose any technical background in math or logic. The first seven chapters cover all the basic components of a first course in symbolic logic, including truth tables, rules for devising formal proofs of validity, multiple quantifiers, properties of relations, enthymemes, and identity. (One exception is that truth trees are not discussed.) The five operator symbols used are: (.) and, (v) or, ( ) not, and also if-then, represented by the sideways U and material equivalence represented by the triple line. There are also four chapters which can be studied without symbolic logic background. Chapter 8 is a study of 7 immediate inferences in Aristotelian logic using A, E, I, O type statements with a detailed proof concerning what existential assumptions are involved. Chapter 9 is a study of classic Boolean syllogism using Venn diagrams to show the validity or invalidity of syllogisms. Chapter 10 is a study of the type of probability problems that are deductive (example: having 2 aces in 5 cards drawn from a randomized deck of cards). Chapter 11 is a study of the types of problems that are often found on standardized tests where certain data are given, and then multiple-choice questions are given where the single correct answer is determined by the data. In the symbolic logic chapters, it is shown many times how putting English statements into symbolic notation reveals the complexity (and sometimes ambiguity) of natural language. Many examples are given of the usage of logic in everyday life, with statements to translate taken from musicals, legal documents, federal tax instructions, etc. Several sections involve arguments given in English, which must be translated into symbolic notation before proof of validity is given. Chapter 7 ends with a careful presentation of Richard's Paradox, challenging those who dismiss the problem because it is not strictly mathematical. The conclusion of this chapter is the most controversial part of the text. Richard's paradox is used to construct a valid symbolic logic proof that Cantor's procedure does not prove there are nondenumerable sets, with a challenge to the reader to identify and prove which premise of the argument is false. There are several uncommon features of the text. For example, there is a section where it is shown how the rules of logic are used in solving Sudoku puzzles. Another section challenges students to devise arguments (premises and conclusion) that can be solved in a certain number of steps (say 3) only by using a certain 3 rules, one time each (for example, Modus Ponens, Simplification, and Conjunction). In proofs of invalidity, if there are 10 simple statements (for example), there are 1024 possible combinations of truth values that the 10 statements can have. But the premises and conclusions are set up so that only 1 of these combinations will make all the premises true and the conclusion false - and this 1 way can be found by forced truth-value assignments, with no need to take options. Another unusual section of the text defines the five operator symbols as relations (for example, Cxy = x conjuncted with y is true), and then statements about the operators are given to determine whether the statements are true or false. To aid in deciding what sections to cover in a given course or time frame, certain sections are labeled "optional" as an indication that understanding these sections is not presupposed by later sections in the text. Although there are a ton of problems with answers in the text, any teacher using this text for a course can receive free of charge an answer book giving answers to all the problems not answered in the text, plus a few cases of additional problems not given in the text, also with answers. Send your request to [email protected], and you will be sent an answer key using your address at the school where you teach.

Symbolic Logic

Symbolic Logic PDF Author: David W. Agler
Publisher: Rowman & Littlefield
ISBN: 1442217421
Category : Mathematics
Languages : en
Pages : 397

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Book Description
Brimming with visual examples of concepts, derivation rules, and proof strategies, this introductory text is ideal for students with no previous experience in logic. Symbolic Logic: Syntax, Semantics, and Proof introduces students to the fundamental concepts, techniques, and topics involved in deductive reasoning. Agler guides students through the basics of symbolic logic by explaining the essentials of two classical systems, propositional and predicate logic. Students will learn translation both from formal language into English and from English into formal language; how to use truth trees and truth tables to test propositions for logical properties; and how to construct and strategically use derivation rules in proofs. This text makes this often confounding topic much more accessible with step-by-step example proofs, chapter glossaries of key terms, hundreds of homework problems and solutions for practice, and suggested further readings.

Force of Logic

Force of Logic PDF Author: Stephen M. Rice
Publisher: Aspen Publishing
ISBN: 1601566107
Category : Law
Languages : en
Pages : 429

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Book Description
Have you ever read a legal opinion and come across an odd term like the fallacy of denying the antecedent, the fallacy of the undistributed middle, or the fallacy of the illicit process and wondered how you missed that in law school? You’re not alone: every day, lawyers make arguments that fatally trespass the rules of formal logic—without realizing it—because traditional legal education often overlooks imparting the practical wisdom of ancient philosophy as it teaches students how to “think like a lawyer.” In his book, The Force of Logic: Using Formal Logic as a Tool in the Craft of Legal Argument, lawyer and law professor Stephen M. Rice guides you to develop your powers of legal reasoning in a new way, through effective tips and tactics that will forever change the way you argue your cases. Rice contends that formal logic provides tools that help lawyers distinguish good arguments from bad ones and, moreover, that they are simple to learn and use. When you know how to recognize logical fallacies, you will not only strengthen your own arguments, but you will also be able to punch holes in your opponent’s—and that can make the difference between winning and losing. In this book, Rice builds on the theoretical foundation of formal logic by demonstrating logical fallacies through the use of anecdotes, examples, graphical illustrations, and exercises for you to try that are derived from common case documents. It is a hands-on primer that presents a practical approach for understanding and mastering the place of formal logic in the art of legal reasoning. Whether you are a lawyer, a judge, a scholar, or a student, The Force of Logic will inspire you to love legal argument, and appreciate its beauty and complexity in a brand new way.

Deductive Logic

Deductive Logic PDF Author: Warren Goldfarb
Publisher: Hackett Publishing
ISBN: 1603845852
Category : Philosophy
Languages : en
Pages : 309

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Book Description
This text provides a straightforward, lively but rigorous, introduction to truth-functional and predicate logic, complete with lucid examples and incisive exercises, for which Warren Goldfarb is renowned.

Symbolic Logic 4e

Symbolic Logic 4e PDF Author: Dr. Daniel Kern
Publisher: Lulu.com
ISBN: 1365005887
Category : Education
Languages : en
Pages : 180

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Book Description
Designed for a first, college-level course in Symbolic Logic, in class or online. Covers Sentential Logic, Natural Deduction, Truth Trees, Predicate Logic and Quantifier Logic.

Deductive Logic

Deductive Logic PDF Author: Hugues Leblanc
Publisher: Allyn & Bacon
ISBN:
Category : Philosophy
Languages : en
Pages : 474

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Book Description


Sweet Reason

Sweet Reason PDF Author: James M. Henle
Publisher: John Wiley & Sons
ISBN: 1118078683
Category : Philosophy
Languages : en
Pages : 436

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Book Description
Sweet Reason: A Field Guide to Modern Logic, 2nd Edition offers an innovative, friendly, and effective introduction to logic. It integrates formal first order, modal, and non-classical logic with natural language reasoning, analytical writing, critical thinking, set theory, and the philosophy of logic and mathematics. An innovative introduction to the field of logic designed to entertain as it informs Integrates formal first order, modal, and non-classical logic with natural language reasoning, analytical writing, critical thinking, set theory, and the philosophy of logic and mathematics Addresses contemporary applications of logic in fields such as computer science and linguistics A web-site (www.wiley.com/go/henle) linked to the text features numerous supplemental exercises and examples, enlightening puzzles and cartoons, and insightful essays

Logic, Deductive and Inductive

Logic, Deductive and Inductive PDF Author: Carveth Read
Publisher:
ISBN:
Category : Logic
Languages : en
Pages : 404

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Book Description


Principles of Deductive Logic

Principles of Deductive Logic PDF Author:
Publisher: SUNY Press
ISBN: 9781438408552
Category : Language Arts & Disciplines
Languages : en
Pages : 500

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Book Description
Clear focus on its application of formal logic to ordinary English is the most distinctive feature of this textbook for the introductory course in deductive logic. Great care is taken with the appropriate translation into logical languages of ordinary English sentences. Evaluation of these translations promotes a more effective use of ordinary language. The Principles of Deductive Logic presents symbolic logic in a fuller and more leisurely fashion than other introductory textbooks. Early chapters cover informal material, including definition and informal fallacies. The remainder of the text is devoted to the treatment of four distinct artificial languages. The Categorical language is the language of syllogistic logic. The Extended Categorical language enriches this first language with the symbolic connectives for conjunction and negation. The Propositional Connective language and the First-Order language (with identity) are the two basic languages of modern logic. Each language is accompanied by a deductive system, and is used as an instrument for exploring ordinary language, including ordinary arguments The book contains a large number of exercises whose answers are supplied in the back of the book, and many more that can be assigned as homework. A solution's manual is available to instructors upon their request. The request must be written on college or university letterhead.

Logic for Philosophy

Logic for Philosophy PDF Author: Theodore Sider
Publisher: Oxford University Press
ISBN: 0192658816
Category : Philosophy
Languages : en
Pages : 305

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Book Description
Logic for Philosophy is an introduction to logic for students of contemporary philosophy. It is suitable both for advanced undergraduates and for beginning graduate students in philosophy. It covers (i) basic approaches to logic, including proof theory and especially model theory, (ii) extensions of standard logic that are important in philosophy, and (iii) some elementary philosophy of logic. It emphasizes breadth rather than depth. For example, it discusses modal logic and counterfactuals, but does not prove the central metalogical results for predicate logic (completeness, undecidability, etc.) Its goal is to introduce students to the logic they need to know in order to read contemporary philosophical work. It is very user-friendly for students without an extensive background in mathematics. In short, this book gives you the understanding of logic that you need to do philosophy.