Logic and Rational ...

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Logic and Rational Thoughts

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Logic and Rational Thoughts

Author: Year Of Pub : 2006
Product ID: 38368o

Logic and rational thought are among the most important subjects that can be taught and taken in any educational environment. The information learned and skills mastered are necessary for anything beyond rote memorization, robot-like applications of manual tasks, and expressions of merely personal beliefs. Organizing information, understanding issues, making judgments, providing evidence, and drawing conclusions require using logic and rational thought. The question is not whether logic and rational thought are to be used in any of these activities, but how well or poorly are they used. And insofar as being able to make judgments, provide evidence, understand issues, organize information, and draw conclusions are neces¬sary ingredients in leading a happy and productive life, logic and rational thought have an essential bearing on the possible happiness and productivity of any individual.


Since the study of logic and rational thought is as much the mastery of skills as it is the understanding of principles, there are over 2500 examples and exercises in this book providing opportunities for the student to do logic and rational thinking. Answers for the majority of odd numbered exercises are found at the back of the text. Even more exercises are provided with the version of the software package, The LogicWorks, customized by me for Logic and Rational Thought. Further exercises for each chapter of the book, not found in the text or The LogicWorks, are provided by Eric Kraemer. These can be used in various ways-to create tests, for instance. Also accompanying the book is a teachers manual, Solutions and Suggestions which contains answers to all of the even numbered exercises in the text, as well as those answers not found in the text for odd numbered exercises. Continuing to remind the student of the universal scope of logic and rational thought, the examples and exercises in each of these teaching aids draw upon a wide range of topics-acid rock to quantum mechanics; social problems to art history; the stock market to religion.

The LogicWorks is powerful software that can be of enormous help to both you and the student. Many of the exercises in Logic and Rational Thought are found in this program. Thus you can assign the student to work these exercises on the com¬puter. When a mistake is made, the program aids the student in discovering the correct answer. Student work can be graded and the grades recorded for you. You are also informed of how much time the student spent at the computer in working the assigned exercises. The program even allows you to create your own exercises and quizzes to be done by the student outside of the classroom. Work at the com¬puter frees class time for other topics that you might wish to discuss.

Great flexibility is provided in the various types of exercises found in Logic and Rational Thought. In Chapters 2-12 you will discover several groups of exercises at the end of a section. Using one or more of these groups, you can stress purely for¬mal aspects of the study of logic, the application of logic to language and the skills needed in translation into logical notation, or a combination. Characteristically the exercises found in any group in the book are ordered from easiest to most dif¬ficult. In a typical group of fifteen exercises, the first five are easy, the next five are moderate, and the last five are difficult.

A number of exercises ask the students to provide their own opinions about dif¬ferent topics, to justify their opinions, and to share this work with their classmates. These sorts of exercises give you an opportunity to guide the thinking of students as they create their own arguments, definitions, and the like. Even in larger classes the students can be encouraged to. interact with one another outside of the class¬room or lecture hall to work with available software, while you assign creative work at the computer with the interacting program, The LogicWorks.


Learning logic can be compared with learning games such as backgammon or foot¬ball. One advantage of this comparison is that it can help students overcome fears of anything that looks different, and especially if it reminds them of mathematics. Another advantage is that this comparison provides a natural introduction of the notion of strategy or heuristic into the teaching of logic and rational thought. Throughout Logic and Rational Thought strategies are introduced to guide students in the appropriate application of the rules they learn. Often students, when pre¬sented with a set of rules to apply in different exercises, have little grasp of when or how to use these rules. These students are almost certain to become frustrated and do poorly. Students typically find a set of strategies very useful to guide their appli¬cations of rules in concrete situations. No one set of game strategies ever guarantees success in every situation. The strategies in this book are only guides for doing things appropriately. You can develop and introduce more, and different, ones. While insight is always required at some level or another, and it is this insight that separates truly superior players from others, nonetheless properly constructed strategies will help a poor player become better, and perhaps even good.


You will find useful footnotes throughout this book. Frequently these relate to the topic being discussed in the text to other topics. These footnotes provide you with opportunities to explore new subjects while reminding students that they are learning a subject and acquiring skills that go far beyond the boundaries of one course offered in a particular department.

When new terms are introduced, they are set off on a page and immediately defined. Such terms are always accompanied by illustrative examples. At the end of the chapter there is a list in which these new terms are again set forth with their definitions. The Review of New Terms provides a convenient place for the stu¬dent to examine the more fundamental points of a chapter before studying the chapter and in reviewing it. There is some duplication of new terms in a few chap¬ters so that different chapters can be used and others omitted without loss of essential information.


You, the teacher, are by far the most important factor for students in coming to learn and practice logic and rational thought. A lively and well-versed teacher can turn the most unlikely students into avid learners, who enjoy and excel in what they do. But even the best teachers can use aids in their important work. Logic and Rational Thought is offered as a tool to help you teach logic and rational thought better within a wide range of academic environments and pedagogical goals.

Logic and Rational Thought is written with an eye to flexibility in constructing vari¬ous one term courses in contemporary logic, traditional logic, and logic and falla¬cies. Following are some general suggestions concerning how such courses might be constructed. These are general suggestions because each teacher has different needs influenced by personal interests, departmental assignments, the institution in which a course is taught, and the students expected to take that course. Here are several flow charts, each indicating a possible course developed using Logic and Rational Thought. You will, no doubt, think of more.



1. Why Bother With Rational Thought?
2. Logic and Arguments
3. Arguments, Explanations, Descriptions, and Rhetoric
4. Deduction and Induction
5. Some Final Observations
6. Review of New Terms


1. Truth-Functional Logic
2. Statement Variables and Logical Constants
3. Truth-Functional Denial
4. Truth-Functional Conjunction
5. Truth-Functional Disjunction
6. Constants of Punctuation and Scope
7. Constructing Truth Tables
8. Hypothetical Statements and Material Implication
9. Material Equivalence
10. Review of New Terms


1. Shortened Form Truth Tables
2. Contradictory, Tautological, and Contingent Statements
3. Shortened Form Truth Tables: Validity and Invalidity
4. The Reduction Ad Absurdum Method: Validity and Invalidity
5. The Replacement Method: Validity and Invalidity
6. Consistency and Inconsistency
7. Logical Equivalence
8. Review of New Terms


1. Validity and Invalidity
2. Consistency and Inconsistency
3. Contradictory, Tautological, and Contingent Statements
4. Logical Equivalence
5. Review of New Terms


1. Argument Forms
2. Simplification, Commutation of the Dot, and Conjunction
3. Disjunctive Syllogism, Commutation of the Wedge, and Addition
4. Modus Ponens and Modus Tollens
5. Hypothetical Syllogism and Constructive Dilemma
6. Points of Strategy-A Summary Review
7. Review of New Terms


1. Association and Commutation
2. Double Negation and Transposition
3. Distribution and DeMorgans Laws
4. Material Implication and Exportation
5. Equivalence and Tautology
6. Review of New Terms


1. The Conditional Method of Proving Validity
2. The Indirect Method of Proving Validity
3. Demonstrations of Inconsistency
4. Demonstrations of Tautologies
5. Demonstrations of Logical Equivalence
6. Review of New Terms


1. Language
2. Meaning
3. Definitions
4. Constructing Definitions
5. Review of New Terms


1. Cogent and Fallacious Arguments
2. Classifying Fallacies
3. Hindrances to Grasping Fallacies
4. Guides to Catching Fallacies
5. Ambiguity
6. Vagueness
7. Equivocation
8. Relative Words
9. Appeal to Irrelevant Authority
10. Appeal to Pity
11. Appeal to the Masses
12. Appeal to Special Interests
13. Appeal to Ignorance
14. Fake Precision
15. Hasty Conclusion
16. Neglect of Relevant Evidence
17. Review of New Terms


1. Ad Hominem
2. Tu Qyoque
3. Red Herring
4. Straw Man
5. Is-Ought
6. Deceptive Alternatives
7. Wishful Thinking
8. Novelty
9. Confusing Sufficient and Necessary Conditions
10. Questionable Causes
11. Slippery Slope
12. Gamblers Fallacy
13. Circular Argument
14. Inconsistencies
15. Factual Certainty
16. Question Begging
17. Review of New Terms



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