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3. Elements of Reason
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Pattern
Based
Reason
Volume 1A
Printed in Canada
ISBN 0-9697564-5-3

Volume 1 = 1A+1B
bounded together







Foreword
PS. Three Remark
1. What is reason
2. Inductive Ed Principles
2. Communication
3. Elements of Reason
4. Implication Rules [10]
5. Hype & Deception
5. Hype & Ethics
6. Chains of Reason [4]
7.  Longer Chains of Reason
7. Mathematical Induction
8. Language Change [2]
9. Next Chapters, About.
10. Limits to Freedom [2]
11. Accidental Patterns
12. Two Analogies
12.  Knowledge Islands
13. Euclidean Model
13. Euclidean Reason
14 Math: Deductive/Empirical [6]
15. Objectivity
15. Objectivity, More
16 Rules-Patterns Origins [10]
Knowledge & Story Telling
17. Objective Ways
17. Trial & Error Discovery
18. Conciousness
19. Symbols & Logic
20. Pronouns & Symbols
21. Truth Tables I. [3]
22. Contrapositive
22. Vacuously True
24. Indirect Reason More
24PS. Excluded Middle Law
24PS.  Proof by Absurdity
PS. Reality vs Imagination
PS. Ahistorical Logic
Links Elsewhere - Go GoGo
Book Entrance

1A Logic Postscripts
- online only

+Proof by Absurdity alias proof by contradiction
+How the demand for consistency supports the law of the excluded middle
+Reality versus or with the aid of Imagination
+Links for reason, logic and crtical thinking
+History Lost or Missing

Would you like to show yourself or others how to be algebra power users? Professor WhySlopes shouts his methods for algebra skill development are likely to work. Try them. They are different.

Elements of Reason
Chapter 3

Previous Chapter:  Communication of Skills.

About the Next Chapters

Chapters four to eight describe the basic elements of rule- and pattern-based thought and hint at their benefits and limitations. In particular, the next three chapters, Implication Rules, Deception and Chains of Reason describe basic ideas in reason and logic which everyone should master. The practice of deception is not encouraged.

  1. The chapter Implication Rules presents two logic puzzles to test or improve your reading and writing. Each consists of a rule and five questions. Answers are given. 
  2. The chapter Deception describes faulty and misleading ways of reason and persuasion. It describes the hype, hype and hype approach too often used for persuasion in advertisements and public debate. 
  3. The chapter Chains of Reason describes how to directly use rules one at a time or chain them together, one after another, for arriving at conclusions and judgments. 

These three chapters on reason develop skills needed in daily life. They provide a standard or model for arriving at conclusions and making decisions: how to argue politely if you must. They also strengthen basic skills needed in mathematics, science, technology, writing, persuasion and communication. Reason and persuasion touch all skills and all disciplines. The further description of reason and logic relies on the method described and offered in these three chapters.

The chapter Longer Chains of Reason indicates the special role of rule-based reason in mathematics. It describes in a very non-mathematical fashion, the concept of induction, a method used in mathematics to arrive at conclusions. This concept of induction is an example of reason used mainly in mathematics or mathematical subjects.

The chapter A Change of Language introduces the if and only if  and iff forms of writing two-way implication rules. 

When ideas in mathematics or another discipline are described instead of being drawn from implication rules, the role of implication-rule based reason or logic may be forgotten. But in every discipline including mathematics, signs of rule- and pattern-based reason are given by the word and phrases from this, therefore, thus, because, since, as, gives, yields etc. Their presence in any line of thought indicates a demonstration perhaps of why this or that should be.


Next Chapter:  (4)  Implication Rules - seeing the difference is one way to improve reading, writing and thinking abilities. 

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Online Volumes (orders)
1,  Elements of Reason. 1996
1A. Pattern Based Reason  1995
1B. Math Curriculum Notes 1996
2. Three Skills for Algebra  1995
3 .Why.Slopes.&
.More.Math.1995

Site Topics/Sections 

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2   Fractions  
3.  Fractions  with Units  
3. Solving Linear Equations  - 
making alg easier
4. Formulas forwards & Backwards - unifying theme for Algebra
5.  Proportionality, Back- & For-wards - theme at work.
6.  Logic - Math Free, good for precision in  work & studies 
7. Euclidean-Geometry  (leanly)
8. Slopes and Lines 
9. Why Study Slopes - a context 
10.  Quadratics
11  Polynomials
12  Factored Polys - a context
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14  Number Theory, Richly
15. Exponents, Radicals & logs.  
16   Calculus - Examples & Advice 
17.   Real  Analysis 
18  Electric Circuits Etc (So So)
19 Maps, Similarity & Trig, (alt view)
20 Complex numbers  

21 Logic with Symbols+truth tables

22  Consistent Story Telling
23. Even More Logic

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