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Appetizers and Lessons for Mathematics and Reason
  online logic chapters  - the best starting point for further site exploration.  Bon Appetite.

4. Repeat- & Reproduc-ible?
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Pattern
Based
Reason
Volume 1A
Printed in Canada
ISBN 0-9697564-5-3

Volume 1 = 1A+1B
bounded together







4. First Puzzle
4. Second Puzzle
4. IF versus IFF
4. Joking About Logic
4. Imply or Suggest
4. One vs Two-Way Committents
4. Repeat- & Reproduc-ible?
4. Rules Limits & Benefits
4. Accidental Rules
4. Steps for Better Reason
Book Entrance
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

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.

Chapter 4

Repeatable & Reproducible Results

Previous: One- Versus Two-Way Implications

When we do arithmetic, we follow rules. If each of us does not make a mistake, we will get the same result as each other. Each calculation is reproducible. Other people know how it was done. They can repeat it, and see if they agree with our results. When we get a result by following rules or instructions, other people can check our results. All they have to do is follow the same rules.

Just as we have methods for doing arithmetic carefully and precisely, we also have suggested methods for thinking carefully about what to accept, to do or to decide. The ability to read and understand rules or suggestions precisely is needed not only in persuading ourselves or others but also in following recipes, instructions and rule-based reason.

The suggestions or rules which give repeatable and reproducible results are the most certain and possibly the most correct. Reliable rule-based processes give repeatable and reproducible results. These results do not depend on who gets them. For instance, a good recipe can be followed by any cook - provided the cook can find all the ingredients. Results should depend on the recipe, but be independent of the cook.


Chapter Subsections: 4. First Puzzle ] 4. Second Puzzle ] 4. IF versus IFF ] 4. Joking About Logic ] 4. Imply or Suggest ] 4. One vs Two-Way Committents ] [ 4. Repeat- & Reproduc-ible? ] 4. Rules Limits & Benefits ] 4. Accidental Rules ] 4. Steps for Better Reason ]

Next: Limits and Benefits

 

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Parents: Help your Child/Teen Learn covers  Speaking Skills, Reading & Writing Preparing for Science Having Patience, etc

Math How-TOs
1. Arithmetic   2. Algebra   3.  More Algebra  4.  Geometry 5 More Geometry 6.  Calculus
>> densely written 
>> use as skill checklists

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 

 1. Decimal Arith - Video Based ]
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
13 Functions - For-& Back -wards
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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