www.whyslopes.com   << Français :  20 pages >>    
Appetizers and Lessons for Mathematics and Reason
  online logic chapters  - the best starting point for further site exploration.  Bon Appetite.

4. IF versus IFF
Back ] Book Entrance ] Up ] Next ]
Book Entrance ]


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 2, Implication Rules

One Versus Two Way Implications

Previous Section: The Second Puzzle

The two puzzles give examples of implication rules. The first puzzle gives a one-way implication rule, while the second gives a two-way implication rule. The following words should further help you to see the difference between one- and two-way implication rules. Seeing this difference may help you understand better the answers to the above questions. They may also help you answer the five questions again using the two-way implication rule.

  1. A one-way implication rule says that when a first situation occurs, so must a second. It does not say that when the second occurs so must the first. The second situation may occur without the first.
  2. A two-way implication rule says that
    1. when a first situation occurs, so must a second, and
    2. when the second situation occurs, so must the first.

    A two-way rule says that when each situation occurs, so must the other. Therefore if the two-way rule is to be obeyed, when one situation does not occur, neither can the other. 

Seeing or recognizing the difference between one- and two-way implication rules makes you a more careful thinker.

One- and two-way rules, recognized or not, are what we use to reach conclusions or make judgments. One and two-way rules can be used to suggest or persuade us of what needs to be done or avoided.


Chapter Sections: 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: Talking About Logic

 

www.whyslopes.com

site search

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

 Back ] Up ] Next ] [Top of this Page]  
www.whyslopes.com?

Road Safety Message  Do not walk on a road with your back to the traffic - rule of thumb
Please report by
email,  errors in mathematics or grammar or terminology to site author
If a mathematics topic you need is not covered in site pages,  report that as well. Topics in most demand
will be covered first in site growth.  

All trademarks and copyrights on this page are owned by their respective owners.
Copyright to comments & contributions are owned by the Poster. 
The Rest © 1995 onward by site author,   Alan Selby
,  All Rights Reserved.