Appetizers and Lessons for Mathematics and Reason   
www.whyslopes.com          ( Français
 Logic mastery is key to easing or avoiding learning difficulties in work & studies. 

Online Volumes (Book 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  Folders for Instructors & Adults
A. Public Policy Essays
B.  Mathematics  Education Essays  2006-7
C -Logic & Applied Math Program  
    for education,  June 22, 2008 
D. Quebec English Math Ed -  Standards to
 avoid  in course design & teacher education 
E. Help your child or teen
How TOs/ Ref.-08- 2008
1. Arithmetic Reference
2. Algebra 
3. More Algebra 
4. Geometry  
5. More Geometry
6. Calculus
7. Logics in Maths
Direct and Indirect Usage of a Single Rule      Up ] Next ]


Pattern
Based
Reason

understanding & explaining
Reason and Math
Volume 1A
Printed in Canada
ISBN 0-9697564-5-3

To reason often means to persuade someone of the need for an idea or action. That someone could be yourself. So be careful.

Learn More: If  this work  is too your liking, you may also like the foreword of Volume 1, Elements of Reason. with its description of all site volumes. 


YOU are better than YOU think. Show yourself  how:

      |      
//  _   _ \\
/\             /\
  <|  (o)   (o)   |> 
 \     | |      / 

 For better work & study skills, read logic chapters 1 to 5  in  Three Skills for Algebra. Sooner is better. Good luck.

 -/[]\- 
||
   / \_ 
 ||||||||||||||||||||||||||||

 Logic Mastery
 Amazing, Amusing, Amorous,  Delicious, Delightful, Edifying, Strengthening Elixir. 
It eases work & learning difficulties. Makes the hard easier. Opens eyes. Leads to greater precision.
in reading and writing

Do not leave here without it -  Logic mastery  will develops critical thinking, improve reading and writing, and give a firmer base for work and studies at many levels. Good luck.


Explore collaborative whiteboards from groupboardtwiddla  or scriblink.


Conclusions From a Single Rule
Direct and Indirect Usage

Previous: Chains of Reason, Chapter Entrance

Pretend the following implication rule is never disobeyed.

Each time Suzy the cat is on the ground and Suzy sees a dog, Suzy climbs a tree and stays in it for at least five minutes.

Direct Usage

What can we say for sure when Suzy the cat sees a dog? One possible answer is that Suzy the cat stays in a tree for at least five minutes. Another possible answer is that Suzy the cat climbs a tree. A more complete answer is that Suzy the cat climbs a tree and stays there for at least five minutes. Each of these answers or conclusions is correct. The last conclusion or result is fuller and more complete than the others. It gives more information. Which answer or conclusion is wanted here depends on who is interested in what. When many conclusions are possible, we state only those conclusions of interest to us. We do not have to state the most complete conclusion. The choice is ours.

Indirect Usage

What can you say for sure if Suzy the cat has not climbed nor stayed in any tree for at least five minutes? To check your answer, you might have to remember or revisit the questions in the chapter Implication Rules. But you should do this after you have read the following words.


Chapter Subsections: Direct and Indirect Usage of a Single Rule ] Linking and Chaining Two Rules Together ] Linking and Chaining Several Rules Together ] Deductive, Inductive or Empirical Reason ] Chapter 6, Chains of Reason (Deductive Reason), Pattern Based Reason ] Linking and Chaining ] Putting Several Rules Together ] Deductive ]

Next: Linking and Chaining Two Rules Together

 

Foreword +  Chapters 1 to 24

FOREWORD
Three Remarks

1 Introduction
2 Communication
3. Elements of Reason
4 Implication Rules
5. Deception
6 Chains of Reason
7 Longer Chains
For & From Consistency
8. Language Change
9 Next Chapters
10 Responsibility
11 Accidental Patterns
12 Knowledge Islands
13 Euclidean Logic
14 Deductive & Empirical 
     Views of Mathematics

15 Objectivity
16 Origin of Rules
and Patterns
17 Objective Ways

18. Waking up
19. Symbols  & Logic
20. Pronouns or Symbols
21. Truth Tables I.
22. Truth Tables II
22. Biconditional
22. Contrapositive
23. IF-THEN table
24. Indirect Reason Again

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
+Three Remarks
+History Lost or Missing

    |      
//  _   _ \\
/\             /\
<|   (o)   (o)  |> 
     | |     |
   \             /   
\    =   /

Caution: Site advice is approximately correct, for some circumstances, not all. Site How-TOs are logically developed, but not tried and tested. That leaves room for thought and refinement..

 -/[]\- 
||
  _ / \     
 ||||||||||||||||||||||||||||
 



 


 .


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

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 (
email form) All Rights Reserved.