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
16 Private Agreements      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:

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

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 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.


Private Agreements
Chapter 16, section A

Previous: Chapter 16, Origins of Rules and Patterns, Intro

Private agreements involve one- and two-way commitments. We have to be aware of the difference between the two. They provide one of the sources of rules to be formed and argued or talked about. Agreements may say that this and that will be done. The agreements may say that an action will be done by one person or party, if or when another party does something else. The agreements may involve time limits. Agreements between two parties try to define and control what will be done in a manner satisfactory to both. Each party to a contract may try to get the most possible from the other. Whether this is fair or not depends on the situation. Some people like to negotiate from strength. In any event, each would-be party to a possible agreement needs the ability to read and understand rules and obligations in the agreement precisely.

A private agreement or business contract may be broken into a sequence of mutual obligations (clauses): If you do this, I will do that and then that. Then you will do this. A weakness of business contracts lies in the failure to agree in advance to changes forced by circumstances beyond the control of one or both parties. Disagreement or arguments can be avoided if possible stopping and withdrawal points and penalties are agreed to in advance.

The abilities to think, write and read carefully are all needed in negotiating and handling business deals, and the one-way and two-way implication rules which occur in them. Broken or misunderstood promises keep courts and mediators busy with arguments about rights and wrongs. Damages or disappointments may result from a failure to keep or understand a written or oral agreement.

The ability to understand and read exactly agreements, contracts, and in particular the obligations and duties which they create or generate, is most important. Without this ability, disappointments, false expectations and perhaps penalties appear. So to avoid future disputes and disappointments, care has to be taken to see that the wording of an agreement is understood by all. Absence of this care in rushed deals results in false expectations and disappointments. Broken commitments and broken laws may lead to a court or a place of arbitration for arguments over losses and damages.

When disagreements are not settled out of court, people on opposite sides of an argument will put forward opposing sets of reasons. The aim is to show that the other side is wrong, at least in part. Here each side may argue from different positions and for different judgments. In the arguments, reasons and implication rules may be chained together deductively. Several reasons may be given to support one idea or conclusion. Each side of a debate will have different accounts of what happened or of what was originally agreed.


Chapter Sections: [ 16 Private Agreements ] 16 Public Laws ] 16 Physical Laws ] 16 Accidental Patterns ] 16 Reliable(?) Patterns ] 16 Scientific Method ] 16 Reaction to Failed Tests ] 16 Chaos ] 16 Statistical Inference ] 16 End Notes ]

Next: 16, Public Laws in Society, Origins of

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

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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..

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