Appetizers and Lessons for Mathematics and Reason (www.whyslopes.com)
||Définition d'une variable || Algèbre || Arithmetique || Logique ||La raison basée sur les règles et modelés||

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

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to work online with others.

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YOU are better than YOU think. Show yourself  how:  

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Read  logic chapters 1 to 5  in online volume Three Skills for Algebra  for greater skills & confidence in  work 
and study

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 Logic chapters 1 to 5  re- appear not in sequence, as is or longer,  in  Volume 1A,  Pattern Based Reason, Bon Appetite.

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

Logic mastery makes the hard, easier. Logic mastery  leads to better, stronger and richer comprehension.  Logic mastery  improves reading and writing.  Logic mastery ease learning difficulties.  Logic mastery gives a headstart.  In sum, logic mastery  will develops critical thinking, improve reading and writing, and give a firmer base for work and studies at many levels. Good luck.


After logic  (a) continue reading Three Skills for Algebra, chapters 8 to 14  and do so alongside site area on solving liinear Equations ; or (b) see this calculus starter lesson and Volume 3, Why Slopes  & More Math, chapters 2 to 6;

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Caution: Site advice is approximately correct, for some circumstances, not all. That leaves room for thought

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What may be learnt and when depends on how skills and concepts are developed. Making the hard easier and clearer will allow earlier & richer development of skills and concepts.


Try the Twiddla Whiteboard. In principle, it  allows to people to draw and chat together online on a copy of this webpage or a clean sheet. The chat may be via text or audio.  Visit www.twiddla.com to set up whiteboards to work with the webpage of your choice.

For online automated help in senior high school maths & calculus, visit  quickmath.com  For Automatic Calculus and Algebra Help with derivatives, integrals, graphs, linear equations, matrix algebra, visit calc101.com  With  overlap, each site quickmath & calc101offers a different range of services, some free, some not, all based on webmathematica. Good luck.

Responsibility
Chapter 10

In this chapter, we give a short story: a conflict between the owners of a cat and a dog about who or what is responsible for an accident. The murky situation leads into a discussion of cause and effect, and then responsibility versus freedom (the limits of freedom) and the absence of liability. Finally, first principles or patterns for the assignment of responsibility and liability are stated or suggested last.

Fred and Felix

Felix the cat lives in a one-tree park. Imagine every time Fred the dog visits the one-tree park, Felix climbs the tree. On one visit, Felix steps on a rotten branch, falls and breaks a leg. In what sense is Fred the cause of this accident? In what sense is Fred the dog responsible? The argument between the owners of these animals follows

Felix's owner claims that Fred is a mean, vicious dog. So Felix had to climb the tree to escape Fred. The accident would not have occurred without Fred's visit to the park. So according to Felix's owner, Fred was the cause of the accident.

Fred's owner counters that Fred is a very friendly, good-natured dog, not interested in harming Felix. Felix was perfectly safe when Fred visited the one-tree park. Moreover, on the day in question, the broken leg was a result of Felix's unnecessary actions, not Fred's. Fred's owner continues: On the day in question, Fred as usual visited the park to walk about. The idea that Fred is vicious is a figment of Felix's imagination. While Felix climbed the tree every time Fred visited the one-tree park, Felix was climbing the tree at his own initiative. Felix had a false fear of Fred. The cat Felix was therefore responsible by himself for climbing the tree.

Felix's owner then suggests that Fred's owner is responsible for the accident since the latter should know about Felix having a natural fear of dogs. Fred's owner replies …. The argument goes on.

Most of the neighbors listening to this argument agree with Felix's owner. They suggest Fred be punished. Fred's owner refuses. A year later, Felix the cat in chasing a bird climbed into the tree again, and fell on the other leg. Felix the fragile feline lived. Poor Fred was not there to be blamed. (One neighbor who missed the result of the argument wondered where or how is Fred? He did not have enough information to answer this question.


Chapter Subsections: Limits to Freedom ] Principles for Responsibility ]

Next: Limits to Freedom

 

 

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Volume 1A, Pattern Based Reason

 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

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

Vol 1A Postscripts
- online only

+Proof by Absurdity alias proof by contradiction
+How the demand for consistency supports the law of the excluded middle

There is a difference between
knowing how to spend money,
and having money to spend.

There is likewise a difference
between mastering a skill
and having meeting a situation in which it applies.

 



 


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a 1983 McGill. Ph. D. in mathematics
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