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YOU are better than YOU think. Show
yourself how:
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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
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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.
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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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www.whyslopes.com
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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