Employ an online or offline tutor at your own risk from
AU:
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CDN : findatutor.ca
CDN: .i-tutor.ca
CDN: Montreal Tutors
NZ: findatutor.co.nz
UK: tutorhunt.com
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USA: wiziq.com
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YOU are better than YOU think. Show yourself how:
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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.
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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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After logic,
(a) continue reading Three
Skills for Algebra, chapters 8 to 14 and do so alongside site area on solving
linear2007 Equations ; or (b) see this calculus
starter lesson and Volume 3, Why
Slopes & More Math, chapters 2 to 6;
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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Explore collaborative whiteboards from
groupboard, twiddla or
scriblink.
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Accidental Patterns Again
Chapter 16
Previous: Observation of
Physical Laws, Testing Conjectures
Suppose we are given a rule which involves the idea that every time a
first situation A occurs. We can be sure that the rule is correct provided
we can check that every time the first situation A happens, that the second
situation B also occurs. This checking is possible (feasible) if we are reading
a story. In the story the rule may be seen to always hold. So it has been
verified. But, except for written stories describing past or fictional events,
we cannot check that each time the first situation A occurs, the second
situation B happens. An observation
Every time the first situation A happened, the second situation B also
occurred
represents history. Forcing the first situation A to occur will not make the
second situation B occur if the pattern is accidental. For example, suppose two
children have gone to school each day, for the past three weeks. This behavior
or pattern gives no guarantee both will show up every day of the following week.
The behavior of the observed children need not be governed by this pattern. The
explanation of the children's attendance at school lies in a home life or health
status which we have not seen. The pattern seen might have been accidentally
established.
Observing the pattern
Every time the first situation A happened, the second situation B also
occurred
in a given circumstance or setting C suggests the implication rule if A
then B might hold in the circumstance C. Seeing that this pattern holds
several times builds confidence in the reliability or truth of this implication
rule. We may become very confident in the suggested implication rule — and
perhaps take it for granted — but we cannot be sure. We cannot conclude for
certain from observation or experience, that this implication rule is never
disobeyed. In contrast, observing the occurrence of situation A once without the
situation B in the given circumstance C shows that the rule can be disobeyed.
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: Reliable Patterns: Scientific
Method, Prediction, Testing, Correction
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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.
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
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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