Pattern
Based
Reason
understanding & explaining
Reason and Math
Volume 1A
Printed in Canada
ISBN 0-9697564-5-3
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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.
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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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Explore collaborative whiteboards
from groupboard,
twiddla or
scriblink.
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Confidence in Patterns
Chapter 16
Previous: Accidental Patterns
Rules Reliable or Not?
The question of what is not accidental needs to be examined. The concept of a
controlled or reproducible situation provides an answer. In rule-based reason
and processes or methods, we gamble. We build theories on implications we assume
or hope are not disobeyed in the circumstances of interest. A theory here is
given or suggested by a chain of implications and assumptions. Our confidence in
the conclusions provided by these chains depends on the confidence we have in
the chain of implications, assumptions, suggestions and approximations leading
to them. As in arithmetic, a false step may lead to a false conclusion.
Confidence is obtained for some implication rules or patterns through the
idea of reproducibility and repeatability in controllable situations. Confidence
may also be obtained from prediction-based tests. How all this is done will be
described below.
Technology and the rules for the operation and manufacture of devices and
products in it, are all based on the pattern of reproducibility. We rely on this
reproducibility in our everyday lives: plumbing, electricity, automobiles,
radios, airplanes, toasters, ovens, furnaces, etc.
Cooking illustrates the confidence building aspect of reproducibility. By
following instructions and putting together ingredients carefully we can make
certain meals repeatedly. Anyone else following the same instructions with
enough care can also prepare or reproduce the same meal or dish.
Carefully recorded experience in chemistry gives reproducible methods for
making, remaking and classifying different substances. The same substances can
be produced again and again by a chemical process provided the recipes for its
production are followed with enough care. The amount of care required depends on
each recipe. Further, empirical experience in physics and engineering gives
formulas and suggestions for modeling and controlling various situations. This
experience is cumulative — if recorded in some form by means of a written
statement about a device or a procedure which worked or failed. This gives a
verifiable, reproducible science or technology. Recording or remembering what
ideas failed gives paths to avoid and questions to ask.
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: Details of the or a Scientific
Method for Advancing Technical Knowledge
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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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