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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End Notes and Review
Chapter 16
Previous: Statistical Inference
and It Limitations
1. In a rule which suggests that whenever a first situation is made to
happen, a second situation will follow, the first situation is called a possible
cause of the second. The second situation is also said to be a possible effect
or consequence of the first.
2. Human made rules or models for nature's behavior suggest or
describe patterns without explaining why they occur. Science and technology are
mixtures of facts, guidelines and recipes. Some parts are certain or almost
certain. Other parts are less certain. The empirical approach to knowledge tries
to identify those repeatable, reproducible processes: processes that work,
accidentally or otherwise.
3. Scientific and technical knowledge can be viewed as a collection of
theories or recognized patterns and recipes (implication rules). Details
accompanying such rules should say when they do or don't apply – the range of
applicability. Knowledge of this range can be unclear. Our knowledge of the
physical sciences forms both a collection of recorded patterns or recipes
for solving some problems and a collection of unsolved problems.
4. The unsolved problems (or mysteries) say or indicate that more work
is required. We humans have discovered many skills and techniques, wonderful or
not. In any area of application, only a few of these skills are pertinent, that
is, applicable. In any area of application, further skills or techniques are
often required. In technical areas, we find two kinds of knowledge: a knowledge
of processes that work and a knowledge of processes that don't. So more work is
required on them. Whether or not this work is feasible always remains to be
seen.
5. Technical knowledge is based on repeatable and reproducible
methods, along with some trial and error from deliberate experimentation
(sometimes accidents) to find them. As human beings, we can spot or imagine
patterns. From them, we try to predict what will happen.
6. Creativity and subjectivity (guesses, past knowledge and
experience, guidelines/assumptions) are involved in deciding what chains of
implications to form or investigate. Once a chain of implications with an
interesting result or conclusion has been discovered, the result or conclusion
and how it was obtained can be shown to others. The path to such a result or
conclusion can then be repeated by others. Mathematics, engineering, science,
chemistry, cooking, computer science, all these disciplines follow this pattern
of discovery and repetition or reproducibility. Reporting how a conclusion or
goal was obtained or missed is a result. It is a result which informs how
something was done (or missed). We can learn from the experience and the errors
of others and ourselves.
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: Chapter 17, Objective
Ways (Trial and Error Discovery, Etc)
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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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