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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.
Learn to read notes and textbooks like
a lawyer, so that no nuance, no subtlety and no clause escapes your
attention. |
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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.
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Physical Laws
Chapter 16
Previous: Chapter 16, Public Laws in
Society, Origins of Rules and Patterns,
In communities, rules and laws may be debated and then written to control our
behavior. In technical knowledge, rules and patterns we may use or follow are
subject to less debate, but they are (or should be) tested to see in what
circumstances they hold. Here rules and patterns are recognized and discovered
rather than written. But in technical knowledge, we meet the main problem of
inference, that is, inductive thought. It is the problem of finding and/or
identifying reliable rules and patterns. Here rules and patterns to describe how
the physical world behaves are proposed and then tested. Those that fail are
rejected while those that pass are only partially confirmed. Here some rules and
patterns appear more reliable than others. Not all is certain.
Empirically based rules may say or suggest that whenever a first event or
situation is seen or done, a second event occurs. The rules describe links
between different parts of nature. Why these rules or patterns are obeyed is
sometimes unknown. They are only descriptions. They are only observations -
patterns that have been seen.
Rules and theories for physics, mathematics, medicine and machines are
empirical. Empirical knowledge comes from experience and discoveries. This
includes trial and error — the first time we try to do or find something, we
typically make a mistake. Correction of the mistake or mistakes can lead to a
method or recipe that can be repeated and followed again.
Our collective experience and knowledge of physical situations and patterns
are described and summarized through the statement of laws, recipes,
instructions and formulas. The recipes may say when one event occurs, another
event will also occur. This experience may tell us how to control nature, wisely
or not. The recipe you follow in cooking a meal provides an example of this.
Experience may suggest or predict the result of an ill-conceived action or
inaction.
The physical sciences contain different theories (recognized patterns) for
different circumstances. Some theories may overlap. Some may be approximately
true. Some will be better than others. Being approximate, many theories are
incomplete. The theories contain unsolved problems to keep us humble about the
extent of our knowledge. Unsolved problems illustrate the limitations of each
theory, and the need for more work to be done. Comprehension of a theory may be
based on accounts of what has been tried (and has perhaps failed) along with
examples which work and illustrate its concepts.
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: Accidental Patterns, possibility
of refutation, not confirmation
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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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