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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.
| |
Previous: Chapter 15,
Objective Processes, Search for Repeatable and Reproducible Methods (or results)
A rule, law or agreement may say that when one event happens, another event
should also happen or may also happen. Most physical and legal theories, if not
all, use rules which are approximately correct. The rules are like all human
discoveries and creations; some are more reliable than others. The formulation
of laws and rules and agreements by people leads to the chance of error and
incompleteness. Even with uncertainty, once rules or laws or agreements have
been stated, we can use them tentatively, to reach conclusions or judgments.
Locating the weakest links in our reasoning gives us a chance to strengthen or
replace them.
The question of what rules to accept, use or change, and how much confidence
we can have in them is often discussed. This question is debated or negotiated
at various levels in mathematics, philosophy, politics, business and religion.
We think or dream of what might be. We speculate. Then we need to test to see
what parts, if any, of our speculations are correct. We correct what we can and
speculate again. Knowledge here comes from an approximation, or a sequence of
approximations, some better than others.
We find and obtain rules to obey or ignore from at least three sources:
- Private Agreements. The first source occurs in deals between
brothers and sisters, or between business people. These implication rules
suggest that if you do this, then and only then will I do that. These
implications are agreements or promises. The agreements and commitments here
can be one-way or two-way. They may be written or spoken. People get upset
whenever such rules are not obeyed or not understood.
- Public Laws in Society. A second source is given by rules or laws
used to say what is acceptable in society. These govern in part our
behavior. Such laws say what we should or should not do. They may even
specify penalties or punishments for disobeying them. A rule that is not
enforced, or is enforced weakly, is often ignored or forgotten.
- Physical Laws. A third source of rule occurs in technology,
mathematics and science. These record or state our observations of nature
and the patterns it follows. They may describe what has been seen. They
record human experience. Examples of the latter are provided by the recipes
for cooking and operating instructions for machines. Reliable and carefully
followed procedures give reproducible results. Further, recipes and reliable
patterns can be joined together to suggest more recipes and patterns of
behavior.
These three sources of rules or patterns are discussed next.
Chapter Sections: [Origin or Sources of Rules and Patterns] [ 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: 16. Rules from
Private Agreements,
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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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