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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 16. Origins
and Limitations of Rules and Patterns
Rule-based reasoning is in part subjective and in part creative. Results
depend on the rules and the facts you choose to use or happen to know.
Rule-based reason becomes subjective when the starting points and assumptions
required are not obvious.
Each of us may make a different sequence of decisions. Each of us is a person
with a limited and different knowledge of what has been done before. As a result
we may be ignorant of methods helpful in the situations we face. As a result, no
matter how rational (or deductive) we try to be, the decision of what to do, or
how to do it is subjective.
Knowledge of what others have done or tried to do may help and guide our
actions. Without previous know-how and knowledge, we need to improvise and look
for patterns, rules and recipes that work. This is where the search for
objective reason, or simple rules to follow, becomes subjective. Each may have a
different idea of where to look. This is because each person has a different
background and varied preferences. The road to objectivity is in part subjective
and creative.
When new situations occur, experimentation, with a little caution to do no
harm, is needed. The discovery of new objective processes (recipes and
guidelines) is subjective. It depends on our experience. Again, each of us has a
different idea (or no idea) of what to do. When approximations or errors are
made, the results in question become more subjective. They depend on the choice
of the approximation. In time, conventions or standards may be adopted to govern
the approximation and make the procedures in question more reproducible.
Rule-based reason is incomplete. The rules or guidelines for handling some
situations are missing. People make rules or see patterns in the situations
familiar to them. New situations may go beyond the reach of the suggested
patterns and rules. Uncertainty begins where previous rule-based knowledge ends.
So rule-based reason has limits.
- Different people get different conclusions. Subjectively, that is, from
varying individual choice, interest and experience, each may use a different
subset of the available implication rules. As long as the people in question
can correctly describe their reasoning or procedure, their creatively found
results are objective. That is, a result or conclusion becomes objective,
more precisely repeatable, if the instructions to get it, once written, can
be followed successfully by others.
- Different starting points or assumptions may lead to disagreements between
logical and otherwise objective people. Talk between disagreeing parties can
sometimes get people to agree on a common starting point for their reason.
If this occurs, the rule-based reason in question can be followed and
repeated, so that reproducible results and conclusions are obtained. That
is, subjective reason may become objective, or at least agreeable to several
parties. In some circumstances, but not all, we can get firm, sure and
reproducible results and conclusions.
Next: Chapter 17, part II, The Discovery Process
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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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