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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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Three Remarks (Postscripts)
Previous: Foreword
Rules and patterns need to be read and written with precision.
-
If you do not read precisely what is meant, how will you
understand?
-
If you do not write precisely what you mean, who will
understand you?
Volume 1A, Pattern Based Reason,
read slowly, will test and develop precision reading and writing while
pointing to the benefits, origins and limits of rule and pattern-based methods
in thought and deed. Not all is certain. The question of what rules and patterns
are reliable remains open. But in daily life we do assume or rely upon
many rules and patterns. There is no escape.
In science and technology, rules and patterns range from being reliable to
speculative. Engineers and scientists need to know the benefits, origins
and limits of their rules and patterns, that is, when they may be applied
or not.
Mathematics offers the most certain area of rule-based
thought. Physics, chemistry and biology include rules and patterns that can be
tried and tested in lab work (experiments). Biological descriptions of
anatomy can be verified in the lab via dissection - direct verification. . In
contrast, quantum physic and cosmology offers speculations on the origins and
evolution of the universe at the subatomic and macroscopic level- these
speculations provide calculations that sometime work regardless of
justification. Finally, evolution theory in biology is based on or the
fits the clues that come from geology, the dating of fossil layers and
fossils, and the similarity of organisms, adult or embryonic, at the
anatomical and microscopic level. If you accept the dating methods or
how they were established, you will come to a conclusion that the earth is old
and that life did not appear quickly.
There was a dream that empirically discovered rules and patterns would
provide answers. But such rules and patterns have their limitations.
In society, religion, commerce and science, the follower of rule- and
pattern-based thought and methods needs to the know the origins, benefits and
limitations of those rules and patterns, and so see when to apply them and to
when further thought is required.
3. Scale Factors in Science and Society - Ecology and Pattern
Based Reason
Questions of scale appear in society, science and technology. Processes
that appear beneficial and harmless on a small scale may on a larger scale bring
ill-effects. Think of towns on a river. Untreated sewage may leave
river waters drinkable when the towns are small. But the growth of towns and
population may pollute the waters and require remedies. City planners and
designers of industrial processes need to consider the effects of scale.
The unchallenged right to pursue methods or processes that do no harm to
others and yourself, may need to be revisited when a method or process is
practiced on a larger and larger scale, as side effects initially considered
harmless accumulate. Ouch
Rule and pattern based methods with results that appear to be repeatable and
reproducible on a small scale may be rotten on a larger scale due to accumulated
side effects.
Next: Chapter 1, What is Reason. -
Different kinds of Reason
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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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