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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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Previous: Chapter 11, When
do rules and patterns hold accidentally? Reliably?
Recall the difference between one- and two-way implication rules:
A one-way implication rule says that when a first situation occurs, so must
a second. It does not say that when the second occur, so must the first. (The
second situation may occur without the first).
A two-way implication rule says that:
- when a first situation occurs, so must a second, and
- when the second situation occurs, so must the first.
A two-way implication says that when each situation occurs, so must the
other. (Therefore if the two-way rule is to be obeyed, when one situation does
not occur, neither can the other.)
The examples in the chapter Chains of Reason involved one-way implication
rules. They showed that one-way implication rules can sometimes be put together
to get further implication rules. You may remember we had one implication rule
about Charles that was not used to get any conclusion.
One and two-way implications can also be joined. The ways in which this can
be done are described below by analogies with one- and two-way streets, and one-
and two-way doors. These analogies indirectly describe how rule-based knowledge
is put together. In particular, rule-based knowledge is divided into separate
segments. Each segment cannot be reached from another by chains of reason. The
two analogies describing this situation further are presented next.
Two analogies and Ignorable Rooms
One and two-way implications can also be joined. The ways in which this can
be done are described below by analogies with one- and two-way streets, and one-
and two-way doors. These analogies indirectly describe how rule-based knowledge
is put together. In particular, rule-based knowledge is divided into separate
segments. Each segment cannot be reached from another by chains of reason. The
two analogies describing this situation further are presented next.
Next: Chapter 12, Part II, Two Analogies and
Ignorable Rooms
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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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