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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 13, Euclidean
Model for logic and reason.
Clever Mortals
People (clever mortals) have tried to base mathematics, physical sciences and
philosophy on a few true (or reliable) first principles: assumptions, rules,
laws, postulates, axioms or whatever you would call them. One fear in the human
selection of the rules is that they or their consequences may conflict. That is,
they may imply that one situation is and is not possible. To avoid such
contradictions, we are afraid to assume too much. [1]
[1] Contradictions and paradoxes may
appear when deductive reason leads from ideas assumed or thought to be self-evident,
to mutually exclusive claims or predictions. One way to avoid their
appearance is to assume fewer ideas, that is, be more selective in making
assumptions. Yet how selective to be is not always self-evident.
Proof is desired to show that all possible chains of reasons will avoid
contradictions. A contradiction is given by statements that say two exclusive
situations must or will occur simultaneously.
Despite these fears, we assume a few principles and implication rules to
reach or make conclusions. What to assume or take for granted is a question for
philosophers and for practical people as well. In practice, we need rules tested
for the situation at hand. On these we build, while being aware of their
limitations and shortcomings. That is perhaps, the most that can be done.
The search for a foundation of mathematical and physical knowledge has been a
collective effort. It has been pursued via trial and error. Like other human
concepts, the resulting laws/implication rules may be workable and acceptable.
There is no guarantee of completeness or consistency, no matter how much that is
desired.
Caution
Before you rush out to look at Euclid's works, or a modern translation and
formulation of it, note the following. Euclid's works on geometry provided the
model for reason by deduction from clear, self-evident starting points. Our
treatment of geometry and mathematics differs today from that of Euclid. The
presentation of mathematics in schools has changed, and is continuing to change.
So Euclid's works may be hard to read. None the less, Euclid's works still
represent the first example of the axiomatic method in practice. For that it is
remembered.
Next:
as you like.
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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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