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YOU are better than YOU think. Show
yourself how:
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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
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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, 14
Deductive And Empirical Views of Mathematics
Reproducible Results
Arithmetic shows the main idea of objectivity. Namely, a result does not
depend on who or what performs a calculation, but only on the rules for
addition, multiplication, subtraction and division. Except perhaps for round-off
error, arithmetic results are repeatable and reproducible.
Recipes and rule-based processes, when carefully done, give results
independent of who obtains them. In this situation, the results cease to be
subjective — that is dependent on the person getting them – and they depend
only on the context. In this situation, the results are said to be objective.
The main advantage of objective (rule-based) reason and processes is as
follows. Once we have agreed upon the rules and recipes and on the evidence or
ingredients to use, the results obtained are independent of who or what obtains
them. The result could be a number if we are doing arithmetic. It could be a
judgment or a conclusion if we are dealing with people. It may be an action or
product when operating a device or machine.
Rule-based reason is ideal when or if you agree on the rules and information
employed. Disagreement on this, and the ensuing absence of rules or information
needed by them, represents a limit of rule-based reason. Disagreement over what
rules, if any, to apply makes conclusions subjective – that is, dependent on
who obtains them.
Objective reason and empirical processes both rely on the idea of following
previously stated recipes and guidelines, preferably ones that have given good
results in the past. Unfortunately, people singly or in organizations are
capable of repeating and reproducing bad or inferior results as well. Still, for
many problems, rules or recipes for their solution may be known. The recipes
provide solutions for problems that other people have met and solved. These
recipes and guidelines represent the experience and the opinion of others, those
who have investigated or explored the problems before. In arithmetic, science
and technology, this knowledge (recipes, tricks, procedures) is represented by
written or verbal statements of rules, patterns and recipes which may work.
Next: Search for Repeatable and Reproducible Results, and
Departures from Objectivity
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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.
Vol 1A Postscripts
- online only
+Proof by
Absurdity alias proof by contradiction
+How the demand
for consistency supports the law of the excluded middle
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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