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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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Search For Repeatable and Reproducible Methods
Departures From Objectivity
Chapter 15 subsection
The ideal or goal of objectivity is represented in the legal system by the
idea of impartiality. Lawyers, juries and judges interpret evidence and laws.
One aim is to obtain impartial, objective verdicts of guilt or innocence, and
assignments of blame, damages and punishments.
Rules and laws are subject to geographic chances. In different countries, we
have different legal systems. Some are impartial. In these there is an attempt
to apply previously established rules and regulations objectively. In other
systems, the justice may be corrupted by bribes, prejudice, etc. Even in the
more-or-less impartial ones, laws and regulations differ. So what is against a
law or a regulation in one location may be legal in another.
Laws, including commercial ones, often have a moral or religious basis. Moral
and religious ideas often define and differentiate groups. What is considered
polite, or inoffensive in one group, will be impolite or offensive in others.
Laws and regulations in legal systems reflect these differences.
Laws and regulations are often, if not always, subject to human
interpretation. Commercial laws are intended to control or regulate business.
Laws may also define or remove previous obligations or liabilities. The economic
needs, self-interest and desires of people, affect laws.
Lawmakers are further requested by interest groups to write laws in one way
or another. Each group readily accepts laws to control and restrict the behavior
of any other group but itself. Laws as they are being formulated may be changed
minutely to the benefit of one group or another. All of us have different ideas
of what is fair. Our laws themselves are compromises between the views,
principles and interests of several groups, often satisfactory to none. So we
cannot say in advance that a set of laws will be complete and not contradictory.
Circumstances may occur to which the laws apply, but for which the rules are
not intended. Or unforeseen circumstances will occur to which the laws do not
directly apply. This points to the need for a new law or new judgments about the
application of existing laws. Human laws are human creations. And humans
individually or collectively may err. The formulation of laws and rules and
principles by people introduces the possibility of error.
Postscript 2001-01-31 (Online Only): Rules and
regulations are written or drafted by clerks or civil servants in a
government under the direction of a cabinet minister. Most law makers,
following the direction of their parties, typically do NOT read in full
the laws and regulations they pass. In consequence, lawmakers do not know
their own intent in passing a rule. The precise interpretation of an imprecise
rule or law may be left to courts or judges. The latter try to guess the
"original" intent of the law. That is absurd. For
example, the fall 2000 US federal elections with it counting of
votes and voter intent in Florida according to ambiguous or inconsistent laws
and regulation provided an instance of this, and a court battle to
determine the US president.
Approximate Objectivity
Laws and regulations, however obtained, may be applied in an objective
manner. Objectivity may be subject to mitigating circumstances, political
interference, the ability of lawyers, the opinions or morals of judges, etc.
Results may vary or differ due to different laws and mores in different
locations — including your hometown; or due to ad hoc departures from
objective applications and interpretations of existing laws and rules, however
carefully written or not. But the ideal of objectivity with human-made and
human-applied regulation remains.
Next: Chapter 16. Origins
and More Limitations of Rules and Patterns
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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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