Chapter 9. More Elements of Reason
The previous chapters show how reliable rules and patterns can be used to
arrive at conclusions or judgments. This raises the question: how can we
recognize reliable rules and patterns? This second group of chapters on
reason describes the origins, limitations and organization of rule- and
pattern-based knowledge in all arts and disciplines.
The problem of identifying reliable implication rules and reliable
information is described but not solved, except for the description of
empirical methods of coping in science and technology. This
identification problem touches many subjects. Students of critical
thinking, persuasion, philosophy, mathematics, science and technology
should find its discussion in these chapters helpful.
About the Next Chapters
Previous chapters also show how rules and patterns can be used one at a
time or one after another to get conclusions. The use and chaining
together of implication rules is called deductive thinking. The next
group of chapters describe more elements of reason. The chapters in
question, namely
- 10 Responsibility
- 11 Accidental Patterns
- 12 Islands and Divisions of Knowledge
- 13 Euclidean Model of Reason
- 14 Views of Mathematics (somewhat technical)
- 15 Objective Processes
- 16 Origin of Rules and Patterns
- 17 Discovery of Objective Ways
- 18 Sense and Knowledge
give views of reason, persuasion and knowledge in our schools and
communities and in our technical areas of knowledge. These chapters speak
about how and where rules and patterns are needed, written, discovered or
extracted from experience. This information itself is needed to recognize
when and where the rules and patterns can be applied, and to be aware of
their reliability or limitations.
The chapter Responsibility tries to clarify the meaning of
liability and responsibility for actions and accidents. Then it talks
about how liability and responsibility for our actions impose limits on
our freedom. Principles for responsibility are suggested.
The chapter Accidental Patterns describes how human behavior
which we have seen in the past may be accidental or coincidental. So we
can have no expectation of this behavioral pattern continuing. This
raises the problem of identifying which patterns of behavior are reliable
and not just accidental or coincidental. How can we be (almost) sure that
one event causes another? For technical areas of knowledge but not for
human behavior, an answer is given in the chapter Origin of Rules.
This chapter echoes and reinforces the discussion of Accidental
Rules in the chapter Implication Rules.
The chapter Islands and Divisions of Knowledge describes how
one- and two-way implication rules may link together rules and patterns
of our communities and in our technical knowledge. Some parts of
knowledge may be connected to others by chains of reason while other
parts may be separate.
The chapter Objective Processes explains the notion of
objectivity. The following of rules and laws in a fashion which gives
repeatable and reproducible results independent of whom or what applies
them leads to the concept of objective thought and actions in
technological, in community or bureaucratic processes. Processes and
results which are repeatable and reproducible are not necessarily
optimal.
The chapter Origin of Rules and Patterns first describes how
rules and laws are written or agreed to in society. Then it describes how
reliable rules and patterns are recognized in our technical areas of
knowledge (except for mathematics). The inference problem in empirical
thought is to identify, draw, induct or extract from experience or tests,
those rules and patterns which are reliable and not accidental. The word
induct means to draw or extract. Inductive reasoning in empirical thought
(not mathematics) refers to the identification of rules and patterns from
experience.
Inductive reasoning in mathematics refers to the longer
chains of reason associated with the principle of mathematical
induction. The meaning of the phrase Inductive reasoning in mathematics
refers to the longer chains of reason associated with the principle of
mathematical induction.
The chapter Discovery of Objective Ways speaks about the
non-objective, subjective and sometimes creative approaches in which
objective ways are found. Problems for which solutions are not dictated
by others leave room for thought and experimentation. Of course, hard
thought and experimentation can be avoided if we can use a previously
found solution known to work well. Sometimes that is preferable.
The chapter Euclidean Model of Reason describes a two thousand
year old model (and method) for organizing technical knowledge. This
method was first seen in the geometric works of Euclid and his followers.
These works suggest how clear definitions and clear assumptions together
with chains of reason can be used to firmly derive conclusions.
Law-makers, theologians, scientists and mathematicians have often tried
to follow this model in their areas of reason besides geometry. One
reason for studying mathematics was to meet this model. The works of
Euclid suggest an ideal we would like to achieve or approximate as well
as possible.
The chapter Views of Mathematics describes how the first
principles of arithmetic-based mathematics came from experience, and how
by trial and error, calculations that work have been found in many
disciplines. Then this chapter mentions the effort to follow the
Euclidean Model of reason in mathematics and the associated
disappointment. Not all is certain. Finally, the classroom view of
mathematics after elementary school is described. The latter could
skipped on first reading.
The last chapter in this group, Sense and Knowledge , speculates
about the origin of self-consciousness and of our ability to tell and
remember stories, theories or ideas linked together. As usual, more can
be said or suggested in speculation (or rumor mongering) than proven.
Serious students of reason and mathematics will not take the speculation
seriously.
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Teachers & Tutors: Site pages offer better or best practices for providing skills -
simpler than expected & comprehensive but for exercises. For your charges, your duty is to study them alone or in
groups and develop skill building exercises & activities to share. Start now. The effort here is the best I can do.
Others are welcome to refine or exceed it. Please do.
Secondary
Mathematics for Ages 11+, A Practical Approach for home-tutoring or -schooling, or for schools & colleges
with local curriculum control. Study how to include site content - its skill development how-TOs and innovations
into present or future lesson plans - some reading required.
Road
Safety Messages and Questions: When and why should you face
traffic when walking along a road or cycle path? Is it a good
idea to hang limbs outside of cars etc? What gives more
protection in a crash: a car, motorbike or bicycle?
See too, the BBC-Belgium story Texting and
Driving - texting & the impossible test - the article links to a gruesome utube video on the subject
The Logic of Injustice:
How Texas sent
an innocent man to his death - The wrong Carlos. Some judgments are irreversible. Procescution: Where and when prosectors play to win rather than for
justice, guilt beyond a reasonable doubt goes unrespected due to prosecutors who putting winning
first, those innocence before the law may be convicted. Some procescutors offices in continuing to accuse after a pardon
due to reasonable doubt or innocent being shown, may sucessfully oppose compensaton for false convictions
by asserting a pardon individual is still under suspicion. Then the pardoned individual or the latter's estate
is not compensation for years or decade
of improper or false imprisonment, or for execution. Site chapters on Logic
and some in Pattern
Based Reason may slowly lead to greater precision in reading, applying and
writing laws.
May 2012, Composition Starting:
Pre-School and Primary Mathematics - Quantitative Skills, An
Intellectual View, Feedback Welcome:
The 8 Most Popular Site Inlinks
Parent Center: Help your child or teen
learn:
Parent-friendly
Work Booklets for ages 3+ to 13 Use these or others to check
or build skills. Other booklets are available but these booklets
allow parents unsure of themselves in mathematics to help their
children. The selection acquired in Canada is published in the
USA. So it has a US orientation. In retrospect, the selection
shows parents what to check with the booklets or by other ways,
the choice is theirs. But in retrospect, the selection does not
cover integral and fractions liquid weights and measures - ask
the publishers to correct that! For ages 9 to 12 say, parents may
compensate by showing boys and girls how to use weights or mass,
and further measures in food preparation. Beyond that children
may be shown how to measure and calculate angles, lengths and
areas [proportional amounts too] directly or by using maps and
plans drawns to scale. Learning how to gather and measure all the
ingredients, pots and pans for a dish or a meal, along with
cleaning up sets the stage for like activities or experiments in
science courses, and in developing organizational skills,
gives boys and girls a head start. Good luck. At the other
extreme, more comprehensive than light, if your motto is
McCainian: drill, drill, drill then Toronto
mathematician and actor John Mighton's jump math organization has jump math
workbooks for at least grades 3 to 8 for at-home and in-school
use - training sessions for teachers available. Jump math has
been expanding to cover older students. Jump Math Samples: plus
Fractions for
Grades 3-4 & Grades 5-6 [Read] Free Resources grades 1 to 8
[unread - likely to be good]. and
Mathematics
Skills For Ages 3 to 14 - technical!
Skills with take
home value - A few ideas
Basic skills include
time-date-calendar Matters; money matters; map, plan and
scale diagram matters;counting, measuring and figuring;
decision making with logic and likelyhood; being careful and
being aware of the domino effect of mistakes; reading and
writing with precision.
Is your child able to add, subtract and multiply amounts
of money, work with fractions, work with clocks and calendars,
work with maps and plans, and measure length, weight-mass and
volume? Schools may promote your son or daughter without
providing basic skills in reading, writing and
arithmetic.
Arithmetic
and Number Theory Skills
Algebra
Starter Lessons
Geometry
- maps plans trigonometry vectors
More
Algebra
70
Calculus Starter Lessons
Calculus Lessons Elsewhere:
-
How to Ace Calculus: Street Wise Guide - Mostly
Text.
-
Flash
Video for Calculus Phobics
They cover basic topics in ways likely to complement your
notes, your textbooks and site material. When Goldilocks
trespassed in the house of the three bears, she found three bowls
of porridge, two not to her liking, and one just right. Different
bears have different tastes. As invited guest here and elsewhere,
if one or more explanations is not to liking, try another. It may
be better or just right.
Unsolicited Advice
Learning to do and high marks if it comes to easy is often
deceptive - light rather than deep. For that reason, students
with learning difficulties determined not to let it get in their
way may go deeper and farther than those with none. High marks,
if the come easy, may be deceptive - provide a too light and not
a deep mastery. That could have been your problem in secondary
school, one that leads to comprehension shock or difficulties in
calculus and more generally in the first year of college. Bon
Appetite.
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