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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 17, Objective
Ways (Trial and Error Discovery)
Speculation
Consciousness and thought appears in infancy or childhood. There they may be
initially taken for granted or not explicitly noticed. Only later are they
questioned, if they are questioned at all. Vagueness of memory may hide the days
when consciousness and thought began. A few speculative remarks follow. Despite
being written in the third person, the remarks represent this author's image of
his own consciousness, thought and ability to know.
An infant is born. His or her senses of touch, sight, sound, heat, smell and
taste meet a new environment. Coordination comes slowly. As the infant moves,
crawls and then walks, his or her mind (presumably) becomes aware of a
difference between two parts of the surroundings. First, external to the mind is
a body. This body is sensitive to indigestion and other discomforts. Some
maintenance is required. Second, external to the body is an environment of
objects, active, inactive and/or reactive. Here both the body and the
environment external to it impinge on and react with the mind of the infant
child. The boundaries of this body, the skin, especially on the fingers, along
with the ears and the eyes provide sensations of the environment beyond the
body. During exploration, the child may find that some caution is required, say
to avoid repetition of painful experiences due to hot, cold, sharp or hard
surfaces. Interaction with the environment brings sensations, sometimes
pleasurable and sometimes not.
The child learns
In moving objects from here to there, in learning to get dressed and to eat,
and in learning to talk, the child may come to accept the environment. Beyond
this, the child may dream. The dreams of the child are perhaps echoes of recent
experiences or sensations, the suggestions of others, or both. Dreams may be
directed or not in the child's imagination where pleasant thoughts or fears may
govern. (Directed dreams and images are a visual form of thought.)
In growing, the child may learn the difference between mental experiences,
here dreams, and the ongoing physical experiences of the body and its five
senses. The latter need to be given priority. Different times and cultures
may favor a different emphasis. The undirected dreams or images may then be
suppressed or discounted. That is, the child accepts the priority of the five
external senses, the environment they represent, and does not remain or withdraw
fully into the echo or memories of past experiences. Loss of control here may
appear as madness or as a withdrawal from the world given by the physical
senses.
The words of others are external to the child. Words provide information and
instructions. When a noise is heard, a child will identify its source. The
source is often external. But as the child learns to speak, the source is not
external. That is, when a word is spoken, it echoes in the ears and therefore
the mind of the talker.
Then in learning to read or speak silently, the external spoken word is
internalized. [1] In this, the child finds an inner mind
to explore. Silent words echo without an audible use of the vocal chords, if
they are used at all. They are heard in the mind. The infant or child needs to
learn to recognize this silent voice as his or her own, a voice that may remain
one and not be divided.
[1] In Roman days, loss of voice meant the
loss of the ability to read aloud and hence the loss of the ability to read.
Thought appears to involve the formation of images in the mind, the formation
of words on the lips or in the mind, and the formation or the recall of
sensation fragments from the physical senses of sight, sound, touch and heat,
taste and smell. When awake, this thought should or may remain linked to
everyday reality, the sometimes rude external environment.
The thoughts of a person are not usually isolated. Interaction with the
environment, the feeling that it is too hot here; body needs such as hunger; the
voices/actions of others intervene and sometimes direct thoughts and actions.
The words of others in particular pass on ideas and stories. Knowledge itself
may be a reflection or a consequence of the ability to describe, to tell,
understand and remember stories. As the infant child grows, stories as told by
elders (or as written in books) transfer knowledge or pass on the culture and
knowledge of a community. Organized or not, it is food for thought. When
deliberately organized, as in education, this transfer may result in the
accumulation of skills and techniques. In particular the deliberate description
of rules and patterns, and the theories that they form, extends the ability to
follow stories and act upon their content, their plots and the characters that
exist within them.
Next: Chapter 18, part ii, The Child Learns
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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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