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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 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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-/[]\- 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. |
Accidental Rules
The initial one-way implication rule said: When Aunt Jane visits her nephew Tom's home, Tom goes outside to play. This rule describes a pattern. This rule is said to be true if it is never disobeyed. This rule is said to be false if it is disobeyed at least once. We can talk about the truth and falseness of a rule in the past, present, future or in some special situation. Given a rule or a possible pattern, we would like to know in which circumstances it is never disobeyed. The five questions show us how to use this rule when we know it is not disobeyed. A sixth question is What, if anything, can we do to check or guarantee that a given rule is never disobeyed in the circumstances of interest? We could perhaps observe all the visits of Aunt Jane to see that Tom goes out to play each and every time. If he does not once, the rule is false. It has been disobeyed. [3]
In observing some but not all of her past visits, we may see the pattern that when she visits he goes out to play. These observations only describe the past. Patterns observed in the past can or might change in the future. We have to judge how likely this is. In contrast, seeing a rule is not obeyed at least once, or just once, is enough to say the rule is false - not always obeyed. Vocabulary: A situation in which a rule is disobeyed is said to provide a counter-example to the rule. In summary, seeing a rule is obeyed a few times is enough to suggest a pattern. Seeing a rule is obeyed a few times is not enough to imply with complete confidence that it is never disobeyed. Observations may only suggest a pattern is developing. They may lead us to conjecture or guess that the rule will always be obeyed or at least never be disobeyed. A difference between being suspicious and being certain exists. Patterns seen may suggest rules, but not prove them absolutely. A rule which suggests that every time an event occurs, another event will occur cannot be checked or proven absolutely. Such a rule can be assumed for the sake of getting conclusions. When is the rule reliable? What can be done to test our assumptions? Our confidence in the resulting conclusions depends on the reliability of the rules and implications used. The reliability, origin and testing of rules, instructions, recipes, suggestions and implications need more inspection. Where is the proof? Sometimes proof is not available. So we may pretend (assume) a rule is never disobeyed to reach conclusions or to make suggestions from it. Each pretense or assumption represents a weak spot - a possible gamble or source of error, in our reasoning. [4]
More will be said on this subject of what rules are reliable. The chapter Accidental Patterns will echo many of the ideas introduced here. Chapter Subsections: Next: Steps For Clearer or Better Reason |
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