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4. Accidental Rules
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Pattern
Based
Reason
Volume 1A
Printed in Canada
ISBN 0-9697564-5-3

Volume 1 = 1A+1B
bounded together







4. First Puzzle
4. Second Puzzle
4. IF versus IFF
4. Joking About Logic
4. Imply or Suggest
4. One vs Two-Way Committents
4. Repeat- & Reproduc-ible?
4. Rules Limits & Benefits
4. Accidental Rules
4. Steps for Better Reason
Book Entrance
Foreword
PS. Three Remark
1. What is reason
2. Inductive Ed Principles
2. Communication
3. Elements of Reason
4. Implication Rules [10]
5. Hype & Deception
5. Hype & Ethics
6. Chains of Reason [4]
7.  Longer Chains of Reason
7. Mathematical Induction
8. Language Change [2]
9. Next Chapters, About.
10. Limits to Freedom [2]
11. Accidental Patterns
12. Two Analogies
12.  Knowledge Islands
13. Euclidean Model
13. Euclidean Reason
14 Math: Deductive/Empirical [6]
15. Objectivity
15. Objectivity, More
16 Rules-Patterns Origins [10]
Knowledge & Story Telling
17. Objective Ways
17. Trial & Error Discovery
18. Conciousness
19. Symbols & Logic
20. Pronouns & Symbols
21. Truth Tables I. [3]
22. Contrapositive
22. Vacuously True
24. Indirect Reason More
24PS. Excluded Middle Law
24PS.  Proof by Absurdity
PS. Reality vs Imagination
PS. Ahistorical Logic
Links Elsewhere - Go GoGo

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
+History Lost or Missing

Would you like to show yourself or others how to be algebra power users? Professor WhySlopes shouts his methods for algebra skill development are likely to work. Try them. They are different.

Accidental Rules

Previous: Limits and Benefits

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]

[3] Note that this rule will never be disobeyed if Aunt Jane never visits. In the latter case, the rule is said to be vacuously true.

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]

[4] In arithmetic, an error or wrong number early in our calculation casts doubts on the rest of the calculation. Similarly in reason, a false step or assumption casts doubts on the rest of the reasoning and the conclusions drawn from it.

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: 4. First Puzzle ] 4. Second Puzzle ] 4. IF versus IFF ] 4. Joking About Logic ] 4. Imply or Suggest ] 4. One vs Two-Way Committents ] 4. Repeat- & Reproduc-ible? ] 4. Rules Limits & Benefits ] [ 4. Accidental Rules ] 4. Steps for Better Reason ]

Next: Steps For Clearer or Better Reason

 
 

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