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       2. Implication Rules


Chapter 2. Implication Rules

Previous: Introduction to Logic Chapters
Chapter sections:
[chapter intro] First Logic Puzzle ] Second Logic Puzzle ] One-versus Two-Way Implications ] Implications versus Suggestions ]

In this chapter, you will meet two puzzles which show the difference between one- and two-way implication rules. Mastering the difference is a simple, first step, in rule and pattern-based thought. This first step is needed to precisely read rules, definitions and statements in all disciplines, including mathematics.

Are you a careful thinker? Can you understand exactly the meaning of a rule or pattern? Instructions for building or creating provide rules and patterns which say and suggest that when this is done, that should happen. Every cook and dressmaker knows the importance of following instructions carefully. Instructions and suggestions which are not repeatable and results which are not reproducible are not of interest to a cook or dressmaker.

To read rules carefully, do not imagine too much. To decide or choose among opinions and actions, you must understand the exact meaning of written and spoken words. You need this skill to understand, to follow, to write and to change rules, guidelines, instructions and laws, etc.

Use your imagination in language courses. Use your imagination when you are reading novels (and newspaper opinion columns). When reading newspapers or listening to radio and television ask: Is the story presented in a one-sided way? Headlines may suggest conclusions which are not in the stories or the text. Look at the details. Here imagination allows you to guess what the full story might be. But imagination provides only suggestion, not proof. Confidence in suggestions must come after proof is given, not before.

Also use your imagination for poorly written rules to guess their meanings. Guesses and speculations give possible meanings. These may or may not be correct. Proof and evidence, or tests, may decide which among various possibilities, if any, are correct.


Each of us needs to understand fully or as much as is possible, whatever we might be doing or learning. In reasoning, some rules and patterns are reliable. Others are guidelines. Each of us needs to know which is which.

Chapter sections: First Logic Puzzle ] Second Logic Puzzle ] One-versus Two-Way Implications ] Implications versus Suggestions ]

Next Section: First Logic Puzzle

Next Chapter: 3. Chains of Reason - Euclidean Model for Reason

Three Skills
For 
Algebra

understanding & explaining
Reason and Math
Volume 2
Printed in Canada
ISBN 0-9697564-2-9
   Back ] Home ] Next ]

Chapters and Appendices

Home
Postscript: The 4-th Skill For Algebra
Foreword
1. Introduction
2. Implication Rules
3. Chains of Reason
4. Romeo and Juliet
4. Induction Mathematical
5 Knowledge Islands
6  Old Language
7  Arith Skill Check
7. The Next Chapters
8 The Three Skills
8 VNR-Concise-Encyclopedia
PS. What is a Variable
9. Algebra Talk
10 Two More Skills
11 Why Shorthand
12 Shorthand Usage
13 What's Next
14 Compound Interest
15 Linear Equations
PS I.  Distributive Law
PS II. Polynomials
16 Painless Proofs
17 Pythagoras
18 Rules of Algebra
19  Functions & Sets
20 Degrees & Radians
21 What's Next
22. Arith & Geometric Sums
23 Summation Notation
24 Your Money
25 Induction & Recursion
26 What's Next
27 Pronouns in Logic
28 Occurrence Tables
29 Contrapositive
30 Truth Tables
31 Indirect Reason
A. Advice For Learning

Words Before Symbols: 
What is a Variable?
Introduction
Variation between Examples

Variation of Letters

A letter denotes a variable

Cases of Double Variation

Three Notions of a Variable

Constants, Parameters
& Variables

Talking about numbers
Dependent or Independent
Variable, a Matter of Choice


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