Chapters and Appendices

Book Entrance

First Logic Puzzle
Second Logic Puzzle
One-versus Two-Way Implications
Implications versus Suggestions

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

Would you like to show yourself or others how to be  algebra power users?

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

Chapter 2. Implication Rules

Previous Section: One-versus Two-Way Implications

Implications Versus Suggestions

In a dictionary you may find that the verb to imply also means to suggest. Words which say when one event occurs so does or will a second are called suggestions or implications. Suggestions and implications can be true. True here means obeyed or at least not disobeyed. Suggestions and implications can be false. False here means disobeyed. In our reasoning process, we want to say with certainty that when this occurs so will that. In practice, we may have to be content with saying when this occurs, so may that. Knowing which of our rules are sure or which are uncertain identifies the weaknesses in our reasoning processes. The implication rules that are never disobeyed provide the most certain suggestions in reason.

In  logic, when we speak of implication rules, we speak of rules which we hope are never disobeyed. Rules which might be disobeyed are called conjectures, suggestions or guesses. Evidence (persuasion) should be required to convince us that a conjecture or suggestion is a reliable implication. We can imagine or suggest more than we can prove. Caution is advised on hearing a rule. Before applying a rule, you need to know how certain it is. Is it a reliable implication or merely an uncertain suggestion?

Chapter subsections: [ Up ] [ First Logic Puzzle ] [ Second Logic Puzzle ] [ One-versus Two-Way Implications ] [ Implications versus Suggestions ]

Next: Chapter 3: Chains of Reason

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