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: Second Logic Puzzle

One Versus Two Way Implications

The two puzzles give examples of implication rules. The first puzzle gives a one-way implication rule, while the second gives a two-way implication rule. The following words should further help you to see the difference between one- and two-way implication rules. Seeing this difference may help you understand better the answers to the above questions. They may also help you answer the five questions again using the two-way implication rule.

1. A one-way implication rule says that when a first situation occurs, so must a second. It does not say that when the second occurs so must the first. The second situation may occur without the first.
2. A two-way implication rule says that
   1. when a first situation occurs, so must a second, and
   2. when the second situation occurs, so must the first.

   A two-way rule says that when each situation occurs, so must the other. Therefore if the two-way rule is to be obeyed, when one situation does not occur, neither can the other. 

Seeing or recognizing the difference between one- and two-way implication rules makes you a more careful thinker.

One- and two-way rules, recognized or not, are what we use to reach conclusions or make judgments. One and two-way rules can be used to suggest or persuade us of what needs to be done or avoided.

Talking About Logic

As suggested above, you can give people the above rules or similar ones before asking five questions. Before you do this, you should wait for a receptive mood, especially if you are not in a classroom. For the sake of an argument and some fun, you may ask after getting an answer, are you sure? Or you may pretend a correct answer is wrong. Of course, you will admit this ruse later, and explain why you really agree (or disagree) with the answers. The aim is to see how people reason and more importantly to strengthen their thinking skills.

Logic is supposed to give rules for thought, that is rules for arriving at conclusions. Yet the only rule needed in the reasoning shown above is as follows: Read exactly what is written and don't assume nor imagine too much.

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?

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

Next Section:  Implications versus Suggestions

Next Chapter: Chains of Reason - Euclidean Model for Reason

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