Introduction
Chapter 1 

Previous: Three Remarks

To reason often means to persuade someone of the need for an idea or action. That someone could be yourself. In the latter case, reasoning may mean following a line or pattern of thought to arrive at a conclusion, action or decision.

Persuasion or reason can take many forms. There are fair and unfair ways of persuasion. There are sensible and absurd ways as well. Methods for arriving at conclusions and judgments in all disciplines are, or should be where possible, based on the use and recognition of reliable rules and patterns. Where ever there is a presentation of ideas, there is an element of reason or persuasion.

Reason and persuasion are met in the home, in the print and television media, in the classroom and in the work place. Rule-based reasoning, that is logic, and departures from it can be described in and outside of mathematics. The recognition of rules and patterns, methods with repeatable, reproducible and thus verifiable results, provides a basis for science, technology and even accounting.

The first chapters on reason give two logic puzzles to show how rules and patterns can be used to arrive at conclusions or judgments in all subjects, mathematical or not. Logos is the Greek word for thought. The puzzles show the need and so reinforce the ability to precisely read and understand the statements of rules, patterns, instructions and definitions. The two logic puzzles in particular show the difference between one- and two-way implication rules

A one-way implication rule says that when one event occurs, so should another. A two-way implication rule says that when either of two events occurs then so must the other. The terminology of one-way and two-way implication rules may be new to this book. It is a plain language replacement for the more traditional phrasing which speaks of conditional and bi-conditional statements.

Not seeing the difference between one- and two-way implications or suggestions is a source of confusion and false expectations in everyday life, contracts, instructions and technical areas. Recognizing the difference between one-way and two-way rules gives an initial step in mastering rule- and pattern-based thought. Seeing how reliable rules and patterns can be used one-at-a-time or one after each other to arrive at conclusions gives another step.

In mathematics courses, logic is often met as the algebraic or symbolic description and analysis of rule and pattern-based methods used in the discipline (math) for arriving at conclusions. Some rule and pattern reasoning methods developed in response to the conclusion reaching needs of mathematics.

The last chapters in this work introduce the algebraic or symbolic description of logic while leading to an explanation of direct and indirect methods of reason. The description innovatively employs the simple notions of a rule being obeyed, disobeyed or not disobeyed, or never disobeyed to clarify the technical truth-table description of one-way (material) implications. The very last chapter describes the direct and indirect chains of reason and persuasion met in mathematical proofs. Indirect methods are also of service perhaps in the writing and resolution of detective and mystery stories.

In all fields of endeavor and inquiry, the main obstacles to the use of reliable rules and patterns for arriving at conclusions lie first in their identification and second in the identification of reliable information to use with them. To understand or cope with these obstacles, a knowledge is required of the origins of rules and patterns in daily life as well as in science and technology. Science, engineering and technology have empirical, that is experience-based methods, for coping with or circumventing the two obstacles. Here rules, patterns and procedures which give repeatable and reproducible results appear to be the most reliable or trustworthy, although not always optimal. Some rules and patterns appear to be more reliable or secure than others, but not all is certain. 

Next: Chapter 2, Communication of Ideas and Skills

www.whyslopes.com
Volume 1A, Pattern Based Reason

 Chapters 1 to 24

FOREWORD
Three Remarks
1 Introduction
2 Communication
3. Elements of Reason
4 Implication Rules
5. Deception
6 Chains of Reason
7 Longer Chains
For & From Consistency
8. Language Change
9 Next Chapters
10 Responsibility
11 Accidental Patterns
12 Knowledge Islands
13 Euclidean Logic
14 Deductive & Empirical 
     Views of Mathematics
15 Objectivity
16 Origin of Rules
and Patterns
17 Objective Ways
18. Waking up
19. Symbols  & Logic
20. Pronouns or Symbols
21. Truth Tables I.
22. Truth Tables II
22. Biconditional
22. Contrapositive
23. IF-THEN table
24. Indirect Reason Again

To reason often means to persuade someone of the need for an idea or action. That someone could be yourself. So be careful.

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
+Three Remarks
+History Lost or Missing

There is a difference between
knowing how to spend money,
and having money to spend.

There is likewise a difference
between mastering a skill
and having meeting a situation in which it applies.

 .

[Page Top] [ Back ] [ Area Intro ] [ Next ] 
If you find an error, please cut and paste its  web page location (URL) into an Email

Wordy Site Tour:  Not too Bad ,  Vol 2. Foreword,  1A Foreword,  2  Logic Puzzles,  
What is a Variable  Calculus Starter Guide  Vol 1 Foreword,    
 
Favourite Sites:  The World Clock - Time Zones Around the World  
 BBC News  and mathematics portion of  English National Curriculum  

All trademarks and copyrights on this page are owned by their respective owners.
Copyright to comments & contributions are owned by the Poster. 
The Rest © 1995 onward by site author,   Alan Selby
All Rights Reserved.