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Empirical & Deductive REASon       Back ] Home ] Up ]

Chapter 3. Chains of Reason

Previous Section: Linking and Chaining

Deductive, Inductive or Empirical

Deductive reason uses or chains together supposedly (or preferably) never-disobeyed implication rules to suggest, to make or to reach conclusions. See the examples above. The implication rules in question may come from assumptions. The assumptions may be tentative.

The phrase inductive reason has one role in mathematics and another outside of mathematics. To induce (or induct) literally means to draw or extract. When you see a rule or pattern that no one has suggested, you are extracting or drawing that pattern from your observations. This process of recognizing rules and patterns that may hold, accidentally or not, is called inductive reasoning. Inductive reason outside of mathematics refers to the identification and recognition of rules and patterns from data and observations. Here rules and patterns may hold accidentally.

Reason which relies on a single or several, experience-found, rules and patterns to arrive at conclusions is called empirical. The underlying problem of inductive, empirical reason is to extract (infer, draw, induct or identify) from experience, in particular, data and observations, rules and patterns not satisfied merely by accident and which appear to be reliable. Self-deception needs to be avoided here.

Inductive reason inside mathematics refers to another process, namely, the extraction or drawing of conclusions from ladder-like chains of reason. See the next chapter for a more precise image or explanation. The rules or assumptions here are usually so certain, that we deliberately ignore the experience-based origins of mathematical reason.

 

Next Chapter: Longer Chains of Reason, mathematical induction

 

Three Skills
For 
Algebra

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

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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