Logical Foundations of Induction

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Logical Foundations of Induction Author:
Translator: M.F. Zidan
Publisher: www.introducingislam.org
Category: Islamic Philosophy

Logical Foundations of Induction

This book is corrected and edited by Al-Hassanain (p) Institue for Islamic Heritage and Thought

Author: Ayatullah Muhammad Baqir as-Sadr
Translator: M.F. Zidan
Publisher: www.introducingislam.org
Category: visits: 6271
Download: 1332

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Logical Foundations of Induction

Logical Foundations of Induction

Author:
Publisher: www.introducingislam.org
English

This book is corrected and edited by Al-Hassanain (p) Institue for Islamic Heritage and Thought

Alhassanain (p) Network for Islamic Heritage and Thought

Logical Foundations of Induction

(Al-usus al-mantiqiyyah li'l-istiqra ')

MuhammadBaqir As-Sadr

Translated by M.F.Zidan

www.alhassanain.org/english

Table of Contents

Preface to Online Version 6

Introduction 7

The logical foundations of Induction 7

Induction 9

Part 1: Induction and Epistemology 9

Chapter 1: Aristotelian Induction 9

Meanings of Induction 9

Aristotle's perfect induction 9

Criticism of perfect induction 10

Recapitulation 11

Aristotle's imperfect induction 11

The Problem of induction 11

Formal logic and the problem 12

Misunderstanding of formal logic 13

Aristotelian epistemology and induction 13

Formal logic and chance 14

Need of definite formulation 15

The crucial point of difference 15

Chapter 2: Criticism of Aristotelian Induction 17

Indefinite Knowledge 17

Genesis of indefinite Knowledge 17

Aristotelian principle and indefinite knowledge 18

First Objection 18

Second objection 19

Third Objection 19

Fourth Objection 20

Fifth Objection 21

Sixth Objection 21

Seventh Objection 22

Chapter 3: Induction And Empiricism 23

Certainty Attitude 23

On the First and Third Questions 23

Discussion 24

On the second question 24

Answer to that question 24

Probability Attitude 26

Discussions 27

Psychological Attitude 28

Examination of psychological attitude 30

(1) Belief 30

(2) Causality and Reason 31

(3) Causality and Experience 32

(4) Concept of Causality 32

(5) Belief in causality 33

Physiological Explanation of Induction 35

Part 2: Induction And Probability 36

Chapter 1: Calculus of Probability 36

Introduction 36

Axioms of the theory 36

Rules of the Calculus 37

Bernoulli's law of large numbers 38

Chapter 2: The Interpretation of Probability 40

(A) Fundamental Definition 40

The First problem 40

The Second Problem 41

(B) Probability in the Finite Frequency Theory 42

Real and Hypothetical Probabilities 42

New Definition of Probability 44

A. The axioms of the new definition 45

Difficulties of our definition 46

The new definition and the calculus 47

The new definition and inverse probability 47

The definition and the Bags - example 47

Our definition and Bernoulli's law 47

The first example 48

The second example 48

Completeness of our definition 48

New axioms 49

Ground of Dominance Axiom 50

Categorical and Hypothetical indefinite knowledge 50

Conditional knowledge that is real 51

Recapitulation 52

Chapter 3: The Deductive Phase Of Induction 53

Causality 53

First Application 54

Rule of multiplication 54

Application of Dominance Axiom 55

Dominance and the problem of a priori probability 56

Second Application 56

The absence of effect does not occur in both cases 56

Third Application 57

Multiplication or dominance 58

Hypothetical Knowledge And Empirical Causality 58

Fourth Application 59

Chapter 4: Modern Theories of Probability 61

Difficulties of Laplace's theory 62

Keynes and Induction 64

Difficulties of Keynes' Interpretation 65

Causal Relations 66

Logical Justification 66

Philosophical justification 67

Scientific Justification 67

Tactical Justification 67

Another Form of Deductive Phase 68

Requirements of the deductive phase 69

Induction and formal logic 69

Chapter 5: Induction and Certainty 71

Subjective Role in Certainty 71

Kinds of certainty 71

Objective certainty require[s] an axiom 72

The formulation of the postulate 73

Conditions of the Postulate 74

The first form of the postulate 74

Objections and Answers 77

1. Is causality a term in indefinite Knowledge 77

2. Attempt to deny our knowledge of causality 77

3. Misapplication of inductive postulate 78

4. Indefinite Probability 79

The Second Form of the Postulate 80

Reformulation of Aristotle's principle 82

Discussion 84

Objection and Answer 85

Part 3: Human Knowledge And Probability 87

Chapter 1: Classes of Statements 87

Principles of demonstration 87

Principles of other forms of inference 87

Universal empirical statements 89

Intuitive statements 90

Testimonial statements 90

Testimonial statements and a priori probability 92

Solution of the Problem 93

Belief in rational agent 95

Inductive proof of God's existence 95

(3) or by virtue of an unwise maker having non-purposive actions 96

Basic Empirical Statements 99

Inductive ways concerning the first formulation 100

Inductive ways concerning the second formulation 101

Our knowledge of the external world is inductive 103

Belief in the conditions of perception is inductive 103

Resemblance between percepts and realities 104

Beliefs in resemblances of particulars 105

Recapitulation 106

Primitive and innate statements 106

Exceptions 107

Differences between primitive and inductive statements 107

Induction and mathematical statements 108

Chapter 2: Is There A priori Knowledge? 110

Empirical Statements 110

Formal Statements 110

Logical Positivism 112

Criticism 113

Empiricism and Meaning of Statements 114

Reichenbach's Position 116

Russell's Objection 116

Discussion 116

CONCLUSION 118

Notes 119

Preface to Online Version

The basic thesis of this book is that the same logic of induction on which scientific methodology is based can be used to prove the existence of God. The implication of this work is far reaching, for it attempts to layout a unifying, common basis of research in religion, social sciences, and natural sciences.“Our Philosophy” and“The Revealer,The Messenger, and the Message” , the two other books by the same author, are very relevant in this regard and useful for a wider understanding of author's thesis. It is suggested that those readers who wish to read this book in search of only a theistic argument on the existence of God may first want to check the second of the abovementioned books; because that book is written specifically with that purpose in mind. The author himself says in one of the chapters of that book that he has avoided“difficult and complicated constructions and analyses not readily accessible to the average reader” in that book.

As for the present book, as the introduction by the translator testifies, this book is a valuable contribution to philosophy and methodology of science, the probability theory, and theistic argument in support of the existence of God. Given the complexity of argument in this book, the translator’s efforts are commendable. Still, at places, one finds the translation to be lacking. At other times, there are typos. We have tried to correct them (in red marks) in the text as much as possible. (The words in plain red are typos we were certain about, hence we corrected them. The words in brackets are mistakes we were not very sure about. At places we have added some ideas from other works by the same author to make it more accessible. The brackets with [x__] means that text inside was what was there when we scanned the book, but we were not sure about it, so we suggest alternative outside the bracket and quote the original in the [x__] for reader's reference.) We hope that you will find this book useful for your academic pursuit.

Introduction

The logical foundations of Induction

Reading through the history of human thought, it is found that inference which man employs in his intellectual and practical life is mainly divided into deduction and induction. Each of which is distinct in nature and procedure.

In deduction, the conclusion never surpasses the premises; the conclusion is either less than or equal to what is asserted in the premises. Thus, the conclusion is necessarily true if its premises are true; the conclusion, in deduction, follows from its premises by virtue of the principle of non-contradiction.

But, in induction, the conclusion has more in it than what is presented in the premises. The conclusion is not inferred deductively. The procedure in induction is contrary to that made in syllogism.The latter moves from general to particular while the former moves from particular to general. Such move from particular to general cannot have the principle of non-contradiction as its basis, as we can assume the premises to be true and the conclusion false without falling into contradiction. Hence, the principle of non-contradiction does not justify inductive conclusions but leads to a gap when proceeding from particular to general.

In this book, we try to present a reformulation of the theory of knowledge in a scientific, philosophical and objective manner based on the theory of probability so as to fill the gap in the intellectual march of man.

Professor As-Sadr tries in the first chapters of the book to present a critical exposition of rationalism represented in Aristotelian logic based on induction. The Aristotelian logic proves inefficient in filling the gap. Professor As-Sadr moves on to a thorough exposition of the empirical theory with its different trends and its method in bridging the gap. Further, he points out the inefficiency of such logic, being unable to present a substantial explanation that can embrace the inductive proof.

The rest of the book tackles the grounds and principles of the theory of probability with a reformulation of it. Professor As-Sadr successfully presents the theory as a basis for inductive proof. Finally, the eminent Muslim jurist tries to display the domains of human knowledge based on deduction and tries to interpret such knowledge in the same manner as that based on induction. Hence, he crowned his great efforts, sound thinking and broadmindedness in proving through clear evidence that the logical grounds of all scientific inference derived from observation and experiment are the same logical grounds proving the Maker of this universe; a universe abounding in signs of wisdom and sagacity, his inference is inductive by nature and in its implementation of the general way required for the inductive proof in its two phases.

With this logical proof, man faces two confusing alternatives: either to reject the scientific inference as a whole or to accept it and give the inductive inference proving the Maker the same weight as the scientific one.

Through such an objective, scientific method, Professor As-Sadr proves that science and faith are interrelated in their logical and inductive grounds. Hence, we can never separate between both of them in light of the logical standpoint of induction.

Hence, the eminent professor sets the logical rules or empirical proof on the existence of God after expounding the logical correlation between scientific inference and the inductive method to reveal the signs of wisdom and sagacity, hence, the existence of the Maker, We can say that the Muslim thinker, Mohammed As-Sadr , in his book“The logical Foundations of Induction” , opens a new horizon breaking the barriers between the modern scientific method and the postulates of the cultural history to the Muslim thinkers, Professor As-Sadr probed deep into the world of research, mastering his tools, armed with natural science. The professor refuted the pretext with another; the proof with another, enjoying a profound understanding of the western thinking.

“The logical Foundations of Induction” has, thus, crowned all the professor's efforts in the field of intellectual creativity. Professor As-Sadr is considered one of the few thinkers who probed deep into this sophisticated scientific and philosophical domain tackling one of the most serious problems in the philosophy of science and the contemporary scientific method.

Regrettably, the author, though an eminent thinker with authentic, creative concepts and with an invaluable method covering scientific, cultural and religious values, has never enjoyed the glamour he deserves.This book, though one of the author's greatest studies, has never enjoyed due attention whether through translation to other languages or research and studies conducted on such a prolific author's creative work.

Finally, trying to introduce the book of such a great jurist and eminent thinker as Professor As-Sadr , may God bless him, is no easy task. It is an onerous task as the Professor enjoyed broadmindedness and was highly acquainted, with scientific, juristic and ideological knowledge. I hesitated a lot due to the prominent stand of Professor As-Sadr and the grandeur of this book, scientifically and philosophically. I only accepted thishonourable task after the insistence of the publisher and those concerned in this sphere. I accepted such a great responsibility which is considered anhonour . I ask Almighty God to help mefulfil such a task and to be up to the responsibility.

Dr.Ghafer Abbass Hagi

Professor of Islamic Economics

Kuwait University