Alhassanain(p) Network for Heritage and Islamic Thought

Logical Foundations of Induction

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

• Preface to Online Version
• Introduction
• The logical foundations of Induction
• Induction
• Part 1: Induction and Epistemology
• Chapter 1: Aristotelian Induction
• Meanings of Induction
• Aristotle's perfect induction
• Criticism of perfect induction
• Recapitulation
• Aristotle's imperfect induction
• The Problem of induction
• Formal logic and the problem
• Misunderstanding of formal logic
• Aristotelian epistemology and induction
• Formal logic and chance
• Need of definite formulation
• The crucial point of difference
• Chapter 2: Criticism of Aristotelian Induction
• Indefinite Knowledge
• Genesis of indefinite Knowledge
• Aristotelian principle and indefinite knowledge
• First Objection
• Second objection
• Third Objection
• Fourth Objection
• Fifth Objection
• Sixth Objection
• Seventh Objection
• Chapter 3: Induction And Empiricism
• Certainty Attitude
• On the First and Third Questions
• Discussion
• On the second question
• Answer to that question
• Probability Attitude
• Discussions
• Psychological Attitude
• Examination of psychological attitude
• (1) Belief
• (2) Causality and Reason
• (3) Causality and Experience
• (4) Concept of Causality
• (5) Belief in causality
• Physiological Explanation of Induction
• Part 2: Induction And Probability
• Chapter 1: Calculus of Probability
• Introduction
• Axioms of the theory
• Rules of the Calculus
• Bernoulli's law of large numbers
• Chapter 2: The Interpretation of Probability
• (A) Fundamental Definition
• The First problem
• The Second Problem
• (B) Probability in the Finite Frequency Theory
• Real and Hypothetical Probabilities
• New Definition of Probability
• A. The axioms of the new definition
• Difficulties of our definition
• The new definition and the calculus
• The new definition and inverse probability
• The definition and the Bags - example
• Our definition and Bernoulli's law
• The first example
• The second example
• Completeness of our definition
• New axioms
• Ground of Dominance Axiom
• Categorical and Hypothetical indefinite knowledge
• Conditional knowledge that is real
• Recapitulation
• Chapter 3: The Deductive Phase Of Induction
• Causality
• First Application
• Rule of multiplication
• Application of Dominance Axiom
• Dominance and the problem of a priori probability
• Second Application
• The absence of effect does not occur in both cases
• Third Application
• Multiplication or dominance
• Hypothetical Knowledge And Empirical Causality
• Fourth Application
• Chapter 4: Modern Theories of Probability
• Difficulties of Laplace's theory
• Keynes and Induction
• Difficulties of Keynes' Interpretation
• Causal Relations
• Logical Justification
• Philosophical justification
• Scientific Justification
• Tactical Justification
• Another Form of Deductive Phase
• Requirements of the deductive phase
• Induction and formal logic
• Chapter 5: Induction and Certainty
• Subjective Role in Certainty
• Kinds of certainty
• Objective certainty require[s] an axiom
• The formulation of the postulate
• Conditions of the Postulate
• The first form of the postulate
• Objections and Answers
• 1. Is causality a term in indefinite Knowledge
• 2. Attempt to deny our knowledge of causality
• 3. Misapplication of inductive postulate
• 4. Indefinite Probability
• The Second Form of the Postulate
• Reformulation of Aristotle's principle
• Discussion
• Objection and Answer
• Part 3: Human Knowledge And Probability
• Chapter 1: Classes of Statements
• Principles of demonstration
• Principles of other forms of inference
• Universal empirical statements
• Intuitive statements
• Testimonial statements
• Testimonial statements and a priori probability
• Solution of the Problem
• Belief in rational agent
• Inductive proof of God's existence
• (3) or by virtue of an unwise maker having non-purposive actions
• Basic Empirical Statements
• Inductive ways concerning the first formulation
• Inductive ways concerning the second formulation
• Our knowledge of the external world is inductive
• Belief in the conditions of perception is inductive
• Resemblance between percepts and realities
• Beliefs in resemblances of particulars
• Recapitulation
• Primitive and innate statements
• Exceptions
• Differences between primitive and inductive statements
• Induction and mathematical statements
• Chapter 2: Is There A priori Knowledge?
• Empirical Statements
• Formal Statements
• Logical Positivism
• Criticism
• Empiricism and Meaning of Statements
• Reichenbach's Position
• Russell's Objection
• Discussion
• CONCLUSION
• Notes