Part 2   The Theory of Faith and Reason

Hirohumi Hoshika

Chapter 2 Faith and Reason as a Many-to-Many Relationship

Contents

Section 1	The Whole of "The Theory of Faith and Reason"
Section 2	Four Elements of the Christian Faith
Section 3	Five Categories of Methods of Reason
Easy study 1	"Correspondence Theory of Truth" and "Coherence Theory of Truth"
Easy study 2	Classical Deduction― Coherence Theory Application 1
2-1	Inference of Affirming the Antecedent
2-2	Truth Table
Easy study 3	Realism   ― Coherence Theory Application 2-1: Inference 1 of Affirming the Consequent
Easy study 4	Hermeneutics― Coherence Theory Application 2-2: Inference 2 of Affirming the Consequent
Easy study 5	Constructivism― Coherence Theory Application 3
5-1	Intuitionistic Logic
5-2-1	Intuitionistic Logic Semantics
Hard study 5-2-2	Inconsistency between "Rejection of Elimination Laws of Double Negation" and "SemanticsⅡ(5)"
5-2-3	Inconsistency between "Rejection of Excluded Middle" and "Semantics"
5-2-4	"Proof Table"
5-3-1	The World of Intuitionistic Logic as Seen in "Proof Table"
5-3-2	Resolution of the Inconsistency between Intuitionistic Logical Semantics and Syntax
5-3-3	The Strangeness of the Intuitionistic Logic that "A Proposition whose Negation cannot be Proven is Always Proven"
5-3-4	The Strangeness of the Intuitionistic Logic that "The Conclusion Changes depending on Whether the Proposition is Affirmative or Negative"
5-4-1	Intuitionistic Logic as a Solution to the Russell Paradox (Set ver.)
5-4-2	Intuitionistic Logic as a Solution to the Russell Paradox (Propositional Function ver.)
5-4-3	Intuitionistic Logic and Three-Valued Logic
5-4-4	The Semantic World of Intuitionistic Logic, "Knowledge History 01"
5-4-5	Knowledge History Analysis
5-5-1	TypeⅠProof Tables for the Kripke System
5-5-2	TypeⅠα Proof Table for Correctly Expressing Pre-linearity (A→B.∨.B→A)
5-5-3	TypeⅡProof Table for Correctly Expressing de Morgan's Laws (￢.Ａ∧Ｂ: → ￢Ａ∨￢Ｂ)
5-5-4	Heyting Algebra and Kripke Semantics
Easy study 6	Summary of Category of Method of Reason― Realistic Thought／Constructivistic Thought
6-1	Differences depending on Whether Introducing Assumptions is Allowed or not
6-2	Differences in Whether the Subject of Discussion is the World or Knowledge about the World
6-3	The Difference between Truth as being True or not, and Truth as being Provable or not
Section 4	Faith and Reason as a Many-to-Many Relationship
Notes

Summary

This chapter concretises the issue of the relationship between faith and reason to be discussed.

 

In the existing "The theory of Faith and Reason", faith and reason have always been treated as a one-to-one relationship. However, since both "faith" and "reason" are vague concepts, even if we directly confront faith with reason, we will only be able to state something vague.

 

It is difficult to clearly define what faith is and what reason is, but it is true that the Christian faith is made up of several creeds, and that, according to modern philosophy, there are not many ways to exercise reason but only a limited number of ways.

 

In this chapter, we consult the Westminster Confession of Faith for the content of orthodox faith and modern logic for the methods of reason, and from the two-dimensional table obtained by combining them, we extract the issues between faith and reason as a many-to-many relationship. It thereby shows what and how it should be discussed as the argument of faith and reason.

 

The resulting “Many-to-Many Correspondence Table of Faith and Reason” (Section 4) serves as an overview of the entire treatise.

 

The discussion in this chapter includes a "Hard study" that further explores the understanding of the concept of negation in intuitionistic logic as introduced in Shigeki Noya's "Ronrigaku [Logic]", and this part is more difficult than the other parts.

Reading Difficulty Level ★★★★★ Word count 187,000 words