Priest (9.1) An Introduction to Non-Classical Logic, ‘Introduction [to ch.9, “Logics with Gaps, Gluts and Worlds”],’ summary

 

by Corry Shores

 

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[The following is summary of Priest’s text, which is already written with maximum efficiency. Bracketed commentary and boldface are my own, unless otherwise noted. I do not have specialized training in this field, so please trust the original text over my summarization. I apologize for my typos and other unfortunate mistakes, because I have not finished proofreading, and I also have not finished learning all the basics of these logics.]

 

 

 

 

Summary of

 

Graham Priest

 

An Introduction to Non-Classical Logic: From If to Is

 

Part I:

Propositional Logic

 

9.

Logics with Gaps, Gluts and Worlds

 

9.1

Introduction

 

 

 

 

Brief summary:

(9.1.1) In this chapter we will examine ways that we can combine the techniques of both modal logic and many-valued logic, especially with logics that involve strict conditional world semantics and First Degree Entailment. (9.1.2) We will also further elaborate on the notion of non-normal worlds. (9.1.3) At the end of this chapter we will examine logics of constructible negation and connexive logics.

 

 

 

 

 

 

 

Contents

 

9.1.1

[Combining Many-Valued Logic and Modal Logic]

 

9.1.2

[Non-Normal Worlds]

 

9.1.3

[Logics of Constructible Negation and Connexive Logics]

 

 

 

 

 

 

Summary

 

9.1.1

[Combining Many-Valued Logic and Modal Logic]

 

[In this chapter we will examine ways that we can combine the techniques of both modal logic and many-valued logic, especially with logics that involve strict conditional world semantics and First Degree Entailment.]

 

[Priest says that:]

In this chapter, we will see how the techniques of modal logic and many-valued logic can be combined. More specifically, we will look at logics that add some kind of strict conditional with world semantics on top of a many-valued base-logic, specifically, FDE.¹

(163)

1. The most obvious combination of the two techniques is in the construction of simple many-valued modal logics. Since this material breaks the main sequence of development of the book, I cover it in the appendix, chapter 11a.

(163)

[contents]

 

 

 

 

9.1.2

[Non-Normal Worlds]

 

[We will also further elaborate on the notion of non-normal worlds.]

 

[Recall from chapter 4 how we discussed non-normal worlds modal logic semantics (N instead of K logics.) Priest says now that we return to the topic of non-normal worlds, along with the relevant logics involved. This will enable us to further discuss the nature of non-normal worlds.]

The non-normal worlds of chapter 4 will also make a reappearance, giving us some basic relevant logics. This will allow us to discuss further what, exactly, non-normal worlds are.

(163)

[contents]

 

 

 

 

9.1.3

[Logics of Constructible Negation and Connexive Logics]

 

[At the end of this chapter we will examine logics of constructible negation and connexive logics.]

 

[Priest lastly notes that:]

We will end the chapter with a brief look at so called logics of constructible negation, which have close connections with intuitionist logic; and an even briefer look at connexive logics.

(163)

[contents]

 

 

 

 

 

 

From:

 

Priest, Graham. 2008 [2001]. An Introduction to Non-Classical Logic: From If to Is, 2nd edn. Cambridge: Cambridge University.

 

 

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