Priest (13.1) An Introduction to Non-Classical Logic, ‘Introduction [to ch.13: Free Logics],’ 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 II:

Quantification and Identity

 

13.

Free Logics

 

13.1

Introduction

 

 

 

 

Brief summary:

(13.1.1) “The family of free logics is a family of systems of logic that dispense with a number of the existential assumptions of classical logic” (290). (13.1.2) We will examine the semantics of free logics and their tableau systems too. (13.1.3) We will also discuss philosophical questions regarding free logics and existence. (13.1.4) For most of the chapter, we do not include the identity predicate, but we add it at the end to see what happens.

 

 

 

 

 

 

Contents

 

13.1.1

[The Nature of Free Logics]

 

13.1.2

[Semantics and Tableaux for Free Logics]

 

13.1.3

[Existence and Free Logics]

 

13.1.4

[Excluding and Adding the Identity Predicate]

 

 

 

 

 

 

Summary

 

13.1.1

[The Nature of Free Logics]

 

[“The family of free logics is a family of systems of logic that dispense with a number of the existential assumptions of classical logic” (290).]

 

[(ditto)]

The family of free logics is a family of systems of logic that dispense with a number of the existential assumptions of classical logic.

(290)

[contents]

 

 

 

 

 

 

13.1.2

[Semantics and Tableaux for Free Logics]

 

[We will examine the semantics of free logics and their tableau systems too.]

 

[(ditto)]

In this chapter, we will look at the semantics of, and tableau systems for, various free logics.

(290)

[contents]

 

 

 

 

 

 

13.1.3

[Existence and Free Logics]

 

[We will also discuss philosophical questions regarding free logics and existence.]

 

[(ditto)]

We will then discuss how these logics handle some issues concerning existence.

(290)

[contents]

 

 

 

 

 

 

13.1.4

[Excluding and Adding the Identity Predicate]

 

[For most of the chapter, we do not include the identity predicate, but we add it at the end to see what happens.]

 

[(ditto)]

Until further notice, we assume that the language does not contain the identity predicate. In the final part of the chapter, we will see how its addition affects matters.

(290)

[contents]

 

 

 

 

 

 

 

From:

 

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