Priest (15.1) An Introduction to Non-Classical Logic, ‘Introduction [to ch.15, “Variable Domain Modal 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

 

15.

Variable Domain Modal Logics

 

15.1

Introduction

 

 

 

 

Brief summary:

(15.1.1) We turn now to variable domain quantified normal logics. (15.1.2) “We will start with K and its normal extensions. Next we observe how matters can be extended to tense logic” (329). (15.1.3) “There are then some comments on other extensions of the logics involved.” (329). (15.1.4) “The chapter ends with a brief discussion of two major philosophical issues that variable domain semantics throw into prominence: the question of existence across worlds, and the connection (or lack thereof) between existence and the particular quantifier” (329).

 

 

 

 

 

 

Contents

 

15.1.1

[Turning to Variable Domain Quantified Normal Modal Logics]

 

15.1.2

[K, Its Extensions, and Tense Logic]

 

15.1.3

[On Extensions of These Logics]

 

15.1.4

[Existence Across Worlds and the Connection Between Existence and the Particular Quantifier]

 

 

 

 

 

 

Summary

 

15.1.1

[Turning to Variable Domain Quantified Normal Modal Logics]

 

[We turn now to variable domain quantified normal logics.]

 

[Recall from section 14.1.1 that there two kinds of quantified normal modal logics: {1} constant domain quantified normal modal logics, in which “the domain of quantification is the same in all worlds”, and {2} variable domain quantified normal modal logics, in which “the domain may vary from world to world” (308). We will now look at variable domain quantified normal logics.]

In this chapter we will look at the other variety of semantics for quantified modal (and tense) logic: variable domain.

(329)

[contents]

 

 

 

 

 

 

15.1.2

[K, Its Extensions, and Tense Logic]

 

[“We will start with K and its normal extensions. Next we observe how matters can be extended to tense logic” (329).]

 

[(ditto)]

We will start with K and its normal extensions. Next we observe how matters can be extended to tense logic.

(329)

[contents]

 

 

 

 

 

 

15.1.3

[On Extensions of These Logics]

 

[“There are then some comments on other extensions of the logics involved.” (329).]

 

[(ditto)]

There are then some comments on other extensions of the logics involved.

(329)

[contents]

 

 

 

 

 

 

15.1.4

[Existence Across Worlds and the Connection Between Existence and the Particular Quantifier]

 

[“The chapter ends with a brief discussion of two major philosophical issues that variable domain semantics throw into prominence: the question of existence across worlds, and the connection (or lack thereof) between existence and the particular quantifier” (329).]

 

[(ditto)]

The chapter ends with a brief discussion of two major philosophical issues that variable domain semantics throw into prominence: the question of existence across worlds, and the connection (or lack thereof) between existence and the particular quantifier.

(329)

[contents]

 

 

 

 

 

 

 

 

From:

 

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