Priest (21.1) An Introduction to Non-Classical Logic, ‘Introduction [to ch.21, “Many-valued 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

 

21

Many-valued Logics

 

21.1

Introduction

 

 

 

 

Brief summary:

(21.1.1) We turn now to many-valued logics. (21.1.2) We examine many-valued quantification logics in general and later 3-valued logics in particular. (21.1.3) After that we turn to free versions of many-valued logics. (21.1.4) And afterward we examine identity in these logics. (21.1.5) We end with some discussion on supervaluation and subvaluation.

 

 

 

 

 

Contents

 

21.1.1

[Turning to Many-valued Quantification Logics]

 

21.1.2

[Looking Generally at Many-Valued Quantification Logics and to 3-Valued Ones in Particular]

 

21.1.3

[Free Many-Valued Quantification Logics]

 

21.1.4

[Identity]

 

21.1.5

[Super- and Sub- Valuation]

 

 

 

 

 

Summary

 

21.1.1

[Turning to Many-valued Quantification Logics]

 

[We turn now to many-valued logics.]

 

[(ditto)]

In this chapter we leave world-semantics for the time being, and turn to many-valued logics.

(456)

[contents]

 

 

 

 

 

 

21.1.2

[Looking Generally at Many-Valued Quantification Logics and to 3-Valued Ones in Particular]

 

[We examine many-valued quantification logics in general and later 3-valued logics in particular.]

 

[(ditto)]

We will start with a brief look at the general situation concerning many-valued logics, before turning to the special cases of the 3-valued logics of chapter 7 for more detailed consideration.

(456)

[contents]

 

 

 

 

 

 

21.1.3

[Free Many-Valued Quantification Logics]

 

[After that we turn to free versions of many-valued logics.]

 

[(ditto)]

Free versions of these logics are next on the agenda – in particular, now that we have the machinery of truth value gaps at our finger tips, the neutral free logics mentioned in 13.4.7. This will occasion a discussion of the behaviour of the existence predicate in a many-valued logic, and the question of whether it might make good philosophical sense for a statement of existence to have a non-classical value.

(456)

[contents]

 

 

 

 

 

 

21.1.4

[Identity]

 

[And afterward we examine identity in these logics.]

 

[(ditto)]

Next, we turn to the behaviour of identity in many-valued logics, and particularly the 3-valued logics of chapter 7. This will occasion a discussion of whether identity statements may plausibly be taken to have non-classical values.

(456)

[contents]

 

 

 

 

 

 

21.1.5

[Super- and Sub- Valuation]

 

[We end with some discussion on supervaluation and subvaluation.]

 

[(ditto)]

We will finish with a few comments on supervaluations and subvaluations in the context of quantificational logic.

(456)

[contents]

 

 

 

 

 

From:

 

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