## 16 Apr 2018

### Priest (10.1) An Introduction to Non-Classical Logic, ‘Introduction [to ch.10 “Relevant Logics”], summary

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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

10.

Relevant Logics

10.1

Introduction

Brief summary:

(10.1.1) In this chapter Priest will introduce relevant logics, which “are obtained by employing a ternary relation to formulate the truth conditions of →” and which can be made stronger by adding constraints to that ternary relation. (10.1.2) Also we will combine relevant semantics with the semantics of conditional logics “to give an account of ceteris paribus enthymemes” (188).

Contents

10.1.1

[Relevant Logics and Their Ternary Relation and Its Constraints]

10.1.2

[Combining Relevant and Conditional Semantics to Account for Ceteris Paribus Enthymemes]

Summary

10.1.1

[Relevant Logics and Their Ternary Relation and Its Constraints]

[In this chapter Priest will introduce relevant logics, which “are obtained by employing a ternary relation to formulate the truth conditions of →” and which can be made stronger by adding constraints to that ternary relation.]

In this chapter Priest will introduce us to relevant logics. He says that “These are obtained by employing a ternary relation to formulate the truth conditions of →” (188). Although the most basic relevant logic does not have any constraints on this ternary relation, stronger relevant logics can be obtained by adding constraints. [I am not certain, but a “stronger” system might mean that it has more valid formulas. But I could be completely wrong, sorry. See section 4.4.4 for more discussion.]

In this chapter we look at logics in the family of mainstream relevant logics. These are obtained by employing a ternary relation to formulate the truth conditions of →. In the most basic logic, there are no constraints on the relation. Stronger logics are obtained by adding constraints.

(188)

[contents]

10.1.2

[Combining Relevant and Conditional Semantics to Account for Ceteris Paribus Enthymemes]

[Also we will combine relevant semantics with the semantics of conditional logics “to give an account of ceteris paribus enthymemes” (188).]

[As I have not yet summarized anything from chapter 5, I will need to simply quote the next lines.]

We also see how these semantics can be combined with the semantics of conditional logics of chapter 5 to give an account of ceteris paribus enthymemes.

(188)

[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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