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by Corry Shores
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[Logic and Semantics, entry directory]
[Graham Priest, entry directory]
[Priest, Introduction to Non-Classical Logic, entry directory]
[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
14.
Constant Domain Modal Logics
14.1
Introduction
Brief summary:
(14.1.1) We will examine quantified normal modal logics, of which there are two kinds: {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). (14.1.2) “If S is any system of propositional modal logic, CS will denote the constant domain quantified version, and VS will denote the variable domain quantified version” (308). (14.1.3) Here we just examine the semantics and tableaux for constant domain logics, and in the next chapter we do those for variable domain logics. (14.1.4) We exclude identity from our language for now, but we return to it in chapter 16. (14.1.5) We will also examine essentialism. (14.1.6) We lastly expand to tense logic.
[Two Kinds of Quantified Normal Modal Logics]
[Notating the Systems]
[Constant Domain for Now]
[Postponing Identity]
[Essentialism]
[Tense Logic]
Summary
[Two Kinds of Quantified Normal Modal Logics]
[We will examine quantified normal modal logics, of which there are two kinds: {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).]
[(ditto)]
In this chapter we will start to look at quantified normal modal logics. These come in two varieties: constant domain (where the domain of quantification is the same in all worlds), and variable domain (where the domain may vary from world to world).
(308)
[Notating the Systems]
[“If S is any system of propositional modal logic, CS will denote the constant domain quantified version, and VS will denote the variable domain quantified version” (308).]
[(ditto)]
Where it is necessary to distinguish between the two, I will use the following notation. If S is any system of propositional modal logic, CS will denote the constant domain quantified version, and VS will denote the variable domain quantified version.
(308)
[Constant Domain for Now]
[Here we just examine the semantics and tableaux for constant domain logics, and in the next chapter we do those for variable domain logics.]
[(ditto)]
In this chapter we will look at the semantics and tableaux for constant domain logics, saving variable domains for the next.
(308)
[Postponing Identity]
[We exclude identity from our language for now, but we return to it in chapter 16.]
[(ditto)]
For these two chapters we will take it that identity is not part of the language. We will turn to the topic of identity in modal logic in chapter 16.
(308)
[Essentialism]
[We will also examine essentialism.]
[(ditto)]
We will also take a quick look at one of the major philosophical issues to which quantified modal logic gives rise: the issue of essentialism.
(308)
[Tense Logic]
[We lastly expand to tense logic.]
[(ditto)]
The chapter ends by showing how the semantic and tableau techniques of normal modal logic extend to tense logic.
(308)
From:
Priest, Graham. 2008 [2001]. An Introduction to Non-Classical Logic: From If to Is, 2nd edn. Cambridge: Cambridge University.
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