9 - Alethic modality
from Part 2 - Applications
Summary
Introduction
We shall consider three main topics in this chapter. They concern the use of modal logic to translate “possibility” and “necessity”, the GL model for the notion of proof, and the de dicto-de re distinction.
We begin with the application of modal logic to the notions of possibility and necessity, especially as they are expressed in ordinary language. It seems intuitively obvious that the formal notion of possible worlds should elucidate the notion of possibility and its close relative, necessity. But let the reader beware! Intuitive obviousness is sometimes misleading. Care is needed.
The S5 modal logic is often suggested as the system for logical possibility and necessity. If we are going to use S5 to assess the validity of arguments couched in English and containing possibility and necessity terms, then we need to know about the reliability of the S5 account of logical possibility and logical necessity. We have to consider the question of the relationship between S5 possibility and necessity, and the concepts of possibility and necessity embedded in ordinary English. So, without further ado we turn to the possibility and necessity terms of English.
Two kinds of possibility?
It has been suggested that there are two sorts of possibility embedded in ordinary English. First, there is a qualifiable possibility expressed by the phrase “possible for”. Second, there is a variable possibility expressed by the phrase “possible that”.
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- Modal Logics and Philosophy , pp. 139 - 150Publisher: Acumen PublishingPrint publication year: 2009