## 15 Jul 2017

### Priest (2.2) An Introduction to Non-Classical Logic, ‘Necessity and Possibility’, 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 distracting mistakes, because I have not finished proofreading.]

Summary of

Graham Priest

An Introduction to Non-Classical Logic: From If to Is

2. Basic Modal Logic

2.2. Necessity and Possibility

Brief summary:

Modal logic deals with “the modes in which things may be true/false.” Such modes include possibility, necessity and impossibility. Modal semantics can employ the concept of possible worlds, which may be understood provisionally as a world situation that is a variation on our own, with it having slightly (or remarkably) different features. One world is possible relative to another if for example the one could actually become an outcome of the other.

Summary

2.2.1

[Modal logic is concerned with “the modes in which things may be true/false” and this includes such modalities as possibility, necessity and impossibility.]

We will examine modal logic. It “concerns itself with the modes in which things may be true/false, particularly their possibility, necessity and impossibility” (20). Priest notes that these notions are “highly ambiguous,” but we discuss that issue in chapter 3 (20).

2.2.2

[A possible world can be thought of provisionally as our world with slightly different features.]

We will examine semantics for modal logics, and these semantics “employ the notion of a possible world.” Although we elaborate this notion later, Priest offers a basic account now. A possible world can be provisionally understood by imagining our world with slightly different features.

We can all imagine that things might have been different. For example, you can imagine that things are exactly the same, except that you are a centimetre taller. What you are imagining here is a different situation, or possible world. Of course, the actual world is a possible world too, and there are indefinitely many others as well, where you are two centimetres taller, three centimetres taller, where you have a different colour hair, where you were born in another country, and so on.

(20)

2.2.3

[Possible worlds can have relations of relative possibility to one another. For example, a  possible future world situation that can actually follow from a present one is a world that is possible relative to our present one.]

There is another important notion that we will employ, namely, relative possibility. [The idea seems to be that we can think of one possible world converging with another, as for example through the flow of time taking us from our world as it is now to our world as it may be in the future. Suppose right now there is a possible situation we might find ourselves in the future, depending on the actions we take now. So right now that other possible (future) world is possible relevant to the present one. But suppose that enough time passes and we miss the opportunity to make the decisions that will take us down the path to that future situation. It will be like a missed turn on the road, and so at this later date it is not possible relative to our future situation. Recall Nolt’s diagram for this idea in section 13.2 of his Logics.

As the present moves forward, we follow a certain branch of time, cutting off our access to other braches that went off in directions time did not happen to take.]

The other intuitive notion that the semantics employs is that of relative possibility. Given how things are now, it is possible for me to be in New York | in a week’s time, 26 January. Given how things will be in six days and twenty-three hours, it will no longer be possible. (I am writing in Brisbane.) Or, even if one countenances the possibility of some futuristic and exceptionally fast form of travel, assuming that I do not leave Brisbane in the next eight days, it will then be impossible for me to be in New York on 26 January. Hence, certain states of affairs are possible relative to some situations (worlds), but not others.

(21)

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

Also cited:

Nolt, John. Logics. 1997. Belmont, CA: Wadsworth.

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