Possible Worlds

Possible Worlds

Rod Girle
Copyright Date: 2003
Pages: 225
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  • Book Info
    Possible Worlds
    Book Description:

    The idea of a possible world that differs in some way from our "actual" world - a world where, for example, the grass is red or no people exist - can help us analyse and understand a wide range of philosophical concepts, such as counterfactuals, properties, modality, and the notions of possibility and necessity. In Possible Worlds Rod Girle surveys current thinking about possible worlds by Kripke, Lewis, Armstrong, Stalnaker, and others. Beginning with a discussion of "possible for" and "possible that," and imagination and fiction, Girle moves on to analyse Kripke's many logics for possibility and Lewis's counterpart worlds. Epistemic possibility, computation and possible worlds, physically possible worlds, impossible worlds, and real possibility are discussed in separate chapters. How the idea of a possible world can be put to use in different areas of philosophy is examined, as are problems that may arise and the benefits that can be gained.

    eISBN: 978-0-7735-8203-3
    Subjects: Philosophy

Table of Contents

  1. Front Matter
    (pp. i-iv)
  2. Table of Contents
    (pp. v-vi)
  3. Preface
    (pp. vii-viii)
    Rod Girle
  4. CHAPTER 1 Introduction
    (pp. 1-25)

    Possible worlds– the very phrase can set the speculative imagination alight. Leibniz suggested that this world was thebest of all possible worlds.The suggestion has enraged some, bewildered many, satisfied some and set others to pondering. What is this idea ofpossible worlds?

    Many works of narrative fiction, such as novels, films and even television programmes, describepossible worlds.Such worlds usually have some sort of internal consistency, or some sort of internal logic, even when they are quite unrealistic. Although realism is not always important, it can be. This is particularly so with the genre of historical novels...

  5. CHAPTER 2 Possible worlds
    (pp. 26-47)

    In this chapter we will consider the way in which possible worlds came to the aid of logicians working with modal logic. Modal logic is generally seen as the logic of possibility and necessity. Possible worlds have made formal modal logic quite clear and precise. In order to see possible worlds and modal logic in clearer perspective we will consider a little of the historical context.

    Modern formal logic began with Frege’s first-order logic.¹ First-order logic is now seen in philosophy, mathematics, linguistics and computer science as the stepping-off point for virtually all work in logic.² First-order logic includes classical...

  6. Chapter 3 Possible worlds and quantifiers
    (pp. 48-72)

    We begin with the extension of prepositional logic to predicate logic and then to modal predicate logic.¹ We look first, from a logical perspective, at what happens when we translate from ordinary language to predicate logic without modal operators. We focus on a very small fragment of both ordinary language and predicate logic: a fragment large enough to show the impact of possible worlds semantics on a range of topics and problems. We then turn to what happens when possible worlds semantics is added to predicate logic.

    The first thing about translating from ordinary language to predicate logic is that...

  7. CHAPTER 4 Possible worlds, individuals and identity
    (pp. 73-94)

    We begin with the addition of singular terms to predicate logic. Consider again

    the following two sentences:

    4.1.1.Kermit is a frog.

    4.1.2.Kermit is green.

    “Kermit” is a proper name. Proper names aresingular terms,not general terms. They are terms that, in everyday discourse, refer to one and only one individual, one and only one entity in the domain. Proper names like “Emma”, “Socrates”, “Pickwick”, “Pegasus” and “Excalibur” are singular terms. If I say “Emma is a student,” then I am not taken to be talking about all the people who are named “Emma”, but only about one...

  8. CHAPTER 5 Possibility Talk
    (pp. 95-104)

    In this chapter we will consider the ways in which the notions of possibility and necessity, and related notions, are expressed in ordinary language. Ordinary usage¹ will indicate the concepts used, and the interrelations between them. There are also sentences of English that pose considerable difficulties for translation to logics that use possible worlds semantics. At the same time, possible worlds can, in some cases, illuminate the meaning of the propositions expressed by such sentences. Above all, reasoning and arguments involving the notions of possibility and necessity are usually expressed in ordinary language.

    We begin with the distinction, in ordinary...

  9. CHAPTER 6 The possible worlds of knowledge
    (pp. 105-125)

    One of the common uses of modal logic, apart from use in the discussion of logical possibility and necessity, is to provide a logic for knowledge and a logic for belief. These logics have practical applications in artificial intelligence, especially in knowledge representation.

    Logics for knowledge areepistemiclogics,¹ and logics for belief aredoxasticlogics. Nevertheless, the term “epistemic logic” is often taken to encompass both epistemic and doxastic logics. One of the first twentieth-century suggestions for a logic for knowledge came from Lemmon in his paper, “Is There Only One Correct System of Modal Logic?”² We have already...

  10. CHAPTER 7 The possible worlds of belief
    (pp. 126-142)

    Now that we have considered Hintikka’s epistemic logic in terms of its possible world basis, we shift to considering doxastic logic, beginning with Hintikka’s logic and going on to consider something of the groundwork in doxastic logic that Smullyan sets out inForever Undecided.¹We will discuss Smullyan’s use of doxastic logic to show what Godel was saying in his important incompleteness theorems about the limitations of logic. Finally, we consider epistemic and doxastic predicate logic and the closely related questions of existence, quantification into epistemic and doxastic contexts, and thede dicto-de redistinction as it applies to these...

  11. CHAPTER 8 Time and many possible worlds
    (pp. 143-156)

    There is an interpretation of quantum physics that is known as themany worlds interpretation.The interpretation is not, by any means, a majority view, but it is much discussed, and is much beloved by authors of fiction, especially the authors of science fiction. In this chapter we will look at the many worlds interpretation from the perspective of possible worlds.

    Our considerations will be much assisted if we begin by looking at time from a possible worlds perspective. There are logics for time that have been developed on the basis of standard modal logics with possible world semantics. These...

  12. CHAPTER 9 Real possibility
    (pp. 157-180)

    If possibilities are real, what follows? Lots of things. But, if we use possible worlds to explain the nature of possibility, does the reality of possibilities mean that possible worlds must be real?

    Some argue for a “yes” answer. Famously, David Lewis was the chief of those in the twentieth century arguing for a “yes” answer.¹ Perforce, we will spend a great deal of time in this chapter considering Lewis's ideas, but not in detail they deserve. Lewis takes the possibleworldsaccount of possibility and necessity, and some other modal notions such as ought, with utmost seriousness. An analogy...

  13. CHAPTER 10 Impossible possible worlds
    (pp. 181-190)

    One quite surprising development in modal logic has been the development of systems in which there are possible worlds in which some sentences are both true and false. This development has been greeted with incredulous stares of such intensity that the stares directed at Lewis’s claims become shy glances. This development has been extended to the actual world, and there is a group of logicians who claim that there are some contradictions that are true, as well, of course, as being false. Note that they are not claiming thatallcontradictions are true, only thatsomeare. These logicians are...

  14. CHAPTER 11 Unfinished story
    (pp. 191-194)

    I have declared or argued for several quite heretical things. First, I declared in favour of the status of first-order modal logic as an artificial language. I then gave examples that show that the language of classical logic is unreliable for the evaluation of many arguments couched in ordinary language. It was urged that more attention should be paid to the logic–language relationship. Modal logic is more reliable for some argument evaluation than non-modal logic. But we saw that there is much beyond the scope of present modal logic – the present logic of boxes and diamonds.

    I argued for...

  15. Notes
    (pp. 195-206)
  16. Bibliography
    (pp. 207-212)
  17. Index
    (pp. 213-216)