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Figure 8.14
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Since from the structure of W3 the other two worlds can be obtained, among these three worlds a dyadic and transitive relation can be recognized: W1 is accessible to W2, which in turn is accessible to W3, while the symmetrical relation does not hold. |
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8.6.5. Necessary Truths and Accessibility |
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A last remark concerns so-called logical or eternal truths that seem to play such an important role in the current literature about possible worlds. I think that logically necessary propositions cannot be ranked as a kind of property. A logical truth such as 'either p or ~p' is the very condition of possibility of the world structures presented above. Suppose there is a W4 in which the individuals can both have and not have a certain property at the same time. I do not suggest that the possession of a given property can remain undetermined; I simply mean that the signs + and - both have the same value, or none at all. |
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What I am outlining is obviously neither a possible nor an impossible world. It is the very impossibility of setting up a world on the bases of the above criteria. These criteria depend on the principle of identification of mathematical symbols, or on the notion of presence and absence of a property. In the terms we have assumed as primitives, it is impossible to speak of an impossible world. |
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It would be possible to deal with this ghostly W4 if we assumed other criteria, as in physics it is possible to assume a different notion of time to speak of certain elementary particles that seem to travel backward in time. |
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But this is a sort of game that need not be played as far as semiotics of narrative worlds is concerned, at least not insofar as these worlds are produced by human beings speaking to human beings who base their language on the principle of the recognizability and identification of phonemes through possible utterances. |
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Nevertheless, while the world-structure outlined above seems to fit the requirements of narrative worlds (we shall test this hypothesis in the next section), what has been said apropos of logical truths does not seem to be confirmed by our narrative experience. It is possible to imagine a science-fiction novel in which there are closed causal chains, that is, in which A can cause B, B can cause C, and C can cause A. In this novel an individual can travel backward through time and become his own father, or find another self only a little younger, so that the reader no longer under- |
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