Abstract
Fiction poses a set of problems relating to the notion of fictional truth and the reading of a fictional text, which link in with questions regarding counterfactuals and belief change. They are thus problems which modern logic, in this instance nonmonotonic logic, would like, or should like, to deal with. However, logics have, so far, not had much to offer. This paper argues that this is because logicians are not treating the correct problem. They assume in their logics an exogenous factor (similarity between worlds, epistemic entrenchment, selection function, to take but a few examples), whereas what is required is an understanding of this factor and the value it takes. This question essentially involves the dynamics: understanding this factor amounts to giving an account of how it comes to have a particular value in a particular context or at a particular moment. The paper contains a consideration of what should count as the essential tasks of such a theory of dynamics, and a tentative suggestion as to one direction for developing such a theory.
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Notes
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Some, such as Adams (1975), have suggested that one cannot talk of truth or falsity of conditionals in general, and counterfactuals in particular, but only of acceptability; the logic of counterfactuals will thus aim to capture the rules relating acceptable counterfactuals. In this paper, these debates shall be ignored, and the discussion, where relevant, will be formulated in terms of truth.
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Another notable attempt is that of Woods (1974), although he does not propose such a complete analysis of fictional truth.
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“Literary theorists […] have developed a textual semantics based on the idea that the semantic domain projected by the literary text is a non-actual possible or an alternative possible world”, Ryan (1991), p. 553.
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This is the case for Goodman (in so far as the connecting principles are laws and depend on an epistemic entrenchment ordering which may alter through time) and Lowe (p. 49) in the case of counterfactuals; in belief revision, theorists working on iterated revision face the question of changes in the factor (see for example Rott (1999, 2003) for a technical and philosophical discussion).
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This is a very rough characterisation of both disciplines (both now involve structures other than the natural numbers, coding theory now takes more account of information theory, communication theory etc.), but is sufficient for the point made here.
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As Makinson (2005), pp. 28–29 points out, representation theorems are the nonmonotonic equivalent of completeness theorems.
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By dynamics of the frameworks, we mean change in the machinery assumed for evaluating propositions; in the case discussed above, possible worlds and a similarity relation on them. Therefore, traditional forms of dynamic logic (van Benthem 1996) do not take account of the dynamics of their frameworks, in so far as they assume a set of states and relations on them without posing the question of possible changes in the set of states or the relation. Those who have begun to look at this question, at least to a certain degree, are rather theorists working in logics for knowledge change under communication (for example Baltag et al. 1998) and some who consider iterated belief revision (for example, Rott 2006) (See for example van Benthem (2007) for a proposal for relating the two.).
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Put more technically, the suggestion is that a (new) topology be defined on the (old) set of points.
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The notion of proximity and continuity (as proximity of consecutive states) are left loosely specified here, although they correspond to basic notions from topology. In particular, although proximity can be thought of as a distance (ie. the space is a metric space), it need not be – containment or overlap is sufficient (ie. the space is a topological non metric space). See for example Sutherland (1975) for details.
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The example is structurally similar to that considered by Stalnaker (1984), p. 130 sq., as is the reply relying on context-shift.
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Lewis (1981), p. 87.
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See for example Modica and Rustichini (1994).
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This model of context is defended in Stalnaker (1999).
- 20.
This sort of technique is employed, albeit in different forms, by Fagin and Halpern (1988), Modica and Rustichini (1999), and others working on the question of ‘awareness’ in the economics literature. The framework used here differs from the others in several important ways; see Hill (2008, forthcoming), for more details.
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For a development of the discussion in the previous paragraph, and an introduction to the technical notions, see Hill (2006), §§5.1 and 5.2.
- 23.
This is what Goodman (1954), Ch. 1 calls “cotenability”.
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Hill, B. (2012). Fiction, Counterfactuals: The Challenge for Logic. In: Pombo, O., Torres, J., Symons, J., Rahman, S. (eds) Special Sciences and the Unity of Science. Logic, Epistemology, and the Unity of Science, vol 24. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2030-5_17
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