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An Intensional Solution to the Bike Puzzle of Intentional Identity

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Abstract

In a 2005 paper Ólafur Páll Jónsson presents a puzzle that turns on intentional identity and definite descriptions. He considers eight solutions and rejects them all, thus leaving the puzzle unsolved. In this paper I put forward a solution. The puzzle is this. Little Lotta wants most of all a bicycle for her birthday, but she gets none. Distracted by the gifts she does receive, she at first does not think about the bike. But when seeing her tricycle, she is reminded of the bike. The question is how we are to analyse these two occurrences of ‘the bike’ in the absence of a unique bike that Lotta wants. So the semantics of ‘the bike’ needs to be spelt out, and it must be made explicit what the complements of Lotta’s attitudes are. My analysis shows that the attributer’s usage of ‘the bike’ blurs the distinction between a second-order and a first-order intension (a property concept and a property, respectively). My solution can be summed up in this two-premise argument. (a) In the state-of-affairs S, the property of being a bike is the extension of the property concept the property such that Lotta wants an instance of it more than any other; (b) in S, Lotta does not think about/is reminded of the property that she wants an instance of more than any other; (c) therefore, in S Lotta does not think about/is reminded of the property of being a bike. This solution requires looking beyond the confines of denotational semantics, which all of Jónsson’s eight solution candidates belong to.

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Notes

  1. ‘Property of individuals’ and ‘individual-property’ are used interchangeably. Properties are intended as universals and not as tropes, such that they may have several instances.

  2. I hasten to add that I am not assuming that the solution to Jónsson’s puzzle must be in a (neo-) Fregean vein. I merely wish to demonstrate that, and how, such a framework affords a solution, unlike any of those that Jónsson (rightly) rejects.

  3. By ’concept‘ I intend Church’s notion of concept. See, e.g., his (1993).

  4. Cf. Church (1951, p. 111, n. 14), (1956, p. 8, n. 20).

  5. For instance, on an extensionalist interpretation of notional attitudes, since Oedipus sought the slayer of Laios, and Oedipus was it, Oedipus sought Oedipus [himself].

  6. See Materna (2010) for the most recent statement of this distinction, and Duží (2009) for the most recent account of (empirical) definite descriptions, as elaborated in Transparent Intensional Logic.

  7. See Ranta (1994, pp. 125ff).

  8. See Duží et al. (2010, §2.4.3).

  9. See Tichý (1971), Jespersen (2005), and Duží et al. (2010, §2.4).

  10. See Jespersen (2008).

  11. If we wish to be absolutely correct, we say that λwλt [Bike = Φ wt ] yields a function from the domain of possible worlds to the co-domain of functions from times to individual-properties, such that at those worlds and times Bike is the extension of Φ.

  12. See Tichý (1971), (1986), and Duží et al. (2010, Ch. 1).

  13. Church (1956, p. 8, n. 20).

  14. Versions of this paper were read as invited lectures at Convegno internazionale LOGICA & METAFISICA, Department of Philosophy, University of Palermo, 27-29 March 2007, and Department of Analytic Philosophy, Slovak Academy of Sciences, Bratislava, 25 June 2007. The research reported herein was carried out while affiliated with Section of Philosophy, Deft University of Technology. The research was supported by the project GACR 401/10/0792. I am indebted to Marie Duží, Tomis Kapitan, Rasa Paulėkaitė, Gabriel Sandu, and an anonymous referee for this journal, for valuable comments and suggestions.

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Correspondence to Bjørn Jespersen.

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Jespersen, B. An Intensional Solution to the Bike Puzzle of Intentional Identity. Philosophia 39, 297–307 (2011). https://doi.org/10.1007/s11406-010-9269-2

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