An intensional solution to the bike puzzle of intentional identity

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.