Hope is hard to characterise because of the exceptional diversity of its applications, to the point that one may wonder whether there is continuity between ordinary cases of hope and what is often called 'hope against hope'. In this paper, I shall follow the relatively small but growing literature on hope and examine propositional hopes, i.e. hopes of the form 'hoping that p', with a particular focus on recent work by Philip Pettit and Adrienne Martin. I shall do this first by identifying a significant difficulty encountered by what has become known as the 'orthodox definition'. The OD defines hope by means of two necessary and sufficient conditions: A hopes that p if and only if A desires that p and A assigns to p a degree of probability between 0 and 1. On this definition, to hope is to desire an outcome we deem neither certain nor impossible. Note that the relevant probability assignment is subjective: the OD allows, for example, that children can hope for Father Christmas to visit them on Christmas Eve.
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