Simplifying and correcting the treatment of intentionality in Montague semantics
The use of denotational semantics brings into Montague semantics an unified notational description. This helps to expose the counter-intuitive usage of the cap-cup operators, and provides insights on how they are used in the meaning postulates. We observe as well that meaning postulates introduce high-order quantification in PTQ. We conclude that those operators have undesirable properties and that their use in the formalization of intentionality is unnecessary and counter-intuitive.
The main conclusion of this chapter is that we should use neither the cap-cup operators nor meaning postulates in a treatment of intentionality.
Unable to display preview. Download preview PDF.
- 1.The word intension was introduced by [Carnap, 1946] in logical terminology and has been widely used in formal treatments of intentionality. In Philosophy, the word ‘intentionality’ is used when we are dealing with the objects of knowledge, belief and necessity, as opposed to immediate sense objects involved in using the physical senses; see for instance [Malmgren, 1971]. As [Hodges, 1977] says, “Alas for the infelicities of logical terminology”. In general remarks we will be using the word ‘intentionality', but we will use in the logical tradition ‘intension’ and ‘intensional verbs’ (and ‘extension’ and ‘extensional verbs'). Some authors (for instance [Turner, 1988]) use the word ‘intensionality’ where they should be using ‘intentionality'.Google Scholar