"If you turn left at the next corner, you will see a blue house at the end of the street." That sentence-a conditional-might be true even though it is possible that you will not see a blue house at the end of the street when you turn left at the next corner.
A moving van may block your view; the house may have been painted pink; a crow might swoop down and peck out your eyes.
Still, in some contexts, we might ignore these possibilities and correctly assert the conditional.
In this book, Christopher Gauker argues that such context-relativity is the key to understanding the semantics of conditionals.
Contexts are defined as objective features of the situation in which a conversation takes place, and the semantic properties of sentences-conditionals included-are defined in terms of assertibility in a context.
One of the primary goals of a theory of conditionals has to be to distinguish correctly between valid and invalid arguments containing conditionals.
According to Gauker, an argument is valid if the conclusion is assertible in every context in which the premises are assertible.
This runs counter to what Gauker sees as a systematic misreading of the data by other authors, who judge arguments to be invalid if they can think of a context in which the premises are judged true and some other context in which the conclusion is judged false.
Different schools of thought on conditionals reflect fundamentally different approaches to semantics.
Gauker offers his theory as a motive and test case for a distinctive kind of semantics that dispenses with reference relations and possible worlds.