Logic, convention, and common knowledge

This dissertation examines and defends the idea that logic is conventional. It also presents logics for reasoning about knowledge and common knowledge. A fundamental thesis is that logical consequence and logical truth are not simply given; they arise as conventions amongst the users of logic. And, a primary goal of the dissertation is to respond to Quine's argument that conventional accounts of logic must be either trivial or vacuous. Convention is explicated in a game theoretic framework along the lines of Lewis's Convention. A convention is thus a kind of equilibrium in the strategies of players of a game. They coordinate by adopting strategies that consistently yield a certain outcome.;Players coordinating in this manner are assumed to have common knowledge of what is happening. I look in detail at the shared-situation approach to common knowledge as set out by Barwise. This is illustrated via a classic coordination problem distributed computing that was first introduced by Gray, viz: the coordinated attack. Though generally thought to be probably unsolvable, on a realistic understanding of common knowledge (taking into account the cognitive limitations of any knower) a solution is shown to exist.;The solution provided is based on shared situations, and a situation semantics is set out in detail. A corresponding epistemic logic is also presented that is sound and complete with respect to the semantics. This logic introduces knowledge predicates that allow us to represent knowing an individual (including an individual situation) simpliciter as opposed to knowing something involving the individual. One cannot express and reason about common knowledge and shared situations entirely within the logic itself. Another logic is presented that is sufficiently expressive, and it is also shown to be sound and complete.;The last chapter returns to Quine's critique and explains how conventions can arise when common knowledge is available only ex post facto. This provides the final justification for a conventional view of logic: it better accounts for logical behavior than the alternative view.