Logical validity

This dissertation is about logical consequence. The main points I will defend can be summarised as follows. First, I claim that logical consequence can be understood as truth-preservation under all interpretations of the language. There is no need to use modal notions to define consequence. In chapter one, I argue that domain-variation across different interpretations can be understood in purely interpretational terms, if we take quantifiers to be context-sensitive expressions. Secondly, I am sympathetic with a substitutional account of logical consequence, where consequence is preservation of truth under all substitutions of the non-logical vocabulary. In chapter two, I extend the substitutional account to modal logic, where the box is read as "It is substitutionally valid that". Modal logic is seen as a way for the system to reflect upon what is valid. Different readings of the box can be provided by restricting the substitutions relevant for the truth of a modal formula. In the third chapter, I argue that a theory of logical consequence ought to be self-applicable: it should apply to its own language. This is required by our use of logical consequence in philosophical logic, to express the debate between the monist and the pluralist about logical consequence, and to link our theory of what is valid with a theory of valid reasoning and justification. Finally, in the fourth chapter I suggest that a theory of interpretations of a given language will never really capture all the interpretations of that language. I extend the worry even to theories that admit absolute generality and take higher-order talk to be non-reducible to first-order talk. I argue that, regardless of the order of the theory one is speaking from, there is always an order higher that one can take as one's starting point, and at any further order up the hierarchy, more interpretations of any language become available.