J.C. Beall and Greg Restall's Generalised Tarski Thesis is a generalisation of the seemingly diverse conceptions of logical consequence. However, even their apparently general account of consequence makes necessary truth-preservation a necessary condition. Sentences in the imperative mood pose a problem for any truth-preservationist account of consequence, because imperatives are not truth-apt but seem to be capable of standing in the relation of logical consequence. In this paper, I show that an imperative logic can be formulated that solves the problem (...) of imperative consequence by leading naturally to a further generalisation of the GTT. (shrink)

Hilary Putnam's Model-Theoretic argument attempts to dispose of the view that science provides us with a literally true description of the world. It uses the Löwenheim-Skolem Theorem to show that all consistent scientific theories are true of the real world, even if they contradict each other. This is incompatible with the realist conception of truth, which allows only for one version of reality. So, Putnam rejected this conception of truth in favour of his own 'internal realism,' which claims that theories (...) can only be true or false within themselves; within their own framework. However, I demonstrate that the Model-Theoretic argument is unsound. It relies on a false premise – that every consistent theory is true of the real world. Putnam uses a clever manipulation of model theory to attempt to convince us of the truth of this premise, but I show that he commits a fundamental error in his method. (shrink)

Standard definitions of validity are designed to preserve truth from the premises to the conclusion. However, it seems possible to construct arguments that contain sentences in the imperative mood. Such sentences are incapable of being true or false, so the standard definitions cannot capture the validity of these imperative arguments. Bernard Williams offers an argument that imperative inference is impossible: two imperatives will always have different permissive presuppositions, so a speaker will have to change his mind before uttering a second (...) imperative, and so imperatives cannot ever be accumulated into a set of premises. I offer four objections to Williams’ argument: (1) Permissive presuppositions are analogous to conversational implicature, and so should be ignored when formulating imperative arguments. (2) There are other valid argument forms, which Williams does not consider, that do not suffer from different permissive presuppositions. (3) There are explanations for the change in permissive presuppositions in Williams’ example other than a change of mind, so the different permissive presuppositions do not have to prevent accumulation. Finally, (4) Williams accepts enough logical relations between imperatives (contradiction and a form of negation) for a definition of a valid imperative inference to follow naturally. (shrink)

The interrelated logical concepts of validity, entailment, and consequence are all standardly defined in terms of truth preservation. However, imperative sentences can stand in these relations, but they are not truth-apt. This puzzle can be understood as an inconsistent triad: T1 Imperatives can be the relata of the consequence relation. T2 Imperatives are not truth-apt. T3 The relata of the consequence relation must be truth-apt. These three claims cannot all be true. So, to solve the problem of imperative consequence we (...) must reject one of the three claims. Solutions can be categorised into three types: those that reject T1, those that reject T2, and those that reject T3. In this thesis, I first outline and motivate each of these three claims. I then consider, in turn, theories of imperative logic and semantics, all of which fall into one of the three types of solution. I consider and reject two versions of solution type 1, the type that rejects T1. These versions argue that it is impossible for imperatives to stand in logical relations, and attempt to provide alternative explanations for what's happening when it seems like they are doing so. I then consider and reject several versions of solution type 2, the type that rejects T2. These theories claim that, despite appearances based on surface grammar, imperatives are disguised declaratives and thus truth-apt. Each theory proposes a translation schema-- it outlines the truth-conditions for imperatives. Next, I outline several versions of solution type 3, the type that rejects T3. These theories aim to develop a formal account of imperative logic. I reject each of these theories in turn, and finally propose a solution that avoids the problems I raise with the other theories. (shrink)