The Proscriptive Principle and Logics of Analytic Implication

The application of syllogistic is merely the analysis of concepts, a term that presupposes---through the root alphanualpha + lambdaupsilono---a mereological background. In the 1930s, such considerations led William T. Parry to attempt to codify this notion of logical containment in his system of analytic implication AI. Parry's system AI was later expanded to the system PAI. The hallmark of Parry's systems---and of what may be thought of as containment logics or Parry systems in general---is a strong relevance property called the 'Proscriptive Principle' (PP) described by Parry as the thesis that:;No formula with analytic implication as main relation holds universally if it has a free variable occurring in the consequent but not the antecedent.;This type of proscription is on its face justified, as the presence of a novel parameter in the consequent corresponds to the introduction of new subject matter. The plausibility of the thesis that the content of a statement is related to its subject matter thus appears also to support the validity of the formal principle.;Primarily due to the perception that Parry's formal systems were intended to accurately model Kant's notion of an analytic judgment , Parry's deductive systems---and the suitability of the Proscriptive Principle in general---were met with severe criticism. It is the goal of the present work to explore themes related to deductive systems satisfying one form of the Proscriptive Principle or other, with a special emphasis placed on the rehabilitation of their study to some degree.;* In Chapter 2 we identify and develop the relationship between Parry-type deductive systems and the field of 'logics of nonsense.' Of particular importance is Dmitri Bochvar's 'internal' nonsense logic Sigma 0, and we observe that two |---Parry subsystems of Sigma 0---Harry Deutsch's Sfde and Frederick Johnson's RC---can be considered to be the products of particular 'strategies' of eliminating problematic inferences from Bochvar's system.;* The material of Chapter 3 considers Kit Fine's program of state space semantics in the context of Parry logics. Fine---who had already provided the first intuitive semantics for Parry's PAI---has offered a formal model of truthmaking (and falsemaking) that provides one of the first natural semantics for Richard B. Angell's logic of analytic containment AC, itself a |---Parry system. After discussing the relationship between state space semantics and nonsense, we observe that Fabrice Correia's weaker framework---introduced as a semantics for a containment logic weaker than AC---tacitly endorses an implausible feature of allowing hypernonsensical statements. By modelling Correia's containment logic within the stronger setting of Fine's semantics, we are able to retain Correia's intuitions about factual equivalence without such a commitment. As a further application, we observe that Fine's setting can resolve some ambiguities in Greg Restall's own truthmaker semantics.;* Chapter 4 we consider interpretations of disjunction that accord with the characteristic failure of Addition in which the evaluation of a disjunction A ∨ B requires not only the truth of one disjunct, but also that both disjuncts satisfy some further property. We examine semantics for several |---Parry logics in terms of the successful execution of certain types of computer programs and the consequences of extending this analysis to dynamic logic and constructive logic.;* Chapter 5 considers these faults in the particular case in which Nuel Belnap's 'artificial reasoner' is unable to retrieve the value assigned to a variable. This leads not only to a natural interpretation of Graham Priest's semantics for the |---Parry system S fde* but also a novel, many-valued semantics for Angell's AC, completeness of which is proven by establishing a correspondence with Correia's semantics for AC. These many-valued semantics have the additional benefit of allowing us to apply the material in Chapter 2 to the case of AC to define intensional extensions of AC in the spirit of Parry's PAI.;* One particular instance of the type of disjunction central to Chapter 4 is Melvin Fitting's cut-down disjunction. Chapter 6 examines cut-down operations in more detail and provides bilattice and trilattice semantics for the |---Parry systems Sfde and AC in the style of Ofer Arieli and Arnon Avron's logical bilattices.;* Finally, the correspondence between the present many-valued semantics for AC and those of Correia is revisited in Chapter 7. The technique that plays an essential role in Chapter 4 is used to characterize a wide class of first-degree calculi intermediate between AC and classical logic in Correia's setting. (Abstract shortened by ProQuest.).