Thesis (DPhil. ( Information Science))--University of Pretoria, 2003. / Includes bibliographical references

Please read the abstract in the section 00front of this document / Thesis (DPhil (Information Science))--University of Pretoria, 2005. / Information Science / unrestricted

In this thesis I present an account of the formal semantics of counterfactuals that systematically deals with impossible antecedents. This, in turn, allows us to gain a richer understanding of what makes certain thought experiments informative in spite of the impossibility of the situations they consider. In Chapter II, I argue that there are major shortcomings in the leading theories of counterfactuals. The leading theories of counterfactuals (based on classical two-valued logic) are unable to account for counterfactuals with impossible antecedents. In such accounts, everything and anything follows from an impossible antecedent. In Chapter III, I examine some crucial notions such as conceivability, imaginability, and possibility. Herein I argue that there is a distinction to be made between the notions of conceiving and imagining. Conceivability, it turns out, is a sufficient condition for being a case. Recent literature on the semantics for relevance logic have made some use of the notion of a “state”, which differs from a world in that contradictions are true in some states; what is not done in that literature is to clarify how the notion of a state differs from an arbitrary collection of claims. I use the notion of a case as a (modal) tool to analyze counterfactuals with impossible antecedents, one for which, unlike the notion of states, it is clear why arbitrary collections of claims do not count. In Chapter IV, I propose a new account of counterfactuals. This involves modifying existing possible worlds accounts of counterfactuals by replacing possible worlds by the “cases” identified in Chapter III. This theory discerns counterfactuals such as: “If Dave squared the circle, he would be more famous than Gödel” which seems true, from others like: “If Dave squared the circle, the sun would explode”, which seems false. In Chapter V I discuss one of the main pay offs of having an account of counterfactuals that deals systematically with counterfactuals with impossible antecedents. To apply the new account of counterfactual to thought experiments, first we have to transform the thought experiment in question into a series of counterfactuals. I show how this is to be done, in Chapter V. There are two advantages of such an account when we apply it to thought experiments: First, for thought experiments with impossible scenarios, our new account can explain how such thought experiments can still be informative. Secondly, for thought experiments like the Chinese Room, where it is not clear whether there is a subtle impossibility in the scenario or not, this new account with its continuous treatment of possible and impossible cases makes clear why the debate about such thought experiments looks the way it does. The crucial question is not whether there is such an impossibility, but what is the "nearest" situation in which there is a Chinese Room (whether it is impossible or not) and what we would say there (about the intentionality of the room). On traditional accounts, it becomes paramount to deal with the possibility question, because if it is an impossible scenario the lessons we learn are very different from the ones we learn if it is possible. There are no available theories of thought experiments that account for thought experiments with impossible/incomplete scenarios. With the new account of counterfactual and by applying it to thought experiments we over come this difficulty.

In this thesis I present an account of the formal semantics of counterfactuals that systematically deals with impossible antecedents. This, in turn, allows us to gain a richer understanding of what makes certain thought experiments informative in spite of the impossibility of the situations they consider. In Chapter II, I argue that there are major shortcomings in the leading theories of counterfactuals. The leading theories of counterfactuals (based on classical two-valued logic) are unable to account for counterfactuals with impossible antecedents. In such accounts, everything and anything follows from an impossible antecedent. In Chapter III, I examine some crucial notions such as conceivability, imaginability, and possibility. Herein I argue that there is a distinction to be made between the notions of conceiving and imagining. Conceivability, it turns out, is a sufficient condition for being a case. Recent literature on the semantics for relevance logic have made some use of the notion of a “state”, which differs from a world in that contradictions are true in some states; what is not done in that literature is to clarify how the notion of a state differs from an arbitrary collection of claims. I use the notion of a case as a (modal) tool to analyze counterfactuals with impossible antecedents, one for which, unlike the notion of states, it is clear why arbitrary collections of claims do not count. In Chapter IV, I propose a new account of counterfactuals. This involves modifying existing possible worlds accounts of counterfactuals by replacing possible worlds by the “cases” identified in Chapter III. This theory discerns counterfactuals such as: “If Dave squared the circle, he would be more famous than Gödel” which seems true, from others like: “If Dave squared the circle, the sun would explode”, which seems false. In Chapter V I discuss one of the main pay offs of having an account of counterfactuals that deals systematically with counterfactuals with impossible antecedents. To apply the new account of counterfactual to thought experiments, first we have to transform the thought experiment in question into a series of counterfactuals. I show how this is to be done, in Chapter V. There are two advantages of such an account when we apply it to thought experiments: First, for thought experiments with impossible scenarios, our new account can explain how such thought experiments can still be informative. Secondly, for thought experiments like the Chinese Room, where it is not clear whether there is a subtle impossibility in the scenario or not, this new account with its continuous treatment of possible and impossible cases makes clear why the debate about such thought experiments looks the way it does. The crucial question is not whether there is such an impossibility, but what is the "nearest" situation in which there is a Chinese Room (whether it is impossible or not) and what we would say there (about the intentionality of the room). On traditional accounts, it becomes paramount to deal with the possibility question, because if it is an impossible scenario the lessons we learn are very different from the ones we learn if it is possible. There are no available theories of thought experiments that account for thought experiments with impossible/incomplete scenarios. With the new account of counterfactual and by applying it to thought experiments we over come this difficulty.

Thesis (M.A.)--Memorial University of Newfoundland, 2005. / Bibliography: leaves 64-70.

De Morgan monoids are algebraic structures that model certain non-classical logics. The variety DMM of all De Morgan monoids models the relevance logic Rt (so-named because it blocks the derivation of true conclusions from irrelevant premises). The so-called subvarieties and subquasivarieties of DMM model the strengthenings of Rt by new logical axioms, or new inference rules, respectively. Meta-logical problems concerning these stronger systems amount to structural problems about (classes of) De Morgan monoids, and the methods of universal algebra can be exploited to solve them. Until now, this strategy was under-developed in the case of Rt and DMM. The thesis contributes in several ways to the filling of this gap. First, a new structure theorem for irreducible De Morgan monoids is proved; it leads to representation theorems for the algebras in several interesting subvarieties of DMM. These in turn help us to analyse the lower part of the lattice of all subvarieties of DMM. This lattice has four atoms, i.e., DMM has just four minimal subvarieties. We describe in detail the second layer of this lattice, i.e., the covers of the four atoms. Within certain subvarieties of DMM, our description amounts to an explicit list of all the covers. We also prove that there are just 68 minimal quasivarieties of De Morgan monoids. Thereafter, we use these insights to identify strengthenings of Rt with certain desirable meta-logical features. In each case, we work with the algebraic counterpart of a meta-logical property. For example, we identify precisely the varieties of De Morgan monoids having the joint embedding property (any two nontrivial members both embed into some third member), and we establish convenient sufficient conditions for epimorphisms to be surjective in a subvariety of DMM. The joint embedding property means that the corresponding logic is determined by a single set of truth tables. Epimorphisms are related to 'implicit definitions'. (For instance, in a ring, the multiplicative inverse of an element is implicitly defined, because it is either uniquely determined or non-existent.) The logical meaning of epimorphism-surjectivity is, roughly speaking, that suitable implicit definitions can be made explicit in the corresponding logical syntax. / Thesis (PhD)--University of Pretoria, 2020. / DST-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS) / Mathematics and Applied Mathematics / PhD / Unrestricted