This paper starts by criticising some olderaccounts of conditionals based on the so-called `Ramsey Test', and ends by proposing their replacement, in part with a material account, in part with a probabilistic account using epsilon terms. The combined replacement is in fact closer to Ramsey's ideas. But there is also a resemblance between the latter and a more recent account of conditionals, which relates some of them to causality. The comparison provides a basis for assessment of the proposed replacement.

Criticisms have been aired before about the fear of certain Platonic abstract objects, propositions. That criticism extends to the widespread preference for an operator analysis of expressions like ‘It is true, known, obligatory that p’ as opposed to the predicative analysis in their equivalents ‘That p is true, known, obligatory’. The criticism in the present work also concerns Prior’s attitude to Platonic entities of a certain kind: not propositions, i.e., the referents of ‘that’-clauses, but individuals, i.e., the referents of Russell’s (...) ‘logically proper names’. Prior had a close knowledge of theories of individuals, including that of Russell. However, when Prior formulated his tense logic Q he presumed a non-Russellian, pre-suppositional account of individuals, such that they might exist at one time but not at another, and when they did not exist no statement could be made about them. This paper examines the correctness of such a pre-suppositional account of individuals, showing there are features of natural language it cannot account for. It is shown that the required features can be formalised in Hilbert’s epsilon calculus, and that using that calculus substantiates a Russellian understanding of ‘logically proper names’. (shrink)

The epsilon calculus improves upon the predicate calculus by systematically providing complete individual terms. Recent research has shown that epsilon terms are therefore the “logically proper names” Russell was not able to formalize, but their use improves upon Russell’s theory of descriptions not just in that way. This paper details relevant formal aspects of the epsilon calculus before tracing its extensive application not just to the theory of descriptions, but also to more general problems with anaphoric reference. It ends by (...) contrasting a Meinongian account of cross-reference in intensional constructions with the epsilon account. (shrink)

Routley?s Formula says, for instance, that if it is believed there is a man then there is something which is believed to be a man. In this paper I defend the formula; first directly, but then by looking at work by Gensler and Hintikka against it, and at the original work of Routley, Meyer and Goddard for it. The argument ultimately reduces to a central point about the extensionality of objects in Routley, Meyer and Goddard?s intensional system, i.e. in its (...) formulation of transparency. (shrink)

Hilbert’s choice operators τ and ε, when added to intuitionistic logic, strengthen it. In the presence of certain extensionality axioms they produce classical logic, while in the presence of weaker decidability conditions for terms they produce various superintuitionistic intermediate logics. In this thesis, I argue that there are important philosophical lessons to be learned from these results. To make the case, I begin with a historical discussion situating the development of Hilbert’s operators in relation to his evolving program in the (...) foundations of mathematics and in relation to philosophical motivations leading to the development of intuitionistic logic. This sets the stage for a brief description of the relevant part of Dummett’s program to recast debates in metaphysics, and in particular disputes about realism and anti-realism, as closely intertwined with issues in philosophical logic, with the acceptance of classical logic for a domain reflecting a commitment to realism for that domain. Then I review extant results about what is provable and what is not when one adds epsilon to intuitionistic logic, largely due to Bell and DeVidi, and I give several new proofs of intermediate logics from intuitionistic logic+ε without identity. With all this in hand, I turn to a discussion of the philosophical significance of choice operators. Among the conclusions I defend are that these results provide a finer-grained basis for Dummett’s contention that commitment to classically valid but intuitionistically invalid principles reflect metaphysical commitments by showing those principles to be derivable from certain existence assumptions; that Dummett’s framework is improved by these results as they show that questions of realism and anti-realism are not an “all or nothing” matter, but that there are plausibly metaphysical stances between the poles of anti-realism and realism, because different sorts of ontological assumptions yield intermediate rather than classical logic; and that these intermediate positions between classical and intuitionistic logic link up in interesting ways with our intuitions about issues of objectivity and reality, and do so usefully by linking to questions around intriguing everyday concepts such as “is smart,” which I suggest involve a number of distinct dimensions which might themselves be objective, but because of their multivalent structure are themselves intermediate between being objective and not. Finally, I discuss the implications of these results for ongoing debates about the status of arbitrary and ideal objects in the foundations of logic, showing among other things that much of the discussion is flawed because it does not recognize the degree to which the claims being made depend on the presumption that one is working with a very strong logic. (shrink)

Over the last two decades, semantic theory has been marked by a continuing shift from a static view of meaning to a dynamic one. The increasing interest in extending semantic analysis from isolated sentences to larger units of discourse has fostered the intensive study of anaphora and coreference, and this has engendered a shift from viewing meaning as truth conditions to viewing it as the potential to change the "informational context".