Online research in philosophy

Recent work on the logical theory of confirmation has centered on accounts of the confirmation of hypotheses relative to auxiliary assumptions or background theory. Whether such relative confirmation actually increases the credibility of the (relatively) confirmed hypothesis will depend in various ways on the epistemic status of the auxiliaries involved. Most obviously, if the auxiliaries are not themselves credible, confirmation relative to them will not increase the credibility of the hypothesis thus confirmed. A complete theory of confirmation must thus combine an account of relative confirmation with an account of the route from relative confirmation to real confirmation. Some recent criticisms of hypothetico-deductive and bootstrapping accounts of relative confirmation are undermined by failure to appreciate the limitations of relative confirmation.

An intensional semantic system for languages containing, in their logical syntax, sortal quantifiers, sortal identities, (second-order) quantifiers over sortals and the necessity operator is constructed. This semantics provides non-standard assignments to predicate expressions, which diverge in kind from the entities assigned to sortal terms by the same semantic system. The nature of the entities assigned to predicate expressions shows, at the same time, that there is an internal semantic connection between those expressions and sortal terms. A formal logical system is formulated that is proved to be absolutely consistent, sound and complete with respect to the intensional semantic system.

A category of non-standard predicates was introduced by Goodman (1954) while attempting to recast the old riddle of induction in terms amenable to solution within confirmation theory. The New Riddle proved as intractable as the old one but the category of predicates, "mutant" ones, may assist us in understanding cognitive development from neonate vacuity to linguisticallyinformed rational inquiry. This paper proposes a naturalistic explanation of why we tend to reject grue-type predicates as proper bases for induction. Its conclusion is that such predicates violate requirements on normal predicates of languages that are capable of being learned by humans. The explanation does not itself directly address standard epistemological questions associated with mutant predicates but instead focusses on the pragmatic bases of such epistemic practices as induction and finds them unfulfilled by mutant predi-.

This paper considers how to put together two popular ideas in the philosophy of time: detenserism (the view that tense can be analysed in token-reflexive terms) and perdurantism (the view that objects persist through time by having temporal parts. On the most obvious way of doing this, certain problems arise. I argue that to deal with these problems we need a tool that is unfamiliar to most detensers and perdurantists - the distinction between sortal and non-sortal predicates.

This paper examines problems of order and periodicity which arise when the attempt is made to define a confirmation function for a language containing elementary number theory as applied to a universe in which the individuals are considered to be arranged in some fixed order. Certain plausible conditions of adequacy are stated for such a confirmation function. By the construction of certain types of predicates, it is proved, however, that these conditions of adequacy are violated by any confirmation function defined for the type of language in question. Various possible solutions to these difficulties are explored and found to be inadequate. In particular, a proposal which stems from the suggestion to restrict a fundamental principle of confirmation to hypotheses containing only non-positional predicates is cited. This proposal, however, is shown to prevent confirmation functions from taking periodicities into account, and so is deemed unsatisfactory. A general theorem is proved to the effect that if non-positional predicates are taken to satisfy the conditions of adequacy which have been formulated, then no periodicity predicates whatsoever (i.e., predicates used in formulating hypotheses which foretell periodicities) can be subject to these conditions, on pain of contradiction. Yet it seems that periodicity predicates must be subject to these conditions of adequacy if a confirmation function is to recognize periodic occurrences. Thus, an impasse seems to be reached. In the final sections we consider the beginnings of one possible solution to these difficulties. Our proposal involves treating sets of individuals, rather than individuals themselves, as instances of an hypothesis which predicts a periodicity. On this basis we formulate new conditions of adequacy which are free from the previous difficulties and which will permit a confirmation function that satisfies them to take periodicities into account.

Sortal predicates have been associated with a counting process, which acts as a criterion of identity for the individuals they correctly apply to. We discuss in what sense certain types of predicates suggested by quantum physics deserve the title of 'sortal' as well, although they do not characterize either a process of counting or a criterion of identity for the entities that fall under them. We call such predicates 'quantum-sortal predicates' and, instead of a process of counting, to them is associated a 'criterion of cardinality'. After their general characterization, it is discussed how these predicates can be formally described.

Sortal predicates have been associated with a counting process, which acts as a criterion of identity for the individuals they correctly apply to. We discuss in what sense certain types of predicates suggested by quantum physics deserve the title of ‘sortal’ as well, although they do not characterize either a process of counting or a criterion of identity for the entities that fall under them. We call such predicates ‘quantum-sortal predicates’ and, instead of a process of counting, to them is associated a ‘criterion of cardinality’. After their general characterization, it is discussed how these predicates can be formally described.