M. J. Budd; XI—Materialism and Immaterialism, Proceedings of the Aristotelian Society, Volume 70, Issue 1, 1 June 1970, Pages 197–220, https://doi.org/10.1093/a.

The "Dutch Book" argument, tracing back to Ramsey and to deFinetti, offers prudential grounds for action in conformity with personal probability. Under several structural assumptions about combinations of stakes, your betting policy is coherent only if your fair odds are probabilities. The central question posed here is the following one: Besides providing an operational test of coherent betting, does the "Book" argument also provide for adequate measurement of the agents degrees of beliefs? That is, are an agent's fair odds also (...) his/her personal probabilities for those events? We argue the answer is "No!" The problem is caused by the possibility of state dependent utilities. (shrink)

An orthodox review of work on kant from 1955 to 1965 concentrating on (1) the continental school, Holding kant's interest to be in founding a practical-Dogmatic metaphysics, With its main work being done on the early period, Things in themselves, And the categories; (2) questions about the fischer-Trendelenburg controversy on the relation of "transcendentally ideal" to "transcendentally real"; (3) english work throwing light on the aesthetic and on the analytic, With the still obsessive concern for the second analogy; (4) the (...) continuing debate on whether the categorical imperative is a moral criterion, And its relation to the golden rule; and (5) the important work on the concepts of freedom and the highest good. (shrink)

A (normal) system of propositional modal logic is said to be complete iff it is characterized by a class of (Kripke) frames. When we move to modal predicate logic the question of completeness can again be raised. It is not hard to prove that if a predicate modal logic is complete then it is characterized by the class of all frames for the propositional logic on which it is based. Nor is it hard to prove that if a propositional modal (...) logic is incomplete then so is the predicate logic based on it. But the interesting question is whether a complete propositional modal logic can have an incomplete extension. In 1967 Kripke announced the incompleteness of a predicate extension of S4. The purpose of the present article is to present several such systems. In the first group it is the systems with the Barcan Formula which are incomplete, while those without are complete. In the second group it is those without the Barcan formula which are incomplete, while those with the Barcan Formula are complete. But all these are based on propositional systems which are characterized by frames satisfying in each case a single first-order sentence. (shrink)

In a number of publications A.N. Prior considered the use of what he called ‘metric tense logic’. This is a tense logic in which the past and future operators P and F have an index representing a temporal distance, so that Pnα means that α was true n -much ago, and Fn α means that α will be true n -much hence. The paper investigates the use of metric predicate tense logic in formalising phenomena ormally treated by such devices as (...) multiple indexing or quantification over times. (shrink)

The paper investigates interpretations of propositional and firstorder logic in which validity is defined in terms of partial indices; sometimes called possibilities but here understood as non-empty subsets of a set W of possible worlds. Truth at a set of worlds is understood to be truth at every world in the set. If all subsets of W are permitted the logic so determined is classical first-order predicate logic. Restricting allowable subsets and then imposing certain closure conditions provides a modelling for (...) intuitionistic predicate logic. The same semantic interpretation rules are used in both logics for all the operators. (shrink)

The paper introduces a first-order theory in the language of predicate tense logic which contains a single simple axiom. It is shewn that this theory enables times to be referred to and sentences involving ‘now’ and ‘then’ to be formalised. The paper then compares this way of increasing the expressive capacity of predicate tense logic with other mechanisms, and indicates how to generalise the results to other modal and tense systems.

The second highest level of the divided line in Plato’s Republic (510b-511a) appears to be about the entities of mathematics—entities such as particular (though non-physical) triangles. It differs from the highest level in two respects. It involves reasoning from hypotheses, and it uses visible images. This article defends the traditional view that the passage is indeed about these mathematical ‘intermediates’; and tries to show how the apparently different features of the second level are related, by focussing on Plato’s need to (...) give an account of how we can speak of many particulars of the same kind, without assuming that they are imperfect copies, in the way sensible things can be imperfect copies, of forms. (shrink)

In celebrating Arthur Prior we celebrate what he gave to the world. Much of this is measured by what others have made of his ideas after his death. The focus of this paper is a little different. It looks at what Prior himself thought he was accomplishing. In particular it considers Prior’s attitude to the semantic metatheory of the logics that he was interested in. The paper sets out some characteristics of the metalogical study of intensional languages in terms of (...) an indexical theory of truth conditions stated in the language of set theory. In examining Prior’s work using these characteristics, it emerges that Prior had serious reservations about this way of studying modal and tense logics. (shrink)

In Book Γ of the Metaphysics Aristotle states and attempts to prove what he calls the basic principle of the science of being as being: the law of non‐contradiction. In this paper I defend an interpretation of his proof, inspired by Elizabeth Anscombe's 1961 essay in ‘Three Philosophers’, though some of its features were remarked on by Lukasiewicz in 1910, according to which Aristotle is proving this principle only for substance predicates, and that it is to be understood as the (...) basic principle of metaphysics rather than of logic. It is the principle that every substance has an essential nature, and if it is of the essential nature of x to be F then it cannot be of the essential nature of x to be not‐F since then x's being F and x's being not‐F would be the same. He puts it by saying that in such a case F and not‐F would ‘signify the same’ for x. Since they do not, x cannot be both. (shrink)

The paper presents an indexical semantics, based on times and worlds, for some of Prior's logics concerned with issues such as foreknowledge and determinism. In that sense Prior's logic of futurity can be presented as a completely standard modal/tense logic.

Book Information Logical Form and Language. Edited by G. Preyer and G. Peter. Clarendon Press. Oxford. 2002. Pp. x + 512. Hardback, £55. Paperback, £19.99.

Modal logic is the logic of necessity and possibility, of ‘must be’ and ‘may be’. These may be interpreted in various ways. If necessity is necessary truth, there is alethic modal logic; if it is moral or normative necessity, there is deontic logic [see chapter 8]. It may refer to what is known or believed to be true, in which case, there is an epistemic logic [chapter 9], or to what always has been or to what henceforth always will be (...) true, which gives an aspect of temporal logic [chapter 10]. Another interpretation is to read ‘Necessarily p′ as ‘it is provable that p′ This chapter will present the general framework of modal logic applicable to all of these, though with emphasis on alethic modal logics. (shrink)

Urn models were developed by Veikko Rantala to provide a non-standard semantics for first-order logic in which the domains, over which the quantifiers range, are allowed to vary. Rantala uses game-theoretical semantics in his presentation, and the present paper is a study of urn models from a more classical, truth-conditional point of view. An axiomatic system for urn logic is set out and completeness is proved by the method of maximal consistent sets.

«)La véritable philosophie est la sainteté de la raison. La volonté nous aliène et nous assimile à sa fin, l'entendement nous assimile et nous acquiert son objet): voilà pourquoi, en nous donnant à Dieu par un dévouement total, nous pouvons le mieux pénétrer par le regard); la pureté du détachement intérieur est l'organe de la vision parfaite. On ne peut le voir sans l'avoir, l'avoir sans l'aimer, l'aimer sans lui apporter l'hommage de tout ce qu'il est, pour ne retrouver en (...) tout que sa seule volonté et sa seule présence. Ce qu'il est, nous voulons qu'il le soit, quoi qu'il nous en coûte); et ainsi ce qu'il est en soi, il le devient en nous.)» Si l'on en croit l'aveu de Maurice Blondel, il y aurait dans sa réflexion philosophique un chemin de sainteté, voie étroite vers l'Amour qu'emprunte le philosophe d'Aix. Pour tenter d'en saisir le sens, le présent ouvrage entend réexaminer l'ensemble du projet philosophique blondélien au regard de cette nouvelle perspective. (shrink)

This long-awaited book replaces Hughes and Cresswell's two classic studies of modal logic: _An Introduction to Modal Logic_ and _A Companion to Modal Logic_. _A New Introduction to Modal Logic_ is an entirely new work, completely re-written by the authors. They have incorporated all the new developments that have taken place since 1968 in both modal propositional logic and modal predicate logic, without sacrificing tha clarity of exposition and approachability that were essential features of their earlier works. The book takes (...) readers from the most basic systems of modal propositional logic right up to systems of modal predicate with identity. It covers both technical developments such as completeness and incompleteness, and finite and infinite models, and their philosophical applications, especially in the area of modal predicate logic. (shrink)

First published in 2002. Routledge is an imprint of Taylor & Francis, an informa company.