The existential assumptions of traditional logic

There have been and continue to be disagreements about how to consider the traditional square of opposition and the traditional inferences of obversion, conversion, contraposition and inversion from the perspective of contemporary quantificational logic. Philosophers have made many different attempts to save traditional inferences that are invalid when they involve empty classes. I survey some of these attempts and argue that the only satisfactory way of saving all the traditional inferences is to make the existential assumption that both the subject and predicate classes and their complement classes are non-empty for all the propositions we admit. I briefly indicate the room for continued controversy over how properly to interpret Aristotle’s statements regarding these inferences, but find some plausibility in the views of Manley Thompson and A.N.Prior that Aristotle had in mind a particular arrangement of existential import unfamiliar to most contemporary logicians     

Twardowski's theory of modification againts the background of traditional logic

Paper presented at the conference The Social and Philosophical Thought in Galicia and Its Austro-Hungarian Context, Lvov, December 5–7, 1991.     

I. Feuer on guilt and logic

Recent work in the theory of action by analytical philosophers has focused on explaining actions by citing the agent's motivating reason(s). But this ignores a pattern of explanation typical in the social sciences, i.e. situating the agent in a reference group whose members typically manifest that behavior. In some cases the behavior of such groups can itself be shown to be the product of social forces. Two extended examples of this explanatory pattern are studied. In each case the motivating reasons of the agents concerned can scarcely be understood apart from reference to the groups of which the agents are members and the social forces which work on those groups. However, attention to the agent's own reasons for action remains important, in part because of action theory's critical potential to help liberate people from arbitrary, hypostasized social forces.     

Moral Responsibility: The Difference of Strawson,and the Difference it Should Make

P.F. Strawson’s work on moral responsibility is well-known. However, an important implication of the landmark “Freedom and Resentment” has gone unnoticed. Specifically, a natural development of Strawson’s position is that we should understand being morally responsible as having externalistically construed pragmatic criteria, not individualistically construed psychological ones. This runs counter to the contemporary ways of studying moral responsibility. I show the deficiencies of such contemporary work in relation to Strawson by critically examining the positions of John Martin Fischer and Mark Ravizza, R. Jay Wallace, and Philip Pettit for problems due to individualistic assumptions.Thanks to an audience at Carleton University for helpful discussion.     

Algorithmic logic. Multiple-valued extensions

Extended algorithmic logic (EAL) as introduced in [18] is a modified version of extended ⁺-valued algorithmic logic. Only two-valued predicates and two-valued propositional variables occur in EAL. The role of the ⁺-valued logic is restricted to construct control systems (stacks) of pushdown algorithms whereas their actions are described by means of the two-valued logic. Thus EAL formalizes a programming theory with recursive procedures but without the instruction CASE.The aim of this paper is to discuss EAL and prove the completeness theorem. A complete formalization of EAL was announced in [20] but no proof of the completeness theorem was given.     

Notes on conditional logic

This paper consists of some lecture notes in which conditional logic is treated as an extension of modal logic. Completeness and filtration theorems are provided for some basis systems. These notes were originally drafted for a course given at the University of Auckland in 1987 (Philosophy 29.308). The work reported in Section 5 is due to Michael Strevens, who took the course and presented his conception of a filtration in a term paper [5]. The author wishes to thank Strevens for many stimulating discussions and for permission to include his results here