De Finettian Logics of Indicative Conditionals Part I: Trivalent Semantics and Validity

Journal of Philosophical Logic - This paper explores trivalent truth conditions for indicative conditionals, examining the “defective” truth table proposed by de Finetti (1936) and...     

Objecting Vaguely to Pascal's Wager

Philosophical Studies -     

Kripke Bundle Semantics and C-set Semantics

Kripke bundle [3] and C-set semantics [1] [2] are known as semantics which generalize standard Kripke semantics. In [3] and in [1], [2] it is shown that Kripke bundle and C-set semantics are stronger than standard Kripke semantics. Also it is true that C-set semantics for superintuitionistic logics is stronger than Kripke bundle semantics [5].In this paper, we show that Q-S4.1 is not Kripke bundle complete via C-set models. As a corollary we can give a simple proof showing that C-set semantics for modal logics are stronger than Kripke bundle semantics.     

On the Treatment of Incomparability in Ordering Semantics and Premise Semantics

In his original semantics for counterfactuals, David Lewis presupposed that the ordering of worlds relevant to the evaluation of a counterfactual admitted no incomparability between worlds. He later came to abandon this assumption. But the approach to incomparability he endorsed makes counterintuitive predictions about a class of examples circumscribed in this paper. The same underlying problem is present in the theories of modals and conditionals developed by Bas van Fraassen, Frank Veltman, and Angelika Kratzer. I show how to reformulate all these theories in terms of lower bounds on partial preorders, conceived of as maximal antichains, and I show that treating lower bounds as cutsets does strictly better at capturing our intuitions about the semantics of modals, counterfactuals, and deontic conditionals.     

Relational Semantics and Domain Semantics for Epistemic Modals

The standard account of modal expressions in natural language analyzes them as quantifiers over a set of possible worlds determined by the evaluation world and an accessibility relation. A number of authors have recently argued for an alternative account according to which modals are analyzed as quantifying over a domain of possible worlds that is specified directly in the points of evaluation. But the new approach only handles the data motivating it if it is supplemented with a non-standard account of attitude verbs and conditionals. It can be shown the the relational account handles the same data equally well if it too is supplemented with a non-standard account of such expressions.     

Intransitivity and Vague Preferences

This paper is concerned with intransitivity in normative rational choice. It focuses on a class of intransitivities which have received little attention, those involving vague preferences. “Vague preferences” are defined in terms of vague predicates such as “red” or “bald.” Such preferences appear common, and intransitive indifference is argued to be an unavoidable feature of them. Such preferences are argued to undermine intransitive strict preference also. Various formal theories of vagueness are applied to an example of vague preferences, but none of them provide a justification for the transitivity axiom. For helpful comments on earlier drafts and discussions of this material, I am very grateful to John Broome, Rosanna Keefe, Matthew Kramer, Stuart Rachels, Jochen Runde and Adrian Walsh. I owe a large debt to John O’Neill, who suggested an earlier version of the “Tragedy of the Disappearing Commons” example.     

Vague Value

You are morally permitted to save your friend at the expense of a few strangers, but not at the expense of very many. However, there seems no number of strangers that marks a precise upper bound here. Consequently, there are borderline cases of groups at the expense of which you are permitted to save your friend. This essay discusses the question of what explains ethical vagueness like this, arguing that there are interesting metaethical consequences of various explanations.     

Semantics and supervenience

I have presented much of this research in talks at the University of Costa Rica and the University of Texas at Austin. I am grateful to my audiences for their comments and advice. I would like especially to thank Luis Camacho, Nicholas Asher, and Robert Koons. Many of the ideas in the paper stem from an informal seminar on type-free theories held at the University of Texas's Center for Cognitive Science from 1984 to 1987. I am grateful to the participants in that seminar — Ignacio Angelelli, Nicholas Asher, Herbert Hochberg, Hans Kamp, Frederick Kronz, Per Lindström and Mark Sainsbury — for their many insights into type-free semantics, and to the Center for Cognitive Science for providing such a hospitable environment for this work. I have also profited from the criticisms of two anonymous referees. Finally, I am indebted to the University of Texas's University Research Institute and to the National Science Foundation's Information Science and History and Philosophy of Science programs for grant support.     

Against Vague Existence

Philosophical Studies -     

Referentiality and Matrix Semantics

Referential semantics importantly subscribes to the programme of theory of logical calculi. Defined by Wójcicki in [8], it has been subsequently studied in a series of papers of the author, till the full exposition of the framework in [9] and its intuitive characterisation in [10].     

Analyticity and Possible-World Semantics

Standard approaches to possible-world semantics allow us to define necessity and logical truth, but analyticity is considerably more difficult to account for. The source of this difficulty lies in the received model-theoretical conception of a language interpretation. In intuitive terms, analyticity amounts to truth in virtue of meaning alone, i.e. solely in virtue of the interpretation of linguistic expressions. In other words, an analytic sentence should remain true under all variations of ‘extralinguistic reality’ as long as the interpretation is kept constant. However, the received conception of an interpretation as a mapping from language to a model frame hinders keeping the interpretation constant while varying other components of the model. To make room for analyticity, the concept of an interpretation should therefore be revised. The latter should be made richer in content than it has usually been assumed. As a by-product, this revision also gives us a one-dimensional analogue of the influential two-dimensional account of a priori. We are thus able to map out the network of formal connections between the notions of analyticity, apriority, logical truth and necessity.     

Inferentializing Semantics

The entire development of modern logic is characterized by various forms of confrontation of what has come to be called proof theory with what has earned the label of model theory. For a long time the widely accepted view was that while model theory captures directly what logical formalisms are about, proof theory is merely our technical means of getting some incomplete grip on this; but in recent decades the situation has altered. Not only did proof theory expand into new realms, generalizing the concept of proof in various directions; many philosophers also realized that meaning may be seen as primarily consisting in certain rules rather than in language-world links. However, the possibility of construing meaning as an inferential role is often seen as essentially compromised by the limits of proof-theoretical means. The aim of this paper is to sort out the cluster of problems besetting logical inferentialism by disentangling and clarifying one of them, namely determining the power of various inferential frameworks as measured by that of explicitly semantic ones.