J. Robert G. Williams

Generalized Probabilism: Dutch Books and Accuracy Domination

This paper explores De Finetti’s generalized versions of Dutch Book and Accuracy Domination theorems. Following proposals due to Jeff Paris, we construe these as underpinning a generalized probabilism appropriate to belief states against either a classical or a non-classical background. Both results are straightforward corollaries of the separating hyperplane theorem; their geometrical relationship is examined. It is shown that each point of Accuracy Domination for b induces a Dutch Book on b; but Dutch Books may need to be ‘scaled’ in order to find a point of Accuracy-Domination. Finally, diachronic Dutch Book defences of conditionalization are examined in the general setting. The formulation and limitations of the generalized conditionalization this delivers are examined.

DEGREE SUPERVALUATIONAL LOGIC

Supervaluationism is often described as the most popular semantic treatment of indeterminacy. There’s little consensus, however, about how to fill out the bare-bones idea to include a characterization of logical consequence. The paper explores one methodology for choosing between the logics: pick a logic that norms belief as classical consequence is standardly thought to do. The main focus of the paper considers a variant of standard supervaluational, on which we can characterize degrees of determinacy . It applies the methodology above to focus on degree logic . This is developed first in a basic, single-premise case; and then extended to the multipremise case, and to allow degrees of consequence. The metatheoretic properties of degree logic are set out. On the positive side, the logic is supraclassical—all classical valid sequents are degree logic valid. Strikingly, metarules such as cut and conjunction introduction fail.

The possibility of onion worlds: Rebutting an argument for structural universals1

Some argue that theories of universals should incorporate structural universals, in order to allow for the metaphysical possibility of worlds of ‘infinite descending complexity’ (‘onion worlds’). I argue that the possibility of such worlds does not establish the need for structural universals. So long as we admit the metaphysical possibility of emergent universals, there is an attractive alternative description of such cases.

GRADATIONAL ACCURACY AND NONCLASSICAL SEMANTICS

This paper gives a generalization of Jim Joyce’s 1998 argument for probabilism, dropping his background assumption that logic and semantics are classical. Given a wide variety of nonclassical truth-value assignments, Joyce-style arguments go through, allowing us to identify in each case a class of “nonclassically coherent” belief states. To give a local characterization of coherence, we need to identify a notion of logical consequence to use in an axiomatization. There is a very general, ‘no drop in truth-value’ characterization that will do the job. The result complements Paris’s 2001 discussion of generalized forms of Dutch books appropriate to nonclassical settings. §

AN ARGUMENT FOR CONJUNCTION CONDITIONALIZATION

Are counterfactuals with true antecedents and consequents automatically true? That is, is Conjunction Conditionalization: (X ? Y) ? (X > Y) valid? Stalnaker and Lewis think so, but many others disagree. We note here that the extant arguments for Conjunction Conditionalization are unpersuasive, before presenting a family of more compelling arguments. These arguments rely on some standard theorems of the logic of counterfactuals as well as a plausible and popular semantic claim about certain semifactuals. Denying Conjunction Conditionalization, then, requires rejecting other aspects of the standard logic of counterfactuals or else our intuitive picture of semifactuals

Working Parts: Reply to Mellor

Whenever a material thing has parts, those parts are located where that thing is. This is a necessary truth, and needs explaining.

Normative Reference Magnets

The concept of moral wrongness, many think, has a distinctive kind of referential stability, brought out by moral twin earth cases. This article offers a new account of the source of this stability, deriving it from a metaphysics of content: “substantive” radical interpretation, and first-order normative assumptions. This story is distinguished from extant “reference magnetic” explanations of the phenomenon, and objections and replies are considered.