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Is probability the only coherent approach to uncertainty?, Risk Analysis, forthcoming
"... In this paper I discuss an argument that purports to prove that probability theory is the only sensible means of dealing with uncertainty. I show that this argument can succeed only if some rather controversial assumptions about the nature of uncertainty are accepted. I discuss these assumptions and ..."
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In this paper I discuss an argument that purports to prove that probability theory is the only sensible means of dealing with uncertainty. I show that this argument can succeed only if some rather controversial assumptions about the nature of uncertainty are accepted. I discuss these assumptions and provide reasons for rejecting them. I also present examples of what I take to be nonprobabilistic uncertainty. Key Words: Cox’s Theorem, NonClassical Logic, Probability, Uncertainty, Vagueness Uncertainties are ubiquitous in risk analysis and on the face of it, we must contend with a number of quite distinct sorts of uncertainty. There are, of course, many methods on hand to deal with uncertainty, so it is important to select the method best suited to the uncertainty in question. There is, however, a growing push towards dealing with all uncertainty in one fell swoop. That is, it is thought to be desirable to employ a single method capable of quantifying all sources of uncertainty. One candidate for this task is probability theory. For such a program to succeed, a demonstration that all uncertainty is,
Vagueness and Truth
"... In philosophy of logic and elsewhere, it is generally thought that similar problems should be solved by similar means. This advice is sometimes elevated to the status of a principle: the principle of uniform solution. In this paper I will explore the question of what counts as a similar problem and ..."
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In philosophy of logic and elsewhere, it is generally thought that similar problems should be solved by similar means. This advice is sometimes elevated to the status of a principle: the principle of uniform solution. In this paper I will explore the question of what counts as a similar problem and consider reasons for subscribing to the principle of uniform solution. 1 Introducing the Principle of Uniform Solution It would be very odd to give different responses to two paradoxes depending on minor, seeminglyirrelevant details of their presentation. For example, it would be unacceptable to deal with the paradox of the heap by invoking a multivalued logic, ̷L∞, say, and yet, when faced with the paradox of the bald man, invoke a supervaluational logic. Clearly these two paradoxes are of a kind—they are both instances of the sorites paradox. And whether the sorites paradox is couched in terms of heaps and grains of sand, or in terms of baldness and the number of hairs on the head, it is essentially the same problem and therefore must be solved by the same means. More generally, we might suggest that similar paradoxes should be resolved by similar means. This advice is sometimes elevated to the status of a principle, which usually goes by the name of the principle of uniform solution. This principle and its motivation will occupy us for much of the discussion in this paper. In particular, I will defend a rather general form of this principle. I will argue that two paradoxes can be thought to be of the same kind because (at a suitable level of abstraction) they share a similar internal structure, or because of external considerations such as the relationships of the paradoxes in question to other paradoxes in the vicinity, or the way they respond to proposed solutions. I will then use this reading of the principle of uniform solution to make a case for the sorites and the liar paradox being of a kind.
unknown title
"... Tolerant, classical, strict In this paper we investigate a semantics for firstorder logic originally proposed by R. van Rooij to account for the idea that vague predicates are tolerant, that is, for the principle that if x is P, then y should be P whenever y is similar enough to x. The semantics, w ..."
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Tolerant, classical, strict In this paper we investigate a semantics for firstorder logic originally proposed by R. van Rooij to account for the idea that vague predicates are tolerant, that is, for the principle that if x is P, then y should be P whenever y is similar enough to x. The semantics, which makes use of indifference relations to model similarity, rests on the interaction of three notions of truth: the classical notion, and two dual notions simultaneously defined in terms of it, which we call tolerant truth and strict truth. We characterize the space of consequence relations definable in terms of those and discuss the kind of solution this gives to the sorites paradox. We discuss some applications of the framework to the pragmatics and psycholinguistics of vague predicates, in particular regarding judgments about borderline cases. Our aim in this paper is to explore a semantic framework originally proposed by [van Rooij, 2010b] in order to deal with the sorites paradox, and intended to formalize the idea that vague predicates are tolerant. Standardly, the idea of tolerance is expressed
Reaching transparent truth
"... This paper presents and defends a way to add a transparent truth predicate to classical logic, such that T 〈A 〉 and A are everywhere intersubstitutable, where all Tbiconditionals hold, and where truth can be made compositional. A key feature of our framework, called STT (for StrictTolerant Truth), ..."
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This paper presents and defends a way to add a transparent truth predicate to classical logic, such that T 〈A 〉 and A are everywhere intersubstitutable, where all Tbiconditionals hold, and where truth can be made compositional. A key feature of our framework, called STT (for StrictTolerant Truth), is that it supports a nontransitive relation of consequence. At the same time, it can be seen that the only failures of transitivity STT allows for arise in paradoxical cases. 1