Paraconsistent Vagueness: Why Not?

The idea that the phenomenon of vagueness might be modelled by a paraconsistent logic has been little discussed in contemporary work on vagueness, just as the idea that paraconsistent logics might be fruitfully applied to the phenomenon of vagueness has been little discussed in contemporary work on paraconsistency. This is prima facie surprising given that the earliest formalisations of paraconsistent logics presented in Jáskowski and Halldén were presented as logics of vagueness. One possible explanation for this is that, despite initial advocacy by pioneers of paraconsistency, the prospects for a paraconsistent account of vagueness are so poor as to warrant little further consideration. In this paper we look at the reasons that might be offered in defence of this negative claim. As we shall show, they are far from compelling. Paraconsistent accounts of vagueness deserve further attention

Paraconsistent Vagueness: Why Not?

The idea that the phenomenon of vagueness might be modelled by a paraconsistent logic has been little discussed in contemporary work on vagueness, just as the idea that paraconsistent logics might be fruitfully applied to the phenomenon of vagueness has been little discussed in contemporary work on paraconsistency. This is prima facie surprising given that the earliest formalisations of paraconsistent logics presented in Jáskowski and Halldén were presented as logics of vagueness. One possible explanation for this is that, despite initial advocacy by pioneers of paraconsistency, the prospects for a paraconsistent account of vagueness are so poor as to warrant little further consideration. In this paper we look at the reasons that might be offered in defence of this negative claim. As we shall show, they are far from compelling. Paraconsistent accounts of vagueness deserve further attention

An Alleged Tension between Quantum Logic and Applied Classical Mathematics

Timothy Williamson has argued that the applicability of classical mathematics in the natural and social sciences raises a problem for the adoption, in non-mathematical domains, of a wide range of non-classical logics, including quantum logics (QL). We first reconstruct the argument and present its restriction to the case of QL. Then we show that there is no inconsistency whatsoever between the application of classical mathematics to quantum phenomena and the use of QL in reasoning about them. Once we identify the premise in Williamson's argument that turns out to be false when restricted to QL, we argue that the same premise breaks down for a wider variety of non-classical logics. In the end, we also suggest that the alleged tension between these non-classical logics and applied classical mathematics betrays a misunderstanding of the nature of mathematical representation in science.Comment: 22 page

Borderline vs. unknown: comparing three-valued representations of imperfect information

International audienceIn this paper we compare the expressive power of elementary representation formats for vague, incomplete or conflicting information. These include Boolean valuation pairs introduced by Lawry and González-Rodríguez, orthopairs of sets of variables, Boolean possibility and necessity measures, three-valued valuations, supervaluations. We make explicit their connections with strong Kleene logic and with Belnap logic of conflicting information. The formal similarities between 3-valued approaches to vagueness and formalisms that handle incomplete information often lead to a confusion between degrees of truth and degrees of uncertainty. Yet there are important differences that appear at the interpretive level: while truth-functional logics of vagueness are accepted by a part of the scientific community (even if questioned by supervaluationists), the truth-functionality assumption of three-valued calculi for handling incomplete information looks questionable, compared to the non-truth-functional approaches based on Boolean possibility–necessity pairs. This paper aims to clarify the similarities and differences between the two situations. We also study to what extent operations for comparing and merging information items in the form of orthopairs can be expressed by means of operations on valuation pairs, three-valued valuations and underlying possibility distributions

Richard Dietz and Sebastiano Moruzzi (eds.), "Cuts and Clouds: Vagueness, its Nature, and its Logic"

Book Reviews:Richard Dietz and Sebastiano Moruzzi (eds.), Cuts and Clouds: Vagueness, its Nature, and its Logic, Oxford University Press, 2010, 586 pp., ISBN 9780199570386

The Nature and Logic of Vagueness

The PhD thesis advances a new approach to vagueness as dispersion, comparing it with the main philosophical theories of vagueness in the analytic tradition

An Alleged Tension between Quantum Logic and Applied Classical Mathematics

Timothy Williamson has argued that the applicability of classical mathematics in the natural and social sciences raises a problem for the adoption, in non-mathematical domains, of a wide range of non-classical logics, including quantum logics (QL). We first reconstruct the argument and present its restriction to the case of QL. Then we show that there is no inconsistency whatsoever between the application of classical mathematics to quantum phenomena and the use of QL in reasoning about them. Once we identify the premise in Williamson's argument that turns out to be false when restricted to QL, we argue that the same premise breaks down for a wider variety of non-classical logics. In the end, we also suggest that the alleged tension between these non-classical logics and applied classical mathematics betrays a misunderstanding of the nature of mathematical representation in science

An Alleged Tension Between non-Classical Logics and Applied Classical Mathematics

Timothy Williamson has recently argued that the applicability of classical mathematics in the natural and social sciences raises a problem for the endorsement, in non-mathematical domains, of a wide range of non-classical logics. We first reconstruct his argument and present its restriction to the case of quantum logic (QL). Then we show that there is no problematic tension between the applicability of classical mathematical models to quantum phenomena and the endorsement of QL in the reasoning about the latter. Once we identify the premise in Williamson's argument that turns out to be false when restricted to QL, we argue that the same premise fails for a wider variety of non-classical logics. In the end, we use our discussion to draw some general lessons concerning the relationship between applied logic and applied mathematics

Epistemicism and modality

What kind of semantics should someone who accepts the epistemicist theory of vagueness defended in Timothy Williamson’s Vagueness (1994) give a definiteness operator? To impose some interesting constraints on acceptable answers to this question, I will assume that the object language also contains a metaphysical necessity operator and a metaphysical actuality operator. I will suggest that the answer is to be found by working within a three-dimensional model theory. I will provide sketches of two ways of extracting an epistemicist semantics from that model theory, one of which I will find to be more plausible than the other

La irregularidad lógica y lo a priori constitutivo

Lo que llamaré ‘la objeción lógica irregular’ es una línea de ataque en contra del principio común y convincente  de que nuestra justificación de las verdades lógicas se fundamenta en la comprensión de sus conceptos  constituyentes. Esta objeción busca socavar la posibilidad de cualquier conexión constitutiva profunda, en la  epistemología de la lógica (y también más allá), entre la comprensión y la justificación. Mi tesis es que, si bien la objeción lógica irregular no llega a demostrar que este principio tradicional debe ser rechazado, no obstante,  sirve para reforzar algunos refinamientos importantes.What I will call ‘the deviant logician objection’ is one line of attack against the common and compelling tenet  that our justification for logical truths is grounded in our understanding of their constituent concepts. This  objection seeks to undermine the possibility of any deep constitutive connection, in the epistemology of logic  (and also beyond), between understanding and justification. My thesis is that while the deviant logician  objection falls short of proving that this traditional tenet must be rejected, nonetheless it serves to bolster some important refinements