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Barnes, Elizabeth. Arguments Against Metaphysical Indeterminacy and Vagueness
2010, Philosophy Compass 5(11): 953-964.
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Added by: Emily Paul

Abstract: In this paper, I’ll examine some of the major arguments against metaphysical indeterminacy and vagueness. Metaphysical accounts of indeterminacy and vagueness have been decidedly unpopular, and this paper examines some of the major reasons for that unpopularity.

Comment: A really useful overview of the alleged problem of metaphysical indeterminacy, and the main arguments against it. Written extremely clearly, but dealing with complex subject matter, so suitable for either an advanced undergraduate or masters class (or a further reading in an intermediate undergraduate class).

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Bergmann, Merrie. An Introduction to Many-Valued and Fuzzy Logic
2009, Cambridge University Press.
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Added by: Berta Grimau

Publisher’s Note: Professor Merrie Bergmann presents an accessible introduction to the subject of many-valued and fuzzy logic designed for use on undergraduate and graduate courses in non-classical logic. Bergmann discusses the philosophical issues that give rise to fuzzy logic – problems arising from vague language – and returns to those issues as logical systems are presented. For historical and pedagogical reasons, three-valued logical systems are presented as useful intermediate systems for studying the principles and theory behind fuzzy logic. The major fuzzy logical systems – Lukasiewicz, Gödel, and product logics – are then presented as generalisations of three-valued systems that successfully address the problems of vagueness. A clear presentation of technical concepts, this book includes exercises throughout the text that pose straightforward problems, that ask students to continue proofs begun in the text, and that engage students in the comparison of logical systems.

Comment: In the words of the author: 'This textbook can be used as a complete basis for an introductory course on formal many-valued and fuzzy logics, at either the upper-level undergraduate or the graduate level, and it can also be used as a supplementary text in a variety of courses. There is considerable flexibility in either case. The truth-valued semantic chapters are independent of the algebraic and axiomatic ones, so that either of the latter may be skipped. Except for Section 13.3 of Chapter 13, the axiomatic chapters are also independent of the algebraic ones, and an instructor who chooses to skip the algebraic material can simply ignore the latter part of 13.3. Finally, Lukasiewicz fuzzy logic is presented independently of Gödel and product fuzzy logics, thus allowing an instructor to focus solely on the former. There are exercises throughout the text. Some pose straightforward problems for the student to solve, but many exercises also ask students to continue proofs begun in the text, to prove results analogous to those in the text, and to compare the various logical systems that are presented.' The book does include a review of classical propositional and first-order logic, but the students should've taken at least one basic logic course before getting into this material.

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Graff Fara, Delia. Shifting Sands: An Interest-Relative Theory of Vagueness
2000, Philosophical Topics 28(1): 45-81.
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Added by: Emily Paul

Summary: I propose that the meanings of vague expressions render the truth conditions of utterances of sentences containing them sensitive to our interests. For example, ‘expensive’ is analyzed as meaning ‘costs a lot’, which in turn is analyzed as meaning ‘costs significantly greater than the norm’. Whether a difference is a significant difference depends on what our interests are. Appeal to the proposal is shown to provide an attractive resolution of the sorites paradox that is compatible with classical logic and semantics.

Comment: An important paper to use for an advanced UG Philosophy of Language/Metaphysics course. Would definitely need to be a core reading and be taught in a lecture first, as there are many important things going on here.

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Keefe, Rosanna. Theories of Vagueness
2000, Cambridge University Press.
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Added by: Berta Grimau

Publisher’s Note: Most expressions in natural language are vague. But what is the best semantic treatment of terms like ‘heap’, ‘red’ and ‘child’? And what is the logic of arguments involving this kind of vague expression? These questions are receiving increasing philosophical attention, and in this timely book Rosanna Keefe explores the questions of what we should want from an account of vagueness and how we should assess rival theories. Her discussion ranges widely and comprehensively over the main theories of vagueness and their supporting arguments, and she offers a powerful and original defence of a form of supervaluationism, a theory that requires almost no deviation from standard logic yet can accommodate the lack of sharp boundaries to vague predicates and deal with the paradoxes of vagueness in a methodologically satisfying way. Her study will be of particular interest to readers in philosophy of language and of mind, philosophical logic, epistemology and metaphysics.

Comment: This book could be used in a philosophy of logic or a philosophy of language course which had a section on vagueness (either at undergraduate or postgraduate level). The first chapter provides a good main reading for such purpose. The book can also be used in a course focused on vagueness exclusively. The technical discussion is minimized throughout and presupposes only some familiarity with elementary logic.

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Magidor, Ofra, Stephen Kearns. Epistemicism about vagueness and meta-linguistic safety
2008, Philosophical Perspectives 22 (1): 277-304.
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Added by: Berta Grimau

Abstract: The paper challenges Williamson’s safety based explanation for why we cannot know the cut-off point of vague expressions. We assume throughout (most of) the paper that Williamson is correct in saying that vague expressions have sharp cut-off points, but we argue that Williamson’s explanation for why we do not and cannot know these cut-off points is unsatisfactory. In sect 2 we present Williamson’s position in some detail. In particular, we note that Williamson’s explanation relies on taking a particular safety principle (‘Meta-linguistic belief safety’ or ‘MBS’) as a necessary condition on knowledge. In section 3, we show that even if MBS were a necessary condition on knowledge, that would not be sufficient to show that we cannot know the cut-off points of vague expressions. In section 4, we present our main case against Williamson’s explanation: we argue that MBS is not a necessary condition on knowledge, by presenting a series of cases where one’s belief violates MBS but nevertheless constitutes knowledge. In section 5, we present and respond to an objection to our view. And in section 6, we briefly discuss the possible directions a theory of vagueness can take, if our objection to Williamson’s theory is taken on board.

Comment: This paper would work well as a secondary reading in a course on vagueness with a section on epistemicism. For instance, the course could present Williamson's as the main proposal within that tradition and then turn to this paper for criticism and an alternative proposal within the same tradition.

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O'Connor, Cailin. The Evolution of Vagueness
2013, Erkenntnis (S4):1-21.
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Added by: Chris Blake-Turner, Contributed by: Cailin O'Connor

Abstract: Vague predicates, those that exhibit borderline cases, pose a persistent problem for philosophers and logicians. Although they are ubiquitous in natural language, when used in a logical context, vague predicates lead to contradiction. This paper will address a question that is intimately related to this problem. Given their inherent imprecision, why do vague predicates arise in the first place? I discuss a variation of the signaling game where the state space is treated as contiguous, i.e., endowed with a metric that captures a similarity relation over states. This added structure is manifested in payoffs that reward approximate coordination between sender and receiver as well as perfect coordination. I evolve these games using a variation of Herrnstein reinforcement learning that better reflects the generalizing learning strategies real-world actors use in situations where states of the world are similar. In these simulations, signaling can develop very quickly, and the signals are vague in much the way ordinary language predicates are vague – they each exclusively apply to certain items, but for some transition period both signals apply to varying degrees. Moreover, I show that under certain parameter values, in particular when state spaces are large and time is limited, learning generalization of this sort yields strategies with higher payoffs than standard Herrnstein reinforcement learning. These models may then help explain why the phenomenon of vagueness arises in natural language: the learning strategies that allow actors to quickly and effectively develop signaling conventions in contiguous state spaces make it unavoidable

Comment: [This is a stub entry. Please add your comments to help us expand it]

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