Online research in philosophy

Vagueness is an extremely widespread feature of language, famously associated with the sorites paradox. One instance of this paradox concludes that a single grain of sand is a heap of sand, by starting with a large heap of sand and invoking the plausible premise that if you take one grain of sand away from a heap of sand, then you still have a heap. The supervaluationist theory of vagueness states that a sentence is true if and only if it is (...) true on all ways of making it precise. This yields borderline case predications that are neither true nor false, but yet classical logic is preserved almost entirely. The sorites paradox is solved because the main premise comes out false – on each way of making 'heap' precise, there is some first grain that turns a heap into a non-heap – but there is no sharp boundary to 'heap' because it is a different grain on different ways of making 'heap' precise; so, there is no grain of which it is true to say it is that first grain. The theory has a range of merits in comparison with rival theories, such as the epistemic view or degree theories of vagueness. Objections have been made (and answers offered) in relation to its treatment of higher-order vagueness and what it says about truth and validity. Author Recommends Fine, Kit. 'Vagueness, Truth and Logic.' Synthese 30 (1975). 265–300. Reprinted in Keefe and Smith 1997. This is the classic text introducing supervaluationism as a treatment of vagueness. It provides both philosophical discussion and formal modelling, demonstrating the adherence to classical logic that the theory yields. Keefe, Rosanna and Peter Smith, eds. Vagueness: A Reader . Cambridge, MA: MIT Press. This collection includes many classic papers on vagueness, including Fine's paper, cited above, a paper by Dummett that offers (but rejects) a precursor of the supervaluationist view, another less well-known early presentation of the view by Henyrk Mehlberg and discussion and defences of the main rival theories of vagueness. Keefe, Rosanna. Theories of Vagueness . Cambridge: Cambridge University Press, 2000. This book defends a supervaluationist theory of vagueness. It discusses the phenomena of vagueness and what is required of a theory of vagueness, before considering and rejecting the major alternatives in turn. Williamson, Timothy. Vagueness . London: Routledge, 1994. This book defends the epistemic theory of vagueness, which maintains that vague predicates do have sharp boundaries, we just do not know where those boundaries lie. It also contains detailed discussions of opposing theories, including supervaluationism. Unger, Peter. 'The Problem of the Many.' Midwest Studies in Philosophy 5 (1980). Eds. P.A. French, T.E. Uehling Jr and H.K. Wettstein. Minneapolis, MN: University of Minnesota Press. This is the classic presentation of the Problem of the Many, to which a supervaluationist solution is relatively popular. This problem arises because frequently the boundaries of an object – say a cloud – are not sharply delineated. Each of the many ways of drawing the boundary seems to be an object of the type in question – say a cloud – hence the problem that there are many things when there should be just one. The supervaluationist, it seems, can say that there is just one cloud because that is true on each precisification. Williams, J. Robert G. 'An Argument for the Many.' Proceedings of the Aristotelian Society 106 (2006). 409–17. Detailed discussion of Unger's Problem of the Many, especially in relation to the supervaluationist solution. Shapiro, Stewart. Vagueness in Context . Oxford: Oxford University Press, 2006. In this book, Shapiro employs a supervaluationist framework, without endorsing some of the central claims of the standard supervaluationist theory of vagueness. Online Materials http://plato.stanford.edu/entries/vagueness/ http://plato.stanford.edu/entries/sorites-paradox/ http://plato.stanford.edu/entries/problem-of-many/ http://www.st-andrews.ac.uk/~arche/projects/vagueness/bibliography.shtml Sample Syllabus Week I: Introduction to Vagueness Keefe, Theories of Vagueness (especially chapters 1 and 2) Williamson, Vagueness (especially chapters 1 and 2) Week II: Supervaluationist Theory: logic and semantics Keefe, 'Vagueness: Supervaluationism.' Philosophy Compass 3.2 (2008): 315–24, 10.1111/j.1747-9991.2008.00124.x Fine, 'Vagueness, Truth and Logic' Keefe, Theories of Vagueness (especially chapter 7) Week III: Higher Order Vagueness and the D Operator Keefe, Theories of Vagueness (especially chapter 8) Fara, Delia Graff. 'Gap Principles, Penumbral Consequence and Infinitely Higher-Order Vagueness.' Liars and Heaps . Ed. J.C. Beall. Oxford: Oxford University Press, 2003. 195–221. Originally published under the name 'Delia Graff'. Week IV: Truth and Validity Keefe, Theories of Vagueness (especially chapter 8) Keefe, 'Supervaluationism and Validity.' Philosophical Topics 28 (2000). 93–105. Cobreros, 'Supervaluations and Logical Consequence: Retrieving the Local Perspective.' Studia Logica , Special Issue on Vagueness , 2009 Week V: Problem of the Many Unger, "The Problem of the Many" Williams, "An Argument for the Many" Week VI: Rival Theories Williamson, Vagueness (especially chapters 7 and 8) Keefe and Smith, Vagueness: A Reader (e.g. chapters 11, 14–6) Focus Questions 1 How important is it for a theory of vagueness to accommodate penumbral connections? Are there any putative penumbral connections that the supervaluationist cannot accommodate? 2 According to supervaluationism, what does it take for "Katie said that Hannah is tall" to be true? Does the view have implausible consequences for indirect speech reports when vague terms are used? 3 Is higher-order vagueness a problem for supervaluationism? 4 Is there more than one viable option for the account of validity in a supervaluationist framework? 5 Can a supervaluationist account of vagueness accommodate the full extent of context dependence exhibited in the use of vague predicates? (shrink)

Stochastic subgrid models have been proposed to capture the missing variability and correct systematic medium-term errors in general circulation models. In particular, the poor representation of subgrid-scale deep convection is a persistent problem that stochastic parametrizations are attempting to correct. In this paper, we construct such a subgrid model using data derived from large-eddy simulations (LESs) of deep convection. We use a data-driven stochastic parametrization methodology to construct a stochastic model describing a finite number of cloud states. Our model (...) emulates, in a computationally inexpensive manner, the deep convection-resolving LES. Transitions between the cloud states are modelled with Markov chains. By conditioning the Markov chains on large-scale variables, we obtain a conditional Markov chain, which reproduces the time evolution of the cloud fractions. Furthermore, we show that the variability and spatial distribution of cloud types produced by the Markov chains become more faithful to the LES data when local spatial coupling is introduced in the subgrid Markov chains. Such spatially coupled Markov chains are equivalent to stochastic cellular automata. (shrink)

Vlastos, G. Introduction: the paradox of Socrates.--Lacey, A. R. Our knowledge of Socrates.--Dover, K. J. Socrates in the Clouds.--Robinson, R. Elenchus.--Robinson, R. Elenchus, direct and indirect.--Robinson, R. Socratic definition.--Nakhnikian, G. Elenctic definitions.--Cohen, S. M. Socrates on the definition of piety: Euthyphro 10A-11B.--Santas, G. Socrates at work on virtue and knowledge in Plato's Laches.--Burnyeat, M. F. Virtues in action.--Walsh, J. J. The Socratic denial of Akrasia.--Santas, G. Plato's Protagoras and explanations of weakness.--Woozley, A. D. Socrates on disobeying the law.--Allen, R. E. (...) Plato's earlier theory of forms. (shrink)

Introduction: the paradox of Socrates, by G. Vlastos.--Our knowledge of Socrates, by A. R. Lacey.--Socrates in the Clouds, by K. J. Dover.--Elenchus, by R. Robinson.--Elenchus: direct and indirect, by R. Robinson.--Socratic definition, by R. Robinson.--Elenctic definitions, by G. Nakhnikian.--Socrates on the definition of piety: Euthyphro 10A-11B, by S. M. Cohen.--Socrates at work on virtue and knowledge in Plato's Laches, by G. Santas.--Virtues in action, by M. F. Burnyeat.--The Socratic denial of Akrasia, by J. J. Walsh.--Plato's Protagoras and explanations of weakness, (...) by G. Santas.--Socrates on disobeying the law, by A. D. Woozley.--Plato's earlier theory of forms, by R. E. Allen.--Selected bibliography (p. 336-339). (shrink)