The paper discusses some ways in which the phenomenon of borderline cases may be thought to bear on the traditional philosophical idea that certain domains of facts are fully open to our view. The discussion focusses on a very influential argument (due to Tim Williamson) to the effect that, roughly, no such domains of luminous facts exist. Many commentators have felt that the vagueness unavoidably inherent in the description of the facts that are best candidates for being luminous plays an illicit role in the argument. The paper investigates this issue by centring around the idea that vagueness brings with itself borderline cases, and that these in turn generate absence of a fact of the matter and hence epistemically benign lack of knowledge. It is argued that, given the possibility of absence of a fact of the matter, the idea of luminosity should be reformulated using the notion of determinacy, and that the resulting reformulation is not immediately subject to the original anti-luminosity argument. However, it is shown that the specific understanding of determinacy required by this strategy validates a new argument against the reformulated version of luminosity. Moreover, reflection on the connection between mistake and absence of a fact of the matter offers another argument against such version, with the surprising upshot that, granting the soundness of the original anti-luminosity argument, not even the determinacy of a certain fact would guarantee its knowability.
KeywordsBorderline cases Determinacy Ignorance Luminosity Sorites Vagueness
Earlier versions of the material in this paper have been presented in 2008 at the Arché Audit and at the Arché Basic Knowledge Seminar (University of St Andrews); in 2009, at the Formal Epistemology Project Research Seminar (University of Leuven), at a research seminar at the University of Aarhus, at the 5th SOPHA Congress (University of Geneva), at the COGITO Epistemology Seminar (University of Bologna) and at the NIP Formal Epistemology Seminar (University of Aberdeen); in 2010, at the 2nd Workshop on Vagueness and Physics, Metaphysics, and Metametaphysics (University of Barcelona). I’d like to thank all these audiences for very stimulating comments and discussions. Special thanks go to Derek Ball, Annalisa Coliva, Laura Delgado, Dylan Dodd, Julien Dutant, Paul Égré, Gabriel Gomez, Chris Kelp, Hannes Leitgeb, Dan López de Sa, Aidan McGlynn, Sebastiano Moruzzi, Sven Rosenkranz, Ian Rumfitt, Johanna Seibt, Jason Stanley, Brian Weatherson, Robbie Williams and Crispin Wright. I’m particularly grateful to Stew Cohen for his support, feed-back and advice on my luminosity-related work throughout the years. But my greatest intellectual debt here is obviously to Tim Williamson, whose seminal articles on the topic provide much of the foundation for the present investigations. In writing this paper, I have benefitted, at different stages, from an AHRC Postdoctoral Research Fellowship and a UNAM Postdoctoral Research Fellowship, as well as from partial funds from the project FFI2008-06153 of the Spanish Ministry of Science and Innovation on Vagueness and Physics, Metaphysics, and Metametaphysics, from the project CONSOLIDER-INGENIO 2010 CSD2009-00056 of the Spanish Ministry of Science and Innovation on Philosophy of Perspectival Thoughts and Facts (PERSP) and from the European Commission’s 7th Framework Programme FP7/2007–2013 under Grant FP7-238128 for the European Philosophy Network on Perspectival Thoughts and Facts (PETAF).
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