Nonclassical Logic of Vagueness
DOI:
https://doi.org/10.22370/rhv2015iss5pp7-16Keywords:
Sorites, vagueness, fuzzy logic, supervaluationism, subvaluationismAbstract
In this paper, we present a simple overview of the main non classical logics proposed for dealing with the Sorites paradox, that is, weakly paracomplete logics, weakly paraconsistent, and type 1 fuzzy logics. We note some of their advantages and problems and we suggest that the problems can be at least partially overcome by adopting a solution which relies on interval based type 2 fuzzy logics.
References
COOK, Roy (2002). "Vagueness and Mathematical Precision", Mind, New Series, Vol. 111, No. 442.
CORNELIS, Chris & DESCHRIJVER, Glad, et al. (2006). "Advances and challenges in interval-valued fuzzy logic", Fuzzy Sets and Systems 157.
EDGINGTON, Dorothy (1997). "Vagueness by Degrees", en Keefe y Smith (eds), Vagueness: a reader. Massachusetts: MIT Press.
FIELD, Hartry (2003). "Semantic Paradoxes and the Paradoxes of Vagueness", en Beall (ed.), Liars and Heaps. Oxford: Oxford University Press.
FINE, Kit (1975). "Vagueness, Truth and Logic", Synthese, Vol. 30, No. 3/4.
GOGUEN, Joseph (1969). "The logic of inexact concepts", Synthese No.19.
HÁJEK, Petr (2009). "On Vagueness, Truth Values and Fuzzy Logics", Studia Logica, Vol. 91, No. 3.
HYDE, Dominic (2008). Vagueness, logic and ontology. Ashgate new critical thinking in philosophy. New York: Routledge.
HYDE, Dominic (2010). "The prospects of a paraconsistent response to vagueness", en Cuts and Clouds, Dietz & Moruzzi (eds). Oxford University Press.
KEEFE, Rosanna (1998). "Vagueness by Numbers", Mind, New Series, Vol. 107, No. 427.
KEEFE, Rosanna (2000). Theories of vagueness. Cambridge: Cambridge University Press.
NOVÁK, Vilém & DVOŘÁK, Antonin. (2004). "Fuzzy Logic as a Methodology for the Treatment of Vagueness", Research report No. 59. Universidad de Ostrava.
SAINSBURY (1996). "Concepts Without Boundaries", en Keefe y Smith (eds) Vagueness: A Reader. Massachusetts: MIT Press.
SMITH, Nicholas J. J. (2008). Vagueness and degrees of truth. Oxford: Oxford University press.
VAN FRAASSEN, Bas (1966). "Singular Terms, Truth-Value Gaps, and Free Logic", The Journal of Philosophy, Vol. 63, No. 17.
VAN GASSE, Bart & CORNELIS, Chris, et al (2008). "A characterization of interval-valued residuated lattices", International Journal of Approximate Reasoning 49.
VARZI, Achille (2007). "Supervaluationism and its logics", Mind, 116 (463).
WILLIAMSON, Timothy (1994). Vagueness, London: Routledge.
WRIGHT, Crispin (1975). "On the coherence of vague predicates", Synthese, Vol. 30 (3-4).
ZADEH, Lotfi (1965). "Fuzzy sets", Information and Control, Vol 8.
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication, with the work after publication simultaneously licensed under a Creative Commons Attribution License (CC BY-NC-ND 4.0 International) that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).