Editing Vagueness (section)

== Approaches ==
The philosophical question of what the best theoretical treatment of vagueness is—which is closely related to the problem of the [[paradox of the heap]], a.k.a. sorites paradox—has been the subject of much philosophical debate.

=== Fuzzy logic ===
[[File:Fuzzy logic temperature en.svg|thumb|In fuzzy logic, e.g. the predicates ''cold'', ''warm'', and ''hot'' apply gradually (vertical axis, 0 and 1 meaning ''certainly not'' and ''certainly'', respectively) to a given temperature (horizontal axis).]]
{{main|Fuzzy logic}}
One theoretical approach is that of fuzzy logic, developed by American mathematician [[Lotfi Zadeh]]. Fuzzy logic proposes a gradual transition between "perfect falsity", for example, the statement "[[Bill Clinton]] is bald", to "perfect truth", for, say, "[[Patrick Stewart]] is bald". In ordinary logics, there are only two [[truth-value]]s: "true" and "false". The fuzzy perspective differs by introducing ''an infinite number of truth-values'' along a spectrum between perfect truth and perfect falsity. Perfect truth may be represented by "1", and perfect falsity by "0". Borderline cases are thought of as having a "truth-value" anywhere between 0 and 1 (for example, 0.6). Advocates of the fuzzy logic approach have included K. F. Machina (1976)<ref>Machina, K.F. 1976. "Truth, Belief and Vagueness", in ''[[Journal of Philosophical Logic]]'' Vol. 5. pp. 47-78.</ref> and [[Dorothy Edgington]] (1993).<ref>{{cite book| author=Edgington, D.| title=Vagueness by degrees| year=1997| pages=294–316| publisher=MIT Press| editor=Keefe, R. |editor2=Smith, P.| url=http://www.jo_syp.republika.pl/media/vbd.pdf}}</ref>

=== Supervaluationism ===
{{main|Supervaluationism}}
Another theoretical approach is known as "[[supervaluationism]]". This approach has been defended by [[Kit Fine]] and Rosanna Keefe. Fine argues that borderline applications of vague predicates are neither true nor false, but rather are instances of "[[truth value]] gaps". He defends an interesting and sophisticated system of vague semantics, based on the notion that a vague predicate might be "made precise" in many alternative ways. This system has the consequence that borderline cases of vague terms yield statements that are neither true, nor false.<ref>Kit Fine, ''The Limits of Abstraction'' (2002).</ref>

Given a supervaluationist semantics, one can define the predicate "supertrue" as meaning "true on all [[precisification]]s".  This predicate will not change the semantics of atomic statements (e.g. "Frank is bald", where Frank is a borderline case of baldness), but does have consequences for logically complex statements. In particular, the [[tautology (logic)|tautologies]] of sentential logic, such as "Frank is bald or Frank is not bald", will turn out to be supertrue, since on any precisification of baldness, either "Frank is bald" or "Frank is not bald" will be true.  Since the presence of borderline cases seems to threaten principles like this one (excluded middle), the fact that supervaluationism can "rescue" them is seen as a virtue.

=== Subvaluationism<!--'Subvaluationism' redirects here--> ===
{{see also|Dialetheism}}
'''Subvaluationism'''<!--boldface per WP:R#PLA--> is the logical dual of supervaluationism, and has been defended by Dominic Hyde (2008) and Pablo Cobreros (2011). Whereas the supervaluationist characterises truth as 'supertruth', the subvaluationist characterises truth as 'subtruth', or "true on at least some precisifications".<ref>Pablo Cobreros, (2011) "[https://link.springer.com/article/10.1007/s11229-010-9760-0 Paraconsistent Vagueness: A Positive Argument]" ''Synthese'' 183(2): 211–227.</ref>

Subvaluationism proposes that borderline applications of vague terms are both true and false. It thus has "truth-value gluts". According to this theory, a vague statement is true if it is true on at least one precisification and false if it is false under at least one precisification. If a vague statement comes out true under one precisification and false under another, it is both true and false. Subvaluationism ultimately amounts to the claim that vagueness is a truly contradictory phenomenon.<ref>Dominic Hyde and Mark Colyvan (2008) “[https://ojs.victoria.ac.nz/ajl/article/download/1798/1649 Paraconsistent Vagueness: Why Not?]” ''Australasian Journal of Logic'' 6: 107–121.</ref> Of a borderline case of "bald man" it would be both true and false to say that he is bald, and both true and false to say that he is not bald.

=== Epistemicist view ===
{{main|Epistemicism}}
A fourth approach, known as "the [[epistemicist]] view", has been defended by [[Timothy Williamson]] (1994),<ref>Williamson, T. 1994. ''Vagueness'' London: Routledge.</ref> [[Roy Sorensen|R. A. Sorensen]] (1988)<ref>Sorensen, R.A. 1988. ''Blindspots''. Oxford: Clarendon Press.</ref> and (2001),<ref>{{cite book| author=Sorensen, Roy| title=Vagueness and Contradiction| year=2001| publisher=Oxford University Press}}</ref> and [[Nicholas Rescher]] (2009).<ref>[[Nicholas Rescher|Rescher, N.]] 2009. ''Unknowability''. Lexington Books. <br /> Uses [[vagrant predicate]]s to elucidate the problem.</ref> They maintain that vague predicates do, in fact, draw sharp boundaries, but that one cannot know where these boundaries lie. One's confusion about whether some vague word does or does not apply in a borderline case is due to one's ignorance. For example, in the epistemicist view, there is a fact of the matter, for every person, about whether that person is old or not old; some people are ignorant of this fact.

===As a property of objects<!--'Metaphysical vagueness' and 'Ontological vagueness' redirect here-->===

One possibility is that one's words and concepts are perfectly precise, but that objects themselves are vague.  Consider [[Peter Unger]]'s example of a [[cloud]] (from his famous 1980 paper, "The Problem of the Many"): it is not clear where the boundary of a cloud lies; for any given bit of water vapor, one can ask whether it is part of the cloud or not, and for many such bits, one will not know how to answer.  So perhaps one's term 'cloud' denotes a vague object precisely.  This strategy has been poorly received, in part due to [[Gareth Evans (philosopher)|Gareth Evans's]] short paper "Can There Be Vague Objects?" (1978).<ref>{{cite journal| author=Evans, G.| title=Can There Be Vague Objects?| journal=Analysis| year=1978| volume=38| issue=4| pages=208–| doi=10.1093/analys/38.4.208}}</ref> Evans's argument appears to show that there can be no vague identities (e.g. "Princeton = Princeton Borough"), but as Lewis (1988) makes clear, Evans takes for granted that there are in fact vague identities, and that any proof to the contrary cannot be right.  Since the proof Evans produces relies on the assumption that terms precisely denote vague objects, the implication is that the assumption is false, and so the vague-objects view is wrong.

Still by, for instance, proposing alternative deduction rules involving [[Identity of indiscernibles|Leibniz's law]] or other rules for validity some philosophers are willing to defend '''ontological vagueness'''<!--boldface per WP:R#PLA--> as some kind of metaphysical phenomenon. One has, for example, [[Peter van Inwagen]] (1990),<ref>Van Inwagen, Peter. 1990 ''Material Beings''. Ithaca, NY: Cornell University Press.</ref> [[Trenton Merricks]] and [[Terence Parsons]] (2000).<ref>Parsons, Terence. 2000. ''Indeterminate Identity - Metaphysics and Semantics'' Oxford: Clarendon Press.</ref>