Supervaluationism

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In logic, supervaluationism is a semantics for dealing with irreferential singular terms and vagueness.[1] Consider the sentence 'Pegasus likes licorice'. The name 'Pegasus' fails to refer, and there is nothing in the myth that would justify any assignment of values to it, suggesting such a sentence is vacuously true. Yet according to supervaluationism, such borderline statements lack a truth value.[2] Alternatively, consider the statement 'Pegasus likes licorice or Pegasus doesn't like licorice' which is an instance of the valid schema: 'p ∨ ~p' (i.e. 'p or not p'). According to supervaluationism, it should be true regardless of whether or not its disjuncts have a truth value; that is, true in all interpretations. In general, anything true in all precisifications is supertrue; anything false is superfalse.[3]

Example

Let v be a classical valuation defined on every atomic sentence of the language L, and let At(x) be the number of distinct atomic sentences in x. Then there are at most 2^At(x) classical valuations defined on every sentence x. A supervaluation V is a function from sentences to truth values such that, x is super-true (i.e. V(x)=True) if and only if v(x)=True for every v; likewise for super-false.

V(x) is undefined when there are exactly two valuations v and v* such that v(x)=True and v*(x)=False. For example, let Lp be the formal translation of 'Pegasus likes licorice'. Then there are exactly two classical valuations v and v* on Lp, viz. v(Lp)=True and v*(Lp)=False. So Lp is neither super-true nor super-false.

See also

References

  1. ↑ Shapiro, Stewart "Vagueness and Conversation" in Beall, Edited (2003). Liars and Heaps. Oxford Eng.: Clarendon. ISBN 0-19-926481-3. 
  2. ↑ Sorensen, Roy (2006). "Vagueness: Supervaluationism". Stanford Encyclopedia of Philosophy. Retrieved 2012-03-04. 
  3. ↑ "Supervaluation: Definition from Answers.com". Oxford Dictionary of Philosophy. Oxford University Press. 2005. Retrieved 2012-03-04. 

External links

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