philosophical logic Understood in a narrow sense, philosophical logic is the area of logic that studies the application of logical methods to philosophical problems, often in the form of extended logical systems like modal logic. Some theorists conceive philosophic ...

, supervaluationism is a

semantics Semantics is the study of linguistic Meaning (philosophy), meaning. It examines what meaning is, how words get their meaning, and how the meaning of a complex expression depends on its parts. Part of this process involves the distinction betwee ...

for dealing with irreferential singular terms and

vagueness In linguistics and philosophy, a vague predicate is one which gives rise to borderline cases. For example, the English adjective "tall" is vague since it is not clearly true or false for someone of middling height. By contrast, the word " prime" ...

. It allows one to apply the tautologies of

propositional logic The propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. Sometimes, it is called ''first-order'' propositional logic to contra ...

in cases where truth values are undefined. According to supervaluationism, a proposition can have a definite truth value even when its components do not. The proposition "

Pegasus Pegasus (; ) is a winged horse in Greek mythology, usually depicted as a white stallion. He was sired by Poseidon, in his role as horse-god, and foaled by the Gorgon Medusa. Pegasus was the brother of Chrysaor, both born from Medusa's blood w ...

likes

licorice Liquorice (Commonwealth English) or licorice (American English; see spelling differences; ) is the common name of ''Glycyrrhiza glabra'', a flowering plant of the bean family Fabaceae, from the root of which a sweet, aromatic flavouring is ...

", for example, is often interpreted as having no truth-value given the assumption that the name "Pegasus" fails to refer. If indeed reference fails for "Pegasus", then it seems as though there is nothing that can justify an assignment of a truth-value to any apparent assertion in which the term "Pegasus" occurs. The statement "Pegasus likes licorice or Pegasus doesn't like licorice", however, is an instance of the valid schema

p \vee \neg p

("''

p

or not-

p

''"), so, according to supervaluationism, it should be true regardless of whether or not its disjuncts have a truth value; that is, it should be true in all interpretations. If, in general, something is true in all precisifications, supervaluationism describes it as "supertrue", while something false in all precisifications is described as "superfalse". Supervaluations were first formalized by

Bas van Fraassen Bastiaan Cornelis "Bas" van Fraassen (; ; born 5 April 1941) is a Dutch-American philosopher noted for his contributions to philosophy of science, epistemology and formal logic. He is a Distinguished Professor of Philosophy at San Francisco Stat ...

.Free Logic (Stanford Encyclopedia of Philosophy)
/ref>

Example abstraction

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 a formula ''x''. There are then 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 supertrue (i.e. ''V''(''x'')=True)

if and only if In logic and related fields such as mathematics and philosophy, "if and only if" (often shortened as "iff") is paraphrased by the biconditional, a logical connective between statements. The biconditional is true in two cases, where either bo ...

''v''(''x'')=True for every ''v''. Likewise for superfalse. ''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". There are then exactly two classical valuations ''v'' and ''v''* on ''Lp'', namely ''v(Lp)''=True and ''v''*''(Lp)''=False. So ''Lp'' is neither supertrue nor superfalse.

References

External links

Stanford Encyclopedia of Philosophy The ''Stanford Encyclopedia of Philosophy'' (''SEP'') is a freely available online philosophy resource published and maintained by Stanford University, encompassing both an online encyclopedia of philosophy and peer-reviewed original publication ...

*
Supervaluationism as a response to vagueness
*
Supervaluationism as a response to the Sorites Paradox
{{Formal semantics Semantics Theories of deduction

Example abstraction

See also

References

External links