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 philosophical ...

, supervaluationism is a

semantics Semantics (from grc, σημαντικός ''sēmantikós'', "significant") is the study of reference, meaning, or truth. The term can be used to refer to subfields of several distinct disciplines, including philosophy Philosophy (f ...

for dealing with irreferential

singular term A singular term is a paradigmatic referring device in a language. Singular terms are of philosophical importance for philosophers of language, because they ''refer'' to things in the world, and the ability of words to refer calls for scrutiny. Over ...

s 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" is ...

. It allows one to apply the tautologies of

propositional logic Propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. It deals with propositions (which can be true or false) and relations b ...

in cases where

truth values In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values (''true'' or '' false''). Computing In some progra ...

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

Pegasus Pegasus ( grc-gre, Πήγασος, Pḗgasos; la, Pegasus, Pegasos) is one of the best known creatures in Greek mythology. He is a winged divine stallion usually depicted as pure white in color. He was sired by Poseidon, in his role as hor ...

likes

licorice Liquorice (British English) or licorice (American English) ( ; also ) is the common name of ''Glycyrrhiza glabra'', a flowering plant of the bean family Fabaceae, from the root of which a sweet, aromatic flavouring can be extracted. The liq ...

", 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 van Fraassen (; born 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 State University and ...

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

Example abstraction

Let ''v'' be a classical valuation defined on every

atomic sentence In logic and analytic philosophy, an atomic sentence is a type of declarative sentence which is either true or false (may also be referred to as a proposition, statement or truthbearer) and which cannot be broken down into other simpler sentences ...

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" (shortened as "iff") is a biconditional logical connective between statements, where either both statements are true or both are false. The connective is bicondi ...

''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'') combines an online encyclopedia of philosophy with peer-reviewed publication of original papers in philosophy, freely accessible to Internet users. It is maintained by Stanford University. Eac ...

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

Example abstraction

See also

References

External links