In
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 for dealing with
irreferential singular terms and
vagueness. It allows one to apply the
tautologies of
propositional logic 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", 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
("''
or not-
''"), 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.
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 2At(''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 ''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.
See also
* Kripke semantics
*Sorites paradox
The sorites paradox (; sometimes known as the paradox of the heap) is a paradox that results from vague predicates. A typical formulation involves a heap of sand, from which grains are removed individually. With the assumption that removing a sing ...
* Subvaluationism
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
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