Validity in Predicate Logic
G. J. Mattey
Winter, 2009 / Philosophy 112
Valid Arguments in Natural Language
•Arguments in natural language consist of a set of sentences serving as premises
and a single sentence serving as the conclusion.
•A natural language argument is valid if and only if it is not possible for all the
premises to be true and the conclusion false.
•Validity of natural language arguments can be evaluated by transcribing them
into Predicate Logic and applying the semantics to the transcribed arguments.
Valid Arguments in Predicate Logic
•Truth and satisfaction in an interpretation are the most basic semantical proper-
ties of sentences of Predicate Logic.
•These properties can be used to determine the truth-value, in an interpretation,
of a Predicate Logic sentence (conclusion) relative to a set of Predicate Logic
sentences (premises) in an argument of Predicate Logic.
•The goal is to determine whether there is an interpretation in which all the
premise-sentences have the value t and the conclusion-sentence has the value
f.
•If there is such an interpretation, it is a counterexample, and the transcribed
argument is invalid.
•If there are no counterexamples, then the transcribed argument is valid.
Determining Invalidity
•To show that an argument of Predicate Logic is invalid, one produces an inter-
pretation to serve as a counterexample.
•Producing a counterexample requires the specification of a domain, as well as
the designations of the names and function symbols, and the extensions of the
predicates occurring in the sentence.
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