procedures, for Ж to have meaning it must be possible to assign quantities QεK
to sentences. To put this another way sentences cannot be flagged by integer
valued quantities, they have to be flagged by real valued ones. In traditional
radical interpretation truth is an ab initio concept, for maximum compatibility
with this real valued generalizations of truth are required. Possible choices for
real valued truth are probabilities or fuzzy truth values.
8.2 Probabilistic and Fuzzy Tarski Truth Theory
Radical interpretation is in part motivated by Tarski’s truth theory. Usually this
applies bivalent truth values to formal languages. Church (1956) [7] p.25 seems
to use the term ”logical form” where ”bivalence” has been used here. Davidson
(1984) [8] p.19 appears to follow Church’s usage. In other words they require
integer valued flags, but here it is advocated that real valued flags are necessary.
There are formalized languages which do not require that truth is bivalent but
is real valued, examples of these are fuzzy logic and probability theory. As has
been argued in the previous section real values should be used for describing
truth in natural languages. There appears to be no reason why Tarski’s truth
theory cannot be modified to include statements which involve probabilities or
fuzzy truth values, although this appears not to have been explicitly done in
the literature. Instead of defining a relation: ”Assignment a satisfies formula F
in structure S : define a relation: ”Assignment a gives formula F the value p in
the structure S” in the probability case, p will be a real number between 0 and
1.
9 Summary
9.1 Peroration
So what does a speaker take a sentence such as ”Snow is white.” to mean?
Stripping away multitudinous provisos the essentially old view of radical inter-
pretation would be along the lines:
In a formal Tarski truth theory the truth of such a statement would
be ascertained by comparison with the statement in another formal
language. For learning a first natural language with no language
to compare it to, the truth of a previously unheard statement is
judged by seeing how well it matches the listeners previous model of
the language and the external information available. The external
information available is taken more often than not to be useful rather
than misleading. Having judged a statement to be true the speaker
then deduces that it is in accurate correspondence to the exterior
world. Having information that accurately portrays the exterior
world must entail knowing what it means; meaning is implicated by
the above reasoning and is a derivative concept from it.
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