and P a procedure with which the indirect correspondence I can be recovered.
Notationally this could be expressed as D&P → I . The usual view of radical in-
terpretation requires that sentences are bivalent, or two-valued; this means that
the truth values ”True” or the truth value ”False” can be assigned to them.
Here the possibility of assigning any quantity to (or labeling, or marking, or
tagging . . . ) sentences is referred to them as being flagged. The existence of a
name strategy, especially in colour perception, shows that there is no unique way
of achieving this; for example, quantitative experiments could be constructed
in which subjects would be required to state how blue or green a chip is, the
quantitative results would depend on whether a name strategy was being de-
ployed, then true or false sentences could be constructed to describe these quan-
titative differences, but these would have different truth values depending on
whether a name strategy was being deployed. This ambiguity of truth values
necessitates that a disambiguating procedure (i.e. a procedure which removes
any amgibuity) be given. The form that such a procedure could take is the
re-writing, hopefully in a bounded finite number of steps B , of the original sen-
tences which are bivalent. An example of a re-writing procedure is what is here
called a brittle re-write procedure. This can be described as follows: suppose
that sentences can be given a single definite value, c.f. Urquhart (1986) [48], of
say:
U = {f alse, almostf alse, almosttrue, true}; (1)
then the original set of sentences can be replaced by a larger set of sentences
having just the values true or false, this can be done by posing the four additional
sentences: ”The previous sentence is False, Almost False, Almost True, True”
all four of which are true or false. Another example, is to suppose that, instead
of the sentences being bivalent it is possible to assign a set of labels or quantities
Q to a sentence, for instance
Q = {H appy and Good, H appy and Bad, Sad and Good, Sad and B ad}; (2)
again for additional sentences, such as: ”The previous sentence has the quality
Q”, can be constructed which are bivalent. This approach really falls under the
scope of Davidson’s program, (1984) [8] p.133, it is just the requirement that
there should be a procedure for matching sentences without logical form (i.e. bi-
valent sentence) the gerrymandered part of a language where sentences do have
logical form. It might be thought straightforward, for the circuitous correspon-
dence of colours, to implement such a procedure; however first two problems
have to be overcome. The first is that the re-write procedure would involve real
variables, the parameters P to be adjusted, such as wavelengths, take values V
on the real line Ж , i.e. V (P) ε Ж; however it seems reasonable to assume that
sentences and truth values can only be stated and assigned sequentially, so that
the total number of truth values available N(T) is an integer valued quantity,
i.e.N (T) ε Z; thus there is the problem of how to segment V(P) so that N(T)
covers all cases, this is an example of the segmentation problem, discussed in
§8.1. The second is that the re-write procedure has to be constructed post-hoc,
after data about responses has been given, but extralinguistic assignment (or
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