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False conclusions are not worth having. They are cognitive effects, but not
positive ones (Sperber & Wilson 1995:
§
3.1-2).The most important type
of cognitive effect achieved by processing an input in a context is a contex-
tual implication, a conclusion deducible from the input and the context
together, but from neither input nor context alone. For example, on seeing
my train arriving, I might look at my watch, access my knowledge of the
train timetable, and derive the contextual implication that my train is late
(which may itself achieve relevance by combining with further contextual
assumptions to yield further implications).
It is interesting that Sperber and Wilson seem to barely mention Anderson and
Belnap's work on relevance logic,
6
and conversely Anderson and Belnap never
cite Sperber and Wilson's work.
7
Gabbay and Woods (2003) is the only work
I know of that makes a connection between them, present company excluded.
I should mention prominently, and that is why this is not just a footnote, that
Gabbay and Woods' topic deserves careful study, and is an interesting alternative
in many ways to the work of Sperber and Wilson and certainly the only work
comparable in extent and detail to theirs. I admit to coming across it only very
recently, and I have not had time to give it the careful study that it deserves.
The whole idea of a
relevant
implication
A
B
is that there is supposed to be
some sort of relevance between the truth of the antecedent
A
and the consequent
B
. What could be more natural then that to interpret
Rabc
as that in the contextof
the information
a
, the information
b
is relevant to the information
c
. If one adopts
Fine'shybridapproachtotheternaryrelation,thismightbesymbolizedas
a
→
c
.
In the words of Sperber and Wilson, “an input is relevant to an individual when its
processing in a context of available assumptions yields a positive cognitive effect.”
“The most important type of cognitive effect achieved by processing an input in a
context is a contextual implication, a conclusion deducible from the input and the
context together, but from neither input nor context alone.”
•
b
≤
6 Absolute Versus Contextual Relevance
Let us write
a
b
to mean that the state of information
a
is relevant all by
itself to the state of information
b
. We shall call this
absolute
relevance, and will
get to
relative
relevance, where relevance depends on a context, in just a few
≤
6
The only exception I know is Wilson and Sperber (1986), where in motivating their
own work to give an explicit account of relevance, they give a series of quotations
intended to demonstrate “considerable scepticism over whether any such account is
in principle possible.” They quote from p. xxi of Anderson and Belnap (1975): “The
diculty of treating relevance with the same degree of mathematical sophistication
and exactness characteristic of extensional logic has led many influential philosopher-
logicians to believe that it was
impossible
to find a satisfactory treatment of the
topic.” This is ironic in that Anderson were clearly doing the same for their own
work.
7
They are not even in the extremely comprehensive bibliography by Robert G. Wolfe
in
Entailment,
vol. II.
