Or robbing Peter (Wason) to pay Paul (Grice).
It all started, for
Newstead, when he submitted for the Journal of Memory
and Language that
"Griceian implicatures and syllogistic reasoning" and it
Grice used to say, "Grice saves; but, mind, there's no
The implicature was that if you, like Peter Wason and Paul
did (Robbing Peter To Pay Paul) take "⊃" to stand for the
'if' in the 'if'
utterance of Wason's AD47 card selection task, you may
SAVE (problems that
may arise if you take a different sort of 'formal
device' to represent
something apparently as
naïf as "if" sounds
But that was precisely Strawson (also called Peter, like Wason,
coincidentally, "Peter without a lesson," as I call him -- since at least
is taking the horseshoe properly) and his mistake.
in the case of Wason's 'if' utterance involved in the AD47 card
task, Leda Cosmides called it "abstract" -- she's no philosopher but
get her drift.
Seriously, it's not so much about the 'subtle grammatical
shift' (or nuance
or conversational implicature) but about how you turn that 'grammar' into logic. Grice, echoing
Russell, used to say that 'grammar' is a 'pretty good guide' to 'logical
form', and I think in
THIS case he did mean 'pretty pretty' (as opposed to
the pretty in pretty complex).
For when we see the abstract 'if'
--surely there are dismissing 'formal devices'
that Grice didn't in his
"Logic and Conversation" lectures,
lists "∀" to stand for "all", "∃" to stand for "some (at least
"ix" to stand for "the".
The Wason subject will first approach the task
syntactically -- and he may
fail at that level.
He will then
approach the task 'semantically'.
And he will test the task
pragmatically. He may wonder: "Is it really
believable that Wason is in
doubt about the truth value of the 'if' utterance?
Don't think so. Is he
teasing me, or trying to tease me? Isn’t it more
likely that Wason just
typed down a true "if" statement — the more so since the
utterance (‘letters on one side, numbers on the other side’
) must also be
taken to be true, if one follows Grice's cooperative
truthful" -- his conversational category of Qualitas).
But back to Step
1 and 2 (syntax-cum-pragmatics), the Wason subject may
feel that the 'if'
utterance needs some sort of predicate, or
quantifiational, logic, and that
its logical form requires the use of predicates and
because of the occurrence of expressions like "one side"
If, like Grice, you are enamoured with System Q (that Myro created
Grice's honour), the way to provide the correct logical form (the middle
second Witters hated that phrase!) formalise Wason's 'iffy' utterance
predicate or quantificational logic should use the following
V for visible
I for invisible
O for vowel
E for even
We now need propositions:
will read as "x is
will read as "x is an even number".
we need a 'relational logic' alla Russell, for the introduction of
predicate 'visible'. For it's not just 'visible' we want, but the ability
to formalise, 'x is on the visible side of card y'. Let
iii. V(x, y)
represent that, where V stands for a dyadic relation).
finally we need again 'relational logic' to represent, 'x is on the
INvisible side of card y'. Let
iv. I(x, y) -- x is on the invisible
side of card y.
symbolise that, where again "I" stands for a dyadic
Now, Wason's iffy utterance can be given the proper logical
∀c(∃x(V(x, c) ∧ O(x)) ⊃ ∃y(I(y, c) ∧ E(y))) ∀c(∃x(I(x, c) ∧ O(x))
y(V(y, c) ∧ E(y)))
After teaching Paul Strawson for a few terms
at St. John's, Grice was
appalled to see that his tutee still committed a
few mistakes. It is these
mistakes (in Strawson's "Introduction to Logical
Theory") that moved Grice to
accept the invitation at Harvard to give the
"Logic and Conversation"
lectures. In the "Prolegomena" Grice explicitly
quotes verbatim from Strawson's
essay on 'if' as a mistake by 'ordinary
language philosophers' who dismiss
pragmatic phenomena -- and that can't
stand the horseshoe's implicatures!
Similarly, and a few years later,
Peter (same first name as Strawson) Wason
ends up finding that some of his
subjects go astray at this point,
replacing the second statement containing
⊃ by a bi-conditional (a different
formal device altogether), or worse, by
a reversed conditional.
Pinker knew this when he says that 'logical'
words in language are
'ambiguous'. He uses that ambiguous 'ambiguous' when
he means is 'Griceian in
nature': utterances containing them have a precise
logical form and trigger
implicatures that can go over Wason's subjects's
(although Pinker uses 'mind' LITERALLY!)
Pinker's list of 'logical words' in the paragraph preceding his précis
Wason's test, one may think he quotes just to reference the PhD by
for the Department of Psychology and Social Relations (Her advisor
Sheldon H. White, not Pinker, granted. From 1982 until 2003, Pinker
the Department of Brain and Cognitive Sciences at MIT, and
the director of the Center for Cognitive
Neuroscience, taking a one-year
sabbatical at the University of California,
Santa Barbara, in 1995–96 (to
which Cosmides is associated). In 2003,
Pinker became the Johnstone Family
Professor of Psychology at
In any case, Pinker's list goes:
"not", "and", "if",
"same", "equivalent", and "opposite".
So, he wouldn't be surprised by a
richer logical form to the Wason task
than the mere
because, while "⊃", note that the expanded logical form in predicate
makes use of "and" ("∧") and one can think of shorter expansions that
"not" (~) if not "opposite", "equivalent" and "opposite".
To sum up, a
certain prejudice (or 'bias') against a logically-based
reasoning (as Grice offers in "Aspects of reason", borrowing some
from his own "Logic and Conversation") cuts off the insights of
from a few applications. Those psychologists like Wason who explore
reasoning -- or worse some of his critics and some of his followers,
hardly the philosophical bunch of them -- seem allergic to formal
as are psychologists of reasoning. This 'bias' may be largely due
simplistic attempts to apply formal theories in a monolithic way.
But since, after Grice, logic has become less monolithic (and open the
gate to implicature -- as he said, "Implicature happens"), psychologists of
reasoning cannot afford to continue avoiding an enriched approach to
form like the
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