It may be pointed out, though, that if the Wason AD47 task is seen as
identifying the truth-conditions that make the 'if' utterance "0" (or
you mustn't), the way we interpret the relevant truth-functor "⊃"
Wason alas does not use) may yield different results, some valid,
and some indeterminate.
A Griceian could suggest or
implicate that subjects engaged in the Wason
AD47 task (the Wason people)
do not use contraposition, but rather construe
the AD47 task as an
instanciation of indicative conditionals.
It should be granted that one
can however contrast this interpretations of
the Wason AD47 task (in
material conditional terms) that ia each
associated with a specific
The "right kind of logic" to be used thus depends on
the interpretation of
the task relevant to a given context.
(and I hope Wason's) issue is broader: to investigate the relation
indicative conditionals and rationality by way of explaining -- any
who cares to read Wason -- the puzzlingly poor results of "The
subjects" to the Wason AD47 task.
To do so, it is useful to understand
what Wason thought was the source and
nature of the subjects'
Does it amount to a failure in rational reasoning?
does the subject understand the task in an unanticipated way?
Researchers on the Wason task generally assume that rational reasoning
not constituted by the (even possibly implicit) knowledge and
propositional logic, not even of the truth tables of the
Anti-Griceians will claim that
an indicative conditional, in particular,
constituting as it does one
important type of natural reasoning, are not and
should not be understood
in the same way as the horseshoe is.
It might be argued that even though
"The Wason subjects" do not apply a
logical rule of inference –
contraposition- when they try to solve the AD47
task, they may be using
another kind of logical strategy.
Fleshing out this strategy might help
us discover the actual cognitive
basis of rationality.
strategies have already been used to prove subjects free from
irrationality: either they are shown to use pragmatic reasoning, which
them to extract relevance of "if" in BI-conditional terms rather than
material implication; or they are
claimed to rely on various
heuristic principles which generally, although
not universally, are truth
Other solutions involve mental models or domain-sensitive
(investigated in schema theory and in social contract
Granted, Grice's approach is limited:
1. A classical
approach only acknowledges full beliefs.
2. A logical approach refers to
objective states of affairs.
3. A logical operator as the horseshoe
necessarily deals with
material implication and a disposition to acquire a belief q
given p have
propositions within their scopes.
But while the propositional connective
⊃ determines new propositions which
are either true or false, it might be
argued that "if" reflects a
subjective process of credence formation rather
than an objective relation between
fact remains that, in whatever ways the acceptability,
the like of a proposition depend on its subjective
acceptability, assertability, and the like of an indicative
depend upon the corresponding subjective conditional probability.
post-Griceians recognise - against Grice, Wason, and Jackson, who
horseshoe + pragmatics interpretation of "if" - that the semantic
characterization of a sentence structured by the indicative conditional
be accounted for in truth-evaluable, belief terms (on pain of
contradiction, as Lewis and Gärdenfors have shown).
reason these post-Griceians offer is that indicative
generally be embedded in others.
[there is] a vowel [on one side of the card], [there is] an even
the other side.
ii. If (if [there is] a vowel
[on one side of the card], [there is] an
even number on the other side)
[the] Grice is right.
If the semantics of such an indicative conditional
has to do with
subjective acceptability, or with a disposition to acquire a
belief q given p,
rather than with propositional truth, the subjects
engaged in the Wason AD47
task may be rational in refraining
interpreting the prescribed rule in terms of contraposition, which
infers from p ⊃ q that not q ⊃ not p.
To understand fully this proposal,
however, it is worth extending the
discussion beyond the limits of the
Wason AD47 task and perhaps attend Grice's
Lectures on Aspects of Reason at
Oxford (only you need a time machine, since
he delivered them at 1979 and
as he said, "they are now outdated, in
Gärdenfors, and Leitgeb observe, the problem is that such a
conditionals fails to explain why a change in one's credence in
will often influence not the credence in the conclusion, but the
placed in the conditional.
The example of reference is:
Hitler had decided to invade England in 1940, he would have won the
Finding out that Hitler did decide to invade England in 1940
would not lead
one to revise the fact that Hitler lost the war.
that the validity of a conditional depends on the total information
available, one should rather drop the belief in the
Reflecting on such examples shows that beliefs in
conditionals cannot be
simply reduced to conditional beliefs.
as one might put it, the explanation of one in terms of the other
as simple and straightforward as one might wish.
If it is understood as a
conditional indicative, reasoning involved in
solving the Wason AD47 task
offers an instantiation of this non-reducibility.
One cannot simply
identify the belief in the conditional rule with a
logical relation between
Let us note, however, that the conditional rule
used in the Wason AD47
task is, at least in some versions of the task, not
similar to the Hitler
Let us see why.
utterance states that if there is a vowel on one side of the
there is an even number on the other side.
There are two ways of
interpreting this task.
In one, the difficulty for the Wason subjects is
having to solve the task
is purely logical and a priori, as Kant would put
The Wason subjects need to determine which possible cases would a
constitute falsifiers of the 'if' utterance.
subjects do not need to inquire about how real states of affairs
like, for they already know that the world is determined, one way
What they need to determine is how they can correctly falsify the
Neither an appraisal of objective probabilities
concerning the world, nor a
capacity to revise one's beliefs when confronted
with a change, seem to be
called for in order to solve the task
One can, however, also imagine another version of the task,
subjects have to make a prediction concerning how the world
the 'if' utterance, now considered as a revisable
In this case, we are close to Hitler's example,
where there exists reasons
that might lead one to reject or falsify the
'if' utterance after all.
Taking a probabilistic reading of the
conditional rule seems much more
justified in this second reading.
For here it makes sense to say that the reasoner needs to use the total
information available to her in order to decide whether to drop the 'iffy'
In this case, in contrast with the former, the estimated
the 'if' utterance has to be revised each time a
counterexample to it is
The 'if' utterance will count
as falsified as a hypothesis if the
probability of being incorrect reaches
a certain critical value.
Such a difference between the two
interpretations of the Wason AD47 task
needs to be taken into account for
evaluating a probablistic style of
For one might argue
that this difference justifies a subject in
representing the task
respectively by a material implication or not -- alla Kleene,
Some Griceians, such as Stalnaker, have insisted that both
representations are formally equivalent.
The principle of
conditional noncontradiction (not both if p then q and if
p then not-q) is
NOT valid for the horseshoe.
The formula (p ⊃ q) & (p ⊃ ~q) is true
whenever p is false.
If this objection is correct, a rational Wason
subject is one who is
justified in using the correct method to solve a
Naïve subjects can obviously not be credited with
considering the dilemma
as to whether Grice thinking of 'if' as the
horseshoe is right or wrong.
Still they have two different ways
available to them for inferring which
are the relevant cards to be turned
over, one in terms of contraposition, the
other in terms of probabilistic
Rational subjects must be granted a procedural knowledge of
how to match a
task with its associated method, even if they cannot
"meta"-represent (shall we say?) such knowledge in appropriate
If one claims that the Wason subjects have been using a
conditional rather than a horseshoe to solve the Wason
AD47 task, three
further questions can be raised.
The first is, how
does a subject recognize which method is contextually
The second is, how can a theorist discover which method was used by the
The third is, what makes a specific decision rational
given a specific
Some may agree that we should pick up the
right logic for the right kind of
The principle of
decision is one of charity.
We should pick up the logic, which can
account for the Wason subjects'
If however, rationality
is taken to be an intrinsic property of a system
rather than an
interpretive relation, charity will not do.
What is first needed is a
descriptive account of the information, which the
subject uses to decide
which logic to use.
Discovering what a Wason subject actually does is a
problem for a theorist
such as Grice, who also needs to deploy appropriate
paradigms to uncover
the cognitive mechanisms involved.
with a probablistic solution is that it explains only why some of
subjects don't choose to turn the card "not q" – they do not
inference based on contraposition.
Nothing is said, however, to explain
why they choose to turn the card "q"
proposal is one that accounts both for what they do and they
It is also one that explores the possible application of the mechanism
other, non-iffy cases of reasoning.
So, at this point, the
probabilistic theory is not vindicated.
Promising avenues might open up
from Leitgeb's proposal of a "sui generis"
conditional belief formation
process, but they remain to be explored in
Our (and indeed
Wason's) third problem consists in explaining what makes a
decision rational given a specific context. It might be suggested
epistemological theory must be offered to explain when and why a
justified, (or entitled to) using a horseshoe analysis, and when
and why he
A reliabilist account cannot be a sufficient account for why a
decision is to be preferred to another in a given
As Strawson once said when attacked by Grice for his treatment
"I only said "if""
"Literally, you said much more than
that!," was Grice's implicatural
Knowledge in flux. Cambridge: MIT Press.
Gibbard, A. Two recent theories of
conditionals. In W.L. Harper, R.
Stalnaker & G. Pearce (Eds.), Ifs:
Conditionals, belief, decision, chance and
Grice, "Indicative conditionals" in "Studies in the Way of
Leitgeb, H. Beliefs in conditionals vs. conditional beliefs. Topoi,
Pears, DF Motivated irrationality.
Ramsey, F.P. Law
and causality. In Foundations of mathematics. London:
Stalnaker, R. Inquiry. Cambridge, Mass.: MIT
Strawson, "'If' and "⊃"", in P.G.R.I.C.E., Philosophical Grounds of
Rationality: Intentions, Categories, Ends.