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Friday, February 26, 2016



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 'false' if
you mustn't), the way we interpret the relevant truth-functor "⊃" (that
Wason  alas does not use) may yield different results, some valid, some not,
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 cognitive strategy.

The "right kind of logic" to be used thus depends on the interpretation of 
the task relevant to a given context.

Grice's (and I hope Wason's) issue is broader: to investigate the relation 
between indicative conditionals and rationality by way of explaining -- any
Griceian who cares to read Wason -- the puzzlingly poor results of "The
Wason  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' difficulty.

Does it amount to a failure in rational reasoning?

Or does the subject understand the task in an unanticipated way?

Researchers on the Wason task generally assume that rational reasoning is 
not constituted by the (even possibly implicit) knowledge and application of
propositional logic, not even of the truth tables of the horseshoe in 
propositional calculus.

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.

Non-formal strategies have already been used to prove subjects free from 
irrationality: either they are shown to use pragmatic reasoning, which leads 
them to extract relevance of "if" in BI-conditional terms rather than as a 
material implication; or they are
claimed to rely on various heuristic  principles which generally, although
not universally, are truth conducive.

Other solutions involve mental models or domain-sensitive rules 
(investigated in schema theory and in social contract theory).

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 
truth-evaluable propositions.

However, both 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
two  propositions.

The Griceian fact remains that, in whatever ways the acceptability, 
assertability, and the like of a proposition depend on its subjective 
probability, the acceptability, assertability, and the like of an indicative 
conditional depend upon the corresponding subjective conditional  probability.

Some post-Griceians recognise - against Grice, Wason, and Jackson, who 
defends a horseshoe + pragmatics interpretation of "if" - that the semantic 
characterization of a sentence structured by the indicative conditional cannot
be accounted for in truth-evaluable, belief terms (on pain of
contradiction, as  Lewis and Gärdenfors have shown).

An additional reason these post-Griceians offer is that indicative 
conditionals cannot generally be embedded in others.

Non-embedded version:

i. If [there is] a vowel [on one side of the card], [there is] an  even
number on the other side.

Embedded version:

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
from interpreting the prescribed rule in  terms of contraposition, which
simply 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

As Stalnaker, Gärdenfors, and Leitgeb observe, the problem is that such a 
reading of conditionals fails to explain why a change in one's credence in
the  premise will often influence not the credence in the conclusion, but the
confidence placed in the conditional.

The example of reference is:

iii. If 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.

Given that the validity of a conditional depends on the total  information
available, one should rather drop the belief in the  conditional.

Reflecting on such examples shows that beliefs in conditionals cannot be 
simply reduced to conditional beliefs.

Or, as one might put it, the explanation of one in terms of the  other
cannot be 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 conditional beliefs.

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.

The 'if' utterance states that if there is a vowel on one side of  the
card, then 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 it.

The Wason subjects need to determine which possible cases would a  priori
constitute falsifiers of the 'if' utterance.

The Wason subjects do not need to inquire about how real states of affairs 
might be like, for they already know that the world is determined, one way
or  the other.

What they need to determine is how they can correctly falsify the 'if' 

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
so understood.

One can, however, also imagine another version of the task, in which 
subjects have to make a prediction concerning how the world objectively reflects 
the 'if' utterance, now considered as a revisable empirical hypothesis.

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 probability of 
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  alternative
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 specific problem.

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 reasoning.

Rational subjects must be granted a procedural knowledge of how to match a 
task with its associated method, even if they cannot explicitly
"meta"-represent  (shall we say?) such knowledge in appropriate conceptual terms.

If one claims that the Wason subjects have been using a probabilistic open 
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 
Wason subject?

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
'if' utterances.

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.

A problem with a probablistic solution is that it explains only why some of
the Wason subjects don't choose to turn the card "not q" – they do not
form the  inference based on contraposition.

Nothing is said, however, to explain why they choose to turn the card "q" 

An appropriate proposal is one that accounts both for what they do and they
don’t do.

It is also one that explores the possible application of the mechanism to 
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
specific decision rational given a specific context. It might be  suggested
that an epistemological theory must be offered to explain when and why  a
subject is justified, (or entitled to) using a horseshoe analysis, and when 
and why he is not.

A reliabilist account cannot be a sufficient account for why a norm of 
decision is to be preferred to another in a given context.

As Strawson once said when attacked by Grice for his treatment of  'if':

"I only said "if""

"Literally, you said much more than that!," was Grice's implicatural  reply.


Gärdenfors, P. 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
time. Dordrecht:  Reidel.
Grice, "Indicative conditionals" in "Studies in the Way of Words"
Leitgeb, H. Beliefs in conditionals vs. conditional beliefs. Topoi, 26, 1, 
Pears, DF Motivated irrationality.
Ramsey, F.P. Law and causality. In Foundations of mathematics. London: 
Routledge & Kegan
Stalnaker, R. Inquiry. Cambridge, Mass.: MIT  Press.
Strawson, "'If' and  "⊃"", in P.G.R.I.C.E., Philosophical Grounds  of
Rationality: Intentions, Categories, Ends.

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