I think this post may be way off-piste. The thing is: why do people who get one
kind of WT partly wrong [e.g. the AD47 example] get another kind entirely right
e.g. where you either know their age of what they are drinking, which of the
following do you need to check further to make sure there is no underage
drinking going on in a club - a 16 year old, a 50 year old, someone with a
beer, someone with a mineral water. Everyone knows it's the 16 year old and
beer drinker who need to be checked for, respectively, what they are drinking
and their age. This problem has exactly the same logical structure as the AD47
problem but it is straightforward for most people where the AD47 is not. Why?
It is not likely that the answer lies in some different grammatical
interpretation of what are, logically, identical problems in their logical
structure - and if you read Pinker you will see enough Wason Tests have been
done to pretty much discount any idea that it is some subtle grammatical shift
of interpretation that explains the divergence.
DL
On Friday, 26 February 2016, 17:21, "dmarc-noreply@xxxxxxxxxxxxx"
<dmarc-noreply@xxxxxxxxxxxxx> wrote:
In a message dated 2/26/2016 11:07:36 A.M. Eastern Standard Time,
donalmcevoyuk@xxxxxxxxxxx writes:
For anyone else following, this translates as: yes, there is no valid
alternative logic e.g. in the AD47 Test, there is only one correct answer - A
and 7.
McEvoy, now I was re-reading his post, wrote about 'do with a laugh', and
he is right in providing what he sees as the implicature behind 'laugh' and
'laughable'.
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
part".
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
war.
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
example.
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'
utteranc.
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'
belief.
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
discovered.
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
approach.
For one might argue that this difference justifies a subject in
representing the task respectively by a material implication or not -- alla
Kleene,
say.
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
appropriate?
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
context?
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'
decision.
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"
instead.
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
detail.
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.
Cheers,
Speranza
REFERENCES:
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,
115-132.
Pears, DF Motivated irrationality.
Ramsey, F.P. Law and causality. In Foundations of mathematics. London:
Routledge & Kegan
Paul.
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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