walter schroyens university of leuven tiensestraat 102 3000 leuven, belgium university of gent h....

Walter Schroyens

University of Leuven

Tiensestraat 102

3000 Leuven, Belgium

University of Gent

H. Dunantlaan 29000 Gent, Belgium

A critical evaluation of the suppositional-conditionaltheory about iffy propositions

A critical evaluation of the suppositional-conditionaltheory about iffy propositionsSchroyens, W. (London, August 18th 2008)

“To boldly go where no man has gone before”?

Something old, something borrowed, … what is new?

Suppositional-conditional theory: singularity, satisficing, dual processing, hypothetical thinking

The devil is in the detail (as is the divine) Pragmatic implicatures and the interpretation(s) of conditionals

New evidence for a family of T4 conditionals, which seems problematical for the T3, suppositional-conditional

“Dragging old cows out of the ditch” (something like “waking sleeping dogs”).

Suppositional-conditional theory presently fails to account for inferential negation effects on AC and presently only has pragmatic implicatures to ‘play with’, which will not do the trick.

“You can’t have your cake and eat it too.”

Explanatory gaps exposed following the Evans et al. logic of direct task comparisons.

University of Leuven

Tiensestraat 102

3000 Leuven, Belgium


“The relevance principle is rooted in the heuristic system whose purpose is to deliver content for analytic processing reflecting relevant knowledge and belief.” (Evans, 2006)

“The singularity principle derives from the consideration that the analytic system is required for hypothetical thinking but has sharply limited processing capacity”. (Evans, 2006)

“The satisficing principle reflects a fundamental ‘bias’ in the analytic system to work with the representation it has unless there is good reason to give it up. …It combines with the singularity principle to convey the idea that in hypothetical thinking, we consider one hypothesis at a time and maintain it until we find a good reason to give it up.” (Evans, 2006)

Singularity principle:

Satisficing principle:

Relevance principleDual processing

analytic system

heuristic system

“None of these three principles is novel in itself, although I am not aware of any other theory that combines them in the way proposed here.” (Evans, 2006, p. 397)


“The relevance principle is rooted in the heuristic system whose purpose is to deliver content for analytic processing reflecting relevant knowledge and belief.” (Evans, in press)

“The singularity principle derives from the consideration that the analytic system is required for hypothetical thinking but has sharply limited processing capacity”. (Evans, in press)

“The satisficing principle reflects a fundamental ‘bias’ in the analytic system to work with the representation it has unless there is good reason to give it up. …It combines with the singularity principle to convey the idea that in hypothetical thinking, we consider one hypothesis at a time and maintain it until we find a good reason to give it up.” (Evans, In press)



Relevance principle

There is an important distinction between two sorts of inference that occur in daily life. On the one hand, the inferences I have so far considered mostly require a conscious and cold-blooded effort. You must make a voluntary decision to try to make them. They may take time and they are at the forefront of your awareness; they are explicit. On the other hand, the inferences that underlie the more mundane processes of intuitive judgment and the comprehension of discourse tend to be rapid, effortless, and outside conscious awareness: they are implicit. (Johnson-Laird, 1983, p. 127, original italics).

Dual processing




“The relevance principle is rooted in the heuristic system whose purpose is to deliver content for analytic processing reflecting relevant knowledge and belief.” (Evans, 2006)

“The singularity principle derives from the consideration that the analytic system is required for hypothetical thinking but has sharply limited processing capacity”. (Evans, 2006)

“The satisficing principle reflects a fundamental ‘bias’ in the analytic system to work with the representation it has unless there is good reason to give it up. …It combines with the singularity principle to convey the idea that in hypothetical thinking, we consider one hypothesis at a time and maintain it until we find a good reason to give it up.” (Evans, 2006)



Relevance principleRelevance principle

Semantic/pragmatic modulation: Context and content “can add information to models, prevent the construction of otherwise feasible models, and aid the process of constructing fully explicit models.” (Jh-L&B,2002) In the first stage, comprehension, reasoners use

their knowledge of the language and their general knowledge to understand the premises: they construct an internal model of the state of affairs that the premises describe….. Only in the third stage is any essential deductive work carried out: the first two stages are merely normal processes of comprehension and description Jh-L&B, 1991, p. 35)



“The relevance principle is rooted in the heuristic system whose purpose is to deliver content for analytic processing reflecting relevant knowledge and belief.” (Evans, in press)

“The singularity principle derives from the consideration that the analytic system is required for hypothetical thinking but has sharply limited processing capacity”. (Evans, in press)

“The satisficing principle reflects a fundamental ‘bias’ in the analytic system to work with the representation it has unless there is good reason to give it up. …It combines with the singularity principle to convey the idea that in hypothetical thinking, we consider one hypothesis at a time and maintain it until we find a good reason to give it up.” (Evans, In press)



Relevance principle

The mechanism is more likely to consist of a device that constructs a single mental model on the basis of discourse, its context and background knowledge. Such knowledge is embodied in the model by default, that is, it is maintained in the model provided that there is no subsequent evidence to overrule it. No attempt is made unless such evidence arises. It is for this reason that the process can be very rapid; it becomes as automatic as any other cognitive skill that calls for no more than a single mental representation at any one time. (Johnson-Laird, 1983, p. 128; original italics, underscoring added)



"individuals should be inferential satisficers; That is, if they reach a credible (or desirable) conclusion, or succeed in constructing a model in which such a conclusion is true, they are likely to accept it, and to overlook models that are counterexamples. Conversely, if they reach an incredible (or undesirable) conclusion, they are likely to search harder for a model of the premises in which it is false. This propensity to satisfice will in turn lead them to be overconfident in their conclusions, especially in the case of arguments that do have alternative models in which the conclusion is false. (Johnson-Laird, 1995, p. 186).

Reasoners tend to neglect models, and so their systematic errors correspond to a proper subset of the models, typically just a single model.. (Jh-L&B,2002,p. 654)

… a false assumption. The theory does not postulate that the search for counterexamples is invariably complete – far from it, as such impeccable performance would be incompatible with observed errors. (Jh-L&B,1991,p.39)

The devil is in the detail (as is the divine)The heuristic-analytic, default-interventionist suppositional-conditional model of

constructing and/or evaluating conditional arguments.

The conditional-inference task:One presents people with conditional inference problems formed by either affirming or denying the antecedent or consequent (production format), or one presents people with a complete argument (problem with conclusion).

0.963 0.700 0.631 0.5520.2

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MP (p therefore q) MT (not-q therefore not-q) AC (q therefore p) DA (not-p therefore not-q)

Infe

renc

e ac

cept

ance

rate

s



Pragmatic implicatures and the truth-table evaluation task

0.04 0.05 0.050.15

0.09

0.48

0.93 0.92

0.07 0.07

0.46 0.31

0.76

0.40

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0.89 0.88

0.49 0.53

0.15 0.120.02 0.04

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Implicit Explicit Implicit Explicit Implicit Explicit Implicit Explicit

TF FT FF TT

True* Irrelevant False

p.qp .not-qnot-p.qnot-p.not-q

TTTFFTFF

T-Case

TFII

Eval.Case

If p then q

TTFTTFFF

T-Case

TIFI

Eval.

TTFTTFFF

T-Case

TIFI

Eval.

if ¬p then ¬q

1. Conditional

if q then p

2. Converse 3. Inverse

this case—applying to a not-p possibility—is a true possibility for the material conditional and not for the ordinary conditional in a

suppositional theory" (Evans et al., 2005,

p.1043)

From the viewpoint of the suppositional conditional … If the

truth of the conditional is determined by the Ramsey test, then not-p cases are indeed irrelevant (Evans et al.,

2007, p. 1773).

The circularity of pragmatic-implicatures explanation. “q therefore p” (AC) is endorsed because people make the (invited) inference “if q then p”

“not-p therefore not-q” (DA) is endorsed because people make the (invited) inference “if not-p then not-p”

Why does one add the converse implicatures in the context of (AC) and the inverse implicatures in the context of DA?

The ad-hoc nature of the pragmatic-implicatures explanation.

“Essentially, these participants expect p and q (or more accurately, true antecedent and true consequent) to go together. If you have one, you have the other (MP, AC); if you do not have one, you do not have the other (DA, MT). Note that this reasoning strategy is symmetrical and non-suppositional, …” (Evans et al., 2007, p. 1782)



Interesting potential solution: Simple-Equivalence reasoning

“The preferred alternative to the initial model would be the model representing the possibility in which both the antecedent and consequent are false (CFF: [~p.~q]). Constructing this preferred alternative is again constrained by the fact that the referred clause is false (as given by the categorical premise: e.g., [~q]). Moreover, this referred clause is implied by or implies the state of affairs that one could not affirm: The inferential clause (e.g., [q]) could not be affirmed when integrating the initial model sets. As such the most obvious alternative would be a situation in which the inferential clause is denied (i.c.,[~q]; see, e.g, Geis & Zwicky, 1971)" (Schroyens et al., 2001, T&R, p. 134).

p q

p

qp q

q

p

q p

not-p

p?

q

q and not-q

not-qp q

False(p) not-p null

not-p p q

not-q

q?

p

p and not-p

False(q)

MP AC MT DA

The incompetence of syntactic “Reductio Ad Absurdum” reasoning to interveneThe analytic system’s functionality/teleology is that of testing putative inferences. Suppositional-conditional theory’s syntactic Reductio-Ad-Absurdum reasoning mechanism does not, cannot fulfill its job, i.e., it cannot result in a ascertained falsification/rejection of the ‘heuristically’ generated hypothesis.

The lack of “interventionist” reasoning on the affirmation problems.



what is proposed is that heuristic process often cue default mental models that imply …

default responses, inferences, or decisions. Analytic processes may or may not intervene

in order to revise or replace such default models and to inhibit default heuristic

responding.” (Evans, 2006, p. 382)

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94%

61%

74%

74%

50%

59%

37%

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MP(q) MP(¬q) AC(p) AC(¬p) MT(¬p) MT(¬¬p) DA(¬q) DA(¬¬q)

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rat

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The lack of “interventionist” reasoning on the affirmation problems.Both Simple-Equivalence reasoning and Reductio-Ad-Absurdum reasoning involve processing of double negatives, which accounts for the negation effects on DA and MT.

The theory does not provide an explanation of the negation effect on AC.

To provide an explanation it can only play with the pragmatic-implicatures/simple-equivalence inferences, but tweaking the P-I/S-E parameter (e.g., “negative conclusion bias”) fails:

i) If negation somehow has its effect in deriving AC via pragmatic-implicatures/S.E-inferences then the negation effect should be larger when a task triggers more pragmatic-implicatures/S.E-inferences. When the task yields more fallacies, it follows from the model that more P-I/S.E inferences have been made. Hence, tasks yielding higher AC rates (when p is affirmative) should yield larger negation effects (whereas in fact the opposite is the case; the negation effects become smaller).



The status of simple-equivalence reasoning and its relation with pragmatic implicatures needs to be clarified



Summary: some problems that have to have to be dealt with.

a) The theoretically incongruent status of the syntactic reductio-ad-absurdum strategy.

b) The absence of ‘interventionist’ (a.k.a., test/validation) procedures for AC/MP.

The lack of ‘interventionist’ (a.k.a., test/validation) procedures needs to be dealt with.

Potential solution:Follow the lead of Mental-models theory: As illustrated in Schroyens et al. (2001, T&R), a semantic test/validation procedures solves both issue (a) and issue (b). Moreover, Schroyens (2008, CJEP) shows that a search for counter-examples is the dominant test strategy.

"…in the conditional reasoning task, contrary to the claims of the mental model theory, it is not necessary to represent ¬p¬q explicitly as a true possibility to produce the valid conditional inference pattern, MP and MT. It is only necessary to consider that the conditional cannot hold when p and ¬q are together. …" (Evans et al, 2003, p. 334).

Evans et al. flirted with this solution, but committed to the syntactic procedure:

You can’t have your cake and eat it tooComparing apples and oranges: The Evans et al.-logic of cross-task comparisons.

“We find this [model theory] account [of the irrelevancy effect] highly implausible for the following reasons. When presented with a minor premise for the MT argument, people must succeed in fleshing-out the not-p and not-q cases as a true possibility around 70% of the time ... Recall our example:

If there is an A on the card then there is a 3 on the cardThere is not a 3 on the card

How is it then possible that, in the truth table task, a not-A and not-3 case is evaluated as irrelevant on the majority of occasions?” Evans et al., 2005 (p. 1043, italics added; also see, Evans, 2007, PNB&R, p. 58; Handley, Evans, & Thompson, 2006, JEP:LMC).

Proclaimed fact*: P(FF(Irrelevant)) > .50An explanatory gap ofminimally 20%. (.50 vs. .30)

Possible versus necessary inferences.

implicit versus explicit negations

Schroyens, Handley, Evans, Schaeken (2003, QJEP, Experiment 2).

0.04 0.05 0.050.15

0.09

0.48

0.93 0.92

0.07 0.07

0.46 0.31

0.76

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0.89 0.88

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0.15 0.120.02 0.04

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Implicit Explicit Implicit Explicit Implicit Explicit Implicit Explicit

TF FT FF TT

True* Irrelevant False

Possible or true?

Schroyens (2008, Cogsci 2008)

Comparing apples and oranges:

You can’t have your cake and eat it too: A serving of ones own (poisened) cake …

If TF(p and not-q) is judged false, then people reasoned towards a ‘biconditional’ interpretation.TF(p and not-q) is judged false in .53[.46,.61] of the cases. Why is it then that so few people reason towards a ‘biconditional’ interpretation in the sentence-probability task?

Schroyens, Schaeken, Dieussaert (2008, Experiment 2, Experimental Psychology):Biconditional probability= TT+FF/(TT+FFTF+FT) = 4%

An explanatory gap ofabout 44%. (.48 vs. .04)

However, if it is the converse implicature that is added, then FF remains irrelevant, which means that people should reason towards a biconditional-defective truth-table and should, thus*, reason towards the defective-biconditional probability.

A re-analyses of Evans et al. (2005, Experiment 2)

AND IF IFF D_IF D_IFF

8% (4/48) 8% (4/48) 8% (4/48) 62% (30/48) 17% (8/48)*

If FF(not-p and not-q) is judged true, then people have reasoned towards a ‘biconditional’ interpretation by adding the inverse implicature. FF is judged True* in .48[.41,.54] of the cases. Why is it then that so few people reason towards a ‘biconditional’ interpretation in the sentence-probability task?

Schroyens, Schaeken, Dieussaert (2008, Experiment 2, Experimental Psychology):Biconditional probability= TT+FF/(TT+FFTF+FT) = 4%

DA is endorsed in about .63[.59,.67] of cases, indicating a pragmatic implicature is made in about 63% of cases. Why is then that only 4 to 17% of people add such pragmatic implicatures in the sentence-probability tasks.




“Distinguishing between the theories seems to us to be very difficult, because neither is formulated in a strictly testable fashion. For example, theorists of both persuasions refer to an unspecified

pragmatic component that is needed to account for the marked effect of problem content and context on deductive reasoning. For

inference rule theorists such pragmatic influences may add ``invited inferences' ' to the necessary inferences provided by the mental

logic, whereas for mental model theorists pragmatic factors influence the likelihood of certain models being represented or fleshed out, with consequent effects on the reasoning observed.

Another problem is that both kinds of theorists are flexible in their proposals about the application of their reasoning mechanism. It is

always possible to adduce an ad hoc account of an unexpected phenomenon on the grounds of whether or not a rule was applied

or whether or not a model was formed.” (Evans et al., 1996, QJEP, p.1089).

To boldly go where no man has gone before?Mental-model theory’s T4 interpretation of conditionals


Case

TrueFalseTrueTrue

TrueFalseTrue/FalseTrue/False

TrueFalseIrrelevantIrrelevant

Neither False nor TrueFalseNeither False nor TrueNeither False nor True

T1 T2 T3 T4

The causes of the paradoxes are twofold. First, they throw semantic information away. Their premises contain more semantic information, that is, rule out more possibilities, than do their conclusions. Naive reasoners do not spontaneously draw conclusions that throw information away by adding disjunctive alternatives (Johnson-Laird & Byrne, 1991). Second, the judgment of the truth or falsity of assertions containing connectives, such as conditionals and disjunctions, is a meta-ability. That is, it calls for a grasp of the meta-linguistic predicates true and false, which refer to relations between assertions and the world (see, e.g., Jeffrey, 1981). In contrast, a task that taps directly into the interpretation of assertions is to judge what is possible. (Johnson-Laird & Byrne, 2002, p. 652)

True (not-p and not-p) therefore True (if p then q)

Reasoning from versus reasoning about the truth of a propositionThe core-meanings’ true possibilities (by definition the cases that are possible, given that the conditional is true) do

not make the conditional true. In going from the truth of a case, to the truth of a general claim (universal conditional) one is faced with the induction problem (a.k.a.,semantic-information loss, the raven paradox, the

verification problem).

To boldly go where no man has gone before?Mental-model theory’s T4 interpretation of conditionals

0.02 0.03 0.050.18

0.12

0.84

0.52

0.180.33

0.45

0.45

0.11

0.04

0.70

0.45 0.70

0.33

0.08

0.03

0.870.75

0.25 0.220.11 0.10 0.08

0%

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T/F/I T/F/I/C T/F/I T/F/I/C T/F/I T/F/I/C T/F/I T/F/I/C

TF (p.¬q) FT (¬p.q) FF (¬p.¬q) TT (p.q)

True Corroboratory Irrelevant False

0.00 0.030.10 0.14

0.240.31

0.76

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0.020.06

0.10

0.36 0.14

0.44

0.21

0.42

0.020.03

0.67

0.39 0.60

0.17

0.020.06

0.950.89

0.14 0.110.02 0.08

0.00 0.03

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T/F/I T/F/I/C T/F/I T/F/I/C T/F/I T/F/I/C T/F/I T/F/I/C

TF (p.¬q) FT (¬p.q) FF (¬p.¬q) TT (p.q)

True None/Corroboratory Irrelevant False

Schroyens (in press, QJEP, Experiment 2)

Schroyens (in press, Experiment 3: strict-truth condition)

O Makes the rule [strictly speaking] false

O Makes the rule [irrefutably] true

O Is irrelevant regarding the rule

O Is relevant but neither makes the rule false, nor does it make the rule [irrefutably] true: The figure is not excluded by the rule and it thus makes it less likely the rule is not true.

O Shows the rule is false,O Neither shows the rule is false, nor shows the rule is irrefutably true: The combination supports the rule, without proving it true or false.O Shows the rule is true.O Is irrelevant.

To boldly go where no man has gone before?Mental-model theory’s T4 conditional

TFFI

Eval.

1 + 2

TFFT

Eval.

1 + 3

AND D_IFF IFF D_IF IF P_X (VFIV) Other

Schroyens (in press, Exp2, Standard-truth groups)

Truth 0.0 5.4 8.1 32.4 8.1 32.4 13.5

Corroboration 0.0 0.0 10.8 10.8 16.2 10.8 51.4

Schroyens (in press, Exp2, Strict-truth groups)

Truth 0.0 4.8 4.8 42.9 9.5 19.0 19.0

Corroboration 0.0 0.0 11.1 11.1 30.6 25.0 22.2

Schroyens (in preparation, Experiment 1, N = 114)

Truth 0.0 11.4 42.1 16.7 4.4 6.1 19.3

Corroboration 0.0 1.8 31.6 5.3 23.7 7.0 30.7

Schroyens (in preparation, Experiment 2, N = 105)

Truth 2.9 6.7 38.1 20.0 9.5 12.4 10.5

Corroboration 0.0 2.7 21.0 5.7 41.0 11.4 18.1


TTTFFTFF

T-Case

TFII

Eval.Case

If p then q

TTFTTFFF

T-Case

TIFI

Eval.

TTFTTFFF

T-Case

TIFI

Eval.

if ¬p then ¬q

1. Conditional

if q then p

2. Converse 3. Inverse

That ‘s all for now. …

questions?

walter schroyens university of leuven tiensestraat 102 3000 leuven, belgium university of gent h....

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