Thinking and reasoning with everyday causal conditionals Jonathan Evans Centre for Thinking and Language School of Psychology University of Plymouth

PART 1 WORKING WITH DAVID OVER Five things you need to know

1. DAVID NEVER STOPS WORKING Expect phone calls any time, any day engaging you in deep philosophical debate David thinks logic is by far the most interesting topic of conversation Now, Jonathan, the reason that T3 conditionals cannot deal with the case of counterfactuals … Sunday morning 9.00 am

2. DAVID KNOWS EVERYTHING YOU DO AND MUCH MORE BESIDES David has read everything there is to read on –Philosophical logic –Philosophy of science –Philosophy of mind –Psychology of reasoning –Psychology of judgement and decision making David also reads history for relaxation

3. DAVID IS A ROAD HAZARD He never stops talking logic to the driver Now, if we apply the principle of least possible change …

4. DAVID IS A TRANSNATIONAL “ A transnational person establishes a permanent nationality opposed to that assigned at birth” David was born as a Brit trapped in an American body David prefers everything that is British where it differs from the American He may be the first American born person to think that cricket is a more interesting game than baseball

5. DAVID ARGUES ABOUT EVERYTHING I argue, therefore I am at least a logical possibility … EVANS-OVER LAW The time taken to finish a book is proportional to the square of the number of authors who are collaborating to write it. WARNING Do not write a book with this man (I did it twice)

PART 2 THINKING WITH CAUSAL CONDITIONALS Collaborative research with David Over and Simon Handley

Probabilistic truth table task A new method invented by David Over For conditionals like If Queen Elizabeth dies then Prince Charles will become King How likely is it that: Queen Elizabeth dies and Prince Charles becomes King ___ Queen Elizabeth dies and Prince Charles does not become King ___ Queen Elizabeth does not die and Prince Charles becomes King ___ Queen Elizabeth does not die and Prince Charles does not become King __ 100% Time period specified as next five years (causal, diagnostic) or last five years (counterfactual)

Conditionals used in causal contexts in everyday real world examples Causal conditional (next five years) If Queen Elizabeth dies then Prince Charles will become King Counterfactual conditional (last five years) If Queen Elizabeth had died than Prince Charles would have become King Diagnostic conditional (in five years time) If Prince Charles has become King then Queen Elizabeth has died

Hypothetical thinking theory (HTT) Evans, Over and Handley (2003) Three principles of hypothetical thinking –Singularity – one hypothesis explored at a time –Relevance – most relevant hypothesis cued by context (by default the most probable) –Satisficing – current hypothesis maintained unless there is a good reason to give it up. Biases are not just due to heuristics, but also to satisficing on single mental simulations. Many examples discussed in my new book: Hypothetical thinking: Dual processes in reasoning and judgement (Psychology Press, in press)

Suppositional theory of conditionals Evans and Over (2004) put forward a suppositional theory of thinking which can be seen as a special case of HTT People evaluate conditionals, if p then q, by a single mental simulation based on the supposition of p. The conditional is believable to the extent that q is believable in this simulation. (Ramsey test.) Hence, people should equate the probability of a conditional with P(q|p). A number of recently published studies have shown that this is the dominant response for abstract conditionals with given frequency distributions.

Relevant probabilities The probabilistic truth table task yields four subjective probabilities: P(pq), P(p¬q), P(¬pq), P(¬p¬q) From these all relevant probabilities can be computed such as Conditional probability: P(q|p) Material conditional probability: 1 – P(p¬q) Delta rule: P(q|p) - P(q|¬p)

Multiple regression approach In our studies, we computed multiple regressions with three independent predictors. –Dependent variable: P(if p then q) –Independent variables: P(p), P(q|p), P(q|¬p) Regression across conditional statements, both on aggregate data and on individual Ps (not reported here) Example predictions –Suppositional theory: +ve weight of P(q|p) –Material conditional: -ve weight of P(p) –Conjunctive probability: +ve weights of P(p) and P(q|p) –Delta rule: +ve weight of P(q|p), -ve weight of P(q|¬p)

Over, Hadjichristidis, Evans, Handley and Sloman (Cognitive Psychology, in press) Experiment 1 Probability TRUE Experiment 1 Probability FALSE

Over et al. (CP, in press) Experiment 2 Probability (conditional) Experiment 2 Causal strength

Over et al. (CP, in press) Experiment 3 Probability (counterfactual) Experiment 2 Causal strength

Evans et al. (submitted) Probability (Causal conditional) Probability (Diagnostic conditional)

Conditional probability experiments Experiments relate subjective beliefs. Unlike abstract experiments, no frequency distributions are presented Belief in the conditional statements are consistently and strongly predicted by P(q|p) Belief in the conditional is generally independent of P(p). Any relation observed is positive, contrary to material conditional Some significant influence of P(q|¬p) in line with delta P rule, but much smaller than P(q|p)

Causal relationships Belief in causal conditionals is the same as belief in causal strength between p and q Both are largely predicted by P(q|p) Exactly the same applies to counterfactual conditionals, supporting our claim that their mental processing via the Ramsey test is similar Most surprisingly, belief in diagnostic conditionals is also predicted by P(q|p) even though this is P(cause|effect) Hence, Ramsey test does not have to be built from cause to effect

Evans, Handley, Over and Neilens (in preparation) Large scale study of individual differences in reasoning with causal conditionals (N = 160) All participants were given –Test of general intelligence (AH4) –Probability of conditionals task –Probabilistic truth table task –Logical truth table task –Conditional inference tasks On conditional inference tasks, 80 Ss were given deductive and 80 were given pragmatic reasoning instructions

Abstract study Prior to this study, we conducted a similar study with abstract conditionals Key findings in abstract study –High ability participants are more likely to (a) use the conditional probability P(q|p) when judging probability the conditional and (b) to give defective truth tables –Low ability participants are more likely to (a) use the conjunctive probability P(pq) when judging probability of the conditional, (b) are less defective, have more matching bias and a tendency towards conjunctive truth table patterns

Logical truth table task Logic index: judgements of TT case as true and TF case as false False antecedent index FAI: judgements of FT and FF as irrelevant As with abstract study, both are positively correlated with ability (AH4): –Logic index with AH4: =.34 (p,<.01) –FAI with AH4 =.23 (p <.01) Hence, on this task, high ability participants are more suppositional

Probabilistic tasks Broadly in line with previous studies However, P(p) is significantly positive Hence, the conjunctive probability, P(pq), might be used by some participants Individual differences in use of P(q|p) and P(pq) responses have only been investigated previously for abstract tasks Predicted belief in conditional statements

Conditional and conjunctive probability responders Used the same method to separate these two groups as used by Evans et al. (2002) with abstract probability judgement task That is, a multiple regression analysis was performed for each participant using both P(q|p) and P(pq) as predictors across sentences 41 CP subjects were those with positive and significant beta weights only for P(q|p) 33 CON subjects were those with positive and significant beta weights only for P(pq) In contrast with abstract studies only a minority: 74 /160 could be classified in this way

Relation of response type to cognitive ability If whole sample is used (n = 160) then there are no significant relationships If the sub-sample who can be classified as CP or CON is used (n = 74) then significant relationships result as on right Graph shows mean beta weights for two predictors in three ability groups For sub-sample, results replicate abstract study. High ability Ps are more suppositional on this task as well as the truth table task

(BIG) problem for model theory Both abstract and thematic studies show a 3 way relation between High ability – Defective truth table – P(if p then q) = P(q|p) Model theory explanation of defective truth table is that people forget the implicit model Model theory account of P(pq) response is similar Low ability Ps have smaller working memory Hence, model theory must predict Low ability – defective truth table – P(pq) responses

Conditional inference tasks DEDUCTIVE REASONING GROUP –Told to assume the premises and decide whether the conclusion necessarily followed. –Given MP, DA, AC and MT inferences in conclusion evaluation format –Required to make Yes/No decision on each conclusion PRAGMATIC INSTRUCTION GROUP –Given the premises and asked to rate belief in the conclusion given from 0% - 100%.

Individual differences in conditional inference tasks – prior expectations Research with abstract conditionals by Newstead et al (2005) and Evans et al. (submitted) show that –High ability groups make more MP –Low ability groups make more DA, AC –High ability groups tend to make less MT If low ability groups reason more pragmatically then MT may be easier to derive this way In current study, we expected an interaction. That is, high ability participants might reason more deductively, but only with deductive instructions.

Inference rates under deductive instructions Trends as for abstract experiments. Also, DA, AC and MT inference rates are highly correlated across participants, suggesting a common basis for inference, different from MP.

Inference rates under pragmatic instructions (mean belief ratings) Only MP is related to cognitive ability. Confirms that MP inference is different from the other three. Suggests, in general reasoning is more belief based with these instructions.

Interaction between instruction and inference type Deductive instructions boost MP and inhibit other inferences especially for high ability participants.

Modelling conditional inference (pragmatic group) This study provides an opportunity to relate beliefs to conditional inferences, as we have the probabilistic truth table task Hence, can relate inferences to beliefs for each participant on each sentence. For pragmatic group we have rated beliefs for each conclusion. Possible models considered initially included: –Belief in the conditional: P(if p then q) –Belief bias – P(conclusion) –Conditional probability (Oaksford & Chater): P(conclusion|premise)

Modelling method Unusually, we have no need to estimate parameters Each model can predict inference rates from an entirely independent set of measurements – the probabilistic truth table task We did this on a subject by subject basis, correlating observed and predicted ratings of conclusion (pragmatic group) and then averaging correlations across subjects Initial analysis found similar levels of support for the three models mentioned above

Further analysis Although the belief bias model fitted quite well, it is evident that P(conclusion) and P(conclusion|premises) are highly correlated with each other We hence did a multiple regression analysis for each participant using both predictors. This confirmed that the conditional probability model is doing most of the work However, we still have a competitor, in that belief the conditional statement is a decent predictor of inference rates on all inferences. Previous research (including current unpublished studies at Plymouth) confirms this general finding. Note that except in the case of MP, the two models are independent

Combined model A plausible psychological theory of belief based conditional inference is the following When the conditional is unbelievable (and deductive instructions are not given) Ss may simply to decline to make any inference When the conclusion is sufficiently believable, they test the inference by a mental simulation. They suppose the minor premise to be true and compute the likelihood of the conclusion Such a two stage model is multiplicative, that is P(conditional statement). P(conclusion|premise)

Combined model Is conditional sufficiently believable? Suppose premise Is conclusion sufficiently believable? Accept inference Reject inference No Yes No START Mental Simulation

Model fits (mean correlations, n = 80) MPDAACMT Belief in conditional Conditional probability (conc|prem) Combined model

More on model fits Although the fits look modest, they are very much stronger than under deductive instructions (difference is statistically significant) Fits for deductive group mostly result in negative correlations (but small) We are still investigating the best model for the pragmatic group It may be the case that P(q|p) and P(p|q) are highly correlated with our materials In this case P(if p then q) might be expect to correlate with P(Conc|Prem) for all inferences

Conditional inference - conclusions There is a tendency to reason on the basis of beliefs, which is removed by deductive instructions (contrast with belief bias in syllogistic reasoning) MP and AC are more belief-based than DA and MT High ability Ss are less belief based, but only for MP There is pragmatic but not belief based method for DA, AC and MT reasoning that is employed by lower ability participants. These must be implicatures that are cued by the ‘if p then q’ syntax. They tend to be inhibited by high ability participants on both abstract and realistic tasks There may be very high ability participants who can solve MT deductively, but they are absent from the population studied by us and Newstead et al. at Plymouth

General conclusions Both syntactic and semantic factors affect conditional reasoning. Syntactic based reasoning need not be logical Current thinking about dual process theory (Evans, Stanovich) is that analytic processes may be biased as well as heuristic ones. Lower ability Ps may simply engage in less effective analytic reasoning On abstract tasks, only high ability participants process the conditional in suppositional manner. However, these individual differences contradict model theory predictions With realistic conditionals, instructions and ability interact to determine the extent of belief based reasoning