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I'll present some old and more recent data about conditional reasoning in children and adolescents within the general framework of mental model theory as a good theory [INAUDIBLE] that. I will begin by presenting some generalities about the importance of psychology of deduction and the two former ways to theorize this prediction of deduction, which is mental logic and mental model theory. And I will present some that data about development of mental models. And the new way of understanding, reasoning today, which is the new paradigm psychology based on probabilities.
And I will propose some modified mental model theory of conditional reasoning to account for the main data discovered by this new trend. And I will present some findings for testing the theory with a task known as a truth table task, and another task known as a probability task. And I will ask the difficult question of if there are developmental stages, and the development of reasoning. And the answer is no.
So you can go back It's finished. Let me begin by psychology of deduction. it's an old problem of nature, the nature of deductive reasoning, because human beings are rational, or like to be rational.
And rationality is often seen as the ability to make deductions because [INAUDIBLE] consequence of rules, laws, theorems, and so on. And it underpins scientific reasoning, so deduction is central for human cognition. And the two traditional questions are, what are the cognitive foundations of deductive reasoning, and does deduction depend on logic?
A first response was the mental logic. So mental logic was the idea that there are logical rules in human mind, and these rules are triggered by reading or hearing some premises. And for example, somebody presented with a sentence like, if the box is red, it contains pencils. It was assumed by these theories that people would-- sorry, it's the other one.
And this sentence would activate the logical rule, if p then q. And if people were presented with the second premise of the form of p, the box is red, the idea was that this rule is triggered and produces the conclusion, it contained pencils. And it was mentioned by brain or [INAUDIBLE] that these kinds of rules are probably innate and govern all deductions and reasoning.
But it doesn't work very well, because it's known that conventional logic is monotonic, which means that once a deduction has been reached, it cannot be withdrawn by anything else. And in fact, people withdraw many often conclusions, because when they are presented with new facts, they abandon their first conclusion. For example, in this example, when we know that Mark manages to illegally download new books, it's quite sure that it will not buy this book.
And also, conditionals often do not correspond to any logical connective. For example, if you like Westerns, Rio Bravo is on TV tonight, it's clear that the fact that Rio Bravo is on TV tonight doesn't depend on the fact that you like Westerns or not. So this is not an if, then that can be translated in logical form.
And mental logic applies to logical form sometimes. The idea was that these rules were syntactic in nature, and nobody knows how logical forms could be extracted from sentences to activate this rule. So the following idea proposed by Johnson-Laird was that people reason not with logical rules but from mental models that they construct.
And the idea is that a mental model is just a representation of a possibility once a sentence is true. For example, if the box is red, it contains pencils. People would represent a red box and pencils, and this would be the mental model corresponding to this sentence. And while they are informed that-- oh, and probably they are aware that there are other possibilities, but these possibilities remain implicit in the first time. And when people know that the box is red, this matches his first model, and they can produce the conclusion it contains red pencils.
If the box is blue, this doesn't match this first model, and so the theory assumes that people can construct additional models, for example, a blue box with no pencils inside. And in this case, the confusion could be that it doesn't contain pencils. But people can go further and construct a third model, which is still compatible with the first sentence where the box is blue, but it contains pencils. So that's possible, and in this case there is no conclusions.
This is the idea of the mental model theory. And it can be summarized in this way, first people construct an initial model with an explicit representation of the coocurrence of p and q and an additional implicit model. And the implicit model can be made explicit by a process known as fleshing out.
And here is a constriction of the second bundle, resulting in a biconditional interpretation, in which a red box contained pencils, and those boxes that are not red do not contain pencils. And in a better and more elaborated interpretation, people would be able to construct a third model. And in this case, they reach a conditional interpretation which is a complete and correct interpretation of the first sentence.
This can be summarized as one explicit model for the initial model, two models with one, which is fleshing out for biconditional interpretations, and conditional interpretation with two fleshed out models added to the first representation. And this could have interesting developmental extensions, because it could be imagined that with age, we could imagine in the first place that children should be able first to construct one, and then two, and then three models. And we could have a developmental in terms of an increasing number of models that can be constricted.
And this is the hypothesis we tested first, with the idea that if children are presented with a sentence of the form, if the box is red then it contains pencils, and if they are asked to identify use cases that are incompatible with the conditional, we should have three different types of responses. Because those who are conjunctive in nature, that is understanding if p and q are the conjunction of p and q, that's all, and should identify the three other cases as incompatible with the rule.
Those who adopt a biconditional reading should just identify these two cases as incompatible with the rule. And those probably older that adopt the conditional reading should identify the sole p and not q case as incompatible with conditional. And we presented this kind of task, which is very simple.
For example, the rule is, if you put on a white shirt, then you put on blue trousers. And children are asked to identify those cases where the rule is not obeyed. And we observe the following results.
Third graders mainly adopt a conjunctive interpretation of biconditional. That is, they identify three different cases as incompatible with the rule. And then sixth graders adopt the three interpretations, approximately, with the same frequency. And all the other [INAUDIBLE] favor a conditional interpretation. And so we have a nice developmental trend from a conjunctive to a conditional interpretation with biconditional interpretations constituting something like middle [INAUDIBLE].
And we also tested the relationship between this kind of interpretation and working memory capacity, because the idea was that the number of models that children can construct depends on their working memory capacity. And we used a slightly different task, which is not a task in which people are asked to identify use cases that are incompatible with conditional, but they are asked to produce admissible cases.
So they are given material like this, and they have to produce as many cases as possible corresponding to, if you put on a white shirt, then you put on blue trousers. And we expect that, of course, younger children will only produce one possibility, which is this one. And older children should produce two different cases, which is this one and this one. And finally, some children should even consider that it's possible to have a gray shirt with blue trousers, which is not compatible with the rule.
And at the same time, people were present-- children and adolescents were presented with a counting span asking which children have to count dots in successive cards. And at the end of the series, to have to recall the totals, which is a very difficult task. And these are the results.
We classified population in the low, medium, and high working memory capacity. And these are their main and preferred interpretation of the conditional. And we can see that low span individuals mainly adopted a conjunctive reading and high span individuals adopted a conditional reading, with biconditional reading as my middle [INAUDIBLE]. And the correlation between the number of different possibilities constructed. And working memory span was 0.65, which is not so bad.
We also tested slightly before Phil Johnson-Laird himself as a concept of modulation. Modulation is a main concept of the mental model theory, which assumes that the construction of mental models can be modulated by semantic or pragmatic knowledge, and in such a way that it can facilitate the construction of some models and hinders the construction of other models.
For example, we discovered a strange effect due to binary terms. A binary term is a term that has only one possible alternative. For example, if the pupil is a girl, the only possible alternative is boy. There are just two possibilities. And if the pupil is a girl, then she wears glasses. The other possibility is that boys don't.
And so this leads to what we call a complete representation, in which every case here is matched with one case here. And these binary terms should block the construction of not p q cases of the form a boy wearing glasses. And those predictions or binary terms should induce biconditional interpretations.
And this is what was observed. This is the first slide before with non-binary terms. So you have the traditional developmental trend, from conjunctive to conditional interpretations. And this is the responses with binary terms. And we can see that the developmental trend has disappeared, and everybody produces the predicted biconditional interpretation.
So this worked quite well, but recently many also have charged that most probably the mental logic and the mental model theory were all wrong, because people do not reason in this way. And they most probably reason using probabilities. And the idea is that any of our deductions, all our deductions are based on probabilities and calculated on probabilities.
And these also named their theory the new paradigm psychology of reasoning. And you have here some of these [INAUDIBLE]. And there are two main ideas. The first is that traditional theories of reasoning, like mental logic or mental models, are rooted on formal logic and the idea that reasoning is a process of deductions are true.
And these theories are based on binary deductions like truth, falsity, and so on. And they reject these ideas, assuming that reasoning is a matter of degrees of beliefs, utility, subjective probability. And most probably, reasoning is just probability judgements, and not deduction from truth or falsity.
And they are quite assertive. For example, here you have a quote by Elqayam and Over, "assuming that studying probability judgment will tell us more about the psychology of reasoning and trying to figure out how far people confront binary extension [INAUDIBLE]." So, thank you for this effort.
And these theories are mainly based on conditional, because the main assumptions concerns conditional reasoning. And the first idea that the meaning of conditional is going to be probabilistic in nature, suppositional, based on what the Ramsey test. The Ramsey Test consists, when you assess [INAUDIBLE] p's and q's, [INAUDIBLE] to add p to your stock of knowledge, to your beliefs. And on this basis, to assess the likelihood of q, disregarding, not case.
For example, if you want to assess the validity or the plausibility of a conditional like, if Queen Elizabeth dies, Charles will become King, and you imagine that Elisabeth is dead-- sorry for that.
SPEAKER 1: You want to keep not p, in that case.
PIERRE BARROUILLET: And you try to imagine the probability that Charles becomes king, and probably very high, of course. And people's degree of belief on a conditional should equate, in this case a conditional probability, which is the probability of if p's and q's, just the probability of q given p. And this is very important for this theoretical trend. It is such important that they call this equality z equation, which is the basis of most of the human reasoning, according to a new paradigm, psychology of reasoning.
There are two main empirical evidence for this theory. The first is that, when people are asked to assess the truth value of a conditional, they adopt what we call a defective or de Finetti truth table. De Finetti is the name of the guy who first described this kind of trust table, in which when assessing the truth value of a conditional, the p q case makes a conditional true.
The p not q case makes it false, of course. But the true not p case leaves the truth value of the conditional indeterminate. This is different from the traditional view of logic, in which the conditional has a material implication truth table, in which the conditional is true for these three cases and just false for p not q cases.
So the idea is that not p cases are considered irrelevant for the truth table. For truth value, it's true that when people are asked to judge the truth value of a conditional, very often they adopt this kind of de Finetti trust table. And the other evidence is the probability task. When people are asked to assess the probability of if p then q sentences, very often they add up the conditional probability of q given p. And this has been demonstrated by [INAUDIBLE] and Over, and [INAUDIBLE].
And these two facts are taken as evidence against the mental model theory, because according to the new paradigm theoreticians, the mental model theories should predict not a definitive truth table, but the material implication truth table, in which the three cases constructed should be judged as making the sentence true, and just p not q as making it false. And there should be no response of irrelevance.
And when asked to assess the probability of a conditional, people should give a response in which they should add the probabilities of the three cases that are represented in the conditional interpretation, as I showed before. And this never occurs. Nobody gives this kind of response. So we were confronted with a big problem, because the traditional mental model theory doesn't make the job, and doesn't account for this kind of phenomenon, which is why we proposed a modified mental model theory of conditional reasoning.
And in this modified mental model theory, we assume first that reasoning is a dual process that governs the construction of mental models. The first type of process, Heuristic process based on a system one-- cognitive system named system one, if you want, which is implicit, automatic, fast, not limited by working memory capacity. These heuristic processes should would produce some initial representation. Very simple, default initial representation.
And after the production of this initial representation, analytic processes pertaining to some system two could flesh out the initial representation and construct addition models. But the intervention of this analytic processes is just optional. And sometimes, and in most of the cases, people should only reason from their initial model.
This simple idea makes that the epistemic status of the different models constructed should vary, depending on the nature of the processes governing their construction, because for [INAUDIBLE], the initial model should capture what makes the sentence true. Because these initial models come spontaneously to mind without any reflection. And they appear as the real meaning of the sentence.
So when confronted with cases that match this initial model, people should consider that the sentence is true. But when confronted with cases that match additional models constructed through fleshing out, people should consider that the truth value of the sentence remains indeterminate. It's just when presented with cases that do not match any of the models constructed that they should deem the conditional false.
Let's take an example. Imagine that people are asked to judge the truth value of a sentence like, if there is an A, then there is a five, and we can imagine that people construct an initial model of the form A, 5. When presented with a case that matches this representation, of course people should probably think that the sentence is true, because--
SPEAKER 2: So this is [INAUDIBLE].
PIERRE BARROUILLET: Yeah, exactly. No, no, no, no, [INAUDIBLE]. And imagine now that people still maintain this initial model, and they are presented with a case B,3, and this doesn't match the initial model. So the sentence is not true, in fact, not entirely true.
But if there is some fleshing out, people can observe that B and 3 matches this model here. And in this case, the sentence is not absolutely true, but it's not false. So it's not either true now false. So it's kind of indeterminate truth value.
By contrast, if they are presented with A and 3, this doesn't match the initial model, and it doesn't match none of the constructed model [INAUDIBLE]. And so the sentence is false. And this makes very simple developmental predictions, because imagine that people, children and adolescents, are presented with the truth value task.
So they are given a sentence, a conditional sentence of the form, if p then q, and they are presented with the four different logical cases. And for each of these cases, they have to say if the sentence is true or false, or if one cannot know if it's true or false. Children will adopt a conjunctive interpretation with just one model, should consider that the sentence is true for this model and false for all of the three other cases, because they are not represented at all.
Children who adopt a biconditional reading with adding not being the q model by fleshing out, should consider of course the sentence true for p, q, false for the cases that are not represented in their representation. But they should consider the conditional as indeterminate for a case that matches some models have fleshed out. And here, we should have four people adopting a conditional interpretation, true for p, q, false for p not q, and the indeterminate response for the two cases that match the two models with not p's that have been constructed by fleshing out.
This is the definitive truth table, shown above, the effective truth table produced by adults. And what this theory predicts is that these definitive table should be preceded developmentally by two different response levels. And the hypotheses are quite simple, because we assume that the heuristic system does not develop so much during childhood and adolescence. And so, for a given type of conditional, the initial model should remain largely unchanged through development.
And the case making the conditional proof should just remain stable across age, because models pertaining to the initial model makes a conditional truth. The analytic system, which strongly develops with age, should lead to a rate of indeterminate responses increasing with age strongly, because the analytic system constricts the models for fleshing out and the cases that match the fleshing out models lead to the indeterminate response.
And finally, the analytic system is influenced by a heuristic system in many of the dual process theories. And this should be the source of the moderation effects, describable.
SPEAKER 3: Is it OK to ask questions about that? There's supposed to be-- I mean, in some conceptions they were modular, though. So the heuristic is walled off from the analytic. So they're not supposed to interact in many models. Is it really analytics that's being influenced [INAUDIBLE]?
PIERRE BARROUILLET: In this idea, the idea is that the heuristic system provides the representations on which is the analytic system works. So the idea is that, generally, the heuristic system is responsible for a production of the initial representation, and analytic systems work on this initial representation.
SPEAKER 3: So then it's not really abstract.
PIERRE BARROUILLET: Sorry?
SPEAKER 3: Then the analytical system cannot be abstract, because it's going to be influenced by knowledge.
PIERRE BARROUILLET: It can be abstract in the sense that you can, for example, imagine that there are some abstract roles that can apply to different contents, depending on the nature of the representation constructed from the heuristic system. So the output of the analytic system can be influenced by the heuristic system without supposing that the analytic system doesn't contain, for example, absolutely abstract rules. You can have abstract rules with an output depending on the input, OK?
SPEAKER 3: [INAUDIBLE]
PIERRE BARROUILLET: Could be. We test this theory with a truth testing task. The task is the following, children are presented with a sentence, like if the circle is red then the star is blue. And then they are presented with the content of a box, which appears on screen. And they have to say, for this case, if the sentence is true, false, or one cannot know if it's true or false. In this case, it's false, OK? Because if the circle is red, the star is blue, but it's not. So here, you have to take this box.
And of course, we expect that-- we expect to find these three kinds of responses, conjunctive, defective, biconditional, in which not been acute cases leaves the true value of the conditional indeterminate.
And here are two cases leaving the conditional truth value indeterminate. And this is mainly what you observe. Third graders mainly produced conjunctive responses. Others mainly produce defective conditional response.
This is the effective truth table described by this new paradigm, and sixth and ninth graders mainly produce biconditional responses, with nine graders beginning to produce conditional responses in this case.
And we tested the effect of binary terms in this task, because binary terms should lead to just a construction of the not p not q model for fleshing out. So what the theory predicts is that in a truth table task, people should produce defective biconditional patterns. And this is what we observe with binary terms in [INAUDIBLE] and the consequence of the conditional, many people produce biconditional responses.
Younger participants remain unaffected by the manipulation of binary [INAUDIBLE], most probably because if they produce conjunctive responses, they do not flesh out their model. And so they should remain unaffected by the many predictions of the facility of fleshing out. And the other finding is that there is a strongly reduced developmental difference.
We also tested promises and threats, because these are interesting sentences like, if you [INAUDIBLE] alone, then I'll give you five Euros. [INAUDIBLE] and colleagues, in 1997, demonstrates that this kind of sentence has a strange truth table, in which there are two cases that are judged to make the conditional true, which are the lawn is mown and the child receives five Euros, and the lawn is not mown, and it receives nothing.
These two cases make the conditional true, and two other cases make it false. And this makes sense, because if you promise that if you mow the lawn that then I'll give you five Euros, and the child mows the lawn, you have to give him the five Euros. And if you don't, you are a liar.
And of course, a child who doesn't mow the lawn should receive nothing. Because if it receives something, there is something wrong. And so, this is why this truth table is very simple, with two cases true and two cases false.
And this makes sense because we assume that heuristic processes in this case deliver a two model initial representation. Because correctly understanding this kind of premise is understanding that, if you mow the lawn you will give your five Euros. But if you don't, I don't give you anything, because I want to have my lawn mown and you want five Euros. So it's a good deal.
And there is no fleshing out at all in this, case because there are just an initial model with two representations. And the two other cases are not compatible with the conditional. So there should be no developmental at all, because there is no fleshing out.
And this is what happens. These are the strange equivalence truth tables. And they all produced for premises and for threats even by third graders, because even third graders very often correctly understand premises and threats, fortunately.
[LAUGHTER]
And we also tested-- that's true. And it's very effective, because when you work on reasoning, you can ask your children to make things like this. And you say, and you know, the mental theory predicts that you should understand that. And it works.
We also tested the theory with the probability task. The probability task is a very difficult task. Imagine that you are presented with cards like these of the four different logical cases. Black and white cards with squares or circles.
And you are asked, how likely is the following statement to be true of a card drawn at random from the pack? If the card is black, then there is a square printed on it. It's a strange task.
It's not random. For example, [INAUDIBLE] thought about this kind of task, because it's very complex, in fact. And what people didn't do in this case is to respond in this way.
As the new paradigm predicts, they disregard not p cases that are not taken into account. And they just assess the probability of finding the square in black cards. And the probability is 2/3 in this case. And about 60% of adults respond in this way.
And it has been even demonstrated that, as you will see, many people, even adults, do not respond in this way in the first place. But if you present a second, and a third, and a fourth, and a fifth trial, many of these people move to these kind of responses [INAUDIBLE], surprisingly.
The question is that, very often by the past, when people presented a theory of reasoning, one of the main tests for this theory was the developmental test. For example, in a mental logic approach, our source assumes that all mind is endowed with logical rules. And the best proof of that was to demonstrate that these rules were already present and efficient, even in children, and even in young children age five, four.
And by the way, it's true that, for example, young children are able to produce [INAUDIBLE], which is a rule I show in the first place for the conditional if p then q and p then q. And in the same way, we have seen that.
For example, the minimal representation that is hypothesized by the mental model theory, the initial model p-q, is already present, even in young children. So I reason that what we need with the new paradigm theories is some developmental test of a possible presence of the equation, the conditional probability, even not in young children, of course, but at least in adolescence, for example. At the beginning of adolescence, it should be not so bad.
And so if it's true that conditionals are probabilistic in nature, and if it's true that the question is a core meaning of the conditional, the equation should exhibit some pervasiveness through development types of conditionals, and contents, and so on. And we tested this using our own model with a very simple prediction, which is that how people assess the probability of a conditional, probably in calculating the ratio between the cases that make the rule true and those that are relevant for the truth value of the rule.
And in the same way, the probability that the conditional is false should correspond to the ratio between the number of cases that make the conditional false, divided by the number of cases that are relevant for truth value. But we know that there is an age related evolution of the relevant cases, because remember that irrelevant cases correspond to rules that match the models constructed through fleshing out. And fleshing out strongly develops with age.
So the number of relevant cases vary from one age to another. And so probably just a conditional should evolve with age in a predictable way. And in this way, imagine, for example, children adopting a conjunctive probability in this task. And he has to assess the probability that if the card is black, then there is a square printed on it. That's simple, because there are just two cases that make the conditional true.
So the probability that the said statement is true is two out of eight, because all the cases are relevant here, because the other cases make the conditional false in the conjunctive probability reading. So they should respond that the probability is two out of eight, which is different from somebody adopting a defective biconditional probability, because defective biconditional reading leads to, of course, assuming that there are still two es that make the conditional true.
But these cases are irrelevant, because not p not q has been produced by fleshing out in the biconditional reading. And so the number of relevant cases is not eight, but six. And people will respond two out of six, reflect a defective biconditional reading.
And those that adopt a defective conditional probability should respond, of course, two out of-- but out of three, because all the not p cases are irrelevant now. And so this is the equation described by the new paradigm. And so we presented this very difficult task to sixth, ninth graders, and adults.
And why is there no third graders? We tried to do that, but they never grasped the task, because assess the probability of something that is not true in the first place, because the probability of if, they were reluctant. And this is the same task as presented in adults.
And these are the results. Here you have the conjunctive responses, mainly in grade six. Ninth graders adopted the three ways of reading. And adults produced 60% of conditional reading [INAUDIBLE] the equation. And 40% of them were conjunctive in responses.
And this is not an isolated finding, because this was also observed in the first [INAUDIBLE], both by [? Ivens ?] and by Klaus Bauer. And so we can see that, as the equation is, for example, absolutely absent in sixth graders and rarely produced in ninth graders. And we also found, we looked for [INAUDIBLE] the equation through contents and context. For example, using binary terms.
Remember that binary terms elicit very often a defective biconditional reading. So in the probability tasks, they should elicit defective biconditional responses. And just nonbinary terms should elicit the equation responses just in adults.
And this is what we observed. This is the responses for the probability task with binary terms. And the responses corresponding to the equation are rare. And very often, people produce defective biconditional readings. And so probability that goes with this kind of interpretation.
And we also try with the premises and threats that this is the equivalence reading. And in this case, people should consider that what is the probability of, if you mow the lawn, then I will give you five Euros for a card drawn at random from the pack. And this should be four, because there are four cases that make the conditional true in this case.
Out of eight, because these all making the conditional false, remember. And this is exactly what happens for promises and for threats. Sixth graders, nine graders, and adults very often produce an equivalence reading. And the corresponding equivalence response is a probability task. And--
SPEAKER 4: Nobody [INAUDIBLE]
PIERRE BARROUILLET: No.
SPEAKER 4: [INAUDIBLE]
PIERRE BARROUILLET: By the past, we had Communists in France, but no longer now. Maybe it's too late for this kind of experiment. You're right, these are Swiss people. So this is the reason, probably.
And the last question is are the three level developmental stages, because we have seen that in all the tasks, you have always the same developmental trend, from conjunctive to biconditional, and then conditional interpretation. And we could imagine that the three levels constitute three developmental stages, a la Piaget, if you want.
But it's not at all the case. These are the three tasks we have seen today, the possibility task, tasks in which people have just to say if this case is compatible with a rule, which is considered as true. Or children are asked to produce cases that are compatible with the rule.
This is a truth value task. It is a task in the reverse direction. People are given a case, and they have to judge the truth value of the conditional, which is, in the mental model theory, a more difficult task.
Because remember that mental models are a representation of possible cases. So thinking about possibilities is a natural way of thinking and reasoning. And reasoning about truth values is something like a meta processing and meta reasoning, and it should be more difficult.
And finally, you have the probability task here, which is even more difficult. And you see that the number, for example, the number of biconditional responses in third graders is lower for the truth values and so possibilities task. And these are the other responses, reflecting some misunderstanding of the task.
And this is their response is probably, they are not able to do that. And this is clearer for sixth graders. Sixth graders are-- adopt a biconditional reading with the easiest possibility task. But you can see that they move to the primitive conjunctive interpretation when we move to more difficult tasks.
And this is also the case for ninth graders who are conditional with the simplest task, but just biconditional with a truth value task. And for the probability task, you can even see a lot of conjunctive responses. This is even true for adults.
You can see that the number of conditional responses decreases as the difficulty of the task increases. So the three levels are probably not developmental stages. They are most probably a reflection of a capacity to produce more or less complex representations, interacting with the inherent difficulty of the task.
SPEAKER 4: [INAUDIBLE]
PIERRE BARROUILLET: Ah. This is a kind of mystery, but I think we have an explanation.
SPEAKER 4: But people get, I mean everybody gets it.
PIERRE BARROUILLET: I think we have an explanation, because you can see that the conjunctive interpretation is almost never observed in the other tasks. Most probably, this is not a real conjunctive reading. And we have observed in another experiment, but I don't have the results in these slides.
When adults are presented with a truth value task with only two possibilities. So they are given cases, and for each of these cases, they have to say if the sentence is true or false. But they have just two possibilities, which is true and false. You remove the possibility to say, oh, it's indeterminate irrelevant.
In this case, it appears that you have approximately the same pattern of responses. And with 60% of adults responding in a way which is, in this case, the material implication. The sentence is true for p-q, not p-q, not p not q, and it's just false for p not q. But you have 40% of these adults would judge that the sentence is true for pq and false for both not p cases and p not q case.
And I think that these guys here probably understand that their task in the probability task is to say if the sentence is true or false, with no possible alternative. And in this case, they adopt this kind of truth table for calculating probably. I think this is the solution, because I just mentioned the responses for the probability of true, but we also the same results for the probability of false.
And in this case, when people are asked to say what is the probability that the conditional is false, they respond in a conjunctive way, too. And they assume that the three cases that are different from p-q make the conditional false, which never occurs when, for example, they are thinking about possibilities. All the adults, without any exception, assume that not p cases are compatible with the conditional.
But when asked if these cases make the conditional true or false, sometimes they prefer to say that it makes false. It's kind of a paradox, but I think it can be understood in some ways. It's a very difficult task, in fact.
At the beginning, I didn't grasp the task, in fact, when I read the first time. What is the probability of conditional? And with additional thought, ah, OK, something like that.
Well, some conclusion. So here, we have seen that conditional reasoning strongly evolves with age. We have three developmental levels in every task that are not developmental stages.
Most probably, this is due to the fact that people can construct increasingly complex representations, depending on working memory capacity. But performance is also a function of the cognitive demand of the task. And even if you are able to produce a conditional interpretation in one task, this doesn't mean that you will be able, for example, to produce a response in the probability task corresponding to this conditional interpretation.
And up at least from the study with children, there is no need to assume a probabilistic meaning of the conditional, because a modifiment of another theory can account for [INAUDIBLE] led to promoting these kinds of theories. And it also predicts developmental findings that cannot be predicted and explained by the probabilistic approach of conditional. That's all, thank you.
Pierre Barrouillet of the University of Geneva presents old and recent data about conditional reasoning in children and adults within the framework of Mental Model theory. He proposes a modification of the theory of conditional reasoning based on probabilities.
Recorded April 6, 2015 as part of the Human Development Outreach and Extension program.
