Grado: Doctor.

Especialización: Lógica y Filosofía de la Ciencia

La regla de introducción de la disyunción, esto es, el esquema de la lógica clásica que, a partir de una premisa, lleva a concluir una disyunción transformando la premisa en uno de los términos de tal disyunción, es un problema cognitivo. Esto es así debido a que las personas solo utilizan esta regla en ciertas circunstancias. Por tanto, toda teoría que trate de describir el razonamiento humano tiene que explicar también este fenómeno. Basándose en la teoría de los modelos mentales, Orenes y Johnson-Laird proponen una explicación a este respecto, y este trabajo pretende mostrar que, aunque puede parecer que su explicación es contradictoria con algunos supuestos esenciales y ciertos desarrollos importantes de la teoría mencionada, tal no es verdaderamente el caso. Los puntos clave en este sentido que serán analizados son el modo en que la teoría de los modelos mentales realmente entiende la disyunción y la distinción que este mismo enfoque plantea entre Modelos Mentales y Modelos Completamente Explícitos.

The disjunction introduction rule, that is, the schema in classical logic that, from a premise, leads to conclude a disjunction transforming the premise into a disjunct of that disjunction, is a cognitive problem. This is so because people only use this rule on a few occasions. Therefore, any theory trying to account for human reasoning must explain this phenomenon as well. Based on the mental models theory, Orenes and Johnson-Laird provide such an explanation. In this way, this paper is intended to show that, although it can seem that their account is in contradiction with some essential assumptions and important developments of the aforementioned theory, that is not actually so. The key points in this regard that will be analyzed are the way the mental models theory really understands disjunction and the distinction that this last approach presents between Mental Models and Fully Explicit Models.

Ahabitual phenomenon in human cognition seems
to prove that our reasoning is not absolutely logical, at least if the
criterion assumed to check that is classical logic. In particular, the problem
is a rule that not only is valid in this last logic, but that it can even
considered as a basic schema in that logic. Indeed, Deaño (

Where ‘∨’ represents disjunction.

Or, if preferred,

This schema causes difficulties because most of the time people do not apply it or think that it is incorrect. It is accepted only in certain specific cases. Of course, this fact can lead one to assume, as said, that the human inferential activity is not logical -or that that activity is not necessarily coherent with standard logic- and to think that, if that were so, the rule should be used. However, what is important for this paper in this way is that, obviously, any framework proposed with the intention to explain reasoning cannot ignore this phenomenon. Such a framework has to account for it and predicts the situations in which the rule will be applied and the circumstances in which it will not.

The mental models theory (from now on, MMT) appears to be able to do that. Indeed, Orenes and Johnson-Laird (2012) give an explanation following this last approach that proposes the reasons why people only use DIR on certain particular occasions and the usual behavior is to reject it. Nevertheless, it can be thought that Orenes and Johnson-Laird’s (

In this way, to achieve that goal, firstly, I will comment on Orenes and Johnson-Laird’s (

Actually, the study carried out by Orenes
and Johnson-Laird (

Where ‘¬’ expresses negation and ‘&’ can be understood as conjunction.

This means that p ∨ q can describe [1], i.e., a situation in which both of the disjuncts are true, [2], i.e., a situation in which only the first disjunct (p) is true, or [3], i.e., a situation in which only the second disjunct (q) is true. So, if q is the premise, the second possibility [2] is precisely the problem with DIR, since, as it can be noticed, it indicates that q is false. One example can be helpful to explain this in a clearer way. Let us think about this inference with the formal structure of DIR:

“Viv is here.

Therefore, Pat is here or Viv is here, or both” (Orenes & Johnson-Laird, 2012: 362).

As pointed out and explicitly shown by Orenes and Johnson-Laird (2012: 362), the disjunction embedded into the conclusion can be true in three cases:

Clearly, [2] is incompatible with the premise Viv is here, as it provides that Viv is not here. Thus, this is the cause that people tend not to consider DIR to be correct, since its conclusion includes a possibility that is absolutely inconsistent with the previous information, that is, the premise.

But, as said, there are also cases in which individuals accept the rule and, if a theory wants to exactly describe the way the human deductive activity really works, it should provide an account of them too. As also mentioned, Orenes and Johnson-Laird (

“Lucia wore jewelry.

Therefore, Lucia wore the bracelet or she wore jewelry” (Orenes & Johnson-Laird, 2012: 363).

Now, a modulation process occurs and its result is the elimination of [2] as a possibility for the disjunction in the conclusion:

And the reason is not hard to understand: if pragmatics and the exact meanings of the words are taken into account, according to MMT, it can be thought that it is not possible wearing a bracelet and not wearing jewelry, as the former pragmatically and semantically implies the latter. So Orenes and Johnson-Laird (

Of course, there are works that criticize this account and propose an alternative explanation for the results presented by Orenes and Johnson-Laird (

A first difficulty in Orenes and
Johnson-Laird’s (

The majority response was that [2] and
[3] were the possibilities linked to p ∨ q, [1] and [4] being ignored. [4] is not a problem, since it was
not considered by Orenes and Johnson-Laird (

Likewise, in the case of the modulated inference, only one scenario should have been taken into account:

And this is so because, as indicated, these are the actual possibilities that, following Khemlani et al.’s (

Thus, it can be thought that Khemlani et al.’s (

As explained, [2] is removed because modulation reveals that it is not possible a scenario with the bracelet and without jewelry. Nevertheless, that very modulation process can make the disjunction inclusive, since it shows that [2] is not possible because, as also commented on, whenever there is a bracelet, there is jewelry as well. And this clearly leads to [1] as another possibility. Certainly, modulation does not only eliminate possible scenarios. It can also modify the elements of a particular scenario (

So, given that the possibilities can be the same if the disjunction is understood as exclusive, this is not a great problem for Orenes and Johnson-Laird’s (

Nonetheless, another point that appears to be a true difficulty for that explanation and allow questioning it is the fact that, from the beginning, MMT distinguishes between Mental Models and Fully Explicit Models (see, e.g., Johnson-Laird,

For the case of an exclusive disjunction such as p ∨ q (where ‘∨’ expresses exclusive disjunctive relationship), this means that the initial models, that is, the Mental Models, considered by most individuals are not even [2] and [3], which are the Fully Explicit Models, but simply:

As it can be checked, [5] and [6] correspond to [2] and [3], the difference being that, certainly, in the former what is denied, that is, what is false (¬q in [5] and ¬p in [6]) does not appear. But, if this is so, it must also be admitted that, given a non-modulated inference such as that described above, the scenarios firstly considered are truly these ones:

This, clearly, is not a problem for Orenes and Johnson-Laird’s (

However, although it can seem to be the contrary, the situation does not radically change in the case of the modulated inference either. From what has been said, it is clear that the Mental Models of the example indicated are:

Obviously, it can be thought that, at first, modulation cannot have an influence on [5]. If the information that the jewelry is not worn does not appear, it is impossible to note that the scenario expresses a contradiction (the bracelet is worn and jewelry is not) and has to be removed or modified. So, it could be stated that, as in the previous case of the non-modulated inference, although it is not incoherent with the premise Lucia wore jewelry, [5] cannot be inferred from it (that Lucia wore jewelry does not lead to that she wore the bracelet). In this way, it could also be claimed that really the inference should be considered as incorrect, and that Orenes and Johnson-Laird’s (

Therefore, neither the fact that people tend to interpret disjunction as exclusive nor the differentiation between Mental Models and Fully Explicit Models are a real problem for Orenes and Johnson-Laird’s (

Indeed, Orenes and Johnson-Laird’s (

On the other hand, as said above, other theories present alternative explanations to the one of Orenes and Johnson-Laird (

As far as the results achieved by Orenes and Johnson-Laird (

It is evident that, regardless of the content of q, if this last formula is taken as a premise and it is asked whether or not it follows from it that q is true, most people will respond positively. And this shows that López-Astorga’s (

However, a problem of López-Astorga’s (

In this way, what is truly interesting here of López-Astorga’s (

So, in short, it appears that we can speak about an important strength of MMT. Although an approach such as that of López-Astorga (

Furthermore, although the criticism raised by López-Astorga (