When involved in a conversation, we do not only reinforce the problematic aspect of the issue. As we will see, some of our replies may conversely tend to suppress or to minimize what makes the issue problematic (even if we are unaware of doing so most of the time). The easiest to do is certainly to deny one term of the problematic clause (cf. p.15). Here is a crude example :
[ex_cupboard]
context: A and B had some trouble with moisture in their house. The house had not been heated during the weekend, and the clothes are still cold in the cupboard.
A1- C'est humide même là [dans le placard]
B1- C'est pas humide, c'est froid
A1- It's also wet here [in the cloth cupboard]
B1- It isn't wet. Its cold
A tells she got the impression that everything was wet, even in the cupboard, thus introducing a topic in the undesirable mode (A and B had moisture problems in their house). However, B is able to show that this impression comes from the fact that the clothes are cold. There is no reason left to think that they are wet. B thus performed what we call a direct invalidation by casting doubt on a fact that was used to establish the modality.
Notice that the logical context is modified as the conversation moves on. Here a piece of knowledge (coolness of the clothes) was made "active" by B and had to be added to the logical context. We are going now to consider cases in which the problematic clause itself is modified. We saw one example of this in [ex_Goffman, p.6]. At the beginning, the paradox was represented by the problematic clause :
[ knows( X, Goffman's_books) & not sociologist ( X ) ] => F
In this dialogue, B5 ("I heard about it from a friend who was a sociologist, and he said read this book, ...") has no effect on both terms of the problematic clause, and thus B5 is a direct invalidation. We get nevertheless the feeling that the paradox is invalidated after B5. This can be understood is we notice that the preceding clause is no longer correct and has to be replaced by :
[ knows( X, Goffman's_books) & not sociologist
( X )
& not recommends(Y, X,
Goffman's_books)] => F
It would be amazing that somebody knows Goffman's books without being a sociologist and without having these books recommended. In other words, when denying the last term above, B5 does not invalidate the initial problematic clause, but a modified, augmented, version of this clause.
That is why we speak here of indirect invalidation. Indirect invalidation differs from direct invalidation by the fact that the denied term had been "forgotten" in the problematic clause. When asserting [recommend(friend, B, Goffman's_books)], B5 denies a term which appears as a forgotten premise in the initial context. The possibility of indirect invalidation for a given context is fundamental, and the distinction between direct and indirect invalidation is syntactically obvious as soon as the logical context is expressed in logical form.
The possibility of indirect invalidation should not give the impression that this way of replying is poorly constrained. All the modifications of the problematic clause are indeed not admissible ! The modified paradox has to be accepted by the first speaker. Just imagine A's reaction if B had replied "it's because I am hungry". More precisely, if the problematic clause is (in propositional logic):
[ p1 & p2 & . . . & pn ] => MOD
a direct invalidation is a negation of one of the pi, while an indirect invalidation involves the negation of an added premise pn+1 :
[ p1 & p2 & . . . & pn & pn+1 ] => MOD
An indirect invalidation is admissible as long as the surprised speaker can accept it as denying a forgotten premise pn+1. In other words, this speaker has to accept that what we represent with the preceding clause really represents the actual incompatibility (s)he had brought up.
We should not wonder that some premises like pn+1 may be "forgotten" by the first speaker. After all, any incompatibility noticed in real life presupposes that the world still exists, that people are at a single location at any time, and so on. But requiring that a given fact pn+1 can be recognized as part of the initial incompatibility remains a very strong constraint on what can or cannot be considered as an admissible invalidation. In the preceding excerpt, A would have accepted (without necessarily agreeing) that B denies hypotheses like :
- people do not read a book by chance
- one reads only books of one's domain of competence
- reading a book cannot be the consequence of a bet
- etc.
because these terms can be acknowledged by her as being part of the problematic clause. But presumably, she would not have admitted arguments denying :
- Goffman is blond
- Goffman's books have an even number of pages
- the climate in Oregon is mild
because she would not accept to consider them as part of the incompatibility, and because in this case the truth value of these terms has no effect on the paradox. Notice that in [ex_christmas-tree p.15] the humorous invalidation A4 is an indirect one. It is admissible from a conversational point of view (here we have pn+1 = not made-of-plastic which appears as a forgotten term in the paradox), even if it is obviously false (hence the humorous effect).
The admissibility of an invalidation is totally dependent on what the logical context is or on how this context could be augmented to integrate forgotten premises. Under certain circumstances an artificial system can recognize indirect invalidations when having "conversations" with humans [Dessalles 1991].
Any invalidation (direct or indirect) of a paradoxical context can always be described as an attempt to give an explanation [Dessalles 1992b]. In an undesirable context, an indirect invalidation may be perceived as an attempt to make a suggestion if it mentions future action. We saw examples of suggestions in [ex_doors p.13] (B2, B3, B5, B7). Each of them appears as an indirect invalidation. Let us turn now to another way of making a relevant reply.