All natural conversations do not function in the improbable mode. In other words, one cannot consider each initiating utterance as carrying information, in the restrictive Shannon sense (just consider the utterance : " Hey, you're are there! "). We will describe here a kind of conversation that everybody can experience daily : conversations that go around an amazement, beginning for instance with "That's strange..." or "I never understood why...". We had two examples of such conversations : [ex_Goffman, p.6] and [ex_mercedes, p.9]. In each case, the first speaker is amazed, because incompatible facts are observed to be simultaneously true :
[knows( X, Goffman's_books) & not sociologist( X )] => F
[owns( X, Car ) & big( Car) & not rich( X )] => F
In each case, the topic was not introduced as an event of infinite rarity. The first speaker tells of a fact which appears to her/him as a paradox, as a contradiction between the observed fact and what he knows, but not as a rarity[2]. In each case the logical context allows the interlocutors to draw the negation of the uttered event through a logical proof : B was a priori expected not to know Goffman's books because he was not a sociologist ; Hungarians were expected not to own big cars because they were known to be poor. This is why we speak of contradictions, or paradoxes.
We will see below other reasons to make a qualitative difference between paradox and improbability, and not to consider the former as a limit of the latter. One of these lies in the different forms of replies that are admissible in both cases. But for now, we hold a second condition for a topic to be relevant :
We have yet to observe another kind of topic introduction that is yet quite different from the two preceding ones.
[2] Some facts presented by locutors as paradoxical can even be frequent.