Il paradosso del contesto condiviso

Il paradosso People have to assess certain shared

knowledge.

This knowledge, it turns out, is defined by an infinite number of conditions.

How then can people assess this knowledge in a finite amount of time?

(Clark e Marshall, Reference and mutual knowledge, 1984)

Il Paradosso: qualche esempio dalla teoria dei giochi

1. SU ASPETTATIVE E CREDENZE: John does not simply try to guess what Tom will write, since Tom

will write what he guesses John will write. So the question each has to ask is not simply, “What would I write if I were he?”, but, “What would I write if I were he wondering what he would write if he were I wondering what I would write if I were he … (Schiffer, 1972)

We devote our intelligences to anticipating what average opinion

expects the average opinion to be. And there are some, who practise the fourth, fifth and higher degrees. (Keynes, 1936)

Il Paradosso: qualche esempio dalla teoria dei giochi

1. ANCORA SU ASPETTATIVE E CREDENZE: It is mutually obvious that the universe of all positive numbers has

a “beginning” or “first” number but not a “middle” or “end” (Schiffer, 1972)

1. SU RAZIONALITA’ E NORMALITA’: sufficient degree of rationality (Lewis, Convention, 1969) Of course the speaker may be wrong; and so may the interpreter.

So in the end what must be counted in favour of a method of interpretation is that it puts the interpreter in general agreement with the speaker. (Davidson, 1984)

Il Paradosso nell’interazione linguistica

1. IL SIGNIFICATO INTESO: I problemi riguardanti la comunicazione riguardano la identità, o

una approssimazione soddisfacente nell’interpretazione del significato da parte del ricevente, confrontata con il significato inteso da chi ha inviato la comunicazione

Ritengo che le difficoltà siano ridotte in termini tollerabili (ma mai eliminate) dal momento che c’è un linguaggio che è stato precedentemente reso ragionevolmente chiaro

(Shannon e Weaver, 1948)

Il Paradosso: l’interazione linguistica

1. IL LINGUAGGIO COME CONVENZIONE: A convention … a regularity in behaviour, a system of mutual

expectations, and a system of preferences … it must be common knowledge in the population that they are (Lewis, 1969)

1. LA DISAMBIGUAZIONE DEL LINGUAGGIO: When somebody hears somebody else utter a sound which sounds

to him like the English “nine”, he might sometimes have good reasons to believe that this sound does not refer to the number nine, but belongs to the German language, in which case it refers to the same as the English “no”. (Recanati, 2007)

Il paradosso è ovunque

Mutual knowledge is ubiquitous. It is an essential ingredient in

convention, in meaning and in language in general (Clark e Marshall, 1984)

Ha a che vedere con negoziazioni salariali, negoziazioni tariffarie, gare con pochi contendenti, accordi extra-giudiziali, con il rapporto tra agente immobiliare e cliente. Al di fuori della sfera economica si può andare dalla minaccia di pesanti ritorsioni fino al comportamento che mira ad ottenere il diritto di precedenza da un taxi.

(Schelling, 1960)

Il paradosso è reale

THE ELECTRONIC MAIL GAME (Rubinstein, 1989)

Players’ strategic behaviour under “almost common knowledge” may be very different from that under common knowledge. To emphasize, by “almost common knowledge” I refer to the case when the numbers on the screen are “very large”…

The best expected playoff the player can obtain in any equilibrium is still just as if no electronic mail system existed! The efficient equilibrium is the one where the messages are ignored

Soluzioni al paradosso

Prima: sintattico-formaleSimboli finiti per esprimere credenze infinitarie

Mutual knowledge can then be treated as a single mental entity instead of an infinitely long list of ever more complex mental entities. (Marshall e Clark, 1984)

KtKjKtKj … φMKtj φ

Soluzioni al paradosso

Seconda: filtri di selezioneenunciati selezionati per pertinenza e accessibilità

Relevance theory claims that humans do have an automatic tendency to maximise relevance, not because we have a choice in the matter – we rarely do – but because of the way our cognitive systems have evolved. (Sperber e Wilson, 1995)

We examined the bounded rationality... The core concept is accessibility – the ease with which particular mental contents come to mind…Salience also determines accessibility. (Kahneman e Tversky, 2002)

Soluzioni al paradosso

Seconda: enunciati selezionati per pertinenza e accessibilità

Soluzioni al paradosso

Seconda: enunciati selezionati per pertinenza e accessibilità

Soluzioni al paradosso

Terza: coerenzail contesto cambia continuamente

The context set is of course continually being updated in the course of the conversation. The speech act performed alter the context and this is the point: they do it explicitly by putting forward a piece of information to be accepted and so added to be available background information” (Stalnaker, 1999)

Epistemic logic describes what agents know at the static intermediate stages of an informational process. But really, it is the state-changing actions themselves that seem of primary interest (van Benthem, 2007)

Concludendo Il paradosso: credenze infinitarie per soggetti con risorse finite - fenomeno estremamente esteso - fenomeno reale

3 soluzioni possibili:- Simboli finiti per informazioni infinite- Filtri di accessibilità e pertinenza- Aspetto dinamico e vincoli di coerenza

Bibliografia- Burge, Review of Truth and predication - Donald Davidson, 2007 - Clark e Marshall, Reference and mutual knowledge, 1984- Davidson, Inquiries into truth and interpretation,1984- Harsanyi, Bargaining in Ignorance of the Opponent’s Utility Function, 1957- Kahneman, Nobel Lecture, 2002- Keynes, The General Theory of Employment, Interest and Money, 1936 - Lewis, Convention, 1969- Perry, Self notions, 1990- Recanati, Perspectival thoughts, 2007 - Rubinstein, The electronic mail game: Strategic behaviour under “Almost Common

Knowledge, 1989- Schelling, The strategy of conflict, 1960 - Schiffer, Meaning, 1972 - Shannon e Weaver, A mathematical theory of Communication, 1948 - Sperber e Wilson, Relevance: Communication and cognition, 1995- Stalnaker, Context and content, 1999 - van Benthem, Cognition as interaction, 2007