David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
In Jelle Gerbrandy, Maarten Marx, Maarten de Rijke & Yde Venema (eds.), Essays dedicated to Johan van Benthem on the occasion of his 50th birthday. Amsterdam University Press (1999)
Since Lewis’s (1969) and Aumann’s (1976) pioneering contributions, the concepts of common knowledge and common belief have been discussed extensively in the literature, both syntactically and semantically1. At the individual level the difference between knowledge and belief is usually identified with the presence or absence of the Truth Axiom ( iA → A), which is interpreted as ”if individual i believes that A, then A is true”. In such a case the individual is often said to know that A (thus it is possible for an individual to believe a false proposition but she cannot know a false proposition). Going to the interpersonal level, the literature then distinguishes between common knowledge and common belief on the basis of whether or not the Truth Axiom is postulated at the individual level. However, while at the individual level the Truth Axiom captures merely a relationship between the individuals’ beliefs and the external world, at the interpersonal level it has very strong implications. For example, the following is a consequence of the Truth Axiom: i jA → iA, that is, if individual i believes that individual j believes that A, then individual i herself believes that A. Thus, in contrast to other axioms, the Truth Axiom does not merely reflect individual agents’ “logic of belief”. (The reason why the Truth Axiom is much stronger in an interpersonal context than appears at first glance is that it amounts to assuming that agreement of any individual’s belief with the truth is common knowledge). Given its logical force, it is not surprising to find that it has strong implications for the logic of common knowledge. In particular, if each individual’s beliefs satisfy the strongest logic of knowledge (namely S5 or KT5), the associated common knowledge operator satisfies this logic too. Such is not the case for belief: bereft of the Truth Axiom, even the strongest logic for individual belief (KD45) is insufficient to ensure the satisfaction of the “Negative Introspection” axiom for common belief: ¬ ∗A → ∗¬ ∗A (where ∗ denotes the common belief operator)..
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Daniel Whiting (2012). Does Belief Aim at the Truth? Pacific Philosophical Quarterly 93 (2):279-300.
Joseph Y. Halpern (1996). Should Knowledge Entail Belief? Journal of Philosophical Logic 25 (5):483 - 494.
Hamid Vahid (2009). The Epistemology of Belief. Palgrave Macmillan.
Aviad Heifetz (1999). Iterative and Fixed Point Common Belief. Journal of Philosophical Logic 28 (1):61-79.
Daniel Whiting (2013). Nothing but the Truth: On the Norms and Aims of Belief. In Timothy Chan (ed.), The Aim of Belief. Oxford University Press
Giacomo Bonanno (1999). How to Make Sense of the Com M on P Ri or Assumption Under Incomplete Information. International Journal of Game Theory 28 (3):409-434.
Pierpaolo Battigalli & Giacomo Bonanno (1997). The Logic of Belief Persistence. Economics and Philosophy 13 (1):39-59.
Luc Lismont & Philippe Mongin (2003). Strong Completeness Theorems for Weak Logics of Common Belief. Journal of Philosophical Logic 32 (2):115-137.
Giacomo Bonanno (2000). Common Belief with the Logic of Individual Belief. Mathematical Logic Quarterly 46 (1):49-52.
Added to index2009-01-28
Total downloads23 ( #157,992 of 1,790,292 )
Recent downloads (6 months)9 ( #94,062 of 1,790,292 )
How can I increase my downloads?