ABSTRACT. Up to now theories of semantic information have implicitly relied on logical monism, or the view that there is one true logic. The latter position has been explicitly challenged by logical pluralists. Adopting an unbiased attitude in the philosophy of information, we take a suggestion from Beall and Restall at heart and exploit logical pluralism to recognise another kind of pluralism. The latter is called informational pluralism, a thesis whose implications for a theory of semantic information we explore. (..) challange the assumption that there is one single, true logic (..) Beall & Restall, Logical Pluralism, 2006: when a formal account of semantic information is elaborated, the unique truth of a logic cannot be taken for granted. (..) stronger position: the pre-theoretical notion of informational content does not in itself warrant a unique logic, but also needs a pluralistic formalisation. In other words, a pluralist position about logic may equally have to be reflected in a formal theory of semantic information. (..) Generalised Tarski Thesis (GTT): A conclusion A follows from premises S iff any case in which each premise in X is true is also a case in which A is true. GTT states that there is no unique formalisation of the pre-theoretical notion of consequence when conceived as truth-preservation over all cases. (..) the following picture arises: (a) if cases are taken to be Tarskian Models (complete and consistent), then we get plain classical logic (henceforth, CL), (b) if cases are constructions (consistent but possibly incomplete), the corresponding logic is intuitionistic (IL), and (c) if cases turn out to be situations (both possibly inconsistent and incomplete) we obtain relevant logic (RL). (..) As explained by Beall and Restall, all three logics, classical, intuitionistic and relevant, can be mutually related. (..) TABLE 1 Theorems and properties CL IL RL [ to be copied ] (..) The crux of Beall and Restall's argument lies in the rejection of any view putting forward the most general approach to logical consequence as the ultimate and unique one. (..) If one wants to take disjunctive syllogism as being valid in one sense, but invalid in another, a pluralist account of logical consequence should follow. (..) A relevant logic does not (and cannot) completely exclude classical logic, for situations might indeed be complete and consistent. (..) Semantic information defined as well-formed and meaningful data (GDI). Semantic information as declarative, objective and semantic information (DOS, Floridi, 2004,2005). (..) all too strict fixed and given semantics (informee-independent meaning) (..) Inverse Relation Principle: Whenever there is an increase in available information there is a decrease in possibilities, and vice versa. (Popper, 1959, Barwise, 1997) (..) Generalised Inverse Relationship Principle (GIRP): The informational content of a piece of information, is given by the set of cases it excludes. (..) Looking at the standard formalisation of this principle, as given by Bar-Hillel and Carnap (1952) and Hintikka (1970), it becomes clear at which point logical monism sneaks into the concept of semantic information. (..) despite their differences both the linguistic (Carnap) and the ontological (Dretske) approach remain within the classically based logical framework (..) Using Israel and Perry's (1990) terminology, it can be said that an information report expresses information relative to a situation, not to the world as a whole. On the standard account, situations are primarily conceived as 'limited parts of reality,' but here we shall in the first place be concerned with the ability to model partial information, not with an ontological interpretation of situations. (..) One could say that both accounts agree with respect to the facts: truth in a situation entails truth in all possible worlds containing that situation. However, truth in a set of possible worlds should not entail truth in a situation (not even the 'largest' situation) contained in all those worlds. (..) Looking at information from this broader perspective, it can not only be said that situation semantics provide a natural interpretation for relevant logic, but conversely and more importantly that relevant logics can be seen as the syntax and proof-theory for reasoning about (partial) information. On the pluralist plan, moreover, the acceptance of situation semantics and relevant logic as a natural way to reason about partial information, should not lead to a full rejection of a possible worlds (i.e. classical) analysis of partial information. (..) content is in the first place content for someone, and when it comes to the abstract notion of content for anyone, we ought to conclude that there is no such unique abstraction. (..) An unbiased assessment of the informational content of a message can loosely be characterised as an answer to the question what a sender's evidential situation should be like in order to enable the truthful assertion of the message under consideration. (..) If a pluralist evaluation of informational content has to be a viable alternative, it ought to explain how a fixed meaning requirement can pair up with a context-dependent assignment of informational content. (..) show that the meaning-invariance requirement can be reduced to keeping the local meaning fixed, we first show it represents the only consistent option for a pluralist (..) a pluralist view on content (..) the inherent ambiguity of the classical account and the worldly perspective which motivates its acceptance (..) Hanson: logical consequence as either truth-preservation or content-nonexpansion (..) as pluralists we simply wish to deny that a choice between both needs to be made at all. |