Formalising Semantic Information Lessons from Logical Pluralism

By introducing the notion of logical pluralism, it can be concluded that up to now theories of semantic information have at least implicitly relied on logical monism, the view that there is one true logic. Adopting an unbiased attitude in the philosophy of information, we ought to ask whether logical pluralism could entail informational pluralism. The basic insights from logical pluralism and their implications for a theory of semantic information should therefore be explored. First, it is shown that (i) the general definition of semantic information as meaningful well-formed data does not favour any logical system, (ii) there are nevertheless good reasons to prefer a given logic above some others, and (iii) preferring a given logic does not contradict logical pluralism. A genuine informational pluralism is then outlined by arguing that for every true logic the logical pluralist accepts, a corresponding notion of semantic information arises. Relying on connections between these logics, it can be concluded that different logics yield complementary formalisations of information and informational content. The resulting framework can be considered as a more versatile approach to information than its monist counterparts. 1 Context and motivation Despite several authors’ attention for the multi-faceted character of the concept of information (see Floridi (2003) and Bremer & Cohnitz (2004)), actual attempts to formalise the concept of information all too often tend towards an implicit logical monism (the view that there is a true logic). The core aim of this paper is to provide an alternative for the assumption that there is a single logic of (semantic) information. The plan, however, is not to deny the possibility of a logic of information being better than others, but to provide a conceptual framework in accordance with both the polyvalence of information and the unbiased approach in the philosophy of information. Our starting point is two-fold. On the one hand different theories of semantic information are available, all relying to a certain extent on formal logic. On the other there is the pluralist claim from Beall & Restall (2000) that there is more than one true logic. Basically, the logical pluralist claims that there are several ways to give a precise account of the pre-theoretical notion of logical consequence (and hence of logical truth), and above all that none of these is a priori better than the others. The logical pluralist, however, does not claim that every true logic is suited for all contexts of application. Taking logical