Abstract
ABSTRACT First, I consider a few motivations to idealize epistemic logics1 in such a degree that brings up the problem of logical omniscience [LOP]. I argue that the main motivation to hold omniscience is of a philosophical-scientific2 background (Stalnaker 1991), in the sense philosophers have a not so peculiar way of investigating underlying mechanisms, i.e., the interaction of several different components of complex systems may be better understood in isolation, even if such components are not found isolated in a realistic context. It is defended that the implicit and explicit knowledge distinction (Fagin and Halpern 1988) is compatible that view since idealizations made by modal epistemic logic are so strong that the agents they describe hardly have anything in common with real agents. I conclude by showing how LOP can be accommodated in the logic of being informed (Floridi 2006) using the Inverse Relationship Principle (Barwise and Seligman 1997). 1Epistemic modal logics and the logic of being informed may collapse in many scenarios, as shown in previous articles (blind review omitted). 2Does not necessarily imply in a naturalized epistemology a la (Quine 1981). For a plea for non-naturalism as constructionism see (Floridi 2017).
Highlights
The problem of logical omniscience is connected to the concept that if an agent knows all formulas in a set Γ and φ follows logically from, the agent knows that φ (Fagin et al 1995)
I argue that the main motivation to hold omniscience is of a philosophical-scientific2 background (Stalnaker 1991), in the sense philosophers have a not so peculiar way of investigating underlying mechanisms, i.e., the interaction of several different components of complex systems may be better understood in isolation, even if such components are not found isolated in a realistic context
The problem of logical omniscience in standard modal epistemic and doxastic logics is linked to the axiom K
Summary
One of the main purposes of language is to transmit information about the world. Where p is any sentence used for that purpose, it seems natural to think of content as the information that is semantically encoded in it. As Hintikka (1962) taught us, it is an idealization that serves logic and it is precisely from the tension between the assumptions of an ideal theory and the intended application within a certain logic that this problem arises – the problem of logical omniscience Hintikka summarizes his approach by holding that “in order to speak of what a certain person a knows and does not know, we have to assume a class (‘space’) of possibilities” (Hintikka 2003:19). The other way would be to consider the domain of the application of such logic in an unrestricted way, which includes idealized agents In this second type of conciliation attempt we would interpret the concepts of “belief” or “knowledge” modelled by the theory in a special sense, where the difference between the ideal and the real is explained by the difference between “knowledge” in an ordinary sense and “knowledge” in a technical sense. The interesting question here is what should count as cases of knowledge
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