Openness, Privilege, and Omniscience

Grounding and Omniscience

I’m going to argue that omniscience is impossible and therefore that there is no God. The argument turns on the notion of grounding. After illustrating and clarifying that notion, I’ll start the argument in earnest. The first step will be to lay out five claims, one of which is the claim that there is an omniscient being, and the other four of which are claims about grounding. I’ll prove that t...

Logical omniscience and rational choice

It is well-known that usual doxastic models (epistemic logic, probability) suffer from strong idealizations. By extension, models of decision making that elaborate on these doxastic models (e.g., models of choice under set-theoretic uncertainty ([LR85], chap.13) and the expected utility model) inherit these idealizations. To improve doxastic models is therefore an important aspect of bounded ra...

Delusions of Omniscience

Epistemic and doxastic modal logics (Hintikka [1962]), and the logics of theory change and belief revision (Alchourr6n et. al. [1985], Giirdenfors [1988]) are used for the representation of belief. Both kinds of logic are omniscient in various ways. We address these delusions of omniscience in this paper. We begin by defining three kinds of omniscience logical, deductive, and factual. We will t...

Awareness, Negation and Logical Omniscience

General Epistemic Logics suffer from the problem of logical omniscience, which is that an agent’s knowledge and beliefs are closed under implication. There have been many attempts to solve the problem of logical omniscience. However, according to our intuition, sometimes an agent’s knowledge and beliefs are indeed closed under implication. Based on the notion of awareness, we introduce two kind...

Logical Omniscience and Rational Belief