Philosophy Society Talk
12 August, 2016
Social Sciences Room 161 (SSCI161) at UWA
This coming Friday 12th August at 4:00pm in Social Sciences Room 161 (SSCI161) at UWA we will hear from Hannah Clark-Younger (UWA) who is a logician that will be at UWA for the rest of the year. Title and abstract are below. All welcome!
Logical Omniscience and the Logic of Questions
When we ask and answer questions, we’re engaged in the giving and receiving of information; we’re updating our knowledge. Thus, it makes sense that a dynamic epistemic logic would be suitable for modelling the asking and answering of questions. The problem of logical omniscience pops up when we try to model epistemic agents using modal logic. If our knowledge is represented by some set of possible worlds, then all necessary truths will be represented in that set, because there are no worlds at which they are false. So, using possible worlds leads to all epistemic agents knowing all necessary truths in all our models. Because we are not ideal epistemic agents, this is undesirable. This is especially clear when we consider questions, as it makes perfect sense for us to ask and receive answers to questions about necessary truths, and to learn something new in the process. To solve this problem, one option is to allow our models to contain not only possible worlds, but impossible ones as well. However, if we don’t restrict what impossible worlds are allowed to be like, then we can’t make sense of epistemic agents having any tacit knowledge constrained by logical principles at all: everyone must be completely logically incompetent. On the other hand, it is difficult to restrict the allowable impossible worlds in a principled way that doesn’t continue to model the agents as knowing too much. I introduce the notion of ‘inference capacity,’ which is agent-specific and describes the ability of the agent to make inference leaps. Restricting the allowable impossible worlds to those which could be reached with the agent’s inference capacity allows us to model logically competent, but not omniscient, agents. It also helps to explain how we can come to know new logical principles and necessary truths, sometimes through asking and answering questions.