"Knowledge and Learning in Branching Time"

Abstract:
Usually knowledge is defined relative to an agent. We define it relative to a method and can then avail ourselves of formal learning theory in our analysis of knowledge. In this setting, a method d knows a hypothesis p in a possible world, that is, K(d)p is true in a possible world w, just in case that d realises p in w. d realises p means that d discovers p in the limit. Furthermore, possible worlds are construed as a kind of Ockhamistic chronicles. They consist of an infinite data stream representing what is the case at given moments in time, together with a fixed moment of time representing now. Within this framework we classify the space of temporal indexed hypotheses and introduce two notions of truth: epistemic truth, which is relative to background knowledge; and metaphysical truth, which is time invariant and independent of background knowledge.
Two definitions of knowledge are introduced - a weak notion corresponding to epistemic truth, and a strong one implying metaphysical truth. The corresponding epistemic systems with addition of classical time operators are investigated. The strong version of knowledge is derived in a logically reliable way. Once, however, knowledge is to be extended to the set of temporally indexed hypotheses, it turns out that logical reliability is a restrictive methodological condition. So despite all its virtues, logical reliability can be costly.
All results presented have been acheived in co-operation with Dr. Vincent Hendricks.

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