Speaker:
Fleming Topsoe (University of Copenhagen)
Title:
Philosophy of information
Abstract:
We will start by discussing the "price of information". This will be tied to a probabilistic setting but when we address other concepts related to cognition, such as "truth", "belief", "knowledge" and "perception", this is more abstract and could cover other situations where information is collected. Anyhow, quantitative arguments related to a probabilistic setting will be our main concern. The notion of "score function" which determines the allocation of effort on the way to information, will play a major role. The concept is known from statistical decision theory where it has been used to device schemes which will encourage an "expert" to be honest. Besides score functions, we find that a concept of "control" is important. It helps us to answer the question "what c a n we know". It leads, via game theoretical considerations to a notion of exponential families, understood in a somewhat untraditional way. It provides a main tool, when seen from the point of view of applications, to determine situations of equilibrium and related optimal objects, such as maximum entropy distributions. Three special features of our approach are the following: 1) A largely operational interpretation of Tsallis entropies 2) the natural unit of information, a "nat", is identified as the basic "overhead cost" connected with observation and 3) the central role of a pointwise version of the "fundamental inequality" of information theory is recognized.