The Fundamental Properties of Information-Carrying Relations

The Fundamental Properties of Information-Carrying Relations

Hilmi Demir (Bilkent University, Turkey)
DOI: 10.4018/978-1-61692-014-2.ch002
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Abstract

Philosophers have used information theoretic concepts and theorems for philosophical purposes since the publication of Shannon’s seminal work, “The Mathematical Theory of Communication”. The efforts of different philosophers led to the formation of Philosophy of Information as a subfield of philosophy in the late 1990s (Floridi, in press). Although a significant part of those efforts was devoted to the mathematical formalism of information and communication theory, a thorough analysis of the fundamental mathematical properties of information-carrying relations has not yet been done. The point here is that a thorough analysis of the fundamental properties of information-carrying relations will shed light on some important controversies. The overall aim of this chapter is to begin this process of elucidation. It therefore includes a detailed examination of three semantic theories of information: Dretske’s entropy-based framework, Harms’ theory of mutual information and Cohen and Meskin’s counterfactual theory. These three theories are selected because they represent all lines of reasoning available in the literature in regard to the relevance of Shannon’s mathematical theory of information for philosophical purposes. Thus, the immediate goal is to cover the entire landscape of the literature with respect to this criterion. Moreover, this chapter offers a novel analysis of the transitivity of information-carrying relations.
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Equivalence Relations: A Preliminary Introduction

A relation could have any number of arguments: one, two, three, four and so on. For example, a ‘being in between’ relation requires three arguments, that a is in between b and c, and therefore is a 3-place relation. Similarly, ‘being the father of’ is an example of a 2-place relation with two arguments: the father and the child. These 2-place relations are also called binary relations. Our main focus in this chapter is binary relations, since an equivalence relation is a binary relation with some specific properties.

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