Outline of a theory of strongly semantic information

Abstract

This paper outlines a quantitative theory of strongly semantic information (TSSI) based on truth-values rather than probability distributions. The main hypothesis supported in the paper is that (i) the classic quantitative theory of weakly semantic information (TWSI) is based on probability distributions because (ii) it assumes that truth-values supervene on information, yet (iii) this principle is too weak and generates a well-known semantic paradox, whereas (iv) TSSI, according t o which information encapsulates truth, can avoid the paradox and is more in line with the standard conception of what counts as information. After a brief introduction, section two outlines the semantic paradox entailed by TWSI, analysing it in terms of an initial conflict between two requisites of a quantitative theory of semantic information. In section three, three criteria of information equivalence are used to provide a taxonomy of quantitative approaches to semantic information and introduce TSSI. In section four, some further desiderata that should be fulfilled by a quantitative TSSI are explained. From section five to section seven, TSSI is developed on the basis of a calculus of truth-values and semantic discrepancy with respect to a given situation. In section eight, it is shown how TSSI succeeds in solving the paradox. Section nine summarises the main results of the paper and indicates some future developments.

Semantic information and the correctness theory of truth

“…is not just interesting in itself but provides a reassuring test, since it is perfectly consistent with a theory of strongly semantic information (Floridi (2004c)). In particular, it shows that tautologies and contradictions are pure semantic contents, equally uninformative or, to phrase it differently, that they provide no semantic information about their referents, over and above their contents (in both cases the coin we are tossing has two identical sides, as it were).…”

“…For example, it plays a crucial role in the solution of the so-called Bar-Hillel-Carnap Paradox (Floridi [2004c]) and provides a necessary element for a subjectivist theory of epistemic relevance (Floridi (2008c)). …”

Understanding epistemic relevance

“…2 The classic reference is Shannon andWeaver [1949 rep. 1998], see Jones [1979] for an introduction. 3 The list includes: Bar-Hillel and Carnap [1953], Bar-Hillel [1964], Hintikka and Suppes [1970], Israel and Perry [1990], and Floridi [2004b]. 4 In this sense, theoretical information theory is a branch of probability theory, and applied information theory a branch of engineering, see Cover and Thomas [1991].…”

“…epistemically relevant semantic information), thus satisfying those critics who lament its absence and, because of it, may be skeptical about the utility of using information-theoretical concepts to tackle philosophical problems and cognitive issues in real life. The second goal is to show that such a subjectivist interpretation can (indeed must) be built on a veridical conception of semantic information, thus vindicating a strongly semantic theory of information (Floridi [2004b]) and proving wrong those critics who argue that misinformation can be relevant. This means showing that the second horn of the dilemma outlined above is actually blunt.…”

“…6 This is argued in Floridi [2005b], see Sequoiah-Grayson [forthcoming] for a recent defence. 7 Defenders of the alethically neutral nature of information include Devlin [1991]; Colburn [2000]; Fetzer [2004]; Dodig-Crnkovic [2005]; the latter two criticise Floridi [2004b]. counterfactual revision.…”