In this talk I propose a reestablishment of the traditional theory of semantic information (hereafter TSI, originally proposed by Bar-Hillel and Carnap (1952, 1953)) based on urn semantics, a non-standard system of semantics introduced by Rantala (1979). The aim of a theory of semantic information is to provide criteria for measuring the amount of information carried by sentences. The basic idea behind TSI is that the amount of information of a sentence varies in function of the number of models it has: the more models it has, the less informative it is. Now, a classical consequence of TSI is the so-called scandal of deduction (hereafter SoD) according to which logical truths have null amount of information. SoD is problematic since it does not make room for the ampliative character of formal knowledge. Because of this, recent work on the subject (e.g., Floridi (2004)) rejects TSI despite its good insights on the nature of semantic information. On the other hand, I explore here a more conservative solution: relying on classical works on semantic externalism, I argue that urn semantics correctly characterizes the epistemological conditions of our semantic competence in the use of quantifiers and, consequently, it provides an adequate metatheoretic framework for the formalization of TSI. Moreover, I present some new logical results on urn semantics that shade some light on its formalization of TSI.

References

Bar-Hillel, Y. and Carnap, R. (1952). An outline of a theory of semantic information. Research Laboratory of Electronics, MIT.

Bar-Hillel, Y. and Carnap, R. (1953). Semantic information. The British Journal for the Philosophy of Science, 4(14):147–157.

Floridi, L. (2004). Outline of a theory of strongly semantic information. Minds and machines, 14(2):197–221.

Rantala, V. (1979). Urn models: a new kind of non-standard model for first-order logic. In Game-Theoretical Semantics, pages 347–366. Springer.