Informational mereology

Intuitively, any object can be made to correspond to an informational content, that is, roughly, the totality of information about its structure and composition. The first aim of this paper is to make this notion of informational content precise, based on insights from Bar-Hillel, Carnap, Lewis, and Humberstone. The second aim is to make a start in the formal study of the connections between the informational contents of wholes and the informational contents of their parts, which I call “informational mereology.” To this end, I adopt a two- step, ‘exemplarist’ approach: first, I define a sample theory of informational mereology, QIM (Qualitative Informational Mereology); second, I outline a few variants and extensions of the theory. Among other things, QIM helps to elucidate and connect philosophically interesting notions (such as parthood, duplication, and structural information) and allows us to prove plausible results concerning the informational contents of material wholes and their parts. For instance, QIM entails that the informational content of a whole properly includes the sum of the informational contents of its proper parts, a result that can be seen as an informational rendition of the old dictum “there is more to the whole than the sum of its parts.”