Thursday, May 14, 2009

Mereology - the study of the relations between integral objects and portions of stuff

I was reading a post by Steffen Staab on the Semantic Web email list and ran across a link to a paper on Mereology, which is basically the study of the relations between complete or integral objects and the component parts that comprise the whole object as well as the relations between the parts themselves.

The Wikipedia article on Mereology tells us:

In philosophy, mereology (from the Greek μερος meros part and the ending -logy study, discussion, science) is a collection of axiomatic first-order theories dealing with parts and their respective wholes. In contrast to set theory, which takes the set-member relationship as fundamental, the core notion of mereology is the part-whole relationship. Mereology is both an application of predicate logic and a branch of formal ontology.

The Stanford Encyclopedia of Philosophy article on Mereology tells us:

Mereology (from the Greek μερος, 'part') is the theory of parthood relations: of the relations of part to whole and the relations of part to part within a whole. Its roots can be traced back to the early days of philosophy, beginning with the Presocratics and continuing throughout the writings of Plato (especially the Parmenides and the Thaetetus), Aristotle (especially the Metaphysics, but also the Physics, the Topics, and De partibus animalium), and Boethius (especially De Divisione and In Ciceronis Topica). Mereology occupies a prominent role also in the writings of medieval ontologists and scholastic philosophers such as Garland the Computist, Peter Abelard, Thomas Aquinas, Raymond Lull, Walter Burley, and Albert of Saxony, as well as in Jungius's Logica Hamburgensis (1638), Leibniz's Dissertatio de arte combinatoria (1666) and Monadology (1714), and Kant's early writings (the Gedanken of 1747 and the Monadologia physica of 1756). As a formal theory of parthood relations, however, mereology made its way into our times mainly through the work of Franz Brentano and of his pupils, especially Husserl's third Logical Investigation (1901). The latter may rightly be considered the first attempt at a thorough formulation of a theory, though in a format that makes it difficult to disentangle the analysis of mereological concepts from that of other ontologically relevant notions (such as the relation of ontological dependence). It is not until Leśniewski's Foundations of a General Theory of Manifolds (1916, in Polish) that a pure theory of part-relations was given an exact formulation. And because Leśniewski's work was largely inaccessible to non-speakers of Polish, it is only with the publication of Leonard and Goodman's The Calculus of Individuals (1940) that mereology has become a chapter of central interest for modern ontologists and metaphysicians.

This is quite heavy-duty stuff, but does show the increasing trend for the intersection of computer science and philosophy especially as we get deeper into the Semantic Web.

The original link pointed to the abstract for a paper entitled A Temporal Mereology for Distinguishing between Integral Objects and Portions of Stuff by Thomas Bittner and Maureen Donnelly. It discusses three categories of "stuff":

  • Integral objects, such as a car or computer.
  • Structured stuff, such as blood or the tissue of an organ.
  • Unstructured stuff, such as air and water that is homogenous.

They give the example of the distinction between the liver as an integral object and liver tissue as the structured stuff the comprises the liver. The two are obviously related, but need to be treated distinctly depending on your intentions and purposes.

In the case of blood, we can refer to human blood in general, the blood of a particular human, a sample or portion of the blood of that particular human, and the "structured stuff" within that portion as it might be processed and separated into the components of red and white cells, platelets, and plasma.

This post is primarily intended as more of a bookmark for later reference, so my apologies for not giving a more concise or more detailed account of mereology.

-- Jack Krupansky


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