Yablo Aboutness

“Aboutness” – that is, the question of whether, for given X and Y, X is about Y – is interesting in its own right, and is of interest technically, for example in understanding the foundations of web architecture and the semantic web, and of the engineering of tools such as the information artifact ontology. Stephen Yablo’s book on the subject is a delight to read. He takes quirky examples from his personal life and from literature, and he avoids unnecessary jargon. And it provides plenty of useful insight into the question.

Here is how I understand his model:

The world changes, i.e. there are many different conditions or states it might be in. Borrowing language from dynamical system theory we consider a world state space, whose points are all the potential states of the world. As time advances, the actual world traces out some path through this space.

The notions of subject matter, aboutness, and parthood can be modeled using a lattice of partitions of the world state space. Consider some object X. Ignoring all of the world other than X, X has its own states, in its own state space. X is part of the world, though, so its states are determined by the states of the world – a sort of simplification or projection. Recall that a partition of a set S is a set of nonempty sets (called ‘blocks’) such that (a) distinct blocks are disjoint and (b) the union of all the blocks is S. We can take X’s state space to be a partition of the world state space, and its states to be blocks, as follows: Two world states are in the same X-block (they are X-equivalent) iff they differ only in ways that make no difference as far as X is concerned. When X changes, the world moves from one X-block to another, and when X doesn’t change, the worlds stays in its current X-block.

To help grasp the formalism I like to think of the simple case where the world state space is R³. The world state traces out a path in R³. We may sometimes care only about one of the coordinates, say y but not x or z. y is an ‘object’ with a state space isomorphic to R, but we model it as the partition of R³ with one block of world states (points in R³) for each possible state of y. That is, each y-block is a plane parallel to the xz-plane.

The partitions of the world state space form a lattice, so we can speak of the ordering of partitions (called finer-than or coarser-than depending on which direction it’s written), and of meets and joins and all the usual lattice theoretic stuff. For every entity there is a partition, and if X is part of Y, then X’s partition is coarser than Y’s partition. (Intuitively: smaller things have smaller state spaces / bigger blocks.) So coarser-than models parthood. Coarser-then also models “inherence” of a quality in the thing that has that quality: that Fido’s weight “inheres” in Fido means that Fido’s weight’s partition is coarser than Fido’s partition. (I’m using ‘quality’ in the BFO sense, although I probably really mean ‘dependent continuant’.) Similarly, observe that any proposition (e.g. “Fido weighs 10 pounds”) partitions the world into two blocks: one consisting of states in which the proposition is true, and the other those in which it is false. When a proposition is “about” an entity, its partition is coarser than the entity’s.

I find this uniform treatment of objects, parts, qualities, and propositions to be appealing. It helps explain my discomfort with conventional ontologies like SUO. Consider the following four entities:

1. Fido
2. Fido’s tail
3. Fido’s weight
4. That Fido weighs ten pounds

The SUO top level would say that 1 and 2 are Physical, that 4 is Abstract (because it’s a Proposition), and that 3 doesn’t exist. To me they are all the same kind of thing, just some more “part-like” than others. They ought to be either all Abstract or all Physical. By Yablo’s programme they are just entities with partitions of varying fineness.

Although I’m not always a fan of BFO, it is closer to a uniform treatment. 1, 2, 3 are all continuants. BFO has no propositions (4) but it is not difficult to imagine adding them, and it is pretty clear where they would fit (they would be a particularly “atomic” kind of dependent continuant).