Where grounding and causation part ways: comments on Schaffer

Does the notion of ground, as it has recently been employed by metaphysicians, point to a single unified phenomenon (the “Unity Hypothesis”)? Jonathan Schaffer holds that the phenomenon of grounding exhibits the unity characteristic of a single genus. In defense of this hypothesis, Schaffer proposes to take seriously the analogy between causation and grounding. More specifically, Schaffer argues that both grounding and causation are best approached through a single formalism, viz., that utilized by structural equation models of causation. In this paper, I present several concerns which suggest that the structural equation model does not transfer as smoothly from the case of causation to the case of grounding as Schaffer would have us believe. If it can in fact be shown that significant differences surface in how the formalism in question applies to the two types of phenomena in question, Schaffer’s attempt at establishing an analogy between grounding and causation has thereby been weakened and, as a result, the application of the Unity Hypothesis to the case of grounding once again stands in need of justification.     

The Crooked Path from Vagueness to Four-Dimensionalism

Philosophical Studies -     

Isolation and Non-Arbitrary Division: Frege's Two Criteria for Counting

In §54 of the Grundlagen, Frege advances an interesting proposal on how to distinguish among different sorts of concepts, only some of which he thinks can be associated with number. This paper is devoted to an analysis of the two criteria he offers, isolation and non-arbitrary division. Both criteria say something about the way in which a concept divides its extension; but they emphasize different aspects. Isolation ensures that a concept divides its extension into discrete units. I offer two construals of this: isolation as discreteness, i.e. absence of overlap, between the objects to be counted; and isolation as the drawing of conceptual boundaries. Non-arbitrary division concerns the internal structure of the units we count: it makes sure that we cannot go on dividing them arbitrarily and still find more units of the kind. Non-arbitrary division focuses not only on how long something can be divided into parts of the same kind; it also speaks to the way in which these divisions are made, arbitrarily or non-arbitrarily, as well as to the compositional structure of the objects divided.     

Constitution and Similarity

Whenever an object constitutes, makes up orcomposes another object, the objects inquestion share a striking number of properties. This paper is addressed to the question of whatmight account for the intimate relation andstriking similarity between constitutionallyrelated objects. According to my account, thesimilarities between constitutionally relatedobjects are captured at least in part by meansof a principle akin to that of strongsupervenience. My paper addresses two mainissues. First, I propose independentlyplausible principles by means of which todelineate, in a non-ad-hoc, non-stipulative andnon-circular fashion, those properties whichcan be expected to be shared amongconstitutionally related objects in virtue oftheir being so related from those which ingeneral cannot be expected to be shared, orwhich are shared for other reasons. Secondly,I spell out in detail the nature of thesupervenience-principle at work in thiscontext. My account thus aims at isolating, ina methodologically responsible fashion, theparticular sort of restricted indiscernibilityprinciple which is a component of theconstitution-relation.