The paper presents, motivates, critiques, and proposes revisions to Baker’s Constitution View, which includes her definitions of constitution, derivative features, and numerical sameness. The paper argues that Baker should add a mereological clause to her definition of constitution in order to avoid various counterexamples.
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See Rea (1995) for the original formulation of the problem of material constitution, which consists of five assumptions: (1) The Existence Assumption (Some xs compose something at t), (2) The Essentialist Assumption (If the xs compose y at t, they compose something at t that essentially bears R to any parts it has at any time), (3) The Principle of Alternative Compositional Possibilities (If the xs compose y at t, they compose something at t that doesn’t essentially bear R to any parts it has at any time), (4) The Identity Assumption (If the xs compose y at t and the xs compose z at t, then y = z), and (5) The Necessity Assumption (If x = y, they are essentially identical).
The indiscernibility of identicals says this: ∀x∀y(x = y→(Fx→Fy)).
The converse of a relation Rxy is the relation Ryx. The disjunction of two relations Rxy and Sxy is the relation RxyvSxy. So the disjunction of a relation Rxy and its converse is the relation RxyvRyx.
Throughout the paper, when I can, I simplify the definition.
Throughout the paper, when I can, I drop the reference to time.
A branching case of constitution is any case of constitution where x constitutes y and z, neither y nor z is identical to the other, and neither y nor z constitutes the other.
An equivalence relation is any relation that is symmetric, transitive, and reflexive. A relation R is symmetric iff (i.e., if and only if) ∀x∀y(Rxy→Ryx) and is transitive iff ∀x∀y∀z((Rxy&Ryz)→Rxz). A relation R is reflexive iff ∀xRxx and partially reflexive iff ∀x∀y((RxyvRyx)→Rxx). Every relation that is symmetric and transitive is partially reflexive and so is a partial equivalence relation. But not every relation that is symmetric and transitive is reflexive. So not every relation that is symmetric and transitive is an equivalence relation.
The ancestral of a relation Rxy is the relation: Rxy or there is z1, z2, …, zn such that Rxz1, Rz1z2, …, Rzny.
Baker 2000, pp.99–101 extends the definition of having a feature derivatively so as to include hybrid features. I ignore the extension here.
Translate this: x doesn’t have H at t independently of x’s c-relations to y at t.
A stacking case of constitution is any case of constitution where x constitutes y and y constitutes z.
It also seems Lump should be a statue independently of its c-relations to Pot. But, on (I), this is false for the same reason.
It also seems Statue is not a pot independently of its c-relations to Lump. But, on (I), this is false for the same reason.
It also seems Statue should be a statue independently of its c-relations to Pot. Moreover, it seems Pot should be a lump independently of its c-relations to Statue, and Statue should also be a lump independently of its c-relations to Pot. But, on (I), these claims are all false for the same reason.
It also seems Statue should be a pot derivatively. But, on (D), this is false for the same reason.
In other words, on (I), everything is not a statue independently of its c-relations to Pot. So, on (I), everything that is a statue independently of its c-relations to Pot is such that Pot is a statue independently of Pot’s c-relations to it.
Translate this: it must be that: for any F★ in G-favorable conditions at time t, some G★ spatially coincides with it at t.
Translate this: it could be that: x exists at time t but no G★ spatially coincides with x at t.
Translate the second conjunct: any G★ that spatially coincides with x is identical to y.
The xs compose y iff the xs don’t overlap each other, each of the xs is a part of y, and each part of y overlaps at least one of the xs.
Translate this: it must be that: if x is in G-favorable conditions at time t, then some G★ materially coincides with x at t.
In a de re modal claim, a designator is in the scope of a modal operator or a modal operator is in the scope of a quantifier. In a de dicto modal claim, neither is true.
A relation R is asymmetric iff ∀x∀y(Rxy→∼Ryx) and is anti-symmetric iff ∀x∀y((Rxy&Ryx)→x = y).
Translate this: each of the ys is a mereological part of x, and each mereological part of x mereologically overlaps one of the ys.
Translate this: x is a proper mereological part of a sum that constitutes y at t.
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My thanks to Allan Bäck and John Lizza for comments on a previous draft. My thanks also to Lynne Rudder Baker for her response to my presentation of the paper in a panel discussion devoted to her work on constitution at the IAPRS 2012 Conference.