Slot Theory and Slotite Theory

Abstract

Instantiation-directed slot theorists' believe that properties/relations have slots which are filled by their instances/relata e.g., where Abigail is taller than Bronia, there are two slots in the relation Taller Than such that Abigail fills the first slot and Bronia fills the second. This crude statement of the theory runs into 'The Problem of Filling', whereby a natural understanding of the relation between slots, filling, and instantiation leads to absurd results. This paper examines a variety of solutions to that problem, one of which is an extension of slot theory that adds an additional category of entities, 'slotites'. directed slots.) The second alternative way of understanding slots is instantiationdirected whereby slots are filled by the different relata of the relation (or instances of the property). For instance, Red's slot could be filled by a red ball which instantiates Red whilst Married's slots would be filled by pairs of spouses. In this paper, I focus solely on instantiation-directed slots, since they are the slots which I find most appeal to my metaphysical sensibilities. (Although I suspect that some of the issues discussed in this paper can be ported over to proposition-directed slots.) 1 Start by sketching a (somewhat crude) theory of instantiation-directed slots. It would have the following three pieces of (possibly primitive, possibly non-primitive) ideology:(CSs) '__ is a slot' (which holds of slots). (CSp) '__ is possessed by __' (the first relatum is a slot; the second relatum is a property/relation). (CSf) '__ fills __' (the first relatum is a relatum/instance of a relation/property; the second relatum is a slot possessed by that relation/property).For example, if some x fills the slot possessed by Red then x instantiates Red. And in the case of Taller Than-which has two slots, σ 1 and σ 2 -we would end up with the following bi-conditional:≡ CRUDE : For any x and y, x and y jointly instantiate Taller Than-and x is thereby taller than y-iff x fills σ 1 and y fills σ 2 . The Problem of Filling (POF)≡ CRUDE is too crude (Dixon (2018a: 201-04) also notes the following problem). Imagine: Abigail is taller than Bronia and both are fully grown women of a tall stature; Clare is taller than Damaris, but both are young children who are both short comparable to Abigail and Bronia i.e. neither Clare nor Damaris are taller than Abigail or Bronia. Given filling is a dyadic relation between a relation's relatum and one of its slots: Abigail fills σ 1 whilst Bronia fills σ 2 (for Abigail is taller than Bronia); Clare fills σ 1 and Damaris fills σ 2 (for Clare is taller than Damaris); but then, given ≡ CRUDE , Clare is thereby taller than Bronia. Since that's false, we have a problem. Call this the Problem of Filling (POF for short).This paper discusses how slot theorists can try to solve POF, using it as a chance to survey different slot theories. § §2-4 discuss slot theories which relativise filling to some further entity: instantiations ( §2); sums, pluralities, or ordered tuples ( §3); and spacet...