A metaphysical excursion

We now return, as promised above, to some applications of a theory of col- lections, or perhaps more perspicuously of properties, that makes use of self- instantiantiation in the way we have just been discussing. The first concerns the metaphysical puzzle known as Bradley’s regress, first formulated by the British idealist F.H. Bradley at the end of the XIX century. 34 We now give an outline of the problem, although Bradley originally used the example of a lump of sugar and its properties, we can here use the already familiar example of Moby Dick. As we pointed out, we say that Moby Dick instantiates the prop- erty of being a whale. However, one could note that this instantiation is just another relation, sayI, and so we not only have that M b, but also that IM b, or in Bradley’s words: ‘There is a relationC [I in our example], in whichA[M in our example] andB [b in our example] stand; and it appears with both of them’5_{But if we now try to describe the situation as before when talking about}

M bwe must say something along the lines of that Moby Dick and being a whale are an instantiation of the relationI, which is itself some instantiation relation, and so following Bradley: ‘If so, it would appear to be another relation,D [our second instantiation relation], in whichC, on one side, and, on the other side, A and B, stand.’ 6. Note also that at face value this instantiation relations are different since one is a2-place while the other is a3-place relation. Bradley concludes that:

3_{See for the original formulation (Bradley, 1893, §2)}

4_{The reader who has a preference for more contemporary metaphysical puzzles might want} to consider the effort to explain what grounds the grounding relation, the interested reader able to parse the title are referred to (Litland, 2017), for an instance where self instantiating properties might also be helpful.

5_{See (Bradley, 1893, p. 19).} 6_{See (Bradley, 1893, Ibid.)}

[S]uch a makeshift leads at once to the infinite process. The new relation D can be predicated in no way of C, or ofA and B; and hence we must have recourse to a fresh relation, E, which comes between D and whatever we had before. But this must lead to another,F; and so on, indefinitely. (Bradley, 1893, Ibid.)

Indeed, the idea being that we need an infinite amount of instantiation re- lations to account for, what we could call, the metaphysical glue holding the object and property it instantiates together. Since for any series of properties or objects that instantiate some (n-place) property we can always take a further distinct (n+ 1-place) instantiation relation as relating them and like this ad infinitum. On the metaphysical side, the upshot of the argument seems to be to undercut the idea that objects and properties that they seem to instantiate are really related since our attempt at explaining their interaction leads to an infinite number of relations and so cannot be taken as satisfactory. This is be- cause we seem to be shifting the problem one level up each time without ever actually addressing it.

The literature offers several attempted solutions of this puzzle. Firstly, one could bite the bullet and accept that such a regress is vicious but that it does not arise in the first place. The mischaracterisation in the way we have described the situation lies in the fact that, although we have talked about instantiation as being a relation, it really is not, as David Armstrong puts it:‘We have to allow the introduction of a fundamental tie or nexus: instantiation.’7 _Instead

of a common or garden property, instantiation is the brute metaphysical glue that binds a relation with its relata. And so there is an infinite regress but this is logical and not ontological, since: ‘As we go on expanding the regress, our statements remain true, but no new truth-maker, or ontological ground, is required for all these statements to be true.’, 8_{but just this nexus provided by}

the porperty-like entity of instantiation.9

Another solution stems from a distinction drawn by Francesco Orilia in the ways one can read the regress: an externalist and an internalist one.10 _{In the}

internalist reading we have a single state of affairs containing an infinity of different instantiation relations, however in the externalist reading we have an infinity of states of affairs and these, in turn have finitely many instantiation relations each.11 For Orilia only the internalist regress is a vicious one,12 since this requires us to have states of affairs with infinitely many constituents, as opposed to simply infinitely many finitely-constituted states of affairs. This would force us to admit that the world must have infinite complexity, and this ‘is in conflict (. . . ) with the basic intuition that a simple fact likeF amust have a finite number of primary constituents’,13_{whereas admitting infinite chains of}

evidence as in the externalist reading does not contradict any basic intuition:

That at any given stage we can continue the explanatory task does not show that no 7_{(Armstrong, 1989, p. 109)}

8_{(Armstrong, 1989, p. 110)}

9_{For a discussion of such an approach consult (Allen, 2016, p. 32).} 10_{See (Orilia, 2006, p. 216)}

11_{See (Orilia, 2006) section3.} 12_{See (Orilia, 2006) sections6and7.} 13_{See (Orilia, 2006, p. 228)}

3.2. SELF-INSTANTIATION 65

knowledge or no understanding is provided at any stage. It merely shows that at no stage we know/understand everything that there is to know/understand about the explicandum which gives rise to the explanatory chain. (Orilia, 2006, p. 232)14

More relevant for our focus on self-instantiating properties are approaches that try, as Armstrong does, to stop the regress, but unlike him do take instan- tiation to be a genuine relation. Indeed, the idea here would be to push-back on our assertion above that the several instances of an instantiation relation present in the regress must be different since they have different arities, in the sense that we are dealing with a single relation albeit an unusual one in the sense that it is variably polyadic. This would mean that it can relate different numbers of objects in different instances, and so firstly the instantiation relation is diadic, then, triadic, and so on. Hence we see that, if we allow properties to self-instantiate what we have is that there is no infinite regress since we have that there are only three entities present here, Moby Dick, the property being a whale and the instantiation relation, or better its instances. Even though this relation or, again, its infinite chain of instances of increasing arity, instantiates itself infinitely often.15