I’ve been thinking a lot recently about relations of fundamentality. There are, I think, three relations here: a relation of ontological dependence that holds between entities, a relation of grounding/truth-in-virtue-of that holds between propositions, and the truth-making relation, that holds between an entity and a proposition.
One thing I am interested in is the connection between the relations. One potential connection is the following: if A makes p true and if p grounds q (i.e. if q is true in virtue of p) then A makes q true. This seems pretty plausible. If p grounds q then it doesn’t take anything more for the world to be a q-world than for it to be a p-world: so to make the world a p-world is to make it a q-world.
I’m currently intrigued by the potential of this to allow us to make sense of Fine’s distinction between what there is and what there really is. It would be nice to be allowed to make such a distinction. In particular, I’d like to be able to say that there are abstracta, but that there aren’t really any abstracta. I’d like to say that there are sets, for example, because it’s really useful to be able to talk about such things; but I’d like to deny that there are really any sets because an ontology without sets is, other things’ being equal, preferable to one with.
Now, it’s natural to think that a set is ontologically dependent on its members. Socrates’ singleton depends for its existence on Socrates, and not vice-versa. You might be tempted as well (perhaps as a consequence) to the claim that the proposition the singleton of Socrates exists is true in virtue of Socrates exists. Since Socrates is the truthmaker for Socrates exists the above principle will then imply that Socrates is the truthmaker for the singleton of Socrates exists.
First thought then: we don’t need there to actually be a singleton of Socrates. We only need Socrates, and he makes true all the truths talking about his singleton. Generalising, all we need are the ordinary concrete objects, and we get all the truths about sets for free. (Pure sets will be a bit trickier – but there are any number of stories we might tell here.) So we can secure all the truths we want – we get the benefit of talking about sets – without admitting sets into our ontology.
But that can’t be quite right. We can’t deny the existence of sets and affirm the truth of the proposition the singleton of Socrates exists. But what we can do is accept that there are sets and deny that there are really any sets. The thought is that the singleton of Socrates exists is true (and hence there are sets), and is made true by Socrates; but the singleton of Socrates really exists is not made true by Socrates; in fact, it’s not made true by anything, and so it’s false.
Armstrong says that a exists is always made true by a. I am denying that: I claim that the singleton of Socrates exists is made true not by the singleton of Socrates (since the truthmakers are what there really is, and there aren’t really any sets) but by Socrates. But I can accept a variant of the Armstrong position: that a really exists is always made true by a, which is a fundamental being.
So the thought is that we have a bunch of fundamental entities that do all our truthmaking. Some of the things they make true is that they really exist. Other things that they make true is that some non-fundamental entities exist (but not that they really exist – they don’t!). This is meant to secure all the benefits without the cost. We get the benefit of talking about sets, since all we need to secure that is that we can presuppose that sets exist – we couldn’t care less whether or not they really exist. And we secure a parsimonious ontology: since what we care about here is what there really is – what exists in reality – and sets don’t really exist.
I have no idea whether that is in line with Fine’s thinking on the distinction, but it seems to me not wholly crazy, and worthy of pursuit.
On other news, I’ve been invited to respond to