The question

Supposing that truths require truth-makers, that true propositions are those that correspond to facts, is there a distinctive domain of facts that make true the relational truths? Or is it rather that, if we had collected the facts required to make true the other truths, the non-relational ones, we would then have enough facts to make all truths true?

If the former is the case, let us say that anti-reductionism about relational facts is true; if the latter, that reductionism about relational facts is true. Let us say that a fact is relational if it makes true some relational proposition (a proposition that asserts that a relation holds between some objects), that it is irreducibly relational if, in addition, it does not make true any non-relational propositions, and that it is monadic if it is not irreducibly relational (if it makes true some proposition that does not assert that a relation holds between some objects).

Anti-reductionism (as we will say for short) holds that there are irreducibly relational facts; reductionism (as we will say for short) that while there may be relational facts, there are no irreducibly relational ones.

This is a very fine definition, but is it an interesting issue? Yes, for three reasons:

1. 1. Reasons internal to truth-maker theory. If you are one of those metaphysicians who believes the antecedent of the first sentence of this chapter, that truths require truth-makers, you will naturally be interested in what manner of things you are thereby committed to. Different truth-maker theorists offer different ontologies of facts. These ontologies deal with relational facts in different ways, so independent arguments for one or other view of relational facts give us some grip on which truth-maker ontology is likely to be the right one. In particular, irreducibly relational facts could seem nominalistically unrespectable (Campbell 1990: 97–9).

2. […]