# Speak with the vulgar.

Think with me.

## Another quick objection to Tooley

In “The Nature of Laws” (1977), Michael Tooley claims that it is nomologically true that Fs are Gs just in case a certain relation R—the nomological relation—holds between the universal Fness and the universal Gness. He claims further that this relation-symbol “R” is a theoretical term whose referent is fixed in Ramsey-Lewis style: we specify some constraints C, and then stipulate that R is the unique relation that satisfies C. These are his constraints:

1. R is a two-place relation on universals.
2. R is contingent: there are universals Fness and Gness such that it is neither necessary that R(Fness, Gness) nor necessary that not R(Fness, Gness).
3. R(Fness, Gness) logically entails that all Fs are Gs.

(I’ve left out the complications that are introduced to deal with laws that have different forms, such as “All non-F’s are G’s or H’s” (Tooley doesn’t think there are negative or disjunctive universals). But Tooley thinks there is a different nomological relation associated with each syntactic construction, so this doesn’t make a difference here.)

But it doesn’t look at all plausible to me that these constraints pick out a unique relation (assuming anything satisfies them at all). Look, here’s a non-nomological relation that satisfies conditions 1–4: the relation denoted by the two-place quantifier “All”—that is, the relation that holds between Fness and Gness just in case all Fs are Gs. Tooley hasn’t said anything that would distinguish his nomological relation from such run-of-the-mill categorical relations. This strikes me as a serious problem. Am I missing something?

(I’m working through David Armstrong’s What is a law of nature? now—I’ll see if he adds anything helpful.)

EDIT: I inadvertently left out one of Tooley’s constraints:

1. R is irreducibly second-order.

You might think this might help. You might say in particular that the “All” relation is in fact reducible to less-than-second-order universals only—since, after all, “All(F, G)” holds iff for every x, if Fx then Gx. But this “reduction” involves the concept “for every”, which plausibly involves the “All”-relation in disguise. (Analogously, one might “reduce” a purported nomological relation R by pointing out that “R(F, G)” holds iff it is nomologically necessary that for every x, if Fx then Gx.) I guess I’m not really sure what the rules are for reducing universals.

Armstrong makes a conjecture along the same lines: “I speculate that the laws of nature constitute the only irreducibly second-order relations between universals” (84). So presumably he thinks that either there is no “All”-relation, or else that it is reducible to a lower order. Does anyone have an idea why he would think this?