## Tuesday, February 26, 2019

### More on grounding of universals

The standard First Order Logic translation of “All As are Bs” is:

1. x(A(x)→B(x)).

Suppose we accept this translation and we further accept the principle:

1. Universal facts are always partially grounded in their instances.

Then we have the oddity that the fact that all ravens are black seems to be partially grounded in my garbage can being black. Let R(x) and B(x) say that x is a raven and black, respectively, and let g be my garbage can. Then an instance of ∀x(R(x)→B(x)) is R(g)→B(g), and the latter material conditional is definable as ¬R(g)∨B(g). But a disjunction is grounded in its true disjuncts, and hence this one will be grounded in B(g) (as well as in ¬R(g)).

There are three things to dispute here: the translation (1), the grounding principle (2), and the claim that a material conditional is grounded in its consequent whenever that consequent is true. Of these, I am most suspicious of the translation of the two-place universal quantifier and the grounding principle (2).