Types, Ontology, and a Solution to the (so-called) Paradox of the Ravens

The Paradox

Introduced in the 1940’s by the logician (and once an assistant of Rudolph Carnap) Carl Gustav Hempel, the Paradox of the Ravens (or Hempel’s Paradox, or the Paradox of Confirmation) has continued to occupy logicians, statisticians, and philosophers of science to this day. The paradox arises when one considers what constitutes an evidence for the confirmation of a hypothesis (a statement).

To illustrate what the Paradox of the Ravens is consider the following:

(H1) All ravens are black
(H2) All non-black things are not ravens

H1 is the hypothesis that ‘All ravens are black’, while H2 is the logically equivalent hypothesis that ‘All non-black things are not ravens’. This is represented in standard first-order predicate logic (FOPL) as follows:

(1) and (2) are logically equivalent, thus any evidence/observation that confirms H1 must also (equally) confirm H2 and vice versa. However, while it does sound reasonable that observing black ravens should confirm H1, observing a white ball, a red sofa, a yellow shirt…