By modifying quantitatively the predicate to produce two forms, "All A is all B" and "All A is some B," he extended the range of classification of propositions.
Popper's truth factor Hilpinen identified with that world, in the range of a proposition, closest to the actual world.
Consider the sum function — the sum of the distances of worlds in the range of a proposition from the actual world.
Popper's content or information factor he identified with that world, in the range of a proposition, furthest from the actual world.
Despite this, the range of a proposition is certainly an important aspect of informative content, and it is not immediately obvious why truthlikeness should be sensitive to differences in the way a proposition picks out its range.
So, we first give the range of c. Proposition 4.1 Let the random variable × be non-degenerated, and there exists some λ > 0, such that E exp{λX} < ∞.
On the other hand, min-sum-average also seems to fall within the likeness camp, since it deems truthlikeness to be a non-trivial function of the likenesses of worlds, in the range of a proposition, to the actual world.
Now that we numerical distances between worlds, numerical measures of propositional likeness to, and distance from, the truth can be defined as some function of the distances, from the actual world, of worlds in the range of a proposition.
The incorporation of similarity spheres signals a fundamental break with the pure content approach, and opens up a range of possible new accounts: what such accounts have in common is that the truthlikeness of a proposition is a non-trivial function of the likeness to the actual world of worlds in the range of the proposition.
The Xerostomia Inventory-Dutch version data were subjected to exploratory factor analysis to reveal the range of the 11 proposition responses, possibly providing one latent variable determining the severity of xerostomia.
