If the mixed sentence d ∨ Os is considered to be normative, then (1) is an example of an 'is-ought' inference, and if it is considered to be non-normative, then (2) is an example of an 'is-ought' inference.
In (GH) a mixed sentence φ is derived from a set of purely descriptive sentences (i.e., sentences free of O) only if φ is completely O-irrelevant (that is, predicates in φ within the scope of O can be replaced by other predicates salva valididate).
In any case Carnap's suggestion is as follows (where for convenience terms are used autonymously): Let T be the totality of theoretical postulates, and C be the totality of mixed sentences (the sentences of the theory containing both antecedent and novel terms).
In total, there are 76 seed patterns from 80 annotated mixed sentences, and this set is represented as "MIX" in Table 5.
However, the test has items of a variety of types: following directions (14 items), same-opposites (11), word classification (10), analogies (8), practical items (6), reasoning (5), proverbs (4), arithmetic (4), spatial items (4), mixed sentences (3), cipher decoding (2), and other items (4).
It includes same-opposites, word classifications, analogies, and practical, reasoning, proverbs, arithmetic, spatial, mixed sentences, and cipher-decoding items.
However, the test has items of a variety of types: following directions (14 items), same-opposites (11), word classification (10), analogies (8), practical items (6), reasoning (5), proverbs (4), arithmetic (4), spatial items (4), mixed sentences (3), cypher decoding (2), and other items (4).
Yablo thinks that something like this is true in connection with typical utterances of (pure and mixed) mathematical sentences, e.g., sentences like '3 is prime' and 'The number of Martian moons is 2.' So Yablo is certainly proposing a hermeneutic nominalist view, but it's not clear that his view is best thought of as a kind of hermeneutic fictionalism.
It is crucial to the latter two proposals that any given mixed atomic sentence p has its domain membership essentially, since such membership is what determines the relevant kind of truth.
But what makes it awkward to take Yablo's view as a version of fictionalism is that he seems to think that what (pure and mixed) mathematical sentences really say or, more precisely, what typical utterances of these sentences really say is true and nominalistic in content.
Sher (2005, 2011) deals with the problem of mixed atomic sentences differently.
