If propositions are not genuine objects in the domain over which quantifiers range—as deflationary nominalists like Prior urged—then no well-formed correlation between propositions and classes exists to generate the diagonal.
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The set of input values over which a function is defined.
genuine objects(in ontology (the study of what exists))
Things that actually exist and have real properties, rather than being abstract ideas or just ways of speaking.
propositions(Answer to the question of what metaphysical category propositions belong to)
Entities belonging to a sui generis metaphysical category of their own kind, not reducible to other categories
quantifiers(the logical form Russell said descriptions should take)
Words like 'all,' 'some,' and 'none' that express how many things we're talking about; Russell argued that phrases like 'the king of France' should be understood using these quantity-words rather than as simple names.
range(as used in semantics and philosophy of language)
The set of different situations or contexts where a word can be correctly used in real-world communication.
well-formed correlation(in logic)
A proper, systematic matching or pairing between two types of things that follows logical rules.