Suppose they each satisfy the singular predicate F, and have no proper parts which are F. Suppose there is a join relation which combines particular individuals to make plural individuals only (call it a plural join or 'p-join').
The singular predicate F will be neither cumulative (i.e., it is not true of the joins which are Fs, for example, if 'F' is 'Man', and a, b, and c are each a man, then the plural individual a ∪p b is not a man), nor is it distributive over the proper parts of the atoms of A1 (more on this later).
there is a unique predicate of L′.
Truth for singular sentences, consisting of a name and an arbitrarily complex predicate, is defined thus: A singular sentence is true iff the object denoted by the name satisfies the predicate.
It seems pretty clear, however, that, based on the rules of quote-names for words, this predicate still retains a singular term for a type, the word 'color' just as clearly as "a George W. Bush appearance" still contains a reference to Bush.
An example of p X, t) is 'is the t-th token in X a singular common noun (NN)?' We divided these p predicates into categories as shown in Table 1.
For another example, a singular term (e.g., '1') may be defined using a predicate (e.g., 'is identical to 1').
It turns out that Kant's view that "exists" is not a "real" predicate and Frege's view, that "exists" is not a predicate of individuals (i.e., a predicate that yields a well-formed sentence if one puts a singular term in front of it), has to be abandoned if one is to accept the claim that there are nonexistent objects.
In response, these eight autocracies communicated, consulted and conjured the beginnings of a monarchical community, one predicated on a unique "pan-royal" identity that shared a singular fate.
The λ-notation has the advantage of clearly revealing that the variable x is bound by the term-forming operator λ, which takes a predicate φ and yields a term λx φx (which in some logics is a singular term that can occur in the subject position of a sentence, while in other logics is a complex predicative expression).
