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The other was the 'inflationary' approach, which posited entities corresponding to all statements, thus 'creating' or asserting the existence of things that (Berlin believed) didn't exist at all.
(A numerical sentence is a first-order sentence asserting the existence of some objects. For example, the numerical sentence that there exist at least two objects is: ∃x∃y(x ≠ y).) If van Inwagen is correct, it is indeterminate whether or not the relevant numerical sentence is true, in which case one of the constituent expressions—'∃', 'x', 'y', '~', '=' must be vague.
Erin and Abby, childhood friends, co-authored a book, "Ghosts from Our Past," asserting the existence of ghosts.
When the New Wave quoted Fuller or Hitchcock, they were both asserting the existence of a school and suggesting that it was cutting-edge.
He seemed deliberately to seek an antique religious aura, asserting the existence of moral absolutes in an era that doubted them.
It restricts that principle, however, in two ways: (1) Instead of asserting the existence of sets unconditionally, it can be applied only in conjunction with preexisting sets, and (2) only "definite" formulas may be used.
Similar(42)
On the other hand, some constructions may share some syntactic features with the existential, but they should not be regarded as such: Lei (1993) lists three conditions for a clause to be called an existential: 1) Semantically, it asserts the existence of something, that is, there exists something (New) in someplace (Given).
If the Axiom of Infinity is reformulated to assert the existence of Vω , then the ranks proved to exist as sets by Zermelo set theory are exactly those which appear in the natural model Vω+ω of this theory.
This entails that no such claim can assert the existence of, or otherwise make reference to, anything that is beyond the realm of possible perceptual experience.
For example, it asserts the existence of a set B corresponding to "Either x is an astronaut or x is a natural number".
In application to matters of ontology, realism is standardly applied to doctrines which assert the existence of entities of some problematic or controversial kind.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com