Sentence examples for assert the existence from inspiring English sources
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.
In application to matters of ontology, realism is standardly applied to doctrines which assert the existence of entities of some problematic or controversial kind.
One philosophical feature of traditional analysis, which worries mathematicians whose outlook is especially concrete, is that many basic theorems assert the existence of various numbers or functions but do not specify what those numbers or functions are.
Fixed point theorems are examples of existence theorems, in the sense that they assert the existence of objects, such as solutions to functional equations, but not necessarily methods for finding such solutions.
In 1770 71 Dalrymple published his twovolume Historical Collection of the Several Voyages and Discoveries in the South Pacific Ocean, in which he continued to assert the existence of the continent.
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).
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.
For example, it asserts the existence of a set B corresponding to "Either x is an astronaut or x is a natural number".
