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The argument is an attempt at reducing to absurdity the atheist's assumption that everything exists contingently.
Aquinas asks, What must follow from the assumption, commonly made by atheists, that nothing exists eternally (i.e., that everything exists contingently)?
When we combine this result with the link between quantification and existence, we conclude that everything exists necessarily, which flies in the face of the assumption that we exist only contingently.
That is: Hence, under the actualist's understanding of existence, NE says that everything exists necessarily and hence (by the definitions of '∃' and '◇') that nothing can possibly fail to exist — ~∃x◇~E!x — from which it immediately follows, contrary to CB, that there are no contingent beings, beings (like us) for whom existence and nonexistence are equally possible.
Such an attitude, according to Collier, is necessary in order to understand that everything exists only by way of its dependence on the one supreme substance, God.
Now suppose that everything exists contingently.
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He tells us that everything that exists exists because substances exist: if there were no substances, there would not be anything else.
In fact, Newton accepted the principle that everything that exists, exists somewhere — i.e., in absolute space.
Since there is now something, it seems to follow that not everything exists contingently.
However, unlike the Meinongian, a proponent of this view insists that absolutely everything exists.
Our first challenge, then, is to explain how sentences like 'Ronald McDonald does not exist' are both meaningful and sometimes apparently true without abandoning the theses that absolutely everything exists and all names are devices of direct reference.
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that problem exists
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com