x exists: where x is any given or described object, means, there is some
primary proposition that is known true about x.
A proposition about x is primary if it has the form 'x has F' where F is
some predicate.
For example:
Descartes thinks therefore Descartes exists.
Descartes pees therefore Descartes exists.
Any true statement directly about Descartes implies that Descartes exists.
That is, if we have a primary truth about something then we have proof that,
that thing exists.
But,
Descartes does not think implies Descartes exists, is false.
Descartes does not pee implies Descartes exists, is false.
i.e. primary predications entail existence. And, secondary predications do
not necessarily entail existence.
God is not a pink elephant, does not prove that God exists.
God is not a number, does not prove that God exists.
God exists, means, there is at least one primary truth about God.
God exists, if and only if, we are in possesion of a verifiable truth that
has God as subject.
The theist only needs one such truth to prove, God exists.
The atheist needs to show that all primary truths about God are false to
prove that, God does not exist.
(Yes, it can be done)
x exists, defined as, there is some primary predicate true of x.
x exists, defined as, some F such that Fx is confirmable.
There are things which do not exist, i.e.
there are descriptions which are contradictory.
Things that are described by contradictory predications cannot exist.
Examples:
That which is and is not, does not exist.
That which is not equal to itself, does not exist.
The barber who shaves only those who do not shave themselves, does not
exist.
The class of those classes which are not members of themselves, does not
exist.
That which is omnipotent and omniscient and omnipresent, does not exist.
That which: (Created all things and All created things are good and Evil
exists) does not exist.
etc.