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Full Idea
When you take any propositional function and assert of it that it is possible, that it is sometimes true, that gives you the fundamental meaning of 'existence'.
Clarification
A 'proposition function' says something about something
Gist of Idea
'Existence' means that a propositional function is sometimes true
Source
Bertrand Russell (The Philosophy of Logical Atomism [1918]), quoted by Colin McGinn - Logical Properties Ch.2
Book Ref
McGinn,Colin: 'Logical Properties' [OUP 2003], p.18
A Reaction
Functions depend on variables, so this leads to Quine's slogan "to be is to be the value of a variable". Assertions of non-existence are an obvious problem, but Russell thought of all that. All of this makes existence too dependent on language.