Let it be said that there are no elements x in reality P.
That is, the negation of
is logically equivalent to "For any element x, x does not exist in reality P", or:
Generally, then, the negation of a propositional function's existential quantification is a universal quantification of that propositional function's negation; symbolically,
Hence, for no x does reality P exist.
For more, see: http://plato.stanford.edu/entries/nonexistent-objects/
That is, the negation of
is logically equivalent to "For any element x, x does not exist in reality P", or:
Generally, then, the negation of a propositional function's existential quantification is a universal quantification of that propositional function's negation; symbolically,
Hence, for no x does reality P exist.
For more, see: http://plato.stanford.edu/entries/nonexistent-objects/