Sep 8, 2015 10:26 PM
Let it be said that there are no elements x in reality P.
That is, the negation of
![[Image: d3b4139920731cc0ad9573300c34579f.png]](https://upload.wikimedia.org/math/d/3/b/d3b4139920731cc0ad9573300c34579f.png)
is logically equivalent to "For any element x, x does not exist in reality P", or:
![[Image: 397b97af3c7fda4b5fac969a75cb8bbc.png]](https://upload.wikimedia.org/math/3/9/7/397b97af3c7fda4b5fac969a75cb8bbc.png)
Generally, then, the negation of a propositional function's existential quantification is a universal quantification of that propositional function's negation; symbolically,
![[Image: 751099d807da6376976befe61f05e071.png]](https://upload.wikimedia.org/math/7/5/1/751099d807da6376976befe61f05e071.png)
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/