Similarly, the proposition _No angels are ugly_ implies that _Angels that are ugly do not exist_.

Therefore, writing _x_ for 'devils,' _y_ for 'ugly,' and _[y]_ for 'not-ugly,' we may express A., the universal affirmative, thus: A._x[y]_ = 0.
That is, _x that is not y is nothing_; or, _Devils that are not-ugly do not exist_.

And, similarly, writing _x_ for 'angels' and _y_ for 'ugly,' we may express E., the universal negative, thus: E._xy_ = 0.
That is, _x that is y is nothing_; or, _Angels that are ugly do not exist_.
On the other hand, particular propositions are regarded as implying the existence of their terms, and the corresponding equations are so framed as to express existence.

With this end in view, the symbol v is adopted to represent 'something,' or indeterminate reality, or more than nothing.

Then, taking any particular affirmative, such as _Some metaphysicians are obscure_, and writing _x_ for 'metaphysicians,' and _y_ for 'obscure,' we may express it thus: I._xy_ = v.
That is, _x that is y is something_; or, _Metaphysicians that are obscure do occur in experience_ (however few they may be, or whether they all be obscure).