Existence

What does "Socrates exists." actually mean?

Two positions in interpreting "Socrates exists." can be taken:
 * 1) "exists" is a predicate.
 * 2) "exists" is not a predicate.

In the first case "existence" would describe an attribute, logically equivalent to "Socrates sleeps." and "Socrates is mortal.".

Yet if we negate the proposition ("Socrates does not exist.") we face the dilemma of not being sure what we are talking about.

Kant
For Kant to exist is no predicate in a non-grammatical sense.

He describes the meaning of "unicorns exist" as "certain objects in nature inhere the attributes we require to call them unicorns". Kant's argumentation goes that we only can understand the meaning of a proposition if we realize, how it's truth can be validated in real life. In the given example we are not able to examine unicorns for signs of existence, as doing so would already assume their existence, but we focus on all animals in the world, which' existence is evident, and we test whether any of them inher the required attributes.

Frege, Russell
Frege and Russell suggest that to exist is neither a first-order predicate nor a property of individuals. Frege thought that existence was a property of properties, a second-order property. On his account, if we make an existence claim we are not attributing a property to an individual. Instead, we are saying something about some property (or concept). In particular, we are saying that the number of individuals with that property is not zero. Frege's remarks on the property of existence occur in his discussion of his theory of concepts, in a section where he criticizes the ontological argument for the existence of God (Grundlagen, §53).