The clearest way of asking about what is existence is to ask the
question, what are we saying when we say of something, X that it
exists (or does not exist)? Once we ask the question in this way, one
thing that jumps out is a question that Plato asked, which was how can
we say of X that X does not exist? For, Plato argued, to say that X
does not exist seems to imply a contradiction, since by asking that
question, we seem to be assuming both that that X does X exist, and
yet to be saying of X that it does not exist. After all, it would seem
that when we ask of anything whether it has some property, aren't we
assuming that it exists? For how could it even have a property unless
it exists? If it did not exist in he first place, what would have the
property. For instance, if we ask whether Barack Obama is president,
we must be supposing that something is Barack Obama. Else, of what
are we asking whether he is president? But, then, how could we then
truly say of anything that it does not exist, for of what would we be
asking that question. So the issue is this: to say of something that
it does not exist seems to imply that it does exist. So how could it
even make sense to say that something does not exist? Yet, on the
other hand, all of us know that not only can we say that something
does not exist (for example, Martians do not exist) but it is true
that somethings do not exist (Martians do not exist). So we appear to
be in the following paradoxical pickle: on the one hand we can say
truly that something does not exist, and yet it seems we cannot
sensibly say such a thing because it implies a contradiction.
The inevitable intuition is that to say of something that it exists
(or does not exist) must be different from simply saying of something
that it has a particular property, since for all other properties, we
can deny that something has that property without contradiction, but
we cannot deny that something has the property of existence without
contradiction. So, what kind of property is the property of
existence? Or, as some have argued, despite its surface appearance,
saying of something that it exists is not really saying of that thing
that it has a property, and existence is not a property as it first
appeared, and as the question, what is existence? assumes.