In that case, what does it mean to say that a physical object exists? One might try to fill in the blank in the following: "An object exists, if and only if, it ... ."
A common view is that this question cannot be answered. It has been suggested that "exists" simply cannot be defined. That people very well understand what it means to say that an object exists is not necessarily to say one can define it. This is a very influential view, which many very smart people hold. But the initial assumption will be made here that we can define "exists" for physical objects.
Here is a starting point for this assumption. What is existence contrasted with? There are different kinds of nonexistence. So it has been proposed that the existence of physical objects is an "excluder" concept, as it were a purely negative concept: an item is actually in the world, it is not fictional; it is real, not imaginary; it is an actual phenomenon, it is not part of a false hypothesis; and it is located at the present time, not just at a past, or a future time.
Common sense would seem to have it, however, that there is one basic sense in which physical objects actually do exist, and that is as an object that belongs to the space-time system that is the world with which people are in direct contact. If one can bump into it, it exists. So one might boldly give this following definition:
This sort of definition encounters some serious objections. Consider the following objection, probably the most widespread.
There are many philosophers today, following Hume, Kant, Frege, and Russell, who claim that existence is not a property, or that 'exists' is not a predicate. Sometimes they say that 'exists' is a second-order predicate (or "second-level" predicate); or they make other sorts of claims about it, such as that it is a unique sort of predicate. Typically, the discussions in which this claim arises are discussions of the existence of physical objects. So, for example, the Eiffel Tower exists. This is a true claim; what makes it true? One would like to be able to say that it is the fact that the Eiffel Tower has the property of existence. It seems that the claim asserts that existence is a property of the Eiffel Tower. Yet the philosophers listed--with qualifications the philosophical Wikipedian is encouraged to elaborate--deny that existence is a property. In fact, this is the common view among philosophers today.
One might wonder why it matters at all whether or not existence is a property. Consider: if existence is not a property, then the concept of existence cannot be defined, or at least, not as it has been defined here. The foregoing definition of 'exists' is incorrect, many philosophers would say, just because the definition does treat existence as a property.
Immanuel Kant wrote:
Of this view, one might ask: does this entail that existence is not a property at all? It seems not. If one lists out all the properties of the apple, the list would include 'being located in the universe with which we are in contact'. An advocate of the definability of 'existence' for physical objects might claim that that particular property just is what constitutes the apple's existence. That property would, of course, be included in a list of all of the apple's properties; so Kant's claim, that existence is not another property over and above all its other properties, seems true enough, but that by itself does not mean that existence is not a property at all.
The dialectic definitely does not end there; in fact, we have barely scratched the surface. Much more can be said on both sides. (And we invite ontologists to dive in and supply the missing details.)