The paper deals with the problem whether the number is a property or an object. The authors are convinced that from the logical point of view the number is an object, but from the ontological point of view the number is a special kind of property (briefly spoken the property of a system or a structure). and Prokop Sousedík, David Svoboda
Frege argues that considering Socrates as an object in the proposition “Socrates exists” raises two problems. First, this proposition would be uninformative. Second, its negation entails a contradiction. Attempting to solve these problems, Frege claims that Socrates is representing the concept of a man whose name is Socrates. Therefore, existence is a second-order concept. This paper surveys the main modern theories about the types of existence, in order to find another response to Frege’s problems. For, if Socrates’ existence differs from the type that “exists” implies, “Socrates exists” is informative and its negation is not a contradiction. At last, this paper argues for an idea, in which “existence” is not a concept or property. Existence is the principle of the objects. So, “Socrates exists” is in fact “the existence is Socrates,” and “Socrates does not exist” is “there is no existence that be Socrates.” This idea could be an alternative for responding to Frege’s problems.