  In his second book, Die Grundlagen der Arithmetik (1884),  Frege went on to provide a logical analysis of number statements. His central idea was that a number statement contains an assertion about  a concept. A statement such as ‘Jupiter has four moons’  is to be understood not as predicating of Jupiter the property of  having four moons, but as predicating of the concept moon of  Jupiter the second-level property has four instances,  which can be logically defined. The significance of this construal  can be brought out by considering negative existential statements  (which are equivalent to number statements involving the number 0).  Take the following negative existential statement: