Regarding the second issue Frege states that singular term or expression is called proper name. Let us consider two proper names 'morning star' and 'evening star'. If we make the identity relation between these two proper names, we will find the following propositions.

1. Morning star is same as evening star.
2. Morning star is same as morning star.
3. Evening star is same as evening star.

The first proposition is a contingent truth because the identity relation between two proper names is known through empirical discovery whereas, second and third proposition are always true because of their logical necessity. They are true by virtue of their definitions. So we find two types of propositions, namely, analytic and synthetic. Here, we find three differences between two sorts of propositions.

1. The first proposition is a contingent truth whereas the second and third propositions are necessarily true.
2. The first proposition is an a posteriori truth whereas the other two propositions are true a priorily.
3. The first proposition is informative whereas the other two propositions are uninformative.

The above distinctions imply that someone can know 'the evening star is the evening star' without knowing that the evening star is same as the morning star even though the evening star is same as the morning star. This is so because 'evening star is the evening star' is just the repetition whereas 'evening star is the morning star' is known through astronomical discovery.

Considering the first case (i.e., the identity relation between two objects), we find three different issues. These are as follows:

1. One and the same object may refer to two things. (For example, Venus is a planet refers to both morning star and evening star.)
2. Two objects may refer to one thing as A. (For example, morning star and evening star refer to one object called Venus.)
3. Two objects may refer to two things - A and B respectively.