From Wikipedia
These are puzzles posed by Frege. They are addressed by making a distinction between sense and reference.
First puzzle
The brightest star in morning was called Hesperus, and the brightest star of evening was called Phosphorus. Science later discovered these to be same object, namely, Venus. Consider the two sentences:
- Hesperus is Hesperus.
- Hesperus is Phosphorus.
The first is just a matter of a priori logic, whereas the second is a nontrivial empirical truth. However, given the existing semantics (attributed to Mill), names have no meaning beyond their reference, meaning the second sentence means “Venus is Venus”.
Second puzzle
- Alex believes Hesperus is visible in the evening.
- Hesperus = Phosphorus.
- Therefore, Alex believes Phosphorus is visible in the evening.
This is not valid, but by naive subsitution of identicals it would appear to be so.