One is a problem about identity statements that Frege raised at the beginning of "On Sense and Reference", and another concerns propositional attitude reports.
[3][4] Frege proposed to resolve this puzzle by postulating a second level of meaning besides reference in the form of what he called sense: a difference in the mode of presentation or the way an object can be "given" to the observer.
Frege's puzzle has received a great deal of attention since the attacks on the descriptivist theory of names mounted in the 1970s and 1980s by philosophers such as Keith Donnellan, Saul Kripke, Ruth Barcan Marcus, Hilary Putnam, and David Kaplan.
In view of this problem, many philosophers of language have attempted to work out a solution to the puzzle within the confines of direct-reference theories of proper names.
Some of these philosophers include Nathan Salmon (e.g. in Frege's puzzle and Content, Cognition, and Communication), Howard Wettstein (e.g. in "Has Semantics Rested on a Mistake?