Frege's article, "On Sense and Reference," is pretty complex. Don't worry too much about the last part starting around p. 33 where he gives lots and lots of examples of sentences with subordinate clauses (but do read it!)
Frege is suggesting two puzzles: the Identity Puzzle and the Propositional Attitude puzzle
The Identity Puzzle: how can there be true, informative identity statements, in particular, how can it be that "The Morning Star = "The Evening Star" tells us something about the world rather than merely rehearsing the trivial logical truth that The Morning Star, like everything else, is self-identical?
The Propositional Attitude Puzzle: how come substituting expressions that name the same thing into some contexts doesn't preserve truth value? How come, for example, does substituting "Samuel Clemens" for "Mark Twain" (Samuel Clemens' pen name) in some sentences, change their truth value?
Any questions?
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What is the role of sense in Frege's solution to the counterexamples to the claim that the truth value of a sentence is determined by the reference of its parts? I understand the notion of 'sense' in his observation of the moon example, but can't seem to apply it to expressions. Also, what differentiates sense and idea? He mentions that the sign's sense "may be the common property of many and therefore is not apart of a mode of the individual mind"? How do we determine what the sense of an expression is?
The difference between senses and ideas is that the latter are private--in your head--whereas the former are not. Sense are those unsavory abstracta that Quine et. al. despise. Frege rejects the Lockean notion that ideas (private mental particulars) are the meanings of words because, he notes, they may be idiosyncratic, have all sorts of personal associations, and also because to explain communication it must be that the meaning different individuals grasp is something public to which all have access: not a "mode of the individual mind." To determine the sense of an expression--well one way is to look up the expression in the dictionary.
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