Here is the text I am working with: http://brianrabern.net/sensereference.pdf
As the title of this thread indicates, I am having trouble understanding Frege's argument that the thought of sentence (i.e.. the proposition expressed by a sentence) cannot be its reference but must be its sense, which begins on page 41 of the linked document.
My confusion is manifesting itself as an objection to his argument. Let P(x) be the sentence "x is a body illuminated by the sun," and let x_1 and x_2 stand for "the morning star" and the evening star", respectively. He seems to be arguing that because it's possible that P(x_1) and P(x_2) express different propositions, and therefore have different truth-values according to someone who doesn't know x_1 = x_2, this possibility implies that the thought/proposition of a sentence cannot be the reference of the sentence, since the thought of P(x) isn't invariant under substitution of the terms x_1 and x_2 which have the same reference but different sense, which he said must be satisfied by the reference of the sentence. Does this sound right?
If this is a proper construal of Frege's argument, it seems to lead to a problem for thinking that the reference of a sentence, if it has one at all, is its truth-value. In the above argument, we are saying that because some person Q doesn't know x_1 = x_2, P(x_1) and P(x_2) express different thoughts/propositions for Q. But can't we conclude, in a parallel fashion, that truth-value cannot be the reference of a sentence, since Q thought each sentence has a different truth-value, namely one is true and the other false. Isn't this precisely what Frege is concluding in the above argument, that because one can be possibly regarded as true and the other false, they cannot express the same thought. I don't see why we can't construct a parallel argument to conclude that truth-value cannot be the reference a sentence either, even though this is what Frege goes on to argue, since it is possible that Q regards P(x_1) and P(x_2) as having different truth-values, and therefore the reference doesn't remain invariant under substitution.
Afterthought: When I reread what I wrote above, and reread the relevant section of Frege's paper, I don't think Frege is arguing that because P(x_1) and P(x_2) can possibly be regarded as having different truth-values by someone who doesn't know x_1 = x_2, therefore the thought of a sentence can't be its reference. I think he is simply arguing that because P(x_1) and P(x_2) can possibly regarded as expressing different thoughts by someone who doesn't know x_1 = x_2, that therefore the thought cannot be the reference of a sentence. And if that's the case, I think my objection evaporates. But I am unsure about this and still don't have all of this sorted out in my head. I'll let you be the judge.
Here is another question which may help relieve my confusion. Do P(x_1) and P(x_2) express different thoughts whether one knows x_1 = x_2 or not? I think the answer is yes.
On page 45, in the same paper whose link I gave above, Frege begins discussing the sense and reference of subordinate clauses and its connection with the sense and reference of the entire sentence in which the subordinate clause appears. He considers the example of "Copernicus believes that x" , where x is some sentence, very much similar to Nanhee's examples about Lois Lane. He says something that confuse me and which seems to conflict with his own example and Nanhee's example:
One subordinate can be substituted for the other without harm to the truth.
But how can this be? Taking Nanhee's example, if Lois Lane doesn't know Superman is identical to Clark Kent, then "Lois Lane believes that Superman is awesome" and "Lois Lane believes that Clark Kent is awesome" will have different truth value; substituting these subordinate clauses (sentences) into "Lois Lane believes that x" will produce two sentences with different truth values, which clearly affects the truth value.
What am I misunderstanding? Perhaps I don't understand Frege's example about Copernicus.