# Frege's Argument About the Sense and Reference of a Sentence

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.

EDIT:

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.

EDIT:

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.

• Truth values are objects for Frege, and thus the truth of a sentence is definitely there, irrespective of the fact taht we know of it or not. The sense of a sentence is its thought-content, i.e. the thought expressed by the sentence. Also this is "objective", and it is not affected by what we think about it. Sep 9, 2017 at 14:18
• @MauroALLEGRANZA But why does it seem that Frege's argument hinges on what Q thinks about P(x_1) and P(x_2), given that Q doesn't know x_1 = x_2. For instance, he says "Anybody who did not know that the evening star is the morning star might hold the one thought to be true, the other false. The thought, accordingly, cannot be the reference of the sentence..." It seems unmistakable that he is directly concluding that the thought cannot be the reference from the possibility that a person MIGHT think one is true and the other false. Perhaps he is giving some sort of modal argument. Sep 9, 2017 at 14:48
• You can see Frege's Theory of Sense and Denotation as well as Mark Textor, Frege on Sense and Reference. Sep 9, 2017 at 16:33
• This topic is also being discussed here. According to damonsava, the argument does depend upon what Q believes or thinks about P(x_1) and P(x_2), which is what I suspected. Sep 9, 2017 at 19:16

I do not think a proper reaction to your criticism of Frege's posit (the reference of a sentence is its truth-value) can be made in the stackexchange format. The question, "Whether the truth value is an object or a property?" has a long intellectual history. (cf. https://plato.stanford.edu/entries/truth-values/) But your EDIT question can be answered quickly.

Do P(x_1) and P(x_2) express different thoughts whether one knows x_1 = x_2 or not?

Frege will say the answer depends on how P(x_1) and P(x_2) are employed.

1. As propositions

The same ideas or thoughts can be expressed linguistically in many different ways, and thus distinguished are sentences and propositions. Propositions are defined as unique and unchanging thought-contents (or senses) of sentences. For this reason, the senses of sentences (= propositions) do not depend on whether one knows them or not. They are objective for this reason, as Mauro ALLEGRANZA puts it. Thanks to this objective nature of propositions, Frege was able to posit that the sense of a sentence is a proposition, and the reference of a sentence is its truth-value.

1. As propositional attitudes

If the sentences are used as propositional attitudes, the truth value does differ depending on whether one knows x_1 = x_2 or not.

Lois Lane believes that Superman is awesome. (True)

Lois Lane believes that Clark Kent is awesome. (False)

Lois Lane does not know that Superman = Clark Kent, so, to her, 'Superman is awesome' and 'Clark Kent is awesome' express different thoughts, and thus different truth values.

• Your discussion on propositional attitudes actually ties in with a new, but related, question I have. If you a have a moment, I have edited my question and am wondering if you could take a look. Sep 13, 2017 at 10:57

One key that can help unlocking Frege's argument is to realize that he is talking about two different viewpoints. The first viewpoint is of the thinker (T), the one who makes judgements like "the morning star is the brightest". The second viewpoint is of the attributor (A), the one who observes thinkers like T, and attributes propositional attitudes to them, like "T believes that the morning star is the brightest".

Sense and reference are also attributed by the attributor A to the thinker T. A attributes senses to T according to what A judges to be T's viewpoint. But A attributes references to T according to her own (A's) viewpoint, not from T's viewpoint. Because for A, T may think (=senses) whatever T likes, but T can refer only to what is real, that is to what A believes to be real.

Why do the sentences "the morning star is the brightest" and "the evening star is the brightest" have different senses for T? Because A may observe that T believes e.g. that "the morning star is the brightest" is true, but that "the evening star is the brightest" is false. On the other hand, whatever T believes does not matter to what A judges to be the references of these sentences. Because A judges references from her own (A's) viewpoint, regardless of T's viewpoint.

I think that this answers the main question, as to why Frege's consideration about the senses cannot be repeated about the references. As to the additional question

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 ...

Do P(x_1) and P(x_2) express different thoughts whether one knows x_1 = x_2 or not?

Yes, they express different thoughts. The relevant test is not whether one knows that x1 = x2, but whether one could have not known that x1 = x2. If it is possible not to know that x1 = x2, it implies that they have different senses.

This post is to answer your EDIT 2 question. Your confusion is legitimate since p.45 is indeed very confusing. I am not sure whether the fault is in me, in translation, or in Frege. Due to the unclarity of the text, to answer your question, I extrapolate stuff I learned about Frege’s work in graduate school. On page 45, Frege is in pain to explain the distinction between the sense and denotation of a sentence when it is used in indirect speech. Earlier in the paper, Frege posited that the sense of a sentence is the proposition, and the reference of a sentence is its truth value.

One objection to Frege’s posit comes from the use of a sentence in an indirect speech. The objection goes like this. If the reference of a sentence is its truth value (= thus is objective and unchanging), then we should be able to substitute one true statement with another true statement freely. But in an indirect speech (i.e., when a sentence is used as a subordinate noun clause, like I think that …(called a propositional attitude)), the free substitute is impossible, since the truth value of the whole sentence can change as exemplified in the Lois Lane case. Thus implausible is the posit that the reference of a sentence is its truth value.

Frege’s response to this objection is to distinguish between the direct sense and the indirect sense of a sentence. The direct sense of a sentence is the stand alone meaning of the sentence, i.e, the proposition; thus its reference is its truth value. The indirect sense of a sentence is its meaning to the subject of the main clause (= thought). Due to this distinction, when a sentence is used in an indirect speech, one should ask whether the sentence is used directly or indirectly. If the sentence is used directly, i.e., as a proposition, then its reference is its truth value. Thus you can substitute without harming the truth value of the whole sentence. This is the context where Frege states what you cite:

One subordinate can be substituted for the other without harm to the truth.

But if the sentence in the indirect speech is used to refer to the sense (= thought) of the subject, then a substitution is impermissible. The sense of a sentence changes depending on the circumstance of the subject, and thus senses are not interchangeable. In this case, Frege states

it is not permissible to replace one expression in the subordinate clause by another having the same customary reference. (p. 45)

I hope my explanation has removed some of your confusion. Elementary Logic by Benson Mates has sections on use and mention, and sense and denotation, which might be useful.