Our discussion will focus primarily on pp. 56-65 (209-214 of the JStor version).
Note that the JStor PDF is an older translation, but it is usable. Other relevant papers of Frege's are "On Concept and Object" (JStor) and "Function and Concept", as well as Part I of his Basic Laws of Arithmetic.
There is a major issue about how one of Frege's key terms is to be translated. The German word is "Bedeutung", and it is the term being translated as "reference" in the title of the paper. It is translated "nominatum" in the older translation available through the JStor link, and it has also been translated "denotation". In ordinary German, however, it just means "meaning", and so it is also sometimes translated that way (for example, in Frege's Collected Papers and Posthumous Writings). So "On Sense and Meaning" is the same paper, as is "On Sense and Denotation".
There are places in Frege's writings that he uses "Bedeutung" with its ordinary meaning of "meaning", but it is mostly a technical term for him, and the closest technical term in current philosophical usage is probably "reference". On the other hand, however, Frege uses "Bedeutung" in a somewhat wider sense from how "reference" is typically used, as one will see from Frege's discussion of the question whether sentences have Bedeutungen, i.e., references. And in this usage, it means something more like "semantic value". But our main focus will be on proper names, where "Bedeutung" pretty much does mean "reference", and our real focus will be more on sense than on reference, anyway.
The central purpose of this paper is to establish a distinction between the reference of an expression—primarily, a proper name—and what Frege calls its sense. The reference of a name is the name's bearer: the thing it is a name of. So the reference of the name "Gottlob Frege" is Gottlob Frege, that very person. It is not so easy to say what the sense of the name is, and Frege does not seem to tell us very much about what it is. Rather, as I said, his purpose here is to argue that names do have sense, and that their sense is different from their reference. In particular, the claim is, it is possible for two names to have the same reference but to have different senses.
The argument for this claim is contained in the first pargraph of the paper. It is not an easy argument to understand. Trust me on this.
Frege begins by mentioning a puzzle about identity statements, such as "Hesperus (the evening star) is the same thing as Phosphorous (the morning star)". As it happens, this is true: Hesperus and Phosphorous are both Venus. The puzzle is generated by the fact that such a statement can be informative and, in particular, that such statements need not be analytic or a priori but, as Frege puts it, may "often contain very valuable extensions of our knowledge". The problem, however, is that if identity is a relation between objects, then it looks as if "Hesperus is Phosophorous" and "Hesperus is Hesperus" assert that exactly the same relation obtains, namely, a relation between Venus and itself. But then how can the former be informative and the latter a mere instance of the law of self-identity? How, as it is put, can the one have a different "cognitive value" from the other?
Frege mentions that, for such reasons, he once held himself (in his first book Begriffsschrift, or Conceptual Notation) that identity was not a relation between objects, but was actually a relation between names. Thus, "Hesperus is Phosphorous" was supposed to mean something like: The names "Hesperus" and "Phosphorous" have the same denotation. In the middle of the paragraph, beginning with the words, "But this relation would hold...", Frege argues against this view. To be kind, it is not obvious what argument Frege is giving here. The key seems to be Frege's observation that the relation between a name and its bearer is arbitrary or, perhaps, conventional. But his underlying thought seems to be that the claim that "Hesperus" and "Phosphorous" have the same denotation is a claim about linguistic practice, whereas "Hesperus is Phosphorous" was meant to be a claim about celestial bodies. So the `name view' of identity gets the subject-matter of such statements wrong.
Frege then transitions, without explicit mention, into the development of his own view. He notes that the mere difference of shape (spelling, pronunciation, whatever) between "Hesperus" and "Phosphorous" cannot be what accounts for the difference in cognitive value that we are trying to explain. Rather, there will be a difference in cognitive value only if there is a difference in the "mode of presentation", which Frege illustrates using a geometrical example.
Can you give an example to show that the mere difference of shape (spelling, pronunciation, whatever) between "Hesperus" and "Phosphorous" cannot be what accounts for the difference in cognitive value that we are trying to explain?
Frege then says that each name has a "sense" that "contains" a "mode of presentation" that is associated with that name, but most commentators have simply supposed that the sense is the mode of presentation. In any event, the implication (which Frege makes explicit elsewhere) is that the fact that "Hesperus is Hesperus" and "Hesperus is Phosphorous" have differ in cognitive value is explained by the fact that "Hesperus" and "Phosphorous" have different senses.
It is important to note that the puzzle here, though particularly stark in connection with identity-statements, is not essentially about identity. The sentences "Hesperus is a planet" and "Phosphorous is a planet" also have different "cognitive values" (in German "Erkenntniswert", literally: value for knowledge), and Frege also holds that this difference is explained by the fact that "Hesperus" and "Phosphorous" have different senses. (Frege does not mention this extension of the point here but does so, again, in other places.)
How exactly is the fact that "Herperus" and "Phosphorous" have different senses supposed to explain the difference in cognitive value between "Hesperus is a planet" and "Phosphorous is a planet"? What assumptions about sense and cognitive value must such an explanation make?
In the next few paragraphs (pp. 57-9), Frege states several theses about sense and its relation to reference:
- The sense of a name is a linguistic feature of it, one anyone who understands the name must know.
- Names with the same sense must have the same reference (sense determines reference), but names with the same reference may have different senses.
- It is possible for a name to have sense without having a reference.
- Ordinarily, when one uses a name, one uses it to talk about its reference.
- But when one uses words in 'indirect speech', one uses them to talk about their sense. Thus, if one says, "Lois said that Superman can fly", then one is talking about the sense of Lois's remarks, as is clear from the fact that it is one thing to say that Superman can fly and another to say that Clark can fly. The same is true of such constructs as "Lois believes that Superman can fly". Here it looks as if what one is saying Lois believes is determined by the sense of the name "Superman", since Lois does believe that Superman can fly, but not that Clark can.
Over the next several pargaraphs (pp. 59-62), Frege argues that the sense one associates with a name must "be distinguished from the associated idea", by which he means something like a mental image. The larger point at issue here, though, is whether sense is subjective.
What is Frege's argument that senses are not "ideas"? How much of the argument turns on special features of ideas as oppposed to something else subjective that sense might be? That is: To what extent does the argument show that senses are not only not ideas but are not subjective at all? Perhaps more importantly: What does the way Frege argues here tell us about how he is thinking about 'sense'?
Frege then turns to the question what we should regard as the sense and reference, not of a name, but of a whole (declarative) sentence. Frege says first that "Such a sentence contains a thought", by which he means a certain "objective content, which is capable of being the common property of several thinkers". Frege then argues that the thought "contained" in a sentence cannot be its reference. He then concludes that the thought must instead be the sentence's sense and goes on to argue that the reference of a sentence is just its truth-value. For our purposes, we need not consider the details of this argument, but my own view, for what it is worth, is that Frege's reasons are ultimately logical in character: What lies behind this discussion is the role of truth-functional connectives in formal logic.
What is Frege's argument that the thought "contained" in a sentence cannot be its reference? To what assumptions about thoughts and references does it appeal?
Oddly, Frege does not seem actually to give any argument for the claim that the thought "contained" in a sentence is its sense. Some people therefore have suggested that by a "thought" Frege just means: sense of a sentence, so that "thought" for him is just defined as "sense of a sentence". Does that seem right? What alternative might there be? One might find inspiration for such an alternative in what Frege said earlier about indirect speech.