Frege's Problem of Identity Sentences

Although my proper name is ‘Robert Jonathan Robert’, I commonly respond to the name ‘Jon’. In my philosophy of language class, my name appears on the official class list as ‘Robert Robert’. When Ben (my professor) saw this, he probably asked himself, “Who is Robert Robert? I don’t remember meeting someone who goes by ‘Robert Robert’.” If he were to ask the class “Who is Robert Robert?” and Cory suggested, “Robert Robert is Robert Robert”, Ben’s response might be, “Cory, that bit of language is obvious, uninteresting, trivial and a priori.” But if I offered, “Robert Robert is Jon Robert”, then Ben would probably say, “Thank you Jon. That bit of language is informative, interesting and a posteriori.” However, if ‘Robert Robert’ and ‘Jon Robert’ both refer to me, Robert Jonathan Robert, why would those two sentences differ in cognitive value?

Frege’s problem in cognitive value is based on reference. If two sentences are identical, with the exception of one word, and the different words refer to the same object, then the sentences should convey identical information. In other words, in the following the sentences:
(1) Robert Robert is Robert Robert.
(2) Jon Robert is Robert Robert.
(1) is a priori, uninformative and trivial while (2) is a posteriori, interesting and informative. Frege describes this difference when he wrote: “a=a and a=b are obviously statements of differing cognitive value; a=a holds a priori and, according to Kant, is to be labelled analytic, while statements of the form a=b often contain very valuable extensions of our knowledge and cannot always established a priori.”[i] Since a=a & a=b, there should be no difference in cognitive value, but as Frege shows, there is. This is Gottlob Frege’s problem of cognitive value for identity sentences.

The solution to this problem does not rely on the reference of the words. In (1) & (2), the names ‘Robert Robert’ & ‘Jon Robert’ both refer to me, Robert Jonathan Robert. If both names refer to the same single object (that is, they corefer), then both names have the exact same reference, and thus the solution of Frege’s problem of identity sentences does not involve reference.

Frege’s solution involves sense in opposed to reference. Bits of language are used to convey thoughts. That is, when someone has a thought, they use language to express that thought to another person, and if the goal is achieved, the listener will have the same thought that the speaker did. The thought does not have the same properties as the actual object; it contains the sense of the object[1]. Therefore, when using bits of language to communicate, the word expresses the sense of the object, which in turns determines the object that the word is referring to. In short, sense determines reference.

Frege’s solution is based on sense in that names with the same referent can express different senses. To apply the example, in (1) ‘Robert Robert’ expresses the sense of Robert Jonathan Robert (the student in Ben’s the Philosophy of Language class who has a peculiar name), which determines Robert Jonathan Robert. In the example (2), ‘Jon Robert’ expresses the sense of Robert Jonathan Robert (the tall blond guy who does card tricks), which determines Robert Jonathan Robert. Seeing that there is a difference in sense associated with the two names, there can be different cognitive information transmitted between (1) & (2) even though those names corefer.

Frege’s solution shows that reference is not a factor in the problem of cognitive value, and moreover, it is determined by sense. I will argue that there is at least one case that sense does not determine reference. Take the example of Rufus, who was the product of an evening of promiscuous sex. Rufus’s mom ended up being a single mom and raised Rufus to the best of her abilities. She wanted her son to have a positive male role model in his life but she didn’t want to get involved with another man, so she told Rufus that his father was a decorated war hero who died in battle. Unknown to Rufus, his father ran the local 7-Eleven and is not war hero. He was never enrolled in the military and has never seen a battle. Here is the dilemma, when Rufus says the name ‘Dad’, what does the name refer to? Does he refer to his biological father that contributed to his genetic makeup or does he refer to the man who was a decorated war hero?
I’ve established that Frege’s solution suggests that sense determines reference. So if we use Frege’s solution to examine the dilemma, we find that ‘Dad’ expresses the sense of Rufus’ Dad, (the dead war hero) which determines Rufus’ Dad (the dead war hero) and thus determines the referent as the dead war hero. Yet, the dead war hero does not exist. Intuition suggests that the reference to the name ‘Dad’ is predetermined to refer to Rufus’ biological father. But Frege’s solution does not provide a correlation between Rufus’ dad and the 7-Eleven manager. There seems to be a conflict between theory and data.

The Rufus case offers a counterargument to Frege’s solution in that sense does not determine reference. Frege would probably agree with this counterargument. He could argue that, although it presents a conflict with sense determining reference, it does not provide a counterexample to the solution. The problem is that there is a difference of cognitive value between two sentences with the same reference. The solution is that there is a difference in sense, not reference. Frege would suggest that his theory states that sense determines reference, but it also states that reference does not play a part in the solution. Although the Rufus Case attacks the creditability of how reference is determined, it does not provide a counterexample to the cognitive difference in identity sentences.



[1] For example: If I think of the Empire State Building, my thought does not actually contain the Empire State Building. The Empire State Building has a very substantial mass and is located in New York, not in my thought. What is contained in my thought is the sense of the Empire State Building.
[i] Sense and Reference (in A Translation of Frege's Ueber Sinn Und Bedeutung) Gottlob Frege
The Philosophical Review, Vol. 57, No. 3. (May, 1948), pp. 209-230.
Stable URL: http://links.jstor.org/sici?sici=0031-8108%28194805%2957%3A3%3C209%3ASAR%3E2.0.CO%3B2-X