Some Solutions to Frege's Puzzle
Recall Frege's Puzzle:
1. 'Hesperus = Hesperus' and 'Hesperus = Phosphorus' have the same meaning.
2. 'Hesperus = Hesperus' and 'Hesperus = Phosphorus' have the same cognitive value.
3. 'Hesperus = Hesperus' and 'Hesperus = Phosphorus' do not have the same cognitive value.
where (1) follows from the assumptions
A. The meaning of a term is given by its reference.
B. The meaning of a sentence is given by its parts.
and (2) follows from (1) and the assumption
C. Sameness of meaning implies sameness of cognitive value.
(1), (2), and (3) are plausibly true taken individually but inconsistent taken together. Solutions to Frege's Puzzle, then, will organize according to whether (1), (2), or (3) ends up being rejected. Philosophy being what it is, every alternative has been adopted and vigorously defended. Let us consider some of the options.
First, we might try rejecting (1) but not (A) or (B) with it. There are at most two ways to pull this off; each approach hinges on treating identity statements as special linguistic items or cases. Neither approach has much to recommend it. Thus,
a) The Relata Differ, I
Identity statements are special because 'Hesperus = Hesperus' is about one thing, Hesperus, while 'Hesperus = Phosphorus' is about two things, Hesperus and Phosphorus, and asserts of these two things that they are one and the same thing. Clearly, though, two (distinct) objects cannot be the same object, because if they were, there would not be two (distinct) objects at all, just the one object. No matter how you look at it, if the identity statements are true, there is only one object here: Venus. Our problem, then, is to understand what precisely we are asserting when we make a true (and informative) identity claim.
b) The Relata Differ, II
Identity statements are special because the relata of 'Hesperus = Hesperus' and 'Hesperus = Phosphorus' have nothing to do with the reference of 'Hesperus' or 'Phosphorus' and everything to do with the terms themselves, 'Hesperus' and 'Phosphorus'. The meaning, then, of 'Hesperus = Hesperus' differs from the meaning of 'Hesperus = Phosphorus' because only 'Hesperus' occurs in 'Hesperus = Hesperus', while 'Hesperus' and 'Phosphorus' occurs in 'Hesperus = Phosphorus'.
(b) is at least as confused as (a), and perhaps moreso. For both identity claims are objectively true claims about the world, not claims about the linguistic items flanking the identity sign. Indeed, had they been claims about names, we would have written them as
i. 'Hesperus' = 'Hesperus'
and
ii. 'Hesperus' = 'Phosphorus'
Where (i) is true, but (ii) is false.
Second, we might try rejecting (1) and (B) with it. Known as the Compositionality Principle, (B) asserts that the meaning of a sentence is composed of, or is a function of, the meaning of its parts. There are again at least two ways to do this. Thus
c) Compositionality Fails for Identity Statements
If compositionality is false for identity statements, then even though 'Hesperus' and 'Phosphorus' have the same meaning, it does not follow that 'Hesperus = Hesperus' and 'Hesperus = Phosphorus' do as well.
The problem with this alternative is that we either have to explain what is special about identity statements such that compositionality should hold everywhere else in language but, somehow, be suspended when it comes to simple assertions of identity. If we cannot do that, we are stumped to explain how natural language can be learned at all, for we would have to learn each statement separately. Yet what seems to happen is that we learn 40 or 50 thousand words and rules for putting them together in such a way that we can make indefinitely many assertions and understand new ones without ever having heard them before.
d) Compositionality Skews Linguistic for Identity Statements
This was Frege's initial solution to the problem, which he gave in the Begriffsschrift. Compositionality has to be treated specially for identity statements because they are claims about language itself. Note that this is not (b). Frege is not suggesting that the relata flanking the identity are names. Rather, the identity itself asserts, of the names, that they co-designate. That is,
'Hesperus = Hesperus' asserts that 'Hesperus' and 'Hesperus' co-designate, while,
'Hesperus = Phosphorus' asserts that 'Hesperus and 'Phosphorus' co-designate.
Frege soon saw that this solution would be unsatisfactory. It gets the truth values right, at least, but the original statements are presumably as much about the world as any statement about the world would be. Why, that is, should the identity relation suddenly elevate us to making assertions about language when 'is between' does not?
Frege's final solution is to reject (1) and (A) with it. Thus,
e) Frege's Solution: The Descriptive Theory of Reference
The meaning of a term is not given by its reference. Rather, every term has both a sense and a reference, where the sense of the term determines its reference. Frege calls the sense of a term its "mode of presentation". Hence 'Hesperus = Hesperus' and 'Hesperus = Phosphorus' differ in cognitive value because the same object is (uninformatively) designated under the same mode of presentation in 'Hesperus = Hesperus', while the same object is (informatively) designated under different modes of presentation in 'Hesperus = Phosphorus'. We will need to say much more about these modes of presentation or senses to make sense of this solution, but think of it for now as the claim that the way a term refers to an object in virtue of what is true of the object as expressed in the sense of the term. Since what is true of the object is ordinarily taken to be (some part of) its description, Frege's solution is taken to be a Descriptive Theory of Reference.
Simply because it will be so important later, there is another solution which allows for (1) and (2) but denies (3). Thus,
f) Direct Reference Theories
On this view, the meaning of a term just is its reference and no more. Meaning is not mediated by description, or anything else, for that matter. On this view, our perception of a difference in cognitive value between 'Hesperus = Hesperus' and 'Hesperus = Phosphorus' is a common confusion on our part.