By Murali Ramachandran
School of English & American Studies
University of Sussex
Falmer, Brighton BN1 9QN
This article appeared in: European Review of Philosophy Vol. I (Stanford: CSLI Publications, 1994) pp. 133-41. Some spelling errors have been corrected.
1. Informative Identity and the Metalinguistic View
Some sentences affirming identity, i.e. of the form ‘a is (identical with) b’, identity sentences let us call them, can be informative. But if, as intuition suggests, identity is a (binary) relation between objects, which holds between precisely every object and itself, then sentences of the form ‘a=a’ and ‘a=b’, if true, would seem to affirm precisely the same thing of precisely the same object. The question arises: how, then, can someone can find one identity sentence more informative than another?
Frege, tackling this question in ‘On Sense and Reference’ (OSR), is led to abandon his former view that identity sentences express (affirm) a relation between the referring expressions (terms) therein rather than between the referents of the terms. The objection is not trivial, for, on the face of it, this ‘metalinguistic’ view seems well able to tackle the question of informativeness. It advocates something like (MV):
(MV) ‘M is N’ means: ‘M’ and ‘N’ corefer.
(where ‘M’ and ‘N’ are to be replaced, inside as well as outside quotation marks, by referring expressions). Thus, sentences of the form ‘a=b’ and ‘a=a’ would express different things: the former would express something about two linguistic entities (‘a’ and ‘b’), whereas the latter would express something about just one (‘a’).
Frege argues, however, that, contrary to appearance, (MV) doesn’t really resolve the informativeness problem. My aim in this note is to clarify and defend Frege’s objection. For, what little discussion of the objection there is does not cast it in a good light. Leonard Linsky, for example, intimates that the objection cannot be entirely correct because:
Frege’s early solution to his puzzle [involving identity] is essentially the same as that given in ‘On Sense and Reference’ ... and the geometrical example from the Begriffsschrift is very like the one used in the later essay.
And Nathan Salmon even goes so far as to say that:
From the viewpoint of the theory of ‘Über Sinn und Bedeutung’ [OSR], of all of the objections that have been raised against the ‘Begriffsschrift’ analysis of identity statements, this one of Frege’s must surely be the weakest.
I hope to convince you that Frege’s objection has more going for it than these remarks would suggest. In particular, I shall argue that Linsky’s considerations do not undermine the force of Frege’s objection.
2. Frege’s Objection: An Initial Outline
Frege points out (OSR, pp. 56‑57) that whether two terms are used to refer to the same object or not is arbitrary. As he says, “Nobody can be forbidden to use any arbitrarily producible event or object as a sign for something.” Because of this, his objection continues, the sentence ‘a=b’ would “no longer refer to the subject matter, but only to its mode of designation; we would express no proper knowledge by its means”.
I take Frege’s point to be that, because nothing prevents us from using any expression we like to refer to, or as a sign for, whatever object we like, sentences expressing the coreference of terms reveal (convey) nothing about the objects the terms refer to. (Nothing, that is, save perhaps the fact that the objects are referred to as such‑and‑such.) Thus, metalinguistic readings of identity sentences ‘lose sight’ of the subject matter, viz. the things which are said to be identical. Identity sentences are read as expressing information about how we use terms, i.e. something about linguistic convention, but nothing about the world (or how objects are in the world). What is expressed by identity sentences according to MV, then, is not knowledge ‘proper’. But, as Frege presses (p.57), in many cases, expressing or conveying knowledge about the world—’extralinguistic’ knowledge we may call it—is precisely what we want to do and, presumably, do do when we utter identity sentences.
So, we have something like a reductio of MV here. But, more needs to be said.
3. Radical Versus Conservative Metalinguistic Explanations
To begin with, there is the distinction between what I shall call radical and conservative metalinguistic views of identity to take into account. The first view takes a metalinguistic stance on the relation of identity itself. In direct opposition to the standard picture of identity—as a relation which holds between every object and itself (and no other object pairs)—the radical view takes identity to be a relation which holds only between linguistic entities. Many commentators, including Frege himself (OSR, p. 56), talk as if Frege’s early metalinguistic view was radical in this sense. I don’t dispute this construal—in fact, as we shall see, Frege’s objection is most forceful if it is read as opposing the radical view—but there surely is a simpler and more plausible way of ‘going metalinguistic’ as it were.
Advocates of (MV), to wit, may take an identity sentence to express a proposition about the terms therein but they are not thereby committed to the view that identity itself is a relation which only holds between linguistic entities. Indeed, coreference is surely ‘parasitic’ on identity, in that the coreference relation holds between certain terms in virtue of the identity relation holding between the referents of those terms. If so, converts to (MV), while committed to maintaining that:
‘a=b’ is true if, and only if, the referent of ‘a’ is identical with the referent of ‘b’.
may do so without revising their original view of identity. Their ‘conversion’ would consist, rather, simply in their revision of what identity sentences express.
Now, the point is, the explanation of informative identity sentences given at the beginning of the paper does not require the radical turn; it is available, at much less cost, to such ‘conservative’ metalinguistic accounts too. So, if Frege is to properly motivate his theory of sense, he must reject both kinds of metalinguistic account. We will see that the objection he gives constitutes a knock-down refutation of radical accounts while providing a fairly persuasive reason for rejecting conservative accounts into the bargain.
4. Frege’s Objection: The Regress-Argument
Here is an interim expansion on Frege’s objection adapted from David Wiggins’ regress-argument. On the metalinguistic approach, the identity sentence
(1) The U.S. President in 1994 is Bill Clinton.
for instance, expresses—and owes its informativeness to—the proposition that:
(1a) ‘The U.S. President in 1994’ and ‘Bill Clinton’ corefer.
As we have already noted, however, coreference is parasitic on identity. (1a) is, to all intents and purposes, strictly (logically and, more importantly, ‘informationally’) equivalent to the proposition that:
(1b) ‘The U.S. President in 1994’ refers to the same individual as ‘Bill Clinton’.
which in turn is strictly equivalent to the proposition that:
(1c) The referent of ‘The U.S. President in 1994’ is (identical with) the referent of ‘Bill Clinton’.
Now, the significant point about the radical metalinguistic approach is that it takes identity to be a relation between, and only between, linguistic terms. Hence, it would take the proposition (1c) to affirm, and owe its informativeness to, the proposition that:
(1d) “The referent of ‘The U.S. President in 1994’” and “The referent of ‘Bill Clinton’” corefer.
We thus embark on an infinite regress, and the ultimate explanation of informativeness is forever postponed. Moreover—and this is the central Fregean point—since informativeness is in any case only explained by a series of propositions concerning the coreference of linguistic terms, we never ‘get at’ the objects in the world themselves. So the radical metalinguistic view just cannot account for the proper, extralinguistic, knowledge conveyed by identity sentences.
I think this regress problem lies at the heart of Frege’s objection, but still a bit more needs to be said. For, as Linsky observes, Frege’s Begriffsschrift explanation of informative identity statements is not the simple one I have sketched.
5. Linsky’s Beef
Linsky, it has been noted, considers Frege’s later (OSR) resolution of the informativeness problem to be essentially the same as his earlier (BEG) solution. The charge is not unfounded. After proposing his metalinguistic account or treatment of identity sentences in Begriffsschrift (p. 10), Frege goes on to explain why we sometimes need different terms for the one and the same reference. In a nutshell, it is because one and the same object can be fully ‘determined’ (thought of?) in different ways. For example, the terms Hillary Clinton’s husband and The U.S. President in 1994 each pick out Bill Clinton, but they do so in different ways. Thus we may talk of a term having a way of determining its reference associated with it. When different terms with one and the same referent are associated with different ways of determining that referent, Frege says “the judgement as to equality of content is, in Kant’s sense, synthetic” (BEG, p. 12).
How does this compare with Frege’s later (OSR) resolution of the informativeness problem? To be sure, there are terminological differences. Later-Frege talks of there being a sense connected with each term, in addition to its referent, and the sense is meant to contain a mode of presentation of that referent. An identity sentence will be informative, Frege now maintains, only if the terms therein have (or express) different senses. But a mode of presentation is nothing more than a way of determining the term’s reference. So, as far as the underlying source of the difference in informativeness is concerned, Frege’s later solution is essentially the same as his earlier solution.
Furthermore, it now looks as if the regress problem does not arise. For the Begriffsschrift explanation, on the present reading, doesn’t locate the (extralinguistic) informativeness of (1) in the expressed proposition, (1a), but in the corresponding proposition one associates with (1a). In that case, (1)’s informativeness—and, for that matter, (1a)’s informativeness—is not underpinned by the informativeness of the likes of (1c). Thus, the regress would appear to be blocked at the first stage.
It should perhaps be noted here that although Linsky disputes Frege’s claim that the metalinguistic approach does not resolve the informativeness problem, he does think that Frege’s remarks suggest another reason for rejecting that approach. Namely, its failure to meet, what Linsky calls, the “Church-Langford translation test”—an adequacy test of sorts for theories of meaning. Now, while I suspect that Frege might well regard failure to meet this test as grounds for rejecting a semantic theory, I do not intend to explore the line of reasoning. For, it surely requires the widest stretch of imagination to suppose that Frege was referring to this test when making the remarks Linsky cites (Linsky, p. 7). And, in any case, I think there is still life in Frege’s original objection.
It turns out that Frege’s Begriffsschrift resolution of the informativeness problem does not really undermine his later objection as has been claimed. There is a lacuna in the line of reasoning we have just considered.
6. Frege’s Objection: The Regress Argument Pressed Home
The fact is, appeal to ways-of-determining-reference (or modes of presentation, to use the later terminology), does not circumvent the regress problem as it initially appears. This is easy to see when we inquire into the nature of the propositions which are meant to be properly informative and which we supposedly associate with the uninformative propositions actually expressed by identity sentences. Sticking with our previous example, consider sentence
(1) The U.S. President in 1994 is Bill Clinton.
and the expressed proposition
(1a) ‘The U.S. President in 1994’ and ‘Bill Clinton’ corefer.
What is the associated informative proposition meant to be? Presumably, it has to be to the effect that the mode of presentation associated with ‘The U.S. President in 1994’ and that associated with ‘Bill Clinton’ pick out (or are satisfied by) one and the same individual. But this is just to affirm that the individual picked out by one mode of presentation is identical with the individual picked out by the other. Hence, on the radical metalinguistic view, the informativeness of the associated proposition resides in a metalinguistic proposition affirming the coreference of certain linguistic entities.
We are off on a regress again—albeit a slightly different one—and informativeness is again accounted for by appeal to a series of propositions, none of which, in Frege’s view, affirm proper, extralinguistic information.
So, we have a reductio of radical metalinguistic accounts: it is impossible for them to accommodate and account for genuinely informative identity statements.
7. Conservative Metalinguistic Accounts
Finally, there remains the issue of conservative metalinguistic accounts of identity. How do they fare? Like radical accounts, they make a claim about what identity sentences express: both kinds of account take the literal content of (1) to be given by (1a). So, Frege’s Begriffsschrift explanation of informativeness is still applicable. That is, the genuine informativeness of identity sentences is explained by appeal to propositions one associates with the expressed (genuinely uninformative) metalinguistic propositions. And these associated propositions are determined by the corresponding modes of presentation one associates with the referring expressions mentioned in the expressed propositions.
Now, the problem as I see it is that these associated propositions turn out to be entirely inexpressible. The point is worth spelling out since, if this is indeed the case, it tells against all metalinguistic accounts. Consider, for a change, the identity sentence
(2) Superman is Clark Kent.
and let us suppose, for the sake of argument, that the sense of the name ‘Superman’ (i.e. the mode of presentation one associates with it) is: the man from Krypton and that the sense of ‘Clark Kent’ is: the be-spectacled suitor of Lois Lane. On metalinguistic accounts, (2) actually expresses the proposition that:
(2a) ‘Superman’ and ‘Clark Kent’ corefer.
but it is informative in virtue of our associating the proposition that:
(2b) The man from Krypton is the be-spectacled suitor of Lois Lane.
with (2a). My claim is that this, informative, proposition is simply inexpressible on the present theory: i.e. that no sentence could have the proposition as its literal content. For example, the likely candidate sentence
(3) The man from Krypton is the be-spectacled suitor of Lois Lane.
is no good, since this just comes out expressing the proposition that:
(3a) ‘The man from Krypton’ and ‘the be-spectacled suitor of Lois Lane’ corefer.
I cannot see how any sentence could express the proposition (2b). The same point would apply to any informative identity sentence: the proposition in virtue of which it is informative, the proper knowledge it conveys, would simply be inexpressible.
Is this a good reason for rejecting metalinguistic accounts, however? It seems that it is only so on the assumption that every proposition can be expressed. But Frege himself would surely reject this expressibility principle. For Fregean thoughts, what I am calling propositions, exist in an independent realm and are not ontologically dependent on any thinkers. They are there to be grasped, but some, presumably, may never be, and may not, in any case, be communicable with the language at hand.
This is all well and good, but I think even those who reject the expressibility principle have grounds for concern. Even Frege, it seems to me, would be concerned that there could be determinate propositions which can be communicated, and therefore grasped, but which cannot be expressed. After all, given Frege’s view that “Nobody can be forbidden to use any arbitrarily producible event or object as a sign for something” (OSR, p. 57), he is likely to maintain that it is entirely open to us to use phrases to express any propositions we grasp. Now, given that even on metalinguistic accounts the proper knowledge conveyed by an identity sentence is a proposition like (2b), and that identity sentences are generally uttered with the intention of communicating such propositions, it would seem most reasonable to conclude that such propositions are the literal contents of identity sentences. In any case, a theory which allows such propositions to be expressed is surely preferable to any theory which makes them inexpressible in principle.
As I have implied, this objection against conservative metalinguistic accounts is by no means a refutation of such accounts, but it is I think quite tenable.
Frege’s objection to his former, metalinguistic, account of identity does have more going for it than is generally regarded, certainly more than is suggested by the quotations from Linsky and Salmon.
 Oblique Contexts, Chicago: University of Chicago Press, 1983, p. 6. This view is also held by Charles E. Caton, “The Idea of Sameness Challenges Reflection”, in M. Schirn (ed.), Studies on Frege II: Logic and the Philosophy of Language, Stuttgart: Bad Cannstatt, 1976, pp.167-80. Further references to these authors apply to these works.
 Although the sentences I have used to convey the propositions (1a)-(1c) are different, I would say that we have one and the same proposition here. But no matter: the following objection hinges only on the informational equivalence of these propositions.
 Metaphorical uses of sentences seem to belie this view. For example, it seems unlikely that what is conveyed by an utterance like “Juliet is the sun” can be expressed with a conjunction of literally true sentences. But it is not so implausible to maintain that any determinate proposition which is conveyed (grasped) must be expressible.