De Jure Coreference and Transitivity1 N.A. Pinillos 1. Introduction Theorists have noted an important difference between two ways of referring to the same thing. The pair of expression occurrences in <’Mark Twain’, ‘Mark Twain’> corefer de jure.2 In contrast, the pair in <’Mark Twain’, ‘Samuel Clemens’> corefer de facto. Following Kit Fine (2007), we can say that the de jure pair represent the referent as the same while the second one does not do so. There are roughly three ways of capturing this difference. One could say that de jure coreference between two expression occurrences happen because (a) the occurrences have identical meanings, (b) they have identical syntactic properties, or (c) they enter into a semantic relation not grounded in identity of meaning or syntax. In what follows, I give some reason to think that de jure coreference is not a transitive relation. As a consequence, we can rule out (a) and (b) just on these grounds alone (since identity is a transitive relation). (c) then looks promising. I argue that this gives further support for a relationist semantics along the lines of what Kit Fine has proposed. 2. Two Tests for De Jure Coreference The distinction between de jure and de facto coreference can be grasped at the intuitive level. But we will need sharper tests to get at the hard cases. I propose two here. One concerns knowledge of coreference and the other concerns embedding in ‘belief’ clauses.

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For helpful comments, I would like to thank Stew Cohen, Sam Cumming, Kit Fine, Michael McGlone, Robert May, Michael Nelson, Adam Sennet and conference participants at the 2008 Western APA meeting where parts of this paper were presented. 2 Here is a small sample of theorists who have addressed this issue whether at the level of thought or language (and often using different terminology). J. Campbell (1984), Robert Fiengo and Robert May (1994, 2006), Kit Fine (2007), K. Lawlor (2001), and Ken Taylor (2003).

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Consider the following:

(1) Mark Twain is Mark Twain. (2) The Prime Minister personally invited Mark Twain, but he didn’t show up. (3) The Prime Minister personally invited Mark Twain, but Mark Twain didn’t show up.

Focus on the most natural uses of these sentences such that the italicized occurrences are intended to be coreferential.3 These occurrences exhibit de jure coreference. To get at the heart of the matter, we need to compare (1-3) with their de facto counterparts:

(4) Mark Twain is Samuel Clemens. (5) The Prime Minister personally invited Mark Twain, but he [pointing at Mark Twain but not realizing that the person being pointed to is called ‘Mark Twain’] didn’t show up. (6) The Prime Minister personally invited Mark Twain, but Samuel Clemens didn’t show up. One important difference between (1-3) and (4-6) is that for the former, any hearer who grasps and fully understand those sentence uses must know that the relevant occurrences corefer.4 If they fail to know this, then they failed to fully understand that sentence use. For example, suppose that upon hearing the natural use of (2), one were to respond this

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Throughout this paper I will speak of uses of sentences. This seems like theory neutral way to proceed. We can intuitively recognize that a surface string has a certain use before we make a decision as to whether the use corresponds to a syntactic, semantic or pragmatic phenomenon. 4 Of course I am idealizing that the agent has the ‘reference’ concept or something related.

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way “wait a second, I don’t really know if ‘he’ and ‘Mark Twain’ designate the same man”. The natural reaction is to say that this person fails to understand the intended use of (2). Contrast the above with the de facto examples in (4-6). If we look at (4), for instance, it is possible to fully grasp this sentence use without knowing that the terms corefer. This might happen if one doesn’t believe the identity statement. While such a person might lack knowledge of literary history, he cannot be also blamed for misunderstanding the use of the sentence. Now one important caveat here is that, in (4) for example, a hearer might in fact have personal doubts about whether Mark Twain exists at all. Arguably, this is compatible with her fully grasping the sentence use. We should then say that what the person knows when there is de jure coreference is that there is coreference if there is reference at all. These ideas suggest the following test for de jure coreference:

KNOWLEDGE TEST: To test if coreferential occurrences A and B in discourse D exhibit de jure coreference, check to see if this is true: anyone who fully grasps D thereby knows that if A and B refer at all (A refers to something and B refers to something) then they refer to the same thing. If the answer is ‘yes’ then this is evidence that there is de jure coreference. If not, then this is evidence that there is de facto coreference.5

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I point out that Kit Fine (2007, pg. 40) uses a different test for de jure coreference: “[a pair is de jure coreferential if] anyone who raises the question whether reference was the same would thereby betray his lack of understanding of what you meant.” This test is different from mine since, it seems to me, that one could raise a question about some claim even if it is known.

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It should be clear from the previous remarks that we can use this test to establish that (13) exhibit de jure coreference, while (4-6) exhibit de facto coreference. I introduce another test. This has to do with embedding the uses (1-6) in belief ascriptions. We find that existential generalization on de jure coreferential occurrences is closed under belief. For example, consider (2) which now gives way to (2)’

(2)’ Sally believes that (the Prime Minister invited Mark Twain, but he didn’t show up).

If (2)’ is true, the following will also be true:

(7) Sally believes that the prime minister invited someone who didn’t show up.

(7) follows from (2)’ in part because ‘Mark Twain’ and ‘he’ in (2)’ are de jure coreferential. Contrast this with (5), which if embedded in a similar way (5)’, does not entail (7):

(5)’ Sally believes that the Prime Minister personally invited Mark Twain, but he [pointing at Mark Twain but not realizing that the person being pointed to is called ‘Mark Twain’] didn’t show up.

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Sally may have this belief and still not think that that the person invited was the person who failed to show up (she might think of them as distinct). The entailment does not hold then in part because coreference in the embedded construction is de facto and not de jure. We can use this test then to distinguish de jure from de facto coreference:

BELIEF EMBEDDING TEST: To test whether two coreferential occurrences A, B in a sentence use ‘S believes …A…B…’ are de jure coreferential, check to see whether it entails S believes ∃x(…x...x…). If it does, then this is evidence that A and B are de jure coreferential. If not, then this is evidence that they are de facto coreferential.

I emphasize that the test is just that, a test. It will not be able to cover some cases at the border. First, it is arguable that if Sally believes that Mark Twain is Samuel Clemens, she will believe anyways there is some x such that x is identical to x. But we don’t want to say that ‘Mark Twain’ and ‘Samuel Clemens’ exhibit de jure coreference. Second, if A and B concern fictional names, we might not want to say that the believer thinks the existential generalization. With some further refinement the test can be modified to cover these cases. However, since these issues will not arise in this context (I do not bring up fictional names, for example), I do not want to complicate the tests beyond what is needed. 3. Transitivity Consider the following on their most natural readings. (co-indexing indicates de jure coreference.)

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(8) We were debating whether to investigate both Hesperus1 and Phosphorus2; but when we got evidence of their true identity, we immediately sent probes there 1,2 . (9) As a matter of fact, my neighbor John1 is Professor Smith2, you will get to meet (the real) John Smith1,2 tonight. (10) Hesperus1 is Phosphorus2 after all, so Hesperus-slash-Phosphorus1,2 must be a very rich planet.

(11) Smith1 is wearing a costume, so Sally thinks he2 is someone other than Smith1.6 (12) He1,2 is often in drag, so yesterday Sally thought that Smith1 wasn’t Smith2.

Let us consider (8) first. Here, ‘Hesperus’ and ‘Phosphorus’ are de facto coreferential. Why? First, they are paradigm cases of de facto coreference. Second, using the Knowledge test, it is plausible that one can understand the use of (8) without having genuine knowledge that those occurrences corefer. Imagine someone hearing (8) but merely believing (not knowing) that the occurrences corefer (perhaps they are somewhat skeptical of the astronomical findings). We wouldn’t think that their not knowing (and merely believing) disqualifies them from understanding: such a hard line stance would make communication too hard to achieve. It might objected that the sentence use in (8) presupposes that ‘hesperus’ and ‘phosphorus’ corefer and as a consequence conversational participants must know that coreferential fact (contrary to what I have said here). This objection is off track. Even if 6

Soames (1994) uses a case like this to show that the anaphor in (11) cannot inherit a Fregean sense from the first occurrence of Smith. This is correct since if it did, then Sally couldn’t possibly have the thought (11) ascribes to her.

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there is such a presupposition, this doesn’t require that hearers know it. Presuppositions need not be known, even if the higher order fact that they are presuppositions is something that must be known by competent hearers. 7 Let us now consider ‘there’ in the use of (8). ‘there’ and ‘Hesperus’ are de jure coreferential because (using the knowledge test) one who understands the use of (8) must know that if ‘there’ refers at all it must corefer with ‘Hesperus’. Hearers who understand the use of (8) know that those occurrences can’t refer to different objects. Similarly, hearers who understand the use of (8) must also know that if ‘there’ refers at all, it must corefer with ‘Phosphorus’. Hearers must know that they can’t refer to different things. Hence, the Knowledge test yields that ‘there’ is de jure coreferential with both ‘Hesperus’ and ‘Phosphorus’. The considerations from the last two paragraphs yield the result that de jure coreference is not a transitive relation. In the use of (8), ‘Hesperus’ and ‘Phosphorus’ are each de jure coreferential with ‘there’. But since they are not de jure coreferential with each other, we get the desired result. The reader may check that similar remarks apply to (9) and (10). I turn to (11) and (12) which now concern the Belief Embedding test. Let us look at (12). The last two occurrences of ‘Smith’ must de facto corefer. If they were de jure coreferential, then it should follow that Sally thought that there is an x such that x is not x (an absurd belief). But we don’t suppose that the truth of (12) commits us to that result. Hence we conclude that the last two occurrences of ‘Smith’ are de facto coreferential.

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Presuppositions need not be known: A use of ‘The moon is flat too’ uttered at a meeting of the flat earth society presupposes that the earth is flat, but no one knows that the earth is flat.

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What about ‘He’ in (12)? Of course, here it is important that the pronoun is not accompanied by any deictic demonstration. Under this assumption, we can say that competent speakers must know that the pronoun corefers with each of the uses of ‘Smith’. If someone claimed that they didn’t know whether the pronoun coreferred with the first ‘Smith’ (for example), we would judge that they didn’t understand the intended use of (12). Using the tests, we just saw that the ‘Smith’ occurrences in (12) are de facto coreferential. However, we saw that the pronoun is de jure coreferential with each of the ‘Smith’ occurrences. This shows, again, that de jure coreference is not a transitive relation. The reader may check herself that similar remarks apply to (11). The cases that I have presented point to an unappreciated phenomenon in language. If I may speak loosely, it is possible for speakers to “link” two expression occurrences that are de facto coreferential to a third occurrence in such a way that the third occurrence is committed to be coreferential with the first two. Although the cases may be rare, they are robust. More importantly, these cases tell us a lot about the nature of de jure coreference.8 4. Consequences If de jure coreference is not transitive, then accounts which say that the relation is explained by identity of meaning or identity of syntactic form will be inadequate (because identity is transitive) . This will include Fregean inspired accounts including

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I want to issue a caveat. There might be various competing ways of further analyzing (8-12). It might be thought that the data I have provided should only be given after I have defended particular analyses of these constructions. I do not believe that this is the right way to proceed. Intuitions about sentence uses often count as evidence before any analysis is attempted. This is especially true here, where the data presented rely on simple intuitions about reference, knowledge and entailment.

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two-dimensional semantics. Similarly, syntactic accounts such as Fiengo and May’s (1994, 2006) will also fall short.9 Fine, Fiengo and May and others have made a case that if we take de jure coreference seriously as an independently motivated notion, then we can look with fresh eyes at some long standing problems of philosophy.10 Given that ‘hesperus’ and ‘phosphorus’ designate the same object, Gottlob Frege (1892) worried about finding a semantic difference between pairs such as the following:

(13) Hesperus is Hesperus

(14) Hesperus is Phosphorus

Frege’s point is that (13) and (14) differ in a priori status, cognitive significance and information content. But note also that (13) involves de jure coreference where (14) does not. Continuing with our thought, suppose that the important difference between these two is somehow derived from the de jure/de facto coreference distinction. If so, then given our remarks about intransitivity and de jure coreference, we should not expect that the important difference between the two statements is to be found by appealing to identity of meaning or syntax. As a consequence, Frege’s well-known solution to the problem he posed, which relies on the identity of meaning between the occurrences in (13) but not in (14), is ultimately unsatisfying. This should be a welcome result for direct reference theorists, who have thought that the difference between (13) and (14) cannot be 9

The criticism will also extend to accounts that rely on identity of variables or discourse referents to explain de jure coreference. 10 Fine ,Op. Cit. Fiengo and May, Op. Cit.

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found by positing a distinction in meaning between coreferring proper names anyways. In this regard, the arguments in this paper provide yet another reason to be dissatisfied with the Fregean framework. Finally, let us then turn to Kit Fine’s relationism.11 Kit Fine has argued that (13) is not synonymous with (14) but not in virtue of ‘hesperus’ and ‘phosphorus’ having different meanings. (He is a Millian so he thinks that they do not so differ). Instead, he believes that some meaning facts are irreducibly relational. The relation in question is “coordination”. Thus, in (13) the two ‘Hesperus’ occurrences are coordinated while the corresponding occurrences of ‘hesperus’ and ‘phosphorus’ in (14) are not coordinated. This counts as a difference in semantic properties between the statements and this can help explain the important differences Frege noted. The arguments given in this paper support Fine’s theory, or something close to it.12 Fine’s idea that some meaning facts must be understood in the first place as a relation, and not one that is derived from the identity of some objects, seems like the most plausible way to accommodate the failure of transitivity noted here. Ultimately, the case for or against transitivity will have to face all the evidence, so I do not claim that considerations I have raised in this short paper are conclusive. At the very least, I hope to have indicated how the question of transitivity raised here might be a useful one to ask for those interested in the representational capacity of natural languages. Works Cited Campbell, J. 1987. Functional Role and Truth Conditions: Is Sense Transparent. Aristotelian Society Supplementary Volume LXI 11

Fine, Op. Cit. Fine, Op. Cit. does not endorse failure of transitivity for a single discourse. He does, however, thinks transitivity fails for case of inter-discourse exchange. The arguments he gives there are not related to the ones I have provided here. 12

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Fiengo, R and May, R. 1994. Indices and Identity. MIT Press Fiengo, R. and May, R 2006. De Lingua Belief. MIT Press. Fine, K 2007. Semantic Relationism. Blackwell Publishing Frege, G. 1892. On Sense and Reference. Reprinted in P. Geach and M. Black, (eds.), Translations from the Philosophical Writings of Gottlob Frege. Oxford: Blackwell, 1960 Lawlor, K 2001. New Thoughts About Old Things: Cognitive Policies as the Ground of Singular Concepts. Garland Publishing. Soames, S. 1994. Attitudes and Anaphora. Philosophical Perspectives 8. Taylor. K. 2003. Reference and The Rational Mind. CSLI

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