No Identity without an Entity Luke Manning Abstract Peter Geach’s puzzle of intentional identity is to explain how the claim ‘Hob thinks a witch has blighted Bob’s mare, and Nob wonders whether she (the same witch) killed Cob’s sow’ is compatible with there being no such witch. I clarify the puzzle and reduce it to the familiar problem of negative existentials. That problem is a paradox, of representations that seem to include denials of commitment (implicitly, here), to carry commitment to what they deny commitment to, and to be true. The best proposed solutions can be understood through this paradox; I evaluate them, and defend a new solution. 1 Introduction Peter Geach, in his paper “Intentional Identity” (1967), presents a puzzle concerning this sentence: G Hob thinks a witch has blighted Bob’s mare, and Nob wonders whether she (the same witch) killed Cob’s sow. (1967: 147) He describes the following situation, which I will call the Hob-Nob case. Someone, call her Rita, visits Hob and Nob in Gotham, a village stricken by “witch mania.” Hob tells Rita, “The witch has blighted Bob’s mare,” and Nob tells her, “Maybe the witch killed Cob’s sow.” There is no person whom Hob and Nob suspect is a witch. Hob is not aware of Cob’s sow, nor Nob of Bob’s mare. And there is no definite description, such as ‘the Gotham witch’, which they both think uniquely applies to an alleged witch. Rita does not believe in witches, but she reports their intentional states with G (147–48, 150, 152–53). The puzzle is to make sense of her report, given that the objects of Hob’s and Nob’s intentional states cannot be the same if there are no such objects—i.e., given that there is no identity without an entity. Forty-five years later, Geach’s puzzle still confounds philosophers and linguists. Their responses are as varied as remedies for hiccups, and often as odd. This is largely because there is no consensus what the puzzle is even about. My main goal is to clarify it, and ultimately to reduce it to another problem. In explaining that reduction I also offer a solution. But solving the problem is only a secondary goal—theorists who disagree with details of my solution can still accept the reduction, which clarifies much about this exceptionally hard problem. I begin by clarifying the puzzle. In §2 I explain that it combines the problem of intentional identity with problems of anaphora and mythical terms. But Geach’s aim is to illustrate the first of these, so the many commentators who focus on the latter two miss the point. In §3 I explain the problem of intentional identity in relation to two simpler problems of intentionality that Geach introduces, those of quasirelationality and quasinames. Having clarified the puzzle, in §4 I reduce it (and more generally Geach’s problems of intentionality) to instances of the problem of negative existentials. I present the latter as a paradox, the result of three jointly inconsistent but independently plausible claims. To illustrate this reduction, I consider the three possible kinds of solutions to the paradox, each of which rejects one of the three claims. In doing so, I criticize two popular kinds of solutions: (1) those that seek a reading of G that does not carry commitment to a witch whom Hob and Nob think and wonder about, and (2) those that say Rita would not really deny that there is such a thing. And finally, I defend a solution of the third kind, on which Rita’s

report about Hob and Nob is not literally true, but still pragmatically appropriate. 2 Puzzle pieces Geach’s example G combines three puzzling phenomena. The first is intentional identity, which I discuss in §3. The second, which many of his commentators focus on, is a problematic kind of anaphora. Two kinds of anaphora are unproblematic, or at least have standard analyses. First, consider: 1 A witch cursed the day she was born. 1 is ambiguous, depending on whether the occurrence of ‘she’ is anaphoric on the occurrence of ‘a witch’. Assume that it is; in other words, assume it has this occurrence of ‘a witch’ for its anaphoric antecedent. Then on a common analysis, it is a variable, and its antecedent is a quantifier phrase that binds it. That is captured in the following classical formalization: 1 ∃x(x is a witch ˄ x cursed the day she was born) Second, many anaphoric pronoun-occurrences seem to stand in for further occurrences of their antecedents, or closely related phrases. Geach calls these pronouns of laziness (1967: 150). In the sentence ‘I curse Willow and the day she was born’, the occurrence of ‘she’ is anaphoric on the occurrence of ‘Willow’, and in effect stands in for a second occurrence of that name. But some cases do not fit either of these models. Consider one of Geach’s famous “donkey sentences”: 2 Any man who owns a donkey beats it. (1980: 143) The occurrence of ‘it’ is anaphoric on the occurrence of ‘a donkey’, but does not stand in for a repetition of it—2 is not equivalent to ‘Any man who owns a donkey beats a donkey’. Nor is the occurrence of ‘it’ bound by its antecedent. E.g., in the formalization: 2′ ∀x([x is a man ˄ ∃y(y is a donkey ˄ x owns y)] → x beats y), the last occurrence of ‘y’ is not bound by the occurrence of ‘∃y’. In these problematic cases a pronoun-occurrence functions in some ways like a bound variable-occurrence, but it is outside its antecedent’s scope, making mischief. I call such pronoun-occurrences, and the anaphora involving them, rogue.1 In G, the occurrence of ‘she’ has for its antecedent the occurrence of ‘a witch’. But it seems to lie outside its antecedent’s scope; that scope seems confined to the first conjunct, and maybe within the scope of the occurrence of ‘thinks’ (Geach, 1967: 147, 150). Thus it seems to be rogue. (Likewise, the phrase ‘the same witch’—Geach’s “gloss” on the occurrence of ‘she’ (150)—occurs in G as a pronominal phrase anaphoric on the occurrence of ‘a witch’, and it too seems to be rogue.) Rogue anaphora has been studied extensively, but there is still no consensus on its proper analysis. In any case, it is not the problem Geach means his puzzle to illustrate. Rather, he employs it only to help illustrate intentional identity. Compare one of his other illustrations: 3 A man dreams of the same girl night after night. (1969: 161) (In the situation Geach has in mind, there is no girl whom the man dreams of.) 3 can report multiple intentional states without using anaphora because it has just one occurrence of an intentional operator (‘dreams’). So it might seem to report a single intentional state. In contrast, G unmistakably reports distinct intentional states, and so it better illustrates the problem of intentional identity. Unfortunately it also leads many commentators to think anaphora is essential to the problem of intentional identity.2 They miss Geach’s point. G also involves a third puzzling phenomenon: mythical terms. The term ‘witch’, like the

terms ‘Isis’, ‘unicorn’, and ‘phlogiston’, originated in myth—i.e., widespread false belief. Such terms may raise semantic problems like those of fictional terms such as ‘Spock’, ‘hobbit’, and ‘flubber’. For example, Saul Kripke says, “statements about unicorns, like statements about Sherlock Holmes,…don’t really express propositions,” because the term ‘unicorn’ fails to designate anything (2011b: 67–71; cf. 1980: 156–58). The problems of mythical terms are not well understood—especially those of mythical general terms, as opposed to singular terms. But in any case, they are not what Geach means his puzzle to illustrate.3 He uses ‘witch’ simply because we believe there are no witches, and therefore we see the problem more quickly than we would with 3. He could just as well have used a nonmythical term with an empty extension, such as ‘dinosaur’ (see example 13, below). So although G contains a mythical term, to focus on that is to miss Geach’s point. We must focus instead on the problem of intentional identity. 3 Intentional identity So what is the problem of intentional identity? Contrary to many commentators, it is not Geach’s puzzle about the sentence G; that is only an instance. Indeed, in his four papers discussing intentional identity (1964, 1967, 1969, and 1976), he gives more than a dozen other cases, many of them quite different from G. (I discuss some below.) What they have in common is that they report groups of intentional states that are linked in a certain way. That is a complex phenomenon, so let’s start with simpler issues. First, what does Geach mean by the term ‘intentional’? Like other medieval technical terms in philosophy such as ‘de dicto’ and ‘a priori’, ‘intentional’ is used for at least a half-dozen things, often without noting or fully understanding which one(s). (The spelling ‘intensional’— with an ‘s’—is also used, sometimes in distinction with ‘intentional’. But the distinctions vary, and Geach uses only ‘intentional’, so I ignore ‘intensional’ here.) Geach is aware of this muddle, but he is not sure which alleged features of intentionality are relevant to his problems. So he focuses on examples, such as the operators ‘thinks’, ‘wonders whether’, and ‘admires’. Nearly all of his examples are representational operators: they contribute to reports of representational states such as thinkings, wonderings, and admirations.4 So I assume that Geach’s problems of intentionality concern representational operators. (And note well: I do not assume anything else about intentionality. Geach assumes that intentional operators are nonextensional—i.e., that for an intentional operator Ψ, the extension of ˹Ψα˺ (e.g., its truth value or referent) is not a function of α’s extension.5 In that case, e.g., ˹I admire α˺ and ˹I admire β˺ might differ in extension even though α and β do not. He also assumes that the extension of ˹Ψα˺ is a function of α’s Fregean sense, or more generally some semantic feature of α besides its extension.6 These two assumptions, besides being doubtful,7 are not necessary for stating Geach’s problems of intentionality.) While the problem of intentional identity concerns reports of multiple, linked intentional states, Geach sees related problems in reports of single intentional states; so let’s start with them. There are two classes of single-state intentional reports that he finds problematic. The first, he says, have an indefinite description or existential quantifier phrase such as ‘a witch’ or ‘someone’ following an intentional operator. W.V.O. Quine’s sentence 4 is an example: 4 Ralph believes someone is a spy.8 (1966: 184) According to Geach, 4 is ambiguous. For one thing, it is ambiguous in the familiar ways identified by Bertrand Russell and by Quine. As we know from Russell (1905), it has a scope ambiguity, with these two readings:

4A Someone is such that Ralph believes that she or he is a spy. 4B Ralph believes there is someone such that she or he is a spy. Call 4A the wide scope reading of 4, since ‘someone’ takes wider scope than ‘believes’, and likewise call 4B the narrow scope reading. And as we know from Quine, 4 has a relational/notional ambiguity. In this case, the relational reading is 4A and the notional is 4B, but Quine’s ambiguity is not simply a matter of scope. I will digress for a moment to explain it. A scope reading of a sentence s, where s is otherwise disambiguated, determines for each operator-occurrence o in s, which other operatoroccurrences in s (if any) are part of o’s argument(s). A sentence (otherwise disambiguated) is scope ambiguous if and only if it has multiple scope readings. 4 is scope ambiguous because two operators occur in it, namely the intentional operator ‘believes’ and the quantifier phrase ‘someone’, each of which can belong to an argument of the other. But consider: 5 I want a sloop. Suppose we read the occurrence of ‘a sloop’ as an existential quantifier phrase: ‘A sloop (is such that)’. Then its argument can contain the occurrence of ‘want’—‘A sloop is such that I want it’. But the converse is impossible; ‘want’ takes only noun phrases as arguments (i.e., it is a predicate). Thus 5 is not scope ambiguous. What then are 5’s relational and notional readings? Quine states them, “with some violence to both logic and grammar,” as the wide and narrow scope readings (respectively) of ‘I wish that I have a sloop’ (184); with less violence, he could have used ‘I want that I have a sloop’. Wanting that one has is a plausible substitute for wanting, but it is doubtful that corresponding substitutions are available for every intentional predicate; e.g., there is no propositional attitude corresponding to worshipping or admiring (cf. David Kaplan, 1986: 266–68). Thus Quine gives no plausible analysis of the notional reading. But he does successfully distinguish the kinds of intentional states that the readings report. He says the notional reading reports that “what I seek is mere relief from slooplessness” (1966: 183). In other words, though many sloops might satisfy my wanting, none of them are sloops that I want—I just want a sloop. Thus my wanting is not particular, i.e., it does not purport to represent some particular thing; rather, it is general, i.e., it purports to generalize about things. In terms of this distinction, Quine should say of an intentional report like 5 (i.e., one with an indefinite description or existential quantifier phrase following an intentional operator) that its relational reading says that there is a particular-intentional-state (i.e., it generalizes about such states), while its notional reading reports a certain general representation. By this definition, 4, 5, and many other reports are indeed ambiguous between relational and notional readings. Geach says there is one more kind of reading, besides those that Russell and Quine identify. It is best illustrated in cases lacking Russell’s and Quine’s ambiguities. Suppose Hannibal belongs to the Ba‘alite religion, common in ancient Carthage. Then it is natural to report: 6 Hannibal worships a god. 6 has a wide-scope/relational reading: 6A There is a god whom Hannibal worships. But since ‘worship’, like ‘want’, is an intentional predicate, if we read ‘a god’ as an existential quantifier phrase, then 6 has no narrow scope reading. Nor does it have a notional reading: unlike wanting, worshipping can only be particular; one cannot worship a god, but no god in particular.9 So 6 lacks the two familiar noncommittal readings, i.e., those that do not entail there is anything that Hannibal worships. But since even a nonbeliever would say 6, Geach says there

must be a third kind of noncommittal reading, reporting a particular-intentional-state.10 Call this alleged reading quasirelational. I doubt there is such a reading (more on that later). But we still might say 6 while denying 6A, and it is not obvious how to make sense of that. So whether or not there is a quasirelational reading, there is a real problem with cases like 6; call it the problem of quasirelationality. There is a second class of single-state intentional reports that Geach finds problematic, with intentional operators followed by names, rather than by indefinite descriptions or quantifier phrases. Consider: 7 Hannibal worships Ba‘al. 7 has no Russellian scope ambiguity, since names are not operators and thus have no scope (Geach, 1963: 139, 144). And it lacks a notional reading, for the same reason 6 does: worshipping is particular. It has an obviously committal reading: 7A Ba‘al is such that Hannibal worships him. But even those who do not believe in Ba‘al would say 7. So Geach says it has a noncommittal reading, on which the name ‘Ba‘al’ is used not “as a name,” but in a special, noncommittal way, as what he calls a quasiname. He says quasinames are “introduced only in object position after intentional verbs; the use of them as logical subjects of predication [i.e., in other positions] neither is explained, nor could be justified, by this introduction” (1969: 162). So he thinks 7 is ambiguous between committal and noncommittal readings, depending on whether its occurrence of ‘Ba‘al’ is used as a real name or a quasiname. I doubt ‘Ba‘al’ and 7 are ambiguous in this way. But still, we might say 7 while denying 7A—or say ‘Hannibal worships the god Ba‘al’ while denying 6A—and it is not obvious how to make sense of that. So whether or not there are quasinames, there is a real problem with cases like 7; call it the problem of quasinames. Finally, we can return to the problem of intentional identity. It arises in a class of reports of multiple, linked intentional states. Geach’s first example is: 8 Smith and Brown admire the same poet. (1964: 137–38) In the situation he has in mind—call it the Smith-Brown case—both Smith and Brown have fallen for the Australian literary hoax according to which there was a poet named Ern Malley (1964: 137; 1969: 164–65). 8 has a relational-like reading which Geach calls the real identity reading: 8A There is a poet whom both Smith and Brown admire. But in the Smith-Brown case, we might say 8 even while denying 8A, so Geach thinks 8 has a noncommittal reading. It is not a narrow scope reading: if we read the occurrence of ‘the same poet’ as a quantifier phrase, it cannot be an argument of the intentional predicate ‘admire’. (If it is any quantifier phrase, it is like ‘a certain poet’: ‘a poet’ plus a wide-scope indicator.) Nor is the alleged reading notional, because admiration (like worshipping) is particular. It would be a third kind of noncommittal reading, reporting multiple intentional states that are particular, with some link between them, like the link reported in the real identity reading. Geach calls this alleged reading the intentional identity reading.11 8 is quite different from our main example: G Hob thinks a witch has blighted Bob’s mare, and Nob wonders whether she (the same witch) killed Cob’s sow. For one thing, 8 has only one occurrence of an intentional operator, while G has occurrences of two different intentional operators. And Geach gives examples of many other forms, such as:

3 A man dreams of the same girl night after night. Unlike G, 3 does not name the subject(s) of the reported intentional states, and it reports states of the same subject12 and of the same type—indeed, it is a generalization about indefinitely many states of the same subject and type. And some examples have names following intentional operators: 9 He dreams of Petronella every night. (1969: 161) Geach says this is ambiguous: if ‘Petronella’ is used as a real name, 9 expresses real identity; if a quasiname, intentional identity. Likewise, if the inhabitants of Hob and Nob’s town of Gotham use the name ‘Maggoty Meg’ for the supposed local witch (cf. Geach, 1976: 314), the reporter Rita could say: 10 Hob thinks Maggoty Meg has blighted Bob’s mare, and Nob wonders whether Maggoty Meg killed Cob’s sow. (cf. Nathan Salmon, 2002: 110–11, 117) Like 9, Geach would say 10 has a quasiname reading, expressing intentional identity. So in general, the real identity reading of a report of multiple intentional states either says that those states share objects, or names some particular objects that the states all represent. The alleged intentional identity reading would be the noncommittal analog of the real identity reading. As with alleged quasinames and the alleged quasirelational reading, I doubt there is an intentional identity reading. But we still might say G while denying its real identity reading: GA There is a witch such that Hob thinks she has blighted Bob’s mare and Nob wonders whether she killed Cob’s sow. (Cf. Geach, 1967: 148) Likewise, we might say 8 while denying 8A, or say 3, 9, or 10 while denying their respective real identity readings. And it is not obvious how to make sense of this. So whether or not there is an intentional identity reading, there is a real problem with cases like G, 3, and 8–10; call it the problem of intentional identity. Most commentators do not use this definition of intentional identity, but instead define it in terms of things such as G, anaphora, notional reports, intersubjective reports, or Hob’s alleged thought that exactly one witch has blighted Bob’s mare.13 That is a mistake. Now that I have is correctly and clearly defined the problem, I can reduce it to another, more familiar problem. 4 Reduction Geach seeks a noncommittal reading of G, but as I said, I doubt there is such a reading. For one thing, the noncommittal readings proposed in the literature (some of which I discuss in §5.1) are implausible—even the few that respect Geach’s stipulations about the puzzle and confront the problem of intentional identity as I just defined it. Still, many theorists simply take it as data that there is a noncommittal reading of G (and of other intentional constructions); they do not see these failures as a sign that G is committal. But as I will now argue, we cannot fairly assume, without argument, that G has a noncommittal reading. Recall that we are meant to think of G not merely on its own, but in conjunction with a corresponding denial of commitment, the negation of its real identity reading: D There is no witch such that Hob thinks she has blighted Bob’s mare and Nob wonders whether she killed Cob’s sow. Rather than supposing that Rita asserts G while we implicitly keep D in mind, let’s have her explicitly assert their conjunction, which I call GD. Where Geach seeks a noncommittal reading

of G, we could just as well seek a noncommittal (and thus consistent) reading of GD. But once we make D explicit, we can see that this puzzle is related to the problem of negative existentials. Indeed, in my view it is simply an instance of that problem—though an instance of a type rarely recognized. Before I explain that, I will discuss a more standard example of the problem of negative existentials: 11 Ba‘al does not exist. Cases like 11 are notoriously problematic. But the source of the problem is disputed. I do not assume that the problem is that the name ‘Ba‘al’ fails to refer, or that predicating existence (or nonexistence) is itself problematic.14 Instead, I will offer a new characterization.15 First, a background point. There is a problem in describing denials of commitment without entailing that they are false. For example, if I describe 11 as denying commitment to Ba‘al, I presuppose there is such a thing as Ba‘al, in which case 11 is false. But instead of using the name ‘Ba‘al’, I can mention it. (Note that I must do so in a way that does not entail that 11 mentions it, rather than using it.) So I can describe 11 as a denial of commitment that specifies what is denied by using the name ‘Ba‘al’. So in general, when describing denials of commitment, I will not use their way of specifying what they deny, but rather mention or describe it. Now the problem. 11, or more generally a representation α, seems (to a certain subject or subjects) to satisfy each of the following claims: Denialα: α is or includes a denial of commitment, using specification s of what it denies. Committalα: α carries commitment to there being something that fits specification s. Trueα: α is true. For example, 11 seems (to us) to be true; in contrast, ‘Barack Obama does not exist’ is (to us) obviously false, and unproblematic. (But it will seem true, and be paradoxical, to certain conspiracy theorists.) Second, 11 seems to be a denial of commitment, unlike some other sentences with ‘Ba‘al’, such as ‘Hannibal worships Ba‘al’ or ‘Ba‘al is mighty’. On the relevant sort of use, 11 does not merely mean that a certain sort of thing does not exist now (compare ‘Cleopatra does not exist’ or ‘Dinosaurs do not exist’), but that this sort of thing is not part of our ontology at all. Third, 11 seems to carry commitment to this sort of thing, namely to a referent of the name ‘Ba‘al’. It seems to do so by using the name, rather than mentioning it. (In contrast, ‘There is no god named ‘Ba‘al’’ obviously carries no such commitment, and is not problematic.) So 11 seems to have these three jointly inconsistent features. Thus the so-called problem of negative existentials is a paradox, which we might more aptly call the paradox of true, committal denials of commitment. Strictly speaking, it is a form of paradox. There is a separate paradox of that form for each representation that (to some subject(s)) seems to satisfy the three claims. So, for example, there is a paradox of 11. We can try to solve it by rejecting True11, Denial11, or Committal11, but since each of these claims is independently plausible, we must motivate that rejection. Many theorists would reject Committal11. But we cannot merely reject it out of hand, without argument, because it is plausible. Why is it plausible? First, on a naive and plausible semantics, any use of a proper name carries commitment to that name’s referent. (Alternative semantics have been proposed, but in this era of direct reference theory, none of them have found much popularity.) And second, we can sensibly follow 11 with more talk “about Ba‘al.” For example, I can say, “Ba‘al does not exist. He is just a mythical god. But he is a fairly interesting figure. Let me tell you about him….” Here, the occurrences of ‘he’ and ‘him’ seem to be anaphoric on

‘Ba‘al’, and I seem to be describing Ba‘al himself.16 Thus Committal11 at least seems true. So do Denial11 and True11, which makes 11 genuinely paradoxical. So why think GD is paradoxical in this way? Because it seems to satisfy each of the three jointly inconsistent claims. First, GD seems to include a denial of commitment, namely D. To be precise, let’s abbreviate the noun phrase ‘thing such that Hob thinks it has blighted Bob’s mare and Nob wonders whether it killed Cob’s sow’ as ‘HN’; and let ‘HN-witch’ abbreviate ‘HN that is a witch’. D seems to deny commitment to a HN-witch.17 Second, GD (through G) seems also to carry commitment to a HN-witch (more on that in a moment). And third, GD seems to be true—or at least, Geach assumes it is true in the Hob-Nob case. Why does GD seem to carry commitment to a HN-witch? First, on a naive and plausible semantics, G simply has its real identity reading, which carries commitment to a HN-witch. And since GD simply conjoins G with D (and since ontological commitment cannot decrease by conjunction), GD carries that same commitment. And second, when Rita asserts GD, it is sensible to ask ‘What witch do they have in mind?’, and sensible for her to reply ‘Maggoty Meg’. So even if G and GD do not really carry commitment to a HN-witch, as Geach and others assume, we cannot simply take that for granted; we must motivate a rejection of CommittalGD. So I have restated Geach’s puzzle in terms of the paradox of GD: that each of TrueGD, DenialGD, and CommittalGD seems true, but together they are inconsistent. To solve that paradox, we must reject one of those three claims; and since each claim is independently plausible, we must motivate that rejection. In these terms, Geach rejects CommittalGD. But for the most part, he merely rejects it out of hand; he does not argue that G (on a relevant reading) does not carry commitment to a HN-witch, but merely assumes this. On the other hand, he does try to specify G’s alleged noncommittal reading, so we can treat that as an argument that G has a noncommittal semantics. And it is clear now that this is not our only option. Instead of rejecting CommittalGD, we might reject TrueGD or DenialGD. Indeed, some theorists have done so, and those who reject CommittalGD can no longer reject such solutions out of hand. I evaluate our three options in §5. Beyond the puzzle about G, Geach’s three problems of quasirelationality, quasinames, and intentional identity are all paradoxical in this way. In all three cases, the denial of commitment is typically left implicit, but can be made explicit. For example, instead of 6, we might consider 6˄¬6A, i.e. ‘Hannibal worships a god, but there is no god whom Hannibal worships’. And instead of 7, we might consider 7˄11, i.e. ‘Hannibal worships Ba‘al, but Ba‘al does not exist’. All the cases seem (to a certain subject or subjects) (1) to deny commitment to a certain sort of thing, (2) to carry commitment to that same sort of thing—specifically through reports of intentional states—and (3) to be true. And though it is philosophical tradition to think that all intentional reports have noncommittal readings, Geach’s main examples have no noncommittal reading of either familiar kind (notional or narrow scope). So if they have some other noncommittal readings, we must show this, and not merely assume it. Unfortunately I cannot discuss all types of cases here, so I will focus on the famous case of G, or more explicitly, GD. In the second half of the paper I will illustrate this reduction of Geach’s puzzle to the paradox of GD, by evaluating solutions to the former as solutions to the latter. 5 Solutions Most commentators miss one of the points I discuss in §§1–3, and so misunderstand the puzzle. But Geach and a few others propose solutions that can be put in terms of the paradox of GD,

rejecting either CommittalGD, DenialGD, or TrueGD. I discuss them below, and argue that the third kind of solution is the most plausible. 5.1 Reject CommittalGD If we accept DenialGD and TrueGD, but reject CommittalGD, we must explain how GD—and specifically G—does not carry commitment to a HN-witch. Geach assumes this is the right approach. He never specifies such a reading of G, but in two papers he specifies intentional identity and quasirelational readings of other intentional reports, and his strategies extend to G. In his first paper on the topic, he analyzes the relational and real identity readings and the alleged quasirelational and intentional identity readings. He analyzes 8 (‘Smith and Brown admire the same poet’) as: 8′ For some w, w is a definite description, and Smith and Brown both admire-as-a-poetsomeone-conceived-under-the-ratio-evoked-by w. (1964: 137–38) (The hyphenation indicates an “indivisible relative term.” The ratio a term evokes is a certain one of its semantic values other than its extension, such as its Fregean (customary) sense (cf. 1967: 149).) But he rejects this analysis.18 An 8′-style analysis of G would entail that there is a definite description by which both Hob and Nob purport to represent a witch. But G would seem true even if Hob and Nob each purported to represent a witch by a certain name, without associating the same definite description with that name.19 (Thus the stipulation, as part of the Hob-Nob case (§1 above), that there is no such shared definite description.) Later, he analyzes the alleged quasirelational reading of 12 as 12′: 12 Jones believes some detective can F. 12′ For some α, α is a detective-aspect and Jones believes [α can F]. (1976: 317) (An aspect is more or less a Fregean sense, specifically one suitable to be expressed by a name (313–14). A detective-aspect is an aspect that purports to represent something as a detective (314–15). The bracket notation is a Fregean form of quasiquotation (cf. n 5, above): the extension of ‘[α can F]’, on a given assignment of an aspect to the variable ‘α’, is the Fregean Thought composed of that aspect and the Fregean sense of the predicate ‘can F’.) He says this sort of analysis will extend to intentional identity (318), but he does not say how. By analogy with 8′ and 12′, G’s intentional identity reading would be: G1 For some aspect α, α is a witch-aspect, Hob thinks [α has blighted Bob’s mare], and Nob wonders whether [α killed Cob’s sow].20 I admit it is plausible that Hob’s and Nob’s intentional states involve aspects, or more generally, individual-representations: representations purportedly of individuals, such as ratios, definite descriptions, names, senses of names, etc. But G1 has two main problems. First, on the face of it G does not literally quantify over individual-representations. Of course some theorists, following Frege, will say the surface form of most intentional reports is misleading, and that the logical form really does involve such quantification. That is a substantial and doubtful linguistic claim (cf. n 7), but I will not attack it here. Instead, consider the second problem: G1 says that Hob and Nob share a witch-aspect, but the problem of intentional identity arises even if they do not.21 For suppose Gotham’s witch mania started with Rob. He tells Hob that a certain evil witch has blighted Bob’s mare, and tells Nob that he suspects Maggoty Meg killed Cob’s sow. Hob and Nob then form different witch-aspects; e.g., Hob’s could be expressed as ‘the evil witch’, and Nob’s as ‘the witch Maggoty Meg’. In this case G1 is clearly false, while G still seems true. In

effect, this objection generalizes Geach’s objection to 8′: there need not be any individualrepresentation by which both Hob and Nob purport to represent a witch. Some commentators avoid this problem; they only require that Hob’s and Nob’s relevant individual-representations be related in a certain way. For example, Tyler Burge says Hob and Nob have distinct “applications” (demonstration-like mental acts) in the same historical “quasianaphoric chain” (1983: 97–98). And Walter Edelberg says they have “I-objects” (aka “ideas”) related historically or by “rough similarity of explanatory role” (1992: 572–76, 582–84). Without getting into the details of their psychological and historical notions, I can say their analyses have the form of G2 (which for convenience I state in terms of aspects), for some relation R: G2 For some witch-aspects α and β such that Rαβ, Hob thinks [α has blighted Bob’s mare], and Nob wonders whether [β killed Cob’s sow].22 I agree that in the Hob-Nob case there is a historical relation between Hob’s and Nob’s individual-representations, such as their both tracing back to Rob’s delusion.23 But notice that on such an analysis, G’s surface form is doubly misleading: despite appearances, G not only quantifies over individual-representations, but also predicates a relation between two individualrepresentations. Such strong linguistic claims require strong empirical evidence, as I mentioned above. And while the former claim is at least supported by philosophical tradition, the latter is not (cf. Salmon, 2002: 110–11). Remember that we cannot simply assume, in this context, that G has a noncommittal reading. For one thing, there are competing solutions to the paradox. And it has proven very hard to derive a noncommittal reading of G from a plausible and systematic semantics. So instead of presupposing that such a reading exists, can we give some evidence for it? The only thing I have seen offered as evidence is that the reporter Rita would say G even while believing there is no HN-witch. But this is no evidence at all, as shown by a parallel of Kripke’s ‘schmidentity’ argument (1980: 108; cf. 1979: 113–15). To review: Kripke considers the semantic thesis that ‘is identical with’ cannot stand for a relation holding only between each object and itself, because then a true identity statement would be uninformative, whereas some are informative. In response, he introduces a binary predicate ‘is schmidentical with’, which he stipulates to stand for a relation holding only between each object and itself. Since a sentence such as ‘Cicero is schmidentical with Tully’ can be informative, the informativeness of true identity statements is no evidence for the semantic thesis. By analogy, consider the semantic thesis that G has a noncommittal reading. And compare, as an unambiguously committal substitute, G’s real identity reading, GA. (We need not stipulate its meaning, because we already agree on it.) In the Hob-Nob case, might Rita say GA while not believing there is such a witch? Yes, she might. Compare: we might say ‘There are twelve gods that the ancient Greeks worshipped’, which is unambiguously committal. Of course we might go on to clarify that we do not believe in any such gods, and Rita might clarify that she does not believe in a HN-witch. But such clarification would be needed whether the claims were unambiguously or ambiguously committal. Just as Rita’s uttering GA would not show that it has a noncommittal reading, her uttering G would not show that it has a noncommittal reading. So rejecting CommittalGD, far from being the only legitimate response to the puzzle, now looks wrongheaded. We had better look at other approaches. 5.2 Reject DenialGD

If we accept TrueGD and CommittalGD but reject DenialGD, then we take G to carry commitment to a HN-witch, and we must explain how D does not deny commitment to a HN-witch. Commentators explain this in one of two ways. The first takes the generalization in D, but not the one in G, to have an implicit domain restriction. Thus Terence Parsons reads D as implicitly restricted with an existence predicate—‘there is nothing such that it exists and it is a witch and…’ (1979: 105; 1980: 7; cf. 1974: 577)—while he gives G its real identity reading, the unrestricted generalization GA (1974: 578). Thus GD is consistent, because while it carries commitment to a witch, it denies commitment only to an existent witch. But there are several problems with Parsons’s metaphysics of so-called nonexistent objects (see, e.g., Kit Fine 1984 for discussion), two of which are especially relevant. First, there is no reason to suppose that Rita means to restrict D to existent witches. Since she does not believe in witches, she would deny commitment to them, rather than merely denying that any exist. But Parsons might say she would be wrong not to restrict D. So consider the second problem. If there is a HN (whether a witch or not), then it is a mythical witch. Is a mythical witch in fact a witch— and so possibly a HN-witch? According to Parsons’s theory, yes; and the mythical god Ba‘al is in fact a god, the mythical animal Pegasus is in fact a winged horse, etc. (1975: 77–78; cf. 1980: 52–54). This principle, that mythical objects in fact have the properties ascribed to them in certain myths, I call (mythical) inerrancy. (Parsons also accepts fictional inerrancy; e.g., he says the fictional character Sherlock Holmes is in fact a detective (ibid.). Strictly speaking, he restricts inerrancy to what he calls nuclear properties. He never defines that notion, but he means to rule out the property of existence, among other things.) But as he admits, while “it would be nice to have a theory which makes [inerrancy] true…this looks so much like a confusion” (1975: 78), that “we cannot put too much faith in” it (1980: 53). I agree: a mythical witch is not in fact a witch, just like a fictional detective is not in fact a detective; rather, they are respectively only a witch in myth and a detective in fiction (i.e., according to some myth or work of fiction). But in that case, no HN is a witch, and so GA is false. Thus Parsons’s analysis of GD is false, contrary to TrueGD. The second proposed way to explain how GD does not both deny and carry commitment to the same sort of thing is to say that it only carries commitment to a HN, but denies commitment to a HN-witch. Thus Héctor-Neri Castañeda suggests, at least as a “naive” solution to the puzzle, taking ‘(there is) a witch’ in G “to range not only over existing objects, but also over nonexisting possible objects” (1974: 47–48). And judging from his discussion of other cases (53– 59), he would not say that a HN is actually a witch, but instead that it is thought to be a witch. Similarly, Graham Priest analyzes G as: G3 Sx(x is (believed to be) a witch ˄ Hob thinks that x blighted Bob’s mare ˄ Nob wonders whether x killed Cob’s cow). (2005: 65 n 12) ‘S’ is his existentially unloaded counterpart to ‘∃’, and its domain includes objects that exist at any world or even at no world (12–14). So like Castañeda he can allow that although there is a HN (supposedly verifying G), nothing is actually a HN-witch (verifying D). But it is implausible that G is about nonactual objects. For one thing, it has no explicit modal operators. And while Castañeda and Priest think certain reports of particular-intentional-states are implicitly modal, that raises a problem identified by Kripke.24 They claim (in part) that Hob is thinking about a certain nonactual object, one that in some nonactual world is a witch who has blighted Bob’s mare. But there are infinitely many such objects, so which one does Hob think about? To have a particular-intentional-state of one of them, he must in some way distinguish it

from all the others, either by knowing a description that fits only it, or by his thought having some partly nonrepresentational link to it, such as a causal link through perception, or through the history of a certain name (cf. Burge, 2009: §III). But the Hob-Nob case suggests no such way for Hob to distinguish a particular nonactual object. And for the same reason, there is no way for Nob to have a particular-intentional-state of a relevant nonactual object, let alone for both Hob and Nob to represent the same one (given Geach’s stipulations about the case). In response, Priest simply denies that to have a particular-intentional-state of something, one must distinguish that thing from all others, or even from other obviously relevant things (2005: 141–42). But few will find this response plausible. (I discuss a further problem below, and a third in n 26.) There is another strategy to read G as carrying commitment to a HN, but not a HN-witch: give ‘witch’ a special reading. Nino B. Cocchiarella reads ‘witch’ as ‘intensional witch’ (1989: 30–32). He says intensional witches are not witches, but abstract “intensional objects,” i.e., “concept-correlates, where the correlation is based on a logical projection of the content of the concepts whose correlates they are” (15). In the Hob-Nob case, he seems to think the relevant concept is witch that Hob thinks has blighted Bob’s mare (32). But since he says we only know of intensional objects via their correlated concepts (18), and neither Hob nor Nob uses that concept, he does not explain how they know of (and have particular-intentional-states of) the correlated intensional witch. Furthermore, as far as I can tell, he thinks that each intensional object corresponds to only one “predicable” concept. But suppose (as in §5.1) that while Hob and Nob both believe Rob’s myth, they use different predicable concepts—evil witch versus witch called ‘Maggoty Meg’. In this modification of the Hob-Nob case, GD is still paradoxical, and G still seems true, but the suggested analysis of G is clearly false. (I raise further problems below.) In contrast, Salmon reads ‘witch’ as ‘mythical witch’ (2002: 112–17): G4 There is a mythical witch such that (i) Hob thinks: she has blighted Bob’s mare; and (ii) Nob wonders whether: she killed Cob’s sow. (116) (He also suggests reading ‘witch’ as ‘witch or mythical witch’; see his n 27.) Mythical witches are mythical objects, which he says are abstract objects accidentally created in mistaken theorizing. E.g., the mythical god Ba‘al, we assume, was created by ancient people’s religious practices; and their creation is not really a god: he is only a god according to myth. Likewise, a mythical witch is not a witch.25 (And note that we can think of the same mythical witch under various concepts.) On Salmon’s view, mythical objects are much like fictional objects, except that they originate in myths rather than works of fiction (1998: 291–305). This metaphysics— called creationism, after the claim that such objects are created—reflects how we think and talk of mythical objects in ordinary life, as well as in the human sciences (anthropology, history, etc.) and humanities.26 I agree with Salmon that some mythical witch, rather than a real witch, is a HN. But even if a nonwitch of some kind k is a HN, G does not literally say this; nor does it say that some witchor-k is a HN. Thus David Braun’s objection to Salmon: while G4 mentions mythical witches, G does not, and so G4 is not “a genuine [i.e., literal] reading” of G (2012: §4). I add that since G does not mention intensional witches, Cocchiarella’s analysis is not literal either. (This may also tell against Castañeda’s and Priest’s analyses, because it not clear G says that something thought to be a witch is a HN. But I cannot pursue this here, because we would need to assume some semantics of intentional reports, and unfortunately any such choice of assumptions would be very controversial.)

Cocchiarella and Salmon have responses. Cocchiarella says that ‘witch’ is ambiguous between “being a witch” and “being an intensional witch,” in which case his reading is literal (1989: 30, 32). Why think ‘witch’ is ambiguous in this way? Because, he says, all general terms and predicates are ambiguous between ordinary and intensional senses. But this is implausible. For one thing, the senses of an ambiguous term must be learned separately, as for example we must learn separately the multiple senses of ‘bank’. But surely we do not learn separately, for each ordinary sense of each general term and predicate, a corresponding intensional sense. More likely, there would be a single ambiguity of the copula (cf. Castañeda 1974: 53-59; Fine 1984: 97–99). Furthermore, since Cocchiarella does not clearly specify the alleged intensional senses, we cannot even evaluate his ambiguity claim. Salmon’s response to Braun is better. In a forthcoming paper he says that ‘witch’ is ambiguous between (real) witch and mythical witch; he disambiguates it as ‘witch1’ and ‘witch2’, respectively. He says this real/mythical ambiguity is common in “controversial” terms such as ‘magician’ and ‘fortune teller’; it is, at least, supported by typical dictionary definitions (cf. Kripke, 2011b: 64, on ‘god’). In that case, G4 is a literal reading of G. But this response relies on an alleged special feature of the mythical term ‘witch’, and I argued in §2 that no such feature is essential to the puzzle. For example, suppose Hob and Nob think livestock are threatened by dinosaurs, rather than witches. ‘Dinosaur’ is not a mythical term, and has no relevant ambiguities. So consider the report: 13 Hob thinks a dinosaur has blighted Bob’s mare, and Nob wonders whether it (the same dinosaur) killed Cob’s sow. Geach would say that 13 raises exactly the problem he means to illustrate with G. Regarding this modified Hob-Nob case, Salmon will say that since there are no dinosaurs (i.e., none now exist), any HN is probably a mythical dinosaur. I agree, but again we must distinguish what is true about Hob and Nob from what the report about them literally says. And no literal reading of 13 reads the occurrences of ‘dinosaur’ as meaning mythical dinosaur. Since Salmon has no solution for this variant of Geach’s puzzle, he has not quite solved Geach’s puzzle itself. Assuming he reads D as denying that a witch1 is a HN, he has at most found an equivocal reading of GD, one on which it is not paradoxical in the first place (because DenialGD is obviously, uncontroversially false). But even if there is such a reading of GD, it is irrelevant to the puzzle. 5.3 Reject TrueGD Finally, let’s try accepting both CommittalGD and DenialGD. This allows us to read GD straightforwardly as the conjunction of G’s real identity reading (GA) and its negation, thereby avoiding the semantic problems I discussed in §§5.1–5.2. But then we must reject TrueGD, and explain why Rita says GD even though she does not think it is literally true. Specifically, since (I assume) GD is untrue only because G is untrue, the main thing to explain is why Rita says G. Two commentators take this last approach to the paradox. First, Mark Crimmins describes the Hob-Nob case with G5: G5 There is a witch-generating mode of presentation m such that Hob believes: [m] has blighted Bob’s mare, and Nob wonders whether: [m] killed Cob’s sow. (1998: 40) This is not an analysis of G itself. Rather, he says that if G5 is true, then in a certain pretense, G is true (on its real identity reading).27 I will discuss two problems with this solution. First, although Crimmins does not precisely

explain his notation, G5 seems to be a notational variant of Geach’s shared-aspect analysis G1. And as I argued in §5.1, G raises the problem of intentional identity even if Hob and Nob share no relevant individual-representations—not even witch-generating modes of presentation. So G5 does not plausibly state the real conditions in which G is pretend-true, for some relevant pretense. The related-aspect analysis G2, or something of that form, is more plausible. Second, though Crimmins rejects TrueGD (see n 27), he only describes what is going on with Hob and Nob, rather than why Rita says G, and thus his solution is incomplete. But he gives reasons to say other pretend-true intentional reports. For example, if Ann is very clever and modest, Crimmins says we might say C1, ‘Ann is as clever as Holmes and more modest than Watson’. C1, he says, is pretend-true under the conditions stated in C2—a certain complex sentence about works of fiction, names, and degrees of cleverness and modesty. And he says, in effect, that we would say C1 in order to indirectly assert C2 (2–7; cf. 10–13, 15). So by analogy, he might say Rita utters G in order to indirectly assert G5.28 But indirect communication depends on a shared understanding of what is being communicated, since by definition, it cannot depend merely on what the utterance itself directly communicates (i.e., its conventional meaning). And unless Rita and the listener have a certain sophisticated metaphysics and psychology of myth, they will never think of anything like G5. So we cannot explain Rita’s utterance of G by saying she means to communicate G5, and thus Crimmins’s only suggested explanation is implausible. The other commentator rejecting TrueGD is Robert Howell. In a forthcoming paper (2012: §III), he describes what is going on with Hob and Nob, not in terms of their mental individualrepresentations such as witch-generating modes of presentation, but in terms of the linguistic expressions they use. (He does this to avoid psychological speculation and to simplify exposition; see his nn 20 and 47.) He says (i) there is a term α which Hob nonconsciously assumes to have exactly one referent (specifically, a witch), and a term β which Nob nonconsciously assumes to have exactly one referent (also a witch).29 Furthermore, (ii) Hob’s and Nob’s assumptions about those terms are historically linked: specifically, they both originate in the same “specific witch-existence assumption,” such as a village myth started by Rob. And (iii) Hob expresses his thought by saying ˹α has blighted Bob’s mare˺, and Nob expresses his wonder by saying ˹Maybe β killed Cob’s sow˺. (Note this account has the form of G2; witchaspects are replaced by terms assumed to designate witches, and the relation R is historical.) According to Howell, because (i)–(iii) are true, G is true under the “general witch-existence assumption,” i.e., the assumption that there are witches. (Compare Crimmins: because G5 is true, G is true in a certain pretense.) He also says that Rita, while not really endorsing this assumption, (nonconsciously) accepts it. (This seems to be a technical sense of accepting something: treating it as true without necessarily believing it. Cf. Robert Stalnaker (1984: 79), to whom Howell alludes.) And “in the scope of” that assumption, she asserts G. As with Crimmins’s solution, Howell’s has two main problems. First, even if (i)–(iii) are true, G may not be true under the general witch-existence assumption. I.e., even if there are witches, one can be mistaken in thinking any of them have attacked local livestock. (Compare the Smith-Brown case; it does not follow from the fact that there are poets, and that Smith and Brown sincerely and reflectively assert ‘I admire the poet Ern Malley’, that there is a poet whom they admire.) Instead, Howell should say that Rita accepts either the same specific-witchexistence assumption presupposed by Hob and Nob, or the general assumption that there is such a specific-witch-existence assumption and that is true. If (i)–(iii) are true, then under either of these assumptions, G is true. Second, Howell gives no reason for Rita to utter G. Like Crimmins, and like those who

accept TrueGD (§§5.1–5.2), his main interest is the truth about Hob and Nob, rather than Rita’s report. He does say we have a “primitive preference” for “object-level” reports like G, over sophisticated metalinguistic accounts like (i)–(iii) (ibid.). And maybe he would explain this preference in terms of “the primitive level at which this nonconscious [language] processing occurs” (§I). But he has not yet given such an explanation, and thus he has not explained why Rita utters G. So Crimmins’s and Howell’s solutions are incomplete. But they are not far from completion, as my own solution will show. In my view, Rita’s act of uttering G should be understood in terms of a very general problem: she wants to characterize intentional states that, in her view, presuppose myths or other misrepresentations. Normally, she might characterize intentional states in terms of the objects they represent, as the subjects think of them.30 But she cannot do that here, because either there are no such objects, or they are not really as Hob and Nob think of them. If she is a sophisticated antirealist or creationist, she might think either G2 or G4 is a true report. But even if she understands these, she may not be ready or willing to “shift gears” from the ordinary way of characterizing intentional states to one of these more conceptually and cognitively demanding ways. And if she lacks a definite theory of myth-presupposing intentional states, then she has no way to characterize them as they really are. So what does she do? Our default approach in such cases is to characterize the intentional states from a certain perspective, a perspective we find mistaken. In the Hob-Nob case, Rita characterizes Hob’s and Nob’s intentional states from the perspective of one who believes the witch-myth that those states presuppose.31 But what is it to adopt a perspective other than one’s own? Crimmins describes it as pretending the perspective is correct; Howell, as accepting certain assumptions. I will defer to psychologists, who in the last few decades have got an empirical grip on the phenomenon. They call it simulation.32 We simulate mental states by having similar ones. (E.g., the states involve similar patterns of neural activity.) Thus we use only the mental resources required for having those mental states, and not the resources required for representing them as mental states of certain kinds. In these terms, adopting a perspective is simulating having that perspective. And while adopting a mistaken perspective that is presupposed by certain intentional states, we can simulate characterizing those states as if they were not mistaken, i.e., in terms of their objects, as the subjects think of them, rather than in terms of some sophisticated theory of myth. And so simulation allows us to indirectly characterize mythpresupposing intentional states, by using only the mental resources we use in characterizing more ordinary intentional states. Furthermore, adopting a perspective allows us to comment on it, without having to represent it as a perspective. For example, we can disavow it, or parts of it. Suppose I have adopted the perspective of a Ba‘alite, and assert 7 (‘Hannibal worships Ba‘al’), thereby seeming to commit to the name ‘Ba‘al’ referring. I do not believe in Ba‘al, so I may need to clarify my real (nonsimulated) view. To disavow the commitment, and to disavow Ba‘alism in general, I assert 11 (‘Ba‘al does not exist’). Why 11? Because from within the Ba‘alite perspective, my assertion of 11 is easily understood as disavowing that perspective. Of course, saying 11 is also problematic: since my assertion presupposes the perspective it rejects, it is inconsistent (and thus True11 is false). But it is an easy and effective way to clarify my real view. Metaphorically, I follow Hannibal out on his limb, and then saw off the limb. Since I am on the limb too, I fall into inconsistency. But I succeed both in characterizing his intentional state, and in clarifying that I do not share his perspective.33 This sort of account can also explain Rita’s behavior in the full Hob-Nob case. When she

visits Gotham during an outbreak of witch-mania, she easily, automatically, and probably unwittingly, adopts the perspective of a believer of the local witch-myth—i.e., she simulates belief in the myth. Within this simulation, she simply concludes from what Hob and Nob tell her that there is a HN-witch, and she reports this with G. She does not really think G is true; she is not trying to characterize the intentional states as they really are, but only to characterize them indirectly, from a certain perspective. This is good enough for most purposes, and easier than grasping sophisticated accounts such as G2 and G4. If needed, she could go on to assert D, to clarify that she does not really believe what G literally says. And in this context, where it is common knowledge that Rita only committed to a HN-witch while presupposing a mistaken perspective, her utterance indirectly but effectively communicates the truth about Hob and Nob, without going into obscure metaphysical or psychological details.34 So my solution to the puzzle has three parts. First, there is an analysis of GD: G simply has its real identity reading, and D negates that.35 (So I accept CommittalGD and DenialGD.) Second, there is an account of what is really going on with Hob and Nob, namely Salmon’s creationist account G4. (I also think there is a true noncommittal account of the form of G2.) Third, and most important for solving the paradox, there is a good excuse for rejecting TrueGD, i.e., an account of why Rita says GD even if she does not think it is true. She says it because (i) her default (and maybe only) way to understand Hob and Nob is to adopt the perspective of someone who believes the local witch-myth, (ii) within that perspective she asserts G, and (iii) she asserts D to clarify what she did in uttering G.36 As far as I know, this is the only solution to Geach’s puzzle that (a) respects all of his stipulations about the Hob-Nob case, (b) does not rely on the irrelevant features I discussed in §2, (c) gives a literal, semantically plausible analysis of both G and D, and (d) explains why Rita says both G and D, even if she lacks certain sophisticated views about myth. In summary, I have clarified Geach’s puzzle and reduced it to the paradox of GD, which is an instance of the so-called problem of negative existentials. That reduction clarifies our options for solving the puzzle, and I have argued that the best option is to reject TrueGD, with the motivation I just supplied. From the perspective of Geach’s papers, and that of most of his commentators, this sort of solution was hard to imagine. They seek a noncommittal reading of G. But such a reading is probably just a myth; G literally carries commitment to a HN-witch, just as much as GD literally, inconsistently denies such commitment. So while Geach and most of his commentators have all been seeking the same thing that does not exist, I have shown how to avoid that irony.37 References Anscombe, G.E.M. (1965). “The Intentionality of Sensation: A Grammatical Feature” in Metaphysics and the Philosophy of Mind: Collected Papers, Vol. II (Oxford: Blackwell, 1981), 3–20. Asher, Nicholas (1987). “A Typology for Attitude Verbs and Their Anaphoric Properties.” Linguistics and Philosophy 10:125–97. Berger, Alan (2002). Terms and Truth: Reference Direct and Anaphoric. MIT Press. Braun, David (2012). “Hob, Nob, and Mythical Witches.” In Reference and Referring, edited by William P. Kabasenche, Michael O’Rourke, and Matthew H. Slater (Cambridge, Mass.: MIT Press), 149–87. Forthcoming; based on a presentation given in 2009. Burge, Tyler (1983). “Russell’s Problem and Intentional Identity.” In Agent, Language, and the

Structure of the World: essays presented to Héctor-Neri Castañeda, with his replies, edited by James B. Tomberlin (Indianapolis: Hackett Publishing Company), 79–110. ——— (2009). “Five Theses on De Re States and Attitudes.” In The Philosophy of David Kaplan, edited by Joseph Almog and Paolo Leonardi (New York: Oxford University Press), 246–316. Castañeda, Héctor-Neri (1974). “Thinking and the Structure of the World.” Philosophia 4, 1:3– 40. Cocchiarella, Nino B. (1989). “Conceptualism, Realism, and Intensional Logic.” Topoi 8:15–34. Crimmins, Mark (1998). “Hesperus and Phosphorus: Sense, Pretense, and Reference.” The Philosophical Review 107, 1:1–47. Edelberg, Walter (1986). “A New Puzzle about Intentional Identity.” Journal of Philosophical Logic 15:1–25. ——— (1992). “Intentional Identity and the Attitudes.” Linguistics and Philosophy 15:561–596. ——— (2006). “Intrasubjective Intentional Identity.” Journal of Philosophy 103:481–502. Fine, Kit (1984). “Critical Review of Parsons’ Non-existent Objects.” Philosophical Studies 45:95–142. Geach, Peter Thomas (1958). “History of a Fallacy.” In Geach (1972), 1–13. ——— (1963). “Quantification Theory and the Problem of Identifying Objects of Reference.” In Geach (1972), 139–46. Revised 1969. ——— (1964). “A Medieval Discussion of Intentionality.” In Geach (1972), 129–38. ——— (1967). “Intentional Identity.” In Geach (1972), 146–53. Originally published, without a footnote, in The Journal of Philosophy 64, 20:627–32. ——— (1969). “The Perils of Pauline.” In Geach (1972), 153–65. ——— (1972). Logic Matters (Oxford: Blackwell). ——— (1976). “Two Kinds of Intentionality.” Monist 59:306–20. ——— (1980). Reference and Generality: An Examination of Some Medieval and Modern Theories, third edition (Ithaca: Cornell). First edition 1962. Goldman, Alvin (2006). Simulating Minds: The Philosophy, Psychology, and Neuroscience of Mindreading (Oxford: Oxford University Press). Howell, Robert (2012). “Objects of Fiction and Objects of Thought.” Forthcoming in a volume edited by Stuart Brock and Anthony Everett. Kaplan, David (1986). “Opacity.” In The Philosophy of W.V. Quine, second edition, edited by Lewis Edwin Hahn and Paul Arthur Schilpp (Chicago: Open Court). Kripke, Saul A. (1979). “Speaker’s Reference and Semantic Reference.” In Kripke (2011a), 99– 124. ——— (1980). Naming and Necessity. (Cambridge, Massachusetts: Harvard University Press). ——— (2011a). Philosophical Troubles: Collected Papers, Volume I (New York: Oxford University Press). ——— (2011b). “Vacuous Names and Fictional Entities.” In Kripke (2011a), 52–74. Presented in 1973. ——— (2013). Reference and Existence: The John Locke Lectures (New York: Oxford

University Press). Presented in 1973. Kroon, Frederick W. (2000). “‘Disavowal Through Commitment’ Theories of Negative Existentials.” In Empty Names, Fiction and the Puzzles of Nonexistence, edited by Anthony Everett and Thomas Hofweber (Stanford: CSLI Publications), 95–116. ——— (2003). “Quantified Negative Existentials.” Dialectica 57, 2:149–64. Manning, Luke (2012). Signifying Nothing? How Fiction Represents. Ph.D. thesis, University of California, Santa Barbara. Markman, Keith D., William M. P. Klein, and Julie A. Suhr, editors (2009). Handbook of Imagination and Mental Simulation (New York: Psychology Press). Parsons, Terence (1974). “A Prolegomenon to Meinongian Semantics.” The Journal of Philosophy 71, 16:561–80. ——— (1975). “A Meinongian Analysis of Fictional Objects.” Grazer Philosophische Studien 1:73–86. ——— (1979). “The Methodology of Nonexistence.” The Journal of Philosophy 76, 11:649–62. ——— (1980). Nonexistent Objects (New Haven: Yale University Press). Priest, Graham (2005). Towards Non-Being: The Logic and Metaphysics of Intentionality (New York: Oxford University Press). Quine, Willard Van Orman (1966). “Quantifiers and Propositional Attitudes.” In The Ways of Paradox and Other Essays (New York: Random House), 183–94. Original, 1956. Quine, W.V.O. (1951). Mathematical Logic, revised edition (Cambridge, Massachusetts: Harvard University Press). Roberts, Craige (1996). “Anaphora in Intensional Contexts.” In The Handbook of Contemporary Semantic Theory, edited by Shalom Lappin (Oxford: Blackwell Reference), 215–46. Russell, Bertrand (1905). “On Denoting.” Mind, New Series 14:479–93. Salmon, Nathan (1998). “Nonexistence.” Noûs 32, 3:277–319. ——— (2002). “Mythical Objects.” In Meaning and Truth: Investigations in Philosophical Semantics, edited by Joseph Keim Campbell, Michael O’Rourke, and David Shier (New York: Seven Bridges Press), 105–123. ——— (2005). Reference and Essence, second edition (New York: Prometheus Books). First edition 1981. ——— (2006). “Pronouns as Variables.” Philosophy and Phenomenological Research 72, 3:656–664. Stalnaker, Robert (1984). Inquiry. Cambridge, Mass.: Bradford Books, MIT Press. van Rooy, Robert (2000). “Anaphoric Relations across Attitude Contexts.” In Reference and Anaphoric Relations, edited by Klaus von Heusinger and Urs Egli (Dordrecht: Kluwer), 157–81. 1

Rogue pronoun-occurrences are often called ‘unbound’, but all the above shows is that they are not bound by their antecedents. Indeed, Alan Berger (2002: chs 7–8) and Nathan Salmon (2006) argue persuasively that they are bound by implicit operators. (Thanks to Matt Griffin for suggesting the term ‘rogue’.)

2

They include Walter Edelberg (1986: e.g., 2–4), Nicholas Asher (1987: 126) and Nino B. Cocchiarella (1989: 30). See my 2012 (64 n 4) for more references.

3

Others note this, including Héctor-Neri Castañeda (1974: 47).

4

Geach sometimes follows Jean Buridan in taking deontic, nonrepresentational operators such as ‘owe’ and ‘is obliged’ as intentional (1980: 94, 189; 1964: 130, passim; 1967: 148–49). Elsewhere (1958: 1) he says these are not intentional but modal. Note that his main deontic examples—‘I owe John a horse’ and ‘There is some horse that I owe John’—become representational if we replace ‘owe’ with ‘have promised to give’. He may have temporarily confused those two notions.

5

See his 1964 (138), and 1967 (149–50). The ‘˹’ and ‘˺’ are W.V.O. Quine’s quasiquotation marks (1951: 35–37). The Greek letters are variables taking expressions as values, and the extension of a quasiquoted expression (relative to an assignment of values to Greek-letter variables) is the expression derived by replacing the occurrences of each Greek-letter variable by its value (on that assignment). E.g., if the respective values of the variables ‘ϕ’ and ‘ψ’ are the expressions ‘p’ and ‘q’, then the extension of the expression ‘˹ϕ ˄ ψ˺’ is the expression ‘p ˄ q’.

6

See his 1964 (130–32, 137), 1967 (149), and 1976 (313–18).

7

First, some intentional operators are extensional; as Kripke says, “suppose the Greeks worshipped Zeus, and Zeus is the tenth god mentioned by Livy. Then the Greeks did worship the tenth god mentioned by Livy” (2013: 69). (Cf. Terence Parsons, 1980: 34–35. Geach is sometimes sympathetic to this point; see his 1980: 188–89; and 1976: 319.) Second, there are many familiar arguments against Fregean semantics for intentional reports; see, e.g., Salmon (2005: chs 1–2).

8

Following Quine, I treat ‘is a spy’ as a simple predicate, semantically equivalent to the predicate ‘spies’, rather than treating ‘a spy’ as an indefinite description or existential quantifier phrase.

9

Compare Kripke’s infelicitous example ‘The Greeks worshipped a god, any old god’ (2013: 66–67).

10 See especially Geach’s 1969 (156–60) and 1976 (313–17), and compare his 1967 (151). Note that it is sometimes unclear what sort of reading he seeks. In his earlier papers (1964 and 1967: 148–50), and even in parts of his 1969 (158–59), his devices for indicating the alleged third noncommittal reading—such as changing 5 to ‘I just want a sloop’—indicate the other noncommittal readings. As he sometimes admits, these devices are inadequate (1967: 149; 1969: 158). (For more exegesis, see my 2012, 69–70.) 11 As far as I can tell, the terms ‘real identity’ and ‘intentional identity’ are meant to suggest a distinction between an intentional state’s “real” objects and its “intentional” objects (cf. Geach 1980: 181–82; and G.E.M. Anscombe 1965: 9–10, and cf. 5). But the latter notion is notoriously obscure, and so the suggestion is philosophically counterproductive. Furthermore

(as Salmon noted to me), G does not identify any witches, either in the sense of referring to them, or of being an identity statement (i.e., something of the form ˹α = β˺). The committal reading would better be called (e.g.) correlational, and the alleged noncommittal reading quasi-correlational. 12 Some commentators assume the alleged intentional identity reading concerns multiple subjects, or that the intrasubjective case is unproblematic (e.g., Asher 1987: 152–53). But 3, not to mention the first example in Geach’s 1967 (146–47), tell otherwise. See also Edelberg (2006). 13 Unfortunately, there are far too many mistaken analyses to discuss here. (See my 2012, 85– 95, for a thorough review.) But I will mention one, which is widely cited. Edelberg (1986) claims to show “the asymmetry of intentional identity.” But it is crucial to his cases that the reported attitudes are notional—he always stipulates that the subjects “have no one in mind.” Thus his cases do not illustrate intentional identity, in Geach’s sense. 14 Kripke (2013: 35–37, 148–55) makes a strong case against both those assumptions. 15 I discuss this characterization further in a forthcoming paper. 16 Compare Frederick Kroon (2000: 98–99), who uses such discourse as evidence that the name is used, not merely mentioned. 17 This description of D has a relational/notional ambiguity. I mean it notionally, because in D the negation takes wider scope than the existential quantifier. So I am describing the denial of commitment without entailing that it is false. 18 He seems to reject all of his 1964 analyses due to a counterexample to the relational analysis (1964: 138; 1969: 164). But it is not clear why that problem should affect his intentional identity analysis, so I focus on his other objection. 19 See especially the book-only footnote (1967: 152 n 1). For exegesis see my 2012 (77–85). 20 Compare Mark Crimmins’s solution, discussed in §5.3 below. 21 Craige Roberts (1996: 237) and Salmon (2002: 110) raise this problem. 22 Salmon (2002: 110) reads Geach as suggesting something like G2, rather than G1, presumably on the basis of the generalized objection I discussed in the previous paragraph. But it is not clear that Geach accepts that generalization. 23 Edelberg’s relation of rough similarity of explanatory role is insufficient. Intuitively, if Hob’s and Nob’s individual-representations have historically unrelated sources, the reporter Rita would not say they are thinking of the same witch. Cf. Robert van Rooy (2000: 172–73). 24 See Kripke (1980: 156–58; 2011b: 59). Salmon (2002: 120 n 13) applies this to other modal solutions to Geach’s puzzle, but in my view those solutions have worse problems (see my 2012, 88). 25 Strictly speaking, Salmon says a mythical witch is anything falsely believed to be a witch; a mythical witch created in myth-making is what he calls a wholly mythical witch (112). (Likewise, Ba‘al is a wholly mythical god.) But I will follow him in omitting ‘wholly’.

26 As far as I can tell, Cocchiarella, Parsons, Castañeda, and Priest all mean to reduce mythical objects to objects that would exist (or have whatever sort of “being” they have) regardless of actual representational activity. In a word, these theorists are Platonists, rather than creationists. Creationism better reflects our ordinary concept of (wholly) mythical objects. 27 Oddly, Crimmins says this makes G “genuinely, seriously true,” but it is more sensible to say that G is literally untrue, though true in a pretense. (Compare the next note.) So I will treat him as rejecting TrueGD. 28 Actually he says Rita’s utterance of G is a “genuine, serious assertion” (40; cf. 2–8), but this seems to be another terminological quirk (compare the previous note). It is more sensible to say that her assertion is indirect, and her utterance is pretenseful (though for a serious purpose). 29 Probably, Howell should talk not about terms, but about certain utterances of those terms. E.g., Hob’s and Nob’s assumptions would concern certain of their utterances of the English expression ‘the witch’, rather than the expression itself. Compare his notes 48 and 50. 30 I assume that if she wants to capture how anyone would characterize things, it is Hob and Nob. But the Hob-Nob case does not demand this. E.g., if Rita is reporting on Gotham events from Rob’s perspective, she may not mean to capture how Hob and Nob would characterize things. 31 Note that their intentional states do not presuppose that a witch has blighted Bob’s mare, or killed Cob’s sow. Rather, what they presuppose is a myth that purports to represent a witch de re. Rita’s report G presupposes that same myth, or at least presupposes that some such myth is true. So when she adopts the perspective of a myth-believer, she does not thereby presuppose that Hob’s belief about Bob’s mare is true or justified. For example, she would not say ‘Hob knows a witch has blighted Bob’s mare’. Thanks to an anonymous referee for encouraging me to clarify this. 32 Empirical work reveals simulation in many mental activities, including empathy, representation of motor activity, counterfactual thinking, and engagement with works of fiction. See, e.g., Alvin Goldman (2006) and Keith D. Markman et al. (2009). Crimmins suggests pretense might reduce to simulation (1998: 24–25). And Howell sometimes says that to accept someone’s assumption is to “occupy their standpoint” (§§II–III), which sounds like simulation. 33 Kroon (2003) gives a similar pragmatic account of some other paradoxical denials of commitment. 34 An anonymous referee suggests Rita might say something like ‘Hob incorrectly thinks a witch has blighted Bob’s mare, and Nob wonders whether she killed Cob’s sow’. (I have changed the example to match G more closely.) I agree that the first conjunct, on its own, could effectively communicate her rejection of the myth, if we read it notionally: Hob thinks there is a witch of a certain sort, but he is wrong. But if we read the first conjunct notionally,

the occurrence of ‘she’ in the second conjunct can no longer be anaphoric on the occurrence of ‘a witch’; its use here becomes unclear. On the other hand, the sentence can be literally understood as saying that there is a HN-witch, but that Hob is wrong about her. And that is not Rita’s view in the Hob-Nob case. So although she might assert this sentence to express her rejection of the myth, it would probably be confusing or misleading. 35 Assigning G its real identity reading is part of solving the problem of intentional identity, but it does not solve the problems of rogue anaphora and mythical terms (see §2). 36 Her utterance may be clear enough already; by using the term ‘witch’, she signals to nonbelievers that she is presupposing a myth. But that is a peculiarity of this case. In contrast, if I utter 8, I probably will have to clarify that I do not think there is a poet whom Smith and Brown admire. And D may not be the best clarification of G. She will likely add ‘really’: ‘but really there is no such witch’. Where a representation r is salient, ‘really’ means: not merely according to r. This will encourage the listener to guess that there is a salient representation—namely, the perspective Rita has adopted—and that G, unlike D, is true merely according to that representation. 37 For helpful discussion and comments on earlier versions of this paper, I thank Nathan Salmon, C. Anthony Anderson, Robert Howell, David Braun, Philip Atkins, Nat Tabris, David Friedell, and an anonymous referee.