1 This article appeared in Philosophical Topics 28/1 (Spring 200): 177-192. DIRECT REFERENCE AND VAGUE IDENTITY In 1957, reporters asked maverick producer Mike Todd why he bought a huge 29-carat engagement ring for Elizabeth Taylor. Todd answered “Thirty carats would have been vulgar.” Todd’s quip absurdly implies he knew that 30 carats is the threshold for vulgarity. But most philosophers think stopping here misses the root of the joke. They think there is a more fundamental absurdity; that it is even possible for a single carat to make the difference between a vulgar ring and a non-vulgar ring. We epistemicists defend the possibility. The law of bivalence implies that discriminative terms (ones that apply to some but not all things) have sharp boundaries. Consequently, classical logic permits few degrees of freedom when solving the sorites paradox. One can follow the incoherentists (Wheeler 1967, Unger 1979) and conclude that nothing is vulgar. One can blaze a new path and conclude everything is vulgar. Or one could follow the epistemicists and say that there are some vulgar things, some non-vulgar things, and nothing lies between the Vulgar and the Non-vulgar. Epistemicism goes beyond conservatism about logic. Ordinary vocabulary must also be preserved. We epistemicists think that ordinary words apply to pretty much what ordinary folks assume they apply to. Thus our double conservatism obeys the time-honored dictum Loquendum enim est ut plures, sentiendum ut pauci (Augustine Niphus Comm. In Aristotelem de 1 Gen. Et. Corr., Bk. I, folio 29). “Think with the learned and speak with the vulgar.” Do epistemicists have a passion for precision? Consider the Victorian British bachelor, Phileas Fogg, protagonist of Mike Todd’s 1956 academy award winning film Around the World in 80 Days (based on the Jules Verne story). Fogg insists that his bath water be exactly one foot and three quarters inch deep, that his toast be precisely 83 degrees Fahrenheit, and that breakfast be served at 8:24, not a minute earlier or later. He goes through valets like Elizabeth Taylor went through husbands. Gottlob Frege was like Phileas Fogg. Frege thought vagueness was the product of slap-dash semantics on the fly. Instead of properly defining terms, his fellow mathematicians opportunistically offered a necessary condition here, a sufficient condition there. Since these "definitions" lacked a condition that was both necessary and sufficient, their “concept” has semantic gaps. Frege did not take comfort in the thought that these borderline cases could be adjudicated later in light of future information and interests. This delay jeapordizes possibility proofs (for the possibility could be disqualified by an unanticipated necessary condition) and non-existence proofs (for the impossibility could be disqualified by an unanticipated sufficient condition). Consequently, Frege campaigned for the elimination of vagueness. Epistemicists have no special objection to vagueness and no special love of precision. They merely insist that vague statements conform to standard logic. However, most philosophers follow Frege in thinking that predicates inherit the incompleteness of linguistic intentions. 1 If there are singular propositions, this distracting belief can be bypassed. A singular proposition contains individuals, events, and other concrete things. For instance, `Mike Todd was Elizabeth Taylor’s third husband’ contains Mike Todd and Elizabeth Taylor. That seems self-evident. Except after philosophers ask embarrassing questions: Given that Mike Todd died in a 1958 plane crash, how can he now be a constituent of the proposition? The proposition still exists but he does not! And how old is the Elizabeth Taylor in the proposition? Is she at her current age or at the age when married to Mike Todd? Frege exposed further difficulties by embedding such sentences in modal contexts and belief contexts such as `Eddie Fischer believes that Mike Todd was Elizabeth Taylor’s third husband’. The behavior of these sentences led Frege to conclude that there are no singular propositions. Propositions are only indirectly related to concrete things via the senses that pick out those things. I think Frege went too far. I am amongst those (such as Paul Horwich 1998, 90-92) who believe that there are both singular propositions and general propositions. The case for singular propositions has been considerably strengthened by the work of Keith Donnellan, David Kaplan, Saul Kripke and Ruth Marcus. Their seminal achievements have been amplified by Nathan Salmon and Scott Soames. I will not attempt to improve upon their case for the existence of some singular propositions. Nor will I present any direct arguments in favor of epistemicism. I merely aim to show that epistemicism provides the best 1 explanatory framework for vague statements that express singular propositions. The centerpiece of this project is a specific thesis: the vagueness of some statements arises from vagueness in how the speaker fixes reference. Thus the vagueness of a statement cannot always be traced to its descriptive content or to vagueness in the proposition it expresses (or to constituents of these propositions -- such as vague objects). 1. Vague reference fixing Saul Kripke (1972, 79n) uses the history of astronomy to illustrate the distinction between supplying a synonym for an expression and fixing the reference of an expression. Suppose Urbaine Leverrier introduced `Neptune' by saying "Let us give the name `Neptune' to the planet causing the perturbations in the orbit of Uranus". This ensures that `Neptune' denotes Neptune if it denotes anything at all. Although Leverrier introduced the name `Neptune' into the language by means of a definite description, the name is not synonymous with the definite description. Leverrier could well have believed that had Neptune been knocked off its course a million years ago, then it would not have caused the perturbations in the orbit of Uranus and even that some other planet might have caused the perturbations. As it turns out, Neptune exists. Encouraged by the success of Leverrier's method, astronomers turned their attention to the perturbations of Mercury. They said "Let us give the name `Vulcan' to the planet causing perturbations in the orbit of Mercury." However, their luck did not hold. There is no such planet. 1 Now consider a fanciful intermediate case. Astronomers detect perturbations in Jupiter's orbit and say `Let us give the name `Nepcan' to the planet causing the perturbations in the orbit of Jupiter'. They do find a heavenly body causing the perturbations but it is only a borderline case of a `planet'. The cautious discoverers assign a name to this body in a way that does not assume it is a planet. They say "Let us give the name `Runt' to the body causing the perturbations in the orbit of Jupiter". Reporters ask whether Runt is Nepcan. The Jovian astronomers shrug. They explain that since Runt is a borderline case of `planet', there is no way to tell whether `Nepcan' successfully denotes like `Neptune' or fails to denote like `Vulcan'. `Runt is Nepcan' is a vague identity. Notice there is no temptation to trace the vagueness to a vague object. Nor should there be a temptation to trace the vagueness to a vague sense. The vagueness of the identity `Venus is the loveliest planet' can be traced to the vagueness of the concepts involved in the proposition. But in `Runt is Nepcan' the vagueness is due to a term (`planet') that was merely used to fix the reference of `Nepcan'. `Nepcan' is not synonymous with `the planet causing the perturbations in the orbit of Jupiter'. The astronomer who introduced `Nepcan' could well have believed that if Nepcan had been knocked off its course a million years ago, then it would have caused no perturbations of Jupiter and even that some other object would have caused the perturbations. Since the statement `Runt is Nepcan' involves a singular term that is a borderline case of `empty term', there is a danger 1 that the indeterminacies associated with empty names might be confounded with the indeterminacies associated with vagueness. There are related difficulties when there is unclarity as to how many objects are involved in the situation. A complete theory of vague identities should eventually address these hard cases. But I shall avoid these complications by focusing on a simpler example of vague reference fixing. Suppose explorers say, "Let us give the name `Acme' to the first tributary of the river Enigma". When they travel up the river Enigma they finally reach the first pair of river branches. They name one branch `Sumo' and the other `Wilt'. Sumo is shorter but more voluminous than Wilt. This makes Sumo and Wilt borderline cases of `tributary'. Either Sumo is just a segment of the Enigma and Wilt feeds into the Enigma, or Wilt is a segment of the Enigma and Sumo is the tributary. The vagueness of `tributary' does not threaten to make `Acme' an empty name because `the first tributary of the Enigma' denotes something on all admissible interpretations of `tributary'. `Acme' definitely refers to something even though it is vague whether it refers to Sumo and vague whether it refers to Wilt. Indeed, we know `Either Acme is Sumo or Acme is Wilt'. Since we also know that Sumo and Wilt both exist, we know that Acme exists. So although we know `Either Sumo is the first tributary of the Enigma or Wilt is the first tributary of the Enigma' there is no telling which. Hence, there is no telling whether `Sumo is Acme' or `Wilt is Acme'. We can know that `Acme is brackish' given that we know Sumo and Wilt are each brackish. Thus the vagueness of the 1 reference fixing does not prevent the name from being part of many knowable singular predications.