© LOGOS & EPISTEME, XI, 1 (2020): 19-27 THE CONFLICT OF RIGIDITY AND PRECISION IN DESIGNATION Daniele BERTINI ABSTRACT. My paper provides reasons in support of the view that vague identity claims originate from a conflict between rigidity and precision in designation. To put this stricly, let x be the referent of the referential terms P and Q. Then, that the proposition "that any x being both a P and a Q" is vague involves that the semantic intuitions at work in P and Q reveal a conflict between P and Q being simultaneously rigid and precise designators. After having shortly commented on an example of vague identity claim, I make the case for my proposal, by discussing how reference by baptism conflicts with descriptive attitudes towards understanding conceptual contents. KEYWORDS: vagueness, rigid designators, imprecise designators, identity claims Vague identity claims are very ordinary linguistic items. Consider the following statement: 1. Florentine Neoplatonists are intellectuals working at the court of the Medici during the Renaissance. Such proposition is an identity claim because it can be analysed as follows: 2. For any x, x is a Florentine Neoplatonist if and only if x is an intellectual working at the court of the Medici during the Renaissance. It is plain that someone may doubt that (1) is vague. An historian may claim that at least one individual which worked as intellectual at the court of the Medici during the Renaissance was not a Neoplatonist. This being the case, (2) would result definitely false.1 As a consequence, the interpretation of (1) as an identity claim would exclude that (1) is vague. However, such a reply is problematic because the referential expressions involved in (1), namely, being an intellectual working at the court of the Medici during the Renaissance (MI) and being a Florentine Neoplatonist (FN) are both vague, where vagueness is commonly understood to refer to the existence of fuzzy 1 I'm not assuming that vague propositions are not epistemic; rather, they are epistemic in a non definitive way, namely, they need a precisification of their meaning in order to have a truthvalue. If a proposition is definitely false does not need such a move to acquire a truth-value. As a consequence, it cannot be vague (although, it can contain vague terms as constituent). Daniele Bertini 20 boundaries separating groups of objects. (Let P be a referential term. Suppose that x is clearly a P and that y is clearly not a P. P is vague if borderline cases exist between x and y, and there are therefore fuzzy boundaries between being a P and not being a P. The issue at stake is that a vague term needs a stipulation of its meaning: there are indeed no fixed insights for establishing those objects to which it applies and those to which it does not). For example, both intellectual and Neoplatonism are open to different construals. A jurist or a financial expert is an intellectual worker, but not necessarily an intellectual in the traditional sense, unless the individual has an interest in intellectual concerns which do not relate to their work. As a consequence, being an intellectual is a property which those who serve as intellectual workers may or may not have. Consider a list of all intellectual workers at the court of the Medici during the Renaissance and order them by their depth of interest in intellectual concerns. At one end of the list is an individual with no interest in intellectual concerns, while at the other is somebody interested in nothing but intellectual concerns. All other individuals stand between the two opposites: the smaller the intellectual concerns, the closer to the non-intellectual boundary. Where is the dividing line between being an intellectual and not being an intellectual? Similar considerations hold for FN. For each theoretician working for the Medici consider whether he or she endorsed a qualifying feature of Neoplatonist philosophy, say P (think of a qualifying feature for x-ism as a feature you should endorse if you intend to be counted among x-ists). Now order them by the strength of their endorsement of P. At one end place a theoretician who did not endorse P (and is thus certainly not a Neoplatonist); at the other end place a theoretician who endorsed it at the maximum extent (and thus certainly is a Neoplatonist). Place all other individuals from lower endorsement of P to higher. Where is the dividing line between Neoplatonists and non-Neoplatonists? Now, if MI and FN are vague referential expressions, a claim which concerns the identity of MI and FN turns out to be vague too. Actually, the semantic indeterminacy of such terms infects any proposition which stipulates their identity: if I do not have a non vague individuation criteria for being a MI and a FN, the identity between MI and FN is fluctuating over different construals of their meaning. These lines of reasoning lead then to the conclusion that (1) is a vague identity claim and highlight two points of interest. First, the informational content of (1) is indisputable: the identity claim between MI and FN provides facts about them, because their identities, taken together, convey a representation of reality that can turn out to be true or false. For example, Renaissance scholars debate over The Conflict of Rigidity and Precision in Designation 21 claims like this one to capture relevant facts about the cultural policies of the Medici dynasty, the history of patronage of the arts, the relationship between political power and exhibition of wealthiness, and so on. Second, (1) is vague because MI and FN are imprecise designators.2 By consensus view, a designator is precise if and only if there is something determinately denoted thereby and so it is not vague what the designator picks out; on the contrary, a designator is imprecise if it is not precise.3 My view is that vague identity claims originate from a conflict of rigidity and precision in designation. Conflict here means something along the following lines. In ordinary predication, if a designator is rigid (e.g., a qualified name), the designator picks out precisely a set of objects. Consider a referential expression as red car. According to the ordinary use of the term (which implies a non vague construal of the referential expression red car), when you sign an agreement for buying a red car, you precisely know what you are buying. Or, if your friend standing at the window says to you: hey, there is a wonderful red car out there! you precisely know which kind of object you could see if you walked out there. There are different cars and different degrees of red, but the designator red car individuates precisely a set of objects. On the contrary, if a designator is not precise (e.g., an ambiguous term), the designator cannot individuate rigidly a set of objects. Consider the ambiguous term religion. Whoever has dealt with the difficult task to define what a religion is, perfectly knows how resistant is the term to a strict definition. Actually, some scholars use religion inclusively, others do not. As a consequence, some count as religions what others refute to classify as such. The moral of the story is that, grossly speaking, rigidity and precision in designation stand side by side. If you are a friend of degree approaches in philosophy, you can say that the more a term is rigidly employed, the more the term is precise in designation. Such a conclusion is not true for vague identity claims. In a substantive sense, vagueness consists in that the proportionality of rigidity and precision is broken: the incapability to access commonly agreed methods for establishing what counts as something has for consequence that rigidity and imprecision in designation are simultaneous features of one and the same proposition. This characterization means that a proposition is a vague identity claim if the 2 Garett Evans, "Can There Be Vague Object?"Analysis 38, 4 (1978): 208; Richmond H. Thomason, "Identity and Vagueness," Philosophical Studies 42, 3 (1982): 329-332; David Lewis, "Vague Identity: Evans Misunderstood," Analysis 48, 3 (1988): 128-130. 3 Dominic Hyde, Vagueness, Logic, and Ontology (London & New York: Routledge, 2016), 11617. Daniele Bertini 22 designating behaviour of the involved referential terms fluctuates between rigidity and imprecision. What I mean by the notion of fluctuation can be spelt out as follows. Let P be a vague referential term. The referentiality of P determines that P is used in a rigid way. That is to say, speakers of a language wherein P occurs understand prima facie P as if it individuates a set of objects. Nonetheless, since P is vague, P cannot pick out precisely a set of objects. As a consequence, P is used to refer imprecisely to a set with fuzzy boundaries. Now, while in ordinary predication the rigidity and precision of a referential expression are proportional, in vague predication they are conflicting. Saying that relevantly vague terms in vague identity claims fluctuate between rigidity and imprecision in designation intends to capture that once a term is employed, such a term is employed rigidly, although since it is vague, it cannot be used precisely. To put this more precisely, let x be the referent of the referential term P (and Q). Then, the proposition "that any x being a P (and a Q)" is vague involves that the semantic intuitions at work in P (and Q) reveal the predicative impossibility to establish a proportionality relation between referential rigidity and precision of P (and Q). I will set forth a case as evidence for my thesis. Michelangelo is possibly the most important intellectual among Florentine Neoplatonists. Suppose dividing Michelangelo's lifeline into different segments. Let Mx stands for "Michelangelo at the age of x", so that: M0 stands for Michelangelo's lifeline segment at the age of 0; M1 stands for Michelangelo's lifeline segment at the age of 1; ... ... ... Mx stands for Michelangelo's lifeline segment at the age of x; ... ... ... Mn stands for Michelangelo's lifeline segment at the age of n. The Conflict of Rigidity and Precision in Designation 23 According to Kripke's seminal analysis for proper names, which established the definition of the notion, the name Michelangelo is a rigid designator.4 This means that the use of the name Michelangelo to refer to the individual universally known by that name is rigidly determined. I can conceive counterfactual worlds wherein Michelangelo did not become an artist, was not a Florentine Neoplatonist, or even had never been born. Even so, each of these conceptions refers to the very same individual, Michelangelo.5 Now, each segment of Michelangelo's lifeline is represented by M0, M1, ..., Mx, ..., Mn, abbreviated expression that refer to Michelangelo at a certain age. They are therefore referential terms for Michelangelo and can be used in identity statements where the proper name Michelangelo occurs: M0 is Michelangelo; M1 is Michelangelo; ... ... ... Mx is Michelangelo; ... ... ... Mn is Michelangelo. Since any of these statements has for content the individual universally known as Michelangelo, the proper name Michelangelo works as a rigid designator in each of them, accordingly to Kripke's definition. So far, so good. However, each of M0, M1, ..., Mx, ..., Mn is used imprecisely in referring to Michelangelo, because: (a) any Mx and Mx+1 are continuous over slight temporal changes, and, as a consequence, it cannot be detected what criteria strictly individuate them; (b) they cannot be substituted one for another in statements about Michelangelo within any predicative context. For example, Michelangelo completed his statue David in 1504, when he was 29. So, while it is true that Mi carved David (where i is greater than 29), it is not true that Mi carved it (where i is 4 Saul A. Kripke, Naming and Necessity (Cambridge: Harvard University Press, 1980), 48. 5 Kripke, Naming and Necessity, 77. Daniele Bertini 24 less than 29). As a consequence, if x is less than 29, and y is greater than 29, Mx and My are both Michelangelo, but what is true of Mx is not true of My. It seems evident then that, while it is not vague whether Michelangelo carved David and each of M0, M1, ..., Mx, ..., Mn is Michelangelo (according to the intuition that proper names are rigid designators), M0, M1, ..., Mx, ..., Mn are imprecise designators for the individual known as Michelangelo and constitute a set of vague descriptions for him. Why do they constitute a set of vague descriptions? After all, each member of the set describes Michelangelo: it seems there are no borderline cases in being Michelangelo. To see why they do, consider what mereological constitution is. In a contribution to the debate on the metaphysics of time,6 Ted Sider argues that individuating compounded objects in a given instant of time always raises issues of vagueness because the diachronic composition which determines how an object is numerically distinct from others can be captured in terms which may generate a sorites paradox.7 The core problem consists in that the temporal changes of an object seems to be continuous over a range of slightly indiscernible differences. For example, it is notorious that while in his early years Michelangelo worked mainly as sculptor and painter, in his later years he accepted exclusively jobs in architecture. Naturally, he began to work as architect from his early years, and continued to paint and carve privately in his later years too. As a consequence, although it is true that Michelangelo was mainly a sculptor and a painter in his youth and an architect in his old age, it is not easy to see when the change in his artistic inclinations occurs. According to the logic of Sider's argument, a tri-dimensionalist reading of Michelangelo's life is committed to the acceptance of ontic vagueness. If being a painter and a sculptor is essential to Michelangelo (as it seems reasonable to assume), and being an architect is essential too, Michelangelo fluctuates from being a painter and a sculptor to being an architect; there are fuzzy boundaries between his early and late years. This means that the object Michelangelo had a fluctuating nature, and it is not determinate for which value of i the proposition Mi was mainly a sculptor and a painter is true. On the contrary, a four-dimensionalist reading of Michelangelo's life does not raise such a problem, because if Michelangelo had extended in time, he had temporal parts for which he was a painter and a sculptor, temporal parts for which he was a painter, a sculptor, and to 6 Ted Sider, Four-Dimensionalism: An Ontology of Persistence and Time (Oxford: Clarendon Press, 2001). 7 Achille Varzi, "Change, Temporal Parts, and the Argument from Vagueness," Dialectica 59, 4 (2005): 488-89. The Conflict of Rigidity and Precision in Designation 25 a lesser extent an architect, temporal parts for which he was an architect and to a lesser extent a painter and a sculptor, and, finally, temporal parts for which he was an architect. Now, since Sider holds that ontic vagueness is not an option, in order to block the assumption of this kind of vagueness from the problems related to diachronic composition, it is necessary to endorse a four-dimensionalist theory of time. Varzi and others doubt that such move actually works, since there seems not to be an implicature relation between diachronic composition and fourdimensionalism. Nonetheless, if one inclines to evaluating vagueness as a semantic fact, Sider's argument has to be blocked somewhere. Achille Varzi provides an analytical overview of what costs rejecting one or the other premise of the argument involves.8 However, my view is that one can pursue a strategy which is not set forth by Varzi's conclusions, by denying that Sider's argument should be answered. The point of the matter is actually that, independently of how a theorist approaches the nature of vagueness (whether it be ontic or semantic), vagueness generates from linguistic uses. That is to say, a purely linguistic story about designation, namely, about how vagueness is structurally related to the use of predicates which work rigidly and imprecisely at once, may suffice to provide an account for how vague statements work. Such a story can be compatible with a number of different theories; it might be the case that vagueness is exclusively a semantic fact, as well as that vagueness generates from a linguistic use because of the fluctuating nature of things out there. The key to my approach consists in distinguishing between the individual to which a proper name refers and the conceptions thereof. Although any conception (or counterfactual proposition) of M0, M1, ..., Mx, ..., Mn is a conception of Michelangelo, there is an overwhelming temptation to consider some more relevant to Michelangelo than others. Had Michelangelo not carved the Pietà, David, or Moses, or had he not frescoed the Sistine Chapel, nobody would consider the individual now universally known as Michelangelo as Michelangelo. What I mean is that the name Michelangelo is used not only for an individual (who could have been a different person and is therefore independent of his accomplishments), but also for a conceptual content individuated by reference to the individual: the content is known by accessing relevant descriptions of the man. Which of these descriptions is required to use the name Michelangelo in a proper sense, that is, to refer to the greatest Florentine Neoplatonist? Since at least some of M0, M1, ..., Mx, 8 Varzi, "Change, Temporal Parts, and the Argument from Vagueness," 497-98. Daniele Bertini 26 ..., Mn do not take part in the conceptual content individuated by the name Michelangelo, they are evidently not essential to being Michelangelo. For example, Michelangelo completed the Pietà, his first universally known work, in 1499, when he was 24 years old. Does any Mx where x is less than 24 really belong to the conceptual content individuated by reference to Michelangelo? Suppose that the Pietà is not essential to Michelangelo's artistic production and that the Sistine Chapel fresco, created between 1508 and 1512, is the only necessary work. This being the case, belonging or not to the conceptual content individuated by referring to Michelangelo is marked by a different Mx. My conclusion, in line with the interpretive thinking of art historians and critics, is that M0, M1, ..., Mx, ..., Mn form a set of vague descriptions. All such scholars debate about the same individual, evaluating his life and work andproviding interpretations for his development and artistry. Each description, however, gives a very different account of the same object, and the differences are made possible because Michelangelo is a rigid designator. This does not remove the differences, however; the conceptual content individuated by referring to Michelangelo requires a precisification. Each book, essay, and discussion about him satisfies that requirement exactly. Notoriously, van Inwagen argues for the claim that attributing a proper name by baptism dispenses from providing a description of the named thing; and that such a fact gives a reason in support of ontic vagueness in face of the semantic one.9 However, baptism is a performative act which requires understanding a wide extent of descriptive conditions (for example, anything which is necessary for individuating the baptised thing). Consequently, the possibility of a baptism without description is deceptive. The moral of the story is that vague identity claims reveal a conflict between semantic intuitions concerning designation. Once a term is rigidly introduced by baptism for referring to a thing, it is associated with a series of descriptions of that thing. Although the baptism confers rigidity, the descriptions are counterfactually variable. This variability leaves room for different choices as to which of these descriptions is the cutting line between belonging or not to the conceptual content rigidly designated by the relevant term. If this variability admits precision in giving strict definitions, the work of theoreticians pushes vagueness away, and settles the dispute. On the contrary, whenever different intuitions about the precisification of meaning conflict and compete with each other in a manner which cannot find conclusive reasons in support of any of them, the plurality of slightly different 9 Peter van Inwagen, "How to Reason About Vague Objects,"Philosophical Topics 16, 1 (1988): 255-284. The Conflict of Rigidity and Precision in Designation 27 descriptions for the same conceptual content to which a certain name refers generates a vague approach to the relevant thing. This being the case, the logic of vagueness and its linguistic expression are not able to individuate whether vagueness is a semantic or ontic fact. A supplement of ontological reasoning should be necessary here.