Abstract
What exactly should count as a vague term? The strikingly diverse examples of what is assumed to be vague in the literature reveal that this is, to a large extent, still unclear. It will be argued that this unclarity is a result of the prevalent borderline definition of vagueness. This definition is certainly pictorial but, in most of its formulations, lacks accuracy. The aim of this paper is thus not to solve sorites or to eliminate vagueness but to provide a workable criterion for identifying vague predicates, which seems even more indispensable in law where vagueness implies discretion. While trying to identify vagueness, some light will be shed into the questions of what causes it and how it is to be distinguished from familiar semantic phenomena.
I am grateful to the members of the Lx LTG (in particular to Pedro Moniz Lopes, Jorge Sampaio, David Duarte and Sara Moreira de Azevedo) for their helpful comments and critics on an early version of this paper. A special word of gratitude regarding later feedback goes to Jaap Hage, Izabela Skoczeń and Bojan Spaić, in the context of the II Lx Meeting on Legal Theory, Legal Interpretation and Scientific Knowledge; to Matthias Klatt and the Graz Jurisprudence team (in particular to Héctor Morales and Lisa Sonnleitner), in the context of a workshop held at the Karl Franzens Universität Graz; and, finally, to Tomasz Gizbert-Studnicki and the Jagiellonian Center for Law, Language and Philosophy team, in the context of a presentation held at the Jagiellonian University, Kraków.
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Notes
- 1.
- 2.
Soames (2014, p. 281).
- 3.
Multidimensional vagueness evolved from Timothy Endicott’s concept of extravagant vagueness. Note that what the author called extravagant vagueness has recently come under much debate and it is presently unsure whether it should classify as a case for vagueness. On this see Endicott (2000, pp. 31 ff); Asgeirsson (2015, pp. 425–448); Moreso (2017, pp. 45–69).
- 4.
Russell (1923, pp. 84–92).
- 5.
Which obeys to the following structure: Base step—a collection of one million grains of sand is a heap; Induction step—If a collection of n grains of sand is a heap, then so is a collection of n-1 grains; Conclusion—A collection of one grain of sand is a heap. This sorites formulation was found in Sorensen (2001a, p. 2). For a detailed explanation on sorites see, among others, Williamson (1994, pp. 8–36).
- 6.
Grice (1989, p. 177). This is a very broad definition. The author, in an attempt to differentiate between the semantic and the epistemic reading included “(…) and one’s not knowing is not due to the ignorance of the facts.” Similar but more precise formulations are easily found: Scott Soames defines vague predicates as “those for which a range of borderline cases separate things to which the predicate clearly applies from those to which it clearly does apply”, Soames (2014, p. 282). Note that for this first approximation no distinction is made as to semantic or pragmatic approaches to vagueness.
- 7.
See Sorensen (2018). Alternatively, vagueness is defined through the applicability of the sorites paradox but this is generally thought to be a limiting analysis of the phenomena.
- 8.
Which emerges from the idea that the extension of a predicate is the set of things of which it is true. For the association of the semantic theory with set theory see Mark Sainsbury critically on this point. The idea can be traced back to Bertrand Russel and is widely held in the semantic and philosophic literature on vagueness. See: Sainsbury (1996, pp. 251–264); Russell (1923, p. 85).
- 9.
- 10.
The sorites paradox (the name derives from the Greek word soros, meaning “heap”) is attributed to the logician Eubulides of Miletus who was famous for overall seven puzzles (the Liar, the Hooded Man, The Electra, The ElusiveMan, The Horned Man, The Bald Man, The heap). On a detailed historical overview on sorites: Williamson (1994, pp. 8–36).
- 11.
- 12.
See Charles Sanders Pierce’s entry for “Vague (in logic)” for the dictionary of philosophy and psychology: “A proposition is vague when there are possible states of things concerning which it is intrinsically uncertain whether, had they been contemplated by the speaker, he would have regarded them as excluded or allowed by the proposition. By intrinsically uncertain we mean not uncertain in consequence of any ignorance of the interpreter, but because the speaker’s habits of language were indeterminate; so that one day he would regard the proposition as excluding, another as admitting, those states of things.” Charles Sanders Pierce cited by Sorensen (2001a, b, p. 35). For a critical analysis of the pragmatic account of vagueness see Keefe (2003, pp. 139 ff).
- 13.
Black (1937, pp. 427–455).
- 14.
Gizbert-Studnicki (2000, pp. 35–145).
- 15.
- 16.
- 17.
This is not exactly wrong since strictly speaking both are terms. Term is a word (or words) that may be the subject or predicate of a proposition (subject or singular term and predicate term).
- 18.
“Is red” corresponds to an incomplete (or existential) proposition. Propositions can be divided into existential (is q) and predicational (p is q). The literature on vagueness uses different lexical items, often without a concrete explanation of what is meant: word, concept, term, predicate, sentence, proposition.
- 19.
For this precision see Gizbert-Studnicki (2000, pp. 135–145). The proposed reading corresponds to the distinction of singular term or subject and general term or predicate used in classical propositional logic. The question can be, however, more complicated: besides the complete denial of the distinction, various types of predicates can be identified (syntactical, logical, epistemical, etc.). I wish not to go into this here. It suffices to say that this idea of a propositional predicate is not to be equated with the syntactical predicate (which often do not coincide). On the complexity of the issue, see, for instance, Russel’s analysis of Aristotle in Russell (2004, pp. 197–199).
- 20.
Another question is whether the copula, the verb, can itself be vague. In the adopted basic propositional account p is q this issue will not be further developed. On this see Ajdukiewicz (1975, p. 55).
- 21.
Also, the implied proposition amounts to a new “p is q” where “heap” functions as predicate “q”.
- 22.
It could be argued that where “adequate measures” functions as syntactical subject term, it is truly a subject term composed of a predicate (adequate) and a subject term (measures). For this purpose, there is no need to develop this idea beyond this clarifying note. Regarding the definition of predicate as always demanding one (or more) singular terms see Russell (1940, pp. 45 ff).
- 23.
Soames (2014, p. 283).
- 24.
Williamson (1994, pp. 53–59).
- 25.
This is discussed below in Sect. 5.
- 26.
Going against this idea, the concept of intentional vagueness, according to which a sentence is vague if borderline cases could have been conceivable. On this definition see Sorensen (1998, p. 174).
- 27.
See Section 1 of this paper.
- 28.
Exceptions are Crispin Wright’s account of borderline cases as those items a fully competent thinker might not be able to sort out, Diana Raffman’s claim that a borderline case of F is equivalent to not F and Roy Sorensen’s argument of inquiry resistance. For a detailed understanding see Wright (2016, pp. 190–210); Raffman (2005, pp. 1–31); Sorensen (1998, pp. 174–183).
- 29.
See Crispin Wright, who also provides a detailed account of the arguments behind higher order vagueness in Wright (2010, pp. 523–549).
- 30.
- 31.
The chart was adapted from Soames (2014, p. 284).
- 32.
Pragmatic approaches, by referring to the native speaker, might allude to the linguistic usage, but this is never clearly expressed. Classical semantic criteria as “being convinced of”, “impossible to apply”, “knowing and not knowing” strike me as essentially intuitionistic.
- 33.
Sorensen (1998, p. 174 ff).
- 34.
In the classical semantic/foundational distinction, I am referring the foundational theories of meaning (what gives symbols of language the meanings they have). Explicit reference to the endorsement of a theory of meaning in the works on vagueness, especially in law, is rare.
- 35.
To put it classically: how to explain that “dog” means dog (and not proton)? To this basic question about meaning (origin of semantic properties), no unified answer has been given. Over time, and after abandoning the Socratic definitional theory (the meaning property of a word consists of a certain definition of it, i.e. the specification of its essential attributes), two answers have traditionally been given. According to the first, the meaning of an expression supervenes on the expression’s relation to things in the world (most famously the British empiricists mental image theory); according to the second, the meaning of an expression supervenes on the expression’s role in language (most famously conceptual role semantics). The historical transition from the first to the second is generally imputed to Gottlob Freges Morning and Evening star argument: since both mean different things although attached to the same physical object (Venus), meaning can’t be just a symbol-world relation. See this description in Fodor and Lepore (2002, pp. 9–27).
- 36.
The definitional structure is particularly evident in the debate on incommensurate multidimensionality (extravagant vagueness). See footnote 3 of this paper.
- 37.
The example might be misleading since it corresponds to a complex proposition. The proposition is composed of an existential (something is, exists) and a predicational statement (something that exists has certain properties). “There is” corresponds to the existential statement p is= something is (in your room). “There is a bachelor in your room” corresponds to the complete predicational statement p is q= the something in your room is a bachelor. The fact that “bachelor” syntactically seems to be a subject term should not detract us from understanding that in the relevant underlying sentence p is c, “bachelor” is the predicate, i.e. that propositionally bachelor is the predicate. The proposition might be substituted by “This (in your room) is a bachelor”. I chose to maintain the example despite its ambiguities because of its utility in explaining empirical and conceptual verification.
- 38.
- 39.
For this underlying argumentative structure see Fodor (1990, pp. 121 and 122).
- 40.
Fodor (1990, p. 59).
- 41.
Citing Jerry Fodor: “Cows cause “cow” tokens and (let’s suppose) cats cause “cow” tokens. But “cow” means cow and not cat and cow or cat because there being cat caused “cow” tokens depends on there being cow-caused cow tokens, but not the other way around. “Cow” means cow because (…) non cow-caused “cow” tokens are asymmetrically dependent upon cow caused “cow” tokens”. In Fodor (1990, p. 91).
- 42.
Fodor (1990, p. 129).
- 43.
This notion was adapted from Paul Horwich’s use theory. Here the meaning of a word is the common factor in the explanations of its numerous occurrences, whereby the underlying basis of each word’s meaning is the law governing its usage. A word has regularities of use and among them there is one basic explanatory regularity of use which explains all our uses of the word and thereby accounts for its meaning. See Horwich (2005, p. 26). Horwich identifies meaning constituting properties with acceptance properties. Many of the possible criticisms (circularity of correct use explaining correct use, words having meaning properties without having a single explanatory acceptance property, striking resemblance with the classical definitional theory) to this theory are avoided by maintaining that meaning is just information.
- 44.
- 45.
This notion was adapted from Paul Horwich’s use theory: one basic explanatory regularity of use which explains all our uses of the word and accounts for its meaning. Here Paul Horwich would say that the use of the word, say “bachelor”, presupposes a basic acceptance property, our acceptance of the sentence, “Bachelors are unmarried men.”. For this and other examples of terms like “or”, “red” and “water” functioning along these lines, see Horwich (2005, pp. 26 and 27).
- 46.
Admittingly, “dog” isn’t the best example. Stephen Schiffer uses the term “dog” to criticise Paul Horwich’s account of meaning, arguing that one can hardly sustain a basic acceptance property. Nevertheless, and for my explanatory criteria of use regularities, (1) there is no need for a single explanatory acceptance property and (2) acceptance properties do not account for meaning. The fact that no easy consensus about the explanatory criteria exists, obviously does not suggest that no consensual meaning exists. It simply proves that the consensus regarding the explanation of the commonality in use regularities is contingent and not what constitutes meaning. For the critique see Schiffer (2000, pp. 527–536).
- 47.
Arguing for the opposite direction (that the explanation of meaning via explanatory acceptance criteria constitutes meaning) although apparently confined to an explanatory function (“we must look for the simplest way to explain overall use”) see Horwich (1998, p. 80).
- 48.
- 49.
The debate about what explains extravagant vagueness highlighted the feature of incommensurability as being determinant for this type of vagueness. I argue that the indeterminacy arises not because of the incommensurability of the (multiple) criteria but because it is contested what should count as criteria (whether they are cumulative, exemplificatory, etc.). For literature on this matter see footnote 3.
- 50.
I am not considering the possibility of an alternative reading of “heap” based not only on the numbers but on the configuration of the grains (as lying on top of each other). Nevertheless, the same findings apply, only under this view the term “heap” would be qualified as a case for qualitative vagueness.
- 51.
These three features are added to the general demand of inquiry resistance: vagueness occurs if it is impossible to assess the truth or falsity of the proposition. This demand, taken by itself, would be similar to the classical semantic criteria for borderline cases and in line with the supervalionist approach to vagueness (borderline statements correspond to a truth value-gap).
- 52.
See Footnote 6.
- 53.
I am leaving aside the rather difficult question of how to prove the existence of the law of use which resembles the proof of a customary norm.
- 54.
Waismann (1945, pp. 119–150).
- 55.
- 56.
- 57.
But here it seems, another difference can be drawn: this open textured caused vagueness will tend to disappear. A law of use will emerge which either: (a) includes cats with this characteristic in the symbol “cat”; (b) excludes it or (c) creates a new category, like “zombie cat”.
- 58.
For instance, the singular term is defined as true only of the (one) object to which it refers and general term as severally true of each objects to which it refers. Quine (2013, pp. 87 ff).
- 59.
In Bertrand Russell, vagueness was portrayed in the same sense than generality: as a one-many relation between symbolizing and symbolized systems (blurry photograph analogy). Here vagueness is a “generic image” that functions like a general image in so far as it has multiple applications. See Russell (1923, p. 86). For a critique see Black (1937, pp. 427 and 428).
- 60.
This tendency of predicates to be universals results from the traditional view that only the general term can function both as a subject and as a predicate. See, for instance, Strawson (1959, p. 132). Here, the particular/universal distinction is associated with the reference (subject)/predication (predicate) distinction. Only universals (not particulars) can be predicated. Similarly, Quine (2013, p. 87).
- 61.
The same applies to complex propositions (or atypical predication) like in “A mammal is red” which implies “p is a mammal” where “mammal” is the original predicate. On this see footnote 36.
- 62.
The analysis of an eventual potential disjunctive plurality of objects (generic terms) leads to questions which cannot be pursued here: is there an identity between generic terms and vague terms? Can vagueness be viewed as semantic genericity?
- 63.
Genericity generally results from the quantifier: an implicit quantifier which is obtained by using bare plurals (e.g. “ravens are black”) or an explicit quantifier by using indefinite singulars (e.g., “a raven is black”). They are however other ways to obtain genericity (definite singulars, partitives, indefinite pronouns). For instance, the use of definite singulars (“the raven is black”) does not seem to imply a plurality of propositional subjects but only a space-time dependence. On some of these ways to obtain genericity see Lopes (2017, p. 478).
- 64.
See von Wright (1963, pp. 22–25).
- 65.
It seems that here the plurality of subjects is not propositional but empirical: the proposition can have only one subject but the propositional singular corresponds to a potential empirical plurality which is maintained until it is instantiated by a concrete singular.
- 66.
See on the alternative inclusive disjunctive structure of genericity (in comparison to the exclusive disjunctive structure and in comparison to the conjunctive structure of generality) Lopes (2017, pp. 471–490).
- 67.
Highlighting this confusion (and eventual coexistence) giving as example the predicate “is a game”, Lopes (2017, p. 477). This means again, that both generality and vagueness can be present. Nevertheless, in numerical terms, this confusion will not be very relevant since most cases of vagueness occur in adjectives (not nouns) which are therefore unsusceptible to a generic quantifier added to the predicate. Just compare “This is a heap” to “This is virtuous”.
- 68.
For instance, in Russell (1921, p. 157) where in his example “This is a man” he claims vagueness exists not because man is a general concept (it is) but because the concept of person is vague.
- 69.
Naturally, the identification of borderline cases encompasses both: empirical concreteness, a concrete space-time context for the proposition plus conceptual concreteness, a concrete word-meaning context through the correspondence of the word to its (minimal) meaning: instantiations of regular use.
- 70.
Indicative terms are defined as terms that mean objects (names but also terms denoting qualities and relations). On this classification see Russell (2009, p. 98).
- 71.
Asgeirsson (2015, pp. 425–448).
- 72.
For the sake of simplicity, the focus will be the vagueness of norm sentences, as opposed to other sources, contracts, etc.
- 73.
Poscher (2016, pp. 1–20).
- 74.
Norm is defined as the meaning of a norm sentence, structurally composed of antecedent, deontic operator and consequence. Instead of normative proposition (which here would be the natural counterpart of descriptive propositions used so far), which in legal realm has a different meaning, I adopt the classical notion of norm sentence.
- 75.
But not exclusively. Approximators are expressions that add a more or less judgement. On this see, Sauerland and Stateva (2011, pp. 121 ff).
- 76.
Uli Sauerland and Penka Stateva argue that numbers are vague. In their example “this wine is 3 years old”, three interpretations are possible: (1) “this wine is exactly 3 years old”, here a more precise approximator is used; (2) “the wine is 3 years old”, this is vague, no approximator is used and (3) “this wine is approximately 3 years old”, here a less precise approximator is used. However, in law numbers formulated according to option 2, have an implicit approximator, like exactly (think of adult starting from 18 years). Additionally, according to the proposed definition of vagueness, a number, say 5, is not vague since you can assign a truth value to a proposition containing 5: it either does or does not correspond to an instantiation of the regular use of 5 (here, the regular use of 5 corresponds to 5000 and not 5004). See Sauerland and Stateva (2011, pp. 121 ff).
- 77.
This choice is the result of vagueness. It is often taken to be what vagueness is about (borderline definition). But, as stated before, vagueness isn’t an exclusive disjunctive alternative of meaning. This is not what characterizes vagueness but merely its consequence.
- 78.
It is not unusual to confuse semantic issues (vagueness) with a situation of normative conflict. For instance, Scott Soames distinguishes various ways in which vagueness can arise in the law confusing vagueness with a typical norm conflict situation. See Soames (2014, p. 291). I will not go into detail here. For the conditions for the verification of a normative conflict (overlap of the antecedent of two or more norms and incompatibility of the norm’s consequence) see Duarte (2010, pp. 51 ff).
- 79.
Whereby condition of application is defined as the existence of an opportunity for doing the thing which is in the content of a given norm (and norm content is defined as what ought to or may or must not or be done). Von Wright (1963, p. 73).
- 80.
Here the source of inspiration was the Portuguese Law of Protection of Children in Danger (Lei de Proteção de Crianças e Jovens em Perigo, Lei n.° 147/99, de 1 de setembro).
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Escher, A. (2019). When It Is Vague What Is Vague: Identifying Vagueness. In: Duarte, D., Moniz Lopes, P., Silva Sampaio, J. (eds) Legal Interpretation and Scientific Knowledge. Springer, Cham. https://doi.org/10.1007/978-3-030-18671-5_7
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