This is a defence of the claim that names are predicates with a demonstrative element in their singular use.

We explain two ways of revising a tense logic like kripke's (1963) modal logic by adding predicate modifiers. first we show that modifiers allow us to render valid some mixing formulas--conditionals reversing the order of a quantifier and an operator--within a complete bivalent system. then we show how modifiers enable a tense logic to give analyses close to the surface form for sentences with temporal qualifications of singular terms, e.g., 'toby was fatter then than william is today'.

In this paper I argue that descriptive content associated with a proper name can serve as a truth-conditionally relevant adjunct and be an additional contribution of the name to the truth-conditions. Definite descriptions the so-and-so associated by speakers with a proper name can be used as qualifying prepositional phrases as so-and-so, so sentences containing a proper name NN is doing something could be understood as NN is doing something as NN (which means as so-and-so). Used as an adjunct, the descriptive (...) content of a proper name expresses the additional circumstances of an action (a manner, reason, goal, time or purpose) and constitute a part of a predicate. I argue that qualifying prepositional phrases should be analyzed as predicate modifiers and propose a formal representation of modified predicates. The additional truth-conditional relevance of the descriptive content of a proper name helps to explain the phenomenon of the substitution failure of coreferential names in simple sentences. (shrink)

The Millian view that the meaning of a proper name is simply its referent has long been popular among philosophers of language. It might even be deemed the orthodox view, despite its well-known difficulties. Fregean and Russellian alternatives, though widely discussed, are much less popular. The Predicate View has not even been taken seriously, at least until fairly recently, but finally, it is receiving the attention it deserves. It says that a name expresses the property of bearing that name. (...) Despite its apparent shortcomings, it has a distinct virtue: It straightforwardly reckons with the fact that proper names generally have multiple bearers and are sometimes used to ascribe the property of bearing a name rather than to refer to a particular bearer of the name. It holds that proper names are much the same as common nouns, both semantically and syntactically, with only superficial differences. They both can be quantified and modified. The main difference, at least in English, is that when used to refer a proper name, unlike a common noun, is not preceded by the definite article. The Predicate View accounts for manifestly predicative uses, but to be vindicated, it needs to do justice to the fact that the main use of proper names is to refer. (shrink)

In this article, we describe and attempt to solve a puzzle arising from the interpretation of modified numerals like less than five and between two and five. The puzzle is this: such modified numerals seem to mean different things depending on whether they combine with distributive or non-distributive predicates. When they combine with distributive predicates, they intuitively impose a kind of upper bound, whereas when they combine with non-distributive predicates, they do not. We propose and explore in detail four solutions (...) to this puzzle, each involving some notion of maximality, but differing in the type of maximality involved and in the source of maximality. While the full range of data we consider do not conclusively favor one theory over the other three, we do argue that overall the evidence goes against the view that modified numerals lexically encode a ‘standard’ maximality operator, and suggests the need for a pragmatic blocking mechanism that filters out readings of sentences that are generated by the grammar but intuitively unavailable. (shrink)

This paper offers a new semantic theory of existentials (sentences of the form There be NP pivot XP coda ) in which pivots are (second order) predicates and codas are modifiers. The theory retains the analysis of pivots as denoting generalized quantifiers (Barwise and Cooper 1981; Keenan 1987), but departs from previous analyses in analyzing codas as contextual modifiers on a par with temporal/locative frame adverbials. Existing analyses universally assume that pivots are arguments of some predicate, and that codas (...) are main or secondary predicates. It is shown that these analyses cannot account for the behavior of codas with quantifiers and for the interaction of multiple codas, both of which receive a simple treatment on the proposed theory. The assimilation of codas to frame adverbials explains several semantic properties which have not been analyzed in the semantic literature, and that distinguish existentials from their copular counterparts. Furthermore, it highlights important properties of the semantics of modification and its relation to predication. (shrink)

In Latent Semantic Analysis (LSA) the meaning of a word is represented as a vector in a high‐dimensional semantic space. Different meanings of a word or different senses of a word are not distinguished. Instead, word senses are appropriately modified as the word is used in different contexts. In N‐VP sentences, the precise meaning of the verb phrase depends on the noun it is combined with. An algorithm is described to adjust the meaning of a predicate as it is (...) applied to different arguments. In forming a sentence meaning, not all features of a predicate are combined with the features of the argument, but only those that are appropriate to the argument. Hence, a different “sense” of a predicate emerges every time it is used in a different context. This predication algorithm is explored in the context of four different semantic problems: metaphor interpretation, causal inferences, similarity judgments, and homonym disambiguation. (shrink)

How strongly an agent beliefs in a proposition can be represented by her degree of belief in that proposition. According to the orthodox Bayesian picture, an agent's degree of belief is best represented by a single probability function. On an alternative account, an agent’s beliefs are modeled based on a set of probability functions, called imprecise probabilities. Recently, however, imprecise probabilities have come under attack. Adam Elga claims that there is no adequate account of the way they can be manifested (...) in decision-making. In response to Elga, more elaborate accounts of the imprecise framework have been developed. One of them is based on supervaluationism, originally, a semantic approach to vague predicates. Still, Seamus Bradley shows that some of those accounts that solve Elga’s problem, have a more severe defect: they undermine a central motivation for introducing imprecise probabilities in the first place. In this paper, I modify the supervaluationist approach in such a way that it accounts for both Elga’s and Bradley’s challenges to the imprecise framework. (shrink)

In this paper, I will make the case that an associative account of predication in Hume seems to allow for impossible predicative conceptions—that is, the conceiving of impossible states of affairs involving subjects instantiating properties or qualities—which violate his Conceivability Principle. The natural response is to argue that such conceptions are not clear and distinct, but substantive worries are raised about a number of attempted solutions along these lines. This poses a predicament for Hume scholars: either we must modify or (...) abandon the Conceivability Principle, or reject an associative account of predication, or concede that Hume faces a difficulty he cannot solve. (shrink)

The general concept of a trope – that of a non-shareable character-grounder – admits of a distinction between modifier tropes and module tropes. Roughly, a module trope is self-exemplifying whereas a modifier trope is not. This distinction has wide-ranging implications. Modifier tropes are uniquely eligible to be powers and fundamental determinables, whereas module tropes are uniquely eligible to play a direct role in perception and causation. Moreover, each type of trope theory faces unique challenges concerning character- grounding. Modifier trope theory (...) faces challenges concerning the inscrutability of predication and the incompatibility with bundle theory, whereas module trope theory faces challenges concerning character overdetermination and a collapse into austere nominalism. These differences indicate that the modifier/module distinction divides the advantages of general trope theory and thus presents the trope theorist with a pivotal choice. (shrink)

In the debate between relativism and contextualism about various expressions, the Operator Argument, initially proposed by Kaplan , has been taken to support relativism. However, one widespread reaction against the argument has taken the form of arguing against one assumption made by Kaplan: namely, that certain natural language expressions are best treated as sentential operators. Focusing on the only extant version of the Operator Argument proposed in connection to predicates of personal taste such as “tasty” and experiencer phrases such as (...) “for Anna” ), in this paper I investigate whetherthe reasons offered by Cappelen and Hawthorne against various assumptions of the argument failing in the case of modal, temporal, locationaland precisional expressions transfer to the case of experiencer phrases to undercut support for relativism about predicates of personal taste. My aim is to show that they don’t. Thus, I first show that their considerations against experiencer phrases such as “for Anna” being sentential operators are not decisive. Second, I show that even if granting that such experiencer phrases are not sentential operators, a suitably modified version of the Operator Argument can be defended from the objections they raise. (shrink)

The standard rule of single privative modification replaces privative modifiers by Boolean negation. This rule is valid, for sure, but also simplistic. If an individual a instantiates the privatively modified property (MF) then it is true that a instantiates the property of not being an F, but the rule fails to express the fact that the properties (MF) and F have something in common. We replace Boolean negation by property negation, enabling us to operate on contrary rather than contradictory properties. (...) To this end, we apply our theory of intensional essentialism, which operates on properties (intensions) rather than their extensions. We argue that each property F is necessarily associated with an essence, which is the set of the so-called requisites of F that jointly define F. Privation deprives F of some but not all of its requisites, replacing them by their contradictories. We show that properties formed from iterated privatives, such as being an imaginary fake banknote, give rise to a trifurcation of cases between returning to the original root property or to a property contrary to it or being semantically undecidable for want of further information. In order to determine which of the three forks the bearers of particular instances of multiply modified properties land upon we must examine the requisites, both of unmodified and modified properties. Requisites underpin our presuppositional theory of positive predication. Whereas privation is about being deprived of certain properties, the assignment of requisites to properties makes positive predication possible, which is the predication of properties the bearers must have because they have a certain property formed by means of privation. (shrink)

Persian possesses a number of stative complex predicates with _dâshtan_ ‘to have’ that express certain kinds of mental state. I propose that these _possessive experiencer complex predicates_ be given a formal semantic treatment involving possession of a portion of an abstract quality by an individual, as in the analysis of property concept lexemes due to Francez and Koontz-Garboden (Language 91(3):533–563, 2015 ; Natural Language and Linguistic Theory 34:93–106, 2016 ; Semantics and morphosyntactic variation: Qualities and the grammar of property concepts, (...) Oxford University Press, 2017 ). Augmented with an analysis of prepositional phrases introducing the target of the mental state and an approach to gradability in terms of measure functions (Wellwood in Measuring predicates, PhD dissertation, University of Maryland, College Park, 2014 ), the analysis explains various properties of possessive experiencer complex predicates, including the behavior of target phrases, the ability of the non-verbal element to be modified by a range of adjectives, the direct participation of the non-verbal element in comparative constructions, and the ability of degree expressions to modify both the non-verbal element and the VP containing the complex predicate. Theoretically, the analysis ties transitive mental state expressions to the grammar and semantics of property concept sentences, which are expressed via possessive morphosyntax cross-linguistically, and connects with syntactic proposals that independently argue for a universal underlyingly possessive morphosyntax for mental state predicates (Noonan in Case and syntactic geometry, PhD dissertation, McGill University, 1992 ; Hale and Keyser in Prolegomenon to a theory of argument structure, MIT Press, 2002 ). The work here also motivates modifications to Francez and Koontz-Garboden’s original proposal, and opens new questions in the original empirical domain of the analysis of possessive predicating strategies for the expression of property concept sentences. (shrink)

The purpose of this paper is to outline an alternative approach to introductory logic courses. Traditional logic courses usually focus on the method of natural deduction or introduce predicate calculus as a system. These approaches complicate the process of learning different techniques for dealing with categorical and hypothetical syllogisms such as alternate notations or alternate forms of analyzing syllogisms. The author's approach takes up observations made by Dijkstrata and assimilates them into a reasoning process based on modified notations. The (...) author's model adopts a notation that addresses the essentials of a problem while remaining easily manipulated to serve other analytic frameworks. The author also discusses the pedagogical benefits of incorporating the model into introductory logic classes for topics ranging from syllogisms to predicate calculus. Since this method emphasizes the development of a clear and manipulable notation, students can worry less about issues of translation, can spend more energy solving problems in the terms in which they are expressed, and are better able to think in abstract terms. (shrink)

In a 2010 paper Daley argues, contra Fodor, that several syntactically simple predicates express structured concepts. Daley develops his theory of structured concepts within Tichý’s Transparent Intensional Logic . I rectify various misconceptions of Daley’s concerning TIL. I then develop within TIL an improved theory of how structured concepts are structured and how syntactically simple predicates are related to structured concepts.

Ordinary disposition ascriptions appear to form a semantically heterogeneous class of clauses some of which can be straightforwardly analyzed as possibility claims, and some of which resist a simple quantificational treatment. For example, while “The block is breakable” is true if the block breaks at a relevant possible world, for “The block is fragile” to be true it doesn’t suffice that the block breaks at one of the worlds that matter to the evaluation of the ascription, since the block could (...) break accidentally and yet be sturdy. The contrast has been taken to indicate that sentences like “The block is fragile” don’t introduce mere existential quantification over sets of worlds, and should be represented as claims about sufficient ratios or proportions of worlds. However, recent work has suggested that by pairing the recalcitrant DAs with modified manifestation phrases, we can generalize the standard analysis of existential DAs to the problematic examples, and state a uniform characterization of DAs as claims of possibility. The paper discusses some counterexamples to the view that allegedly non-existential DAs are covert claims of fine-grained possibility, and sketches a hybrid account combining proportional quantification with fine-grained manifestations. (shrink)

This paper consists principally of selections from a much longer work on the semantics of English. It discusses some problems concerning how to represent grammatical modifiers (e.g. slowly in x drives slowly) in a logically perspicuous notation. A proposal of Reichenbach's is given and criticized; then a new theory (apparently discovered independently by myself, Romain Clark, and Richard Montague and Hans Kamp) is given, in which grammatical modifiers are represented by operators added to a first-order predicate calculus. Finally some (...) problems concerning applications of adjectives to that-clauses and gerundive-clauses are discussed. (shrink)

We prove that the theory of the extensional compositional truth predicate for the language of arithmetic with \Delta 0 -induction scheme for the truth predicate and the full arithmetical induction scheme is not conservative over Peano Arithmetic. In addition, we show that a slightly modified theory of truth actually proves the global reflection principle over the base theory.

This study offers syntactic and semantic evidence that there are three types of locative modifiers within the verbal domain that differ with respect to their syntactic base position and interpretation. Two of them are subject to semantic indeterminacy, thereby leading to multiple utterance meanings. The study aims at showing that the full range of interpretations can be derived within a rigid account of lexical and compositional semantics. Locative modifiers are invariably treated as first-order predicates adding a locative constraint. All semantic (...) differences originate from the structural environment they are embedded in and the pragmatic resolution of semantic indeterminacy. The syntactic distribution of locative modifiers is shown to be derivable from interface conditions. (shrink)

This paper is the result of a contribution between ethics and law, which will be used as thought-process tools, to address the complex issue of legal and ethical statuses of GM fish. To find answers, we propose to consider this issue from a wider angle, looking at the relations between the human, animal, and living worlds. We show that it is possible to construct other forms of intellectual logic that, without setting these worlds in opposition, do not lapse into relativism (...) where boundaries are blurred. In this sense, we submit the hypothesis that ordered pluralism should help us to move past a mere Man–Animal relationship to reveal the entire complexity of relationships within mankind and between mankind and other (non-human) worlds alongside it and to which it belongs: the animal and living worlds. With this new logic, “animal ethics” and “animal law” are re-embedded into a set of relationships. This logic emerges from a new consideration: the nature of the contemporary objects we are dealing with. We shall call objects like genetically modified fish “relational objects” in the sense that in order to be apprehended, they utilize a set of relationships of which there are just as many as the dimensions forming them, not as predicates but as primary constituents. Experimentally, in the case of GM fish, we translate this by proposing to typologize legal and ethical considerations induced by multiple relations connected to this object. According to the type of relationship in question, the GM fish will not have the same status; it is a changing object that must be suitably apprehended. (shrink)

A method for constructing continua of logics squeezed between some intermediate predicate logics, developed by Suzuki [8], is modified and applied to intervals of the form [L, L+ ¬¬S], where Lis a predicate logic, Sis a closed predicate formula. This solves one of the problems from Suzuki's paper.

In a previous paper I described a range of nonmonotonic conditionals that behave like conditional probability functions at various levels of probabilistic support. These conditionals were defined as semantic relations on an object language for sentential logic. In this paper I extend the most prominent family of these conditionals to a language for predicate logic. My approach to quantifiers is closely related to Hartry Field's probabilistic semantics. Along the way I will show how Field's semantics differs from a substitutional (...) interpretation of quantifiers in crucial ways, and show that Field's approach is closely related to the usual objectual semantics. One of Field's quantifier rules, however, must be significantly modified to be adapted to nonmonotonic conditional semantics. And this modification suggests, in turn, an alternative quantifier rule for probabilistic semantics. (shrink)

In the Categories Aristotle defined substance as that which is neither predicable of nor in another. In saying that a substance is not predicable of another, Aristotle meant to exclude genera and species from the category substance. Aman is a substance but not man. In saying that a substance is not in another, Aristotle meant to exclude property particulars from the category. A man is a substance, not his color. The Categories treats substances as simples. Though a particular substance, Bucephalus (...) the horse, has parts, it is nevertheless a single entity in the category substance and, hence, incomplex in the way a black thing or a running man are not. Black things and runners are complex because they are aggregates of substances and property particulars. Even if a horse is one substance and, thus, an entity, a horse is made of parts and one may wonder how it is related to its parts, as well as how its being made of parts coheres with the definition of substance given in the Categories. (shrink)

The possibility of error is related to the existence a norm. Connections are spelled out to the notion of infallibility and to that of a modifying predicate, to traditional truth theories in connection with “truth of things”, as well as the primacy of the negative cases, for instance “ false friend”.

In this paper I concern myself with The Superman Puzzle. I argue that the descriptive content associated with proper names, besides determining the proper name’s reference, function as truth-conditionally relevant adjuncts which can be used to express a manner, reason, goal, time or purpose of action. In that way a sentence with a proper name ‘NN is doing something’ could be understood as ‘NN is doing something as NN’. I argue that the substitution of names can fail on modified readings (...) because the different descriptive content of proper names modifies the main predicate differently. Here I present a formal representation of modified predicates which allows one to model intuitively the different truth-conditions of sentences from The Puzzle. (shrink)

The notion of existence is a very puzzling one philosophically. Often philosophers have appealed to linguistic properties of sentences stating existence. However, the appeal to linguistic intuitions has generally not been systematic and without serious regard of relevant issues in linguistic semantics. This paper has two aims. On the one hand, it will look at statements of existence from a systematic linguistic point of view, in order to try to clarify what the actual semantics of such statements in fact is. (...) On the other hand, it will explore what sort of ontology such statements reflect. The first aim is one of linguistic semantics; the second aim is one of descriptive metaphysics. Philosophically, existence statements appear to reflect the distinction between endurance and perdurance as well as particular notions of abstract states and of kinds. Linguistically, statements of existence involve a particular way of drawing the distinction between eventive and stative verbs and between individual-level and stage-level predicates as well as a particular approach to the semantics of bare plurals and mass nouns. (shrink)

The paper is in two parts. In Part I, a semantics for embedded and query uses of interrogatives is put forward, couched within a situation semantics framework. Unlike many previous analyses,questions are not reductively analysed in terms of their answers. This enables us to provide a notion of ananswer that resolves a question which varies across contexts relative to parameters such as goals and inferential capabilities. In Part II of the paper, extensive motivation is provided for an ontology that distinguishes (...) propositions, questions, and facts, while at the same time the semantics provided captures an important commonality between questions and propositions: factsprove propositions andresolve questions. This commonality is exploited to provide an explanation for why predicates such as know carry presuppositions such as factivity and for a novel account of the behaviour of adverbially modified predicates with interrogative, declarative and fact-nominal arguments. (shrink)

In this paper I concern myself with The Superman Puzzle. I argue that the descriptive content associated with proper names, besides determining the proper name's reference, function as truthconditionally relevant adjuncts which can be used to express a manner, reason, goal, time or purpose of action. In that way a sentence with a proper name NN is doing something could be understood as NN is doing something as NN. I argue that the substitution of names can fail on modified readings (...) because the different descriptive content of proper names modifies the main predicate differently. Here I present a formal representation of modified predicates which allows one to model intuitively the different truth-conditions of sentences from The Puzzle. (shrink)

The question in the background of this article is what kind of epistemology can emerge on the basis of the philosophy of life. To answer this question, the theories of Georg Misch and Josef König have been analysed. Both authors differentiate between the analytic discourse of theoretical approaches to the world and the synthetic discourse of non-theoretical objectifications of life which create a human semantic environment. For Misch, the former is constituted with “discursive” and the later with “evocative” utterances. For (...) König as developed in his work “Sein und Denken”, “determining” and “modifying” predicates oppose each other as cardinally different cognitive and epistemological entities. The article focuses on König′s analysis of the genesis and logics of “determining” and “modifying” predication following the strategy of his book. In conclusion some controversies between Misch′s and König′s conceptions of a language constitution of the world are represented and discussed. (shrink)

Although, in the literature, Principle C of Binding Theory is taken not to apply to copular sentences on the basis of English data alone, this study aims to show that this Principle applies to French copular sentences. French displays a dichotomy between predicational copular sentences and other subtypes of copular sentences : while the former use the verb est alone, the latter need an additional form, namely the neuter demonstrative pronoun ce. Evidence is given that, in French, the two terms (...) flanking the copula est cannot be referential because the post-copula term would be bound by the pre-copula one, in accordance with Principle C of Binding Theory. Thus, adding the pronoun ce modifies the structure of the sentence and gives rise to a Topic c’est Focus structure, which escapes Principle C. (shrink)

In my paper, I propose a certain classification of evaluative expressions. I hypothesize that the basic criterion to distinguish between evaluative and descriptive terms is the faultless disagreement test. Next, I discuss a few kinds of phenomena which seem to render this distinction dubious: context–sensitivity, vagueness and using descriptive terms to express evaluative judgments. Further, I investigate Ch. Kennedy’s proposal according to which gradable adjectives can express two kinds of subjectivity. I modify this account by postulating another sub-class of subjective (...) adjectives which are not subjective due to vagueness and which are not evaluative either as they do not necessarily encode any valence. I propose a linguistic test to identify these expressions. Finally, I check where my classification of adjectives places the predicate of personal taste “tasty”. I suggest that “tasty” is both evaluative and experiential and additionally, it carries a condition of its own use, that is the information that can be used to positively assess the taste of something. This, I argue, makes it similar to thin evaluative terms as it carries no descriptive component at all. (shrink)

There is a little known paradox the solution to which is a guide to a much more thoroughgoing solution to a whole range of classic paradoxes. This is shown in this paper with respect to Berry's Paradox, Heterologicality, Russell's Paradox, and the Paradox of Predication, also the Liar and the Strengthened Liar, using primarily the epsilon calculus. The solutions, however, show not only that the first-order predicate calculus derived from Frege is inadequate as a basis for a clear science, (...) and should be replaced with Hilbert and Bernays' conservative extension. Standard second-order logic, and quantified propositional logic also must be substantially modified, to incorporate, in the first place, nominalizations of predicates, and whole sentences. And further modifications must be made, so as to insist that predicates are parts of sentences rather than forms of them, and that truth is a property of propositions rather than their sentential expressions. In all, a thorough reworking of what has been called 'logic' in recent years must be undertaken, to make it more fit for use. (shrink)

I defend a slightly modified version of geach's rule r, I.E., That although both a and b are g, It is possible for a to be the same f as b and a different h than b, Provided that the question whether a and b are the same g is undecidable. Answering those who object to relative identity I claim that they tacitly adhere to a false fregean view, I.E., That one cannot use a singular term to denote an entity (...) x if it is not true that for every y, X=y or not x=y. I show, However, That such terms are, And must be, Used by every empirically oriented language with finite or infinite predicative arsenal, And hence relative identity is more handy than absolute identity. Finally I give a version of leibniz's law for relative identity. (shrink)

We often predicate capacities of substances in such a way so as to modify the way that they exist . However, sometimes a capacity is not for the modification of a substance but for the existence of one. Moreover, we have reason to think that these capacities are just as real as other capacities. If that’s right, then the question arises: if these capacities are real features in the world, what they are real features of? Part I argues that (...) they can’t be capacities of substances, and so they must be capacities of some part of substances. Part II argues that they can’t be capacities of the substance’s integral/substantial parts. Part III argues that a possessor of such capacities would have to be a lot like prime matter in not being characterized by substantial forms. (shrink)

This paper argues that Hindi incorporation is, in fact, pseudoincorporation, involving noun phrases rather than nouns. Furthermore, it shows that there is no requirement that the incorporated nominal form a morphological or even a syntactic unit with the verb. Such loosely aligned nominals can nevertheless be identified as incorporation on the basis of semantic intuitions having to do with number interpretation, anaphora, and certain properties typically associated with lexical processes. Contrary to standard assumptions, it is argued that the targets of (...) pseduo-incorporation are specified for number. Singular incorporated nominals in Hindi are shown to be semantically singular, with number neutrality arising as a consequence of interaction with aspectual specification. Taking aspectual information into account is also shown to have interesting implications for current approaches to the semantics of incorporation, one in which the incorporated nominal introduces a discourse referent, and one in which it functions as a predicate modifier. A closer look at the effect of aspect on anaphora, for example, does not unequivocally support the predicate modification view of pseudoincorporation. The paper also explores the cross-linguistic applicability of the claims made on the basis of Hindi. Most notably, a distinction between Hungarian verbs with respect to incorporation of bare singulars provides striking confirmation of the claims that number morphology is semantically visible in pseudo-incorporation. It also discusses the restrictions on the productivity of pseudo-incorporation in light of the findings for Hindi and Hungarian. (shrink)

This book examines philosophical approaches to linguistic vagueness, a puzzling feature of natural language that gives rise to the ancient Sorites paradox and challenges classical logic and semantics. -/- The Sorites, or Paradox of the Heap, consists in three claims: (1) One grain of sand does not make a heap. (2) One billion grains of sand do make a heap. (3) For any two amounts of sand differing by at most one grain: either both are heaps of sand, or neither (...) one is. The third claim is rendered plausible by an initial conviction that vague predicates like ‘heap’ tolerate small changes. However, the repeated application of a tolerance principle to the second claim yields the further proposition that one grain of sand does make a heap – which contradicts claim number one. Consequently, many philosophers reject or modify tolerance principles for vague predicates. -/- Inga Bones reassesses prominent responses to the Sorites and defends a Wittgensteinian dissolution of the paradox. She argues that vague predicates are, indeed, tolerant and discusses how this finding relates to the paradox itself, to the notion of validity and to the concept of a borderline case . (shrink)