Classes are the objects of the second sort of second-order set theory. They have sets as their members and behave like sets, but paradoxes tell us that many classes cannot be sets. Then, what are classes? Predicativism about classes suggests that classes are predicates of sets, and this article investigates the question from the predicativist point of view in light of recent developments in the use of classes in set theory. Predicativism has been considered too restrictive and unable (...) to accommodate the use of classes in set theory. This diagnosis, however, is only true of a certain specific type of predicativism. In this article, we propose a new type of predicativism, which we call liberal predicativism, and argue that predicativism is still a highly viable option, and our liberal version provides a sufficiently versatile and workable nominalist concept of classes for set theory. (shrink)

In the literature, predicativism is connected not only with the Vicious Circle Principle but also with the idea that certain totalities are inherently potential. To explain the connection between these two aspects of predicativism, we explore some approaches to predicativity within the modal framework for potentiality developed in Linnebo (2013) and Linnebo and Shapiro (2019). This puts predicativism into a more general framework and helps to sharpen some of its key theses.

Predicativists hold that proper names have predicate-type semantic values. They face an obvious challenge: in many languages names normally occur as, what appear to be, grammatical arguments. The standard version of predicativism answers this challenge by positing an unpronounced determiner in bare occurrences. I argue that this is a mistake. Predicativists should draw a distinction between two kinds of semantic type—underived semantic type and derived semantic type. The predicativist thesis concerns the underived semantic type of proper names and underdetermines (...) a view about the semantic type of bare occurrences. I’ll argue that predicativists should hold that bare names are derived individual-denoting expressions. I end by considering what this result means for the relationship between predicativism and other metalinguistic theories of names. (shrink)

In Word and Object, Quine proposed that names be treated as the predicate elements of covert descriptions, expressing the property of being identical to the named individual. More recently, many theorists have proposed a predicativist view according which a referential name expresses the property of being called by that name. Whereas this Being-Called Predicativism has received much attention in the recent literature, Quinean Predicativism has not. This neglect is undeserved. In this paper, I argue, first, that close appositive (...) constructions suggest that names can function as predicates expressing identifying properties of the sort proposed by Quine, and, second, that a predicativist analysis which extends this view to referential names overcomes some of the central objections that have been raised against Being-Called Predicativism. (shrink)

According to predicativism about names, names which occur in argument positions have the same type of semantic contents as predicates. In this paper, I shall argue that these bare singular names do not have the same type of semantic contents as predicates. I will present three objections to predicativism—the modal, the epistemic, and the translation objections—and show that they succeed even against the more sophisticated versions of predicativism defended by Fara and Bach.

Predicativism about names—the view that names are metalinguistic predicates—has yet to confront a foundational issue: how are names represented in the lexicon? I provide a positive characterization of the structure of the lexicon from the point of view Predicativism. I proceed to raise a problem for Predicativism on the basis of that characterization, focusing on cases in which individuals have names which are spelled the same way but pronounced differently. Finally, I introduce two potential strategies for solving (...) the problem, and offer reasons not to be optimistic about either. (shrink)

In this article, we challenge Matushansky’s (Linguistics and Philosophy,21, 573–627, 2008) small clause treatment of proper names in naming constructions. While she is widely credited with establishing, based on cross-linguistic evidence, that names should be viewed as predicates in naming constructions, we present a counterexample from Polish that questions the universal interpretation of the small clause hypothesis (SCH). This leads us to advocate for an alternative analysis of proper names in naming constructions, wherein they are considered components of the argument (...) of a naming verb. We posit that this approach may have deflationist implications for predicativism concerning proper names, as it does not necessitate the existence of primitive name-predicates. We argue that there is no compelling positive evidence for the existence of predicative uses of names whose application conditions cannot be articulated using an equivalent phrase that quotes or mentions the name. Any apparent use of “Delia” as a predicate can be cast either (i) as not really a predicate, but rather an argument mentioning the name “Delia,” or (ii) as a genuine predicate, albeit one with an application condition defined by one of the well-established existing predicates, such as “individual called ‘Delia,’” where the name is mentioned. Predicative uses of names are thus dependent on the mention of names, and so there is a sense in which there are no primitive name-predicates. (shrink)

Consider the following sentences: In every race, the colt won; In every race, John won.John Hawthorne and David Manley say that the difference between these two sentences raises a problem for Predicativism about names. According to the currently more standard version of Predicativism, a bare singular name in argument position, like ‘John’ in , is embedded in a definite description with an unpronounced definite article. The problem is supposed to be that permits a covarying reading that allows for (...) different races to have been won by different colts, while does not permit a covarying reading—it can be true only if there is a single John that won every race. But, the objection runs, if the name ‘John’ is really embedded in a definite description with an unpronounced definite article, then the two sentences are structurally parallel and should not differ with respect to covariation. Appealing to Jason Stanley's ‘Nominal Restriction’ , I show that the difference between the two sentences above not only does not raise a problem for Predicativism but also is actually predicted by it. (shrink)

The view that proper names are uniformly predicates has recently gained prominence. I review linguistic evidence against it. Overall, the linguistic evidence suggests that proper names function as predicates when they appear in a grammatically predicative position and as referential expressions when they are grammatically in a referential position. Conceptual grounds on which the predicativist view might nonetheless be upheld include ‘uniformity’, i.e., that a single semantic value be lexically specified for names in all of their occurrences irrespective of differences (...) in their grammar. However, ‘being a predicate’ or ‘being referential’ are not lexical properties of words but indications for how these grammatically function on an occasion of their use. Moreover, the intuitively referential and intuitively predicative uses of proper names precisely covary with grammatical differences. A proper name is therefore a predicate when it is predicatively used, not when its grammar and meaning are different. Given this grammar-meaning alignment there is no motivation to posit a novel ‘covert syntax’ for names in their referential uses, which breaks this alignment. Cross-linguistic evidence from languages such as Catalan, which features overt determiners in referential uses of proper names, moreover turns out to strongly support the view that the grammar of human language is systematically sensitive to differences in the referential and predicative uses of names. (shrink)

The standard versions of predicativism are committed to the following two theses: proper names are count nouns in all their occurrences, and names do not refer to objects but express name-bearing properties. The main motivation for predicativism is to provide a uniform explanation of referential names and predicative names. According to predicativism, predicative names are fundamental and referential names are explained by appealing to a null determiner functioning like “the” or “that.” This paper has two goals. The (...) first is to reject the predicativists’ explanation of the two types of names. I present three syntactic counterexamples to the predicativists’ account of referential names: incorporation, modification, and measure phrase uses. The second goal is to present a novel strategy to explain the two types of names. I propose that referential names are fundamental but that there are null morphemes available for transforming a name into a count noun (and possibly into other syntactic categories). (shrink)

Recently, and rather startlingly, given the history of the debate about a name's semantic content, some claim that names are in fact predicates -- predicativism. Some of predicativists claim that a name's semantic content involves the concept of being called -- calling accounts that have been traditionally meta-linguistic. However, these accounts fail to be informative. Inspired by Burge's claim that proper names are literally true of the individuals that have them, Fara develops a non-meta-linguistic concept of being called analysed (...) in terms of property attributions. I offer seven separate reasons for rejecting the account, one of which is that Fara's development of the view, at least, has implausible consequences for a theory of name acquisition. I sketch an alternative account of name acquisition that is meta-linguistic in nature, but because it is not offered as a theory of name's content, the standard worries fail to apply. In fact, I argue that an account of name acquisition must be meta-linguistic, and therefore a more nuanced conception of meta-linguistic speech acts is required. The account invokes Austin's performative-constative distinction. It analyses name acquisition as due to performative meta-linguistic speech acts. (shrink)

Overview The debate over the semantics of proper names has, of late, heated up, focusing on the relative merits of referentialism and predicativism. Referentialists maintain that the semantic function of proper names is to designate individuals. They hold that a proper name, as it occurs in a sentence in a context of use, refers to a specific individual that is its referent and has just that individual as its semantic content, its contribution to the proposition expressed by the sentence. (...) Furthermore, a proper name contributes its referent to the proposition expressed by virtue of mechanisms of direct reference to individuals, not by virtue of expressing properties. Predicativists embrace an opposing view according to which proper names are just a special kind of common noun. Their semantic function is to designate properties of individuals. A proper name, as it occurs in a sentence in a context of use, expresses a property, and that property is its contribution to the proposition expr .. (shrink)

Contributing to the debate between referentialist and predicativist accounts of the semantics of proper names, this paper partly endorses a recent trend to reject unitary accounts of their semantics. It does so by restoring a Fregean version of the variety of use account. It criticizes alternative variety of use accounts for not clearly distinguishing pragmatic, syntactic, and semantic issues and argues that, once these are distinguished, the necessity of accepting that names have a variety of uses, and are sometimes logical (...) singular terms and at others logical predicates shows that Frege’s claim, that we should recognize that names have both reference and sense, is vindicated. (shrink)

Clarence Sloat, Ora Matushansky, and Delia Graff Fara advocate a Syntactic Rationale on behalf of predicativism, the view that names are predicates in all of their occurrences. Each argues that a set of surprising syntactic data compels us to recognize names as a special variety of count noun. This data set, they say, reveals that names’ interaction with the determiner system differs from that of common count nouns only with respect to the definite article ‘the’. They conclude that this (...) special distribution of names is best explained by the-predicativism, the view that posits the existence of the null-determiner ‘the’ preceding bare singular names. This essay argues that they have incorrectly discerned the syntactic facts: their critical data point concerning the ungrammaticality of sentences like “The Katherine wants coffee” is mistaken. Such sentences’ grammaticality undermines the Syntactic Rationale and presents serious auxiliary problems for predicativism. (shrink)

In 'The Reference Book' (2012), Hawthorne and Manley observe the following contrast between (1) and (2): -/- (1) In every race John won. (2) In every race, the colt won. -/- The name 'John' in (1) must intuitively refer to the same single individual for each race. However, the description 'the colt' in (2) has a co-varying reading, i.e. a reading where for each race it refers to a different colt. This observation is a prima facie problem for proponents of (...) so-called The-Predicativism which is the view that the name in (1) is really a covert definite description, viz. 'the John'. If the The-Predicativism is correct, (1) and (2) are therefore syntactically equivalent, but this makes it mysterious why only (2) would have a co-varying reading. In a recent paper, Fara (2015) argues that there is a simple and elegant way for proponents of The-Predicativism to explain this contrast. This explanation relies on discerning some subtle syntactic differences between (1) and (2) which in turn are based on assumptions about nominal restrictions a la Stanley and Szabó (2000). In this short paper, I demonstrate that Fara's proposed explanation has a variety of serious shortcomings and hence that the contrast between (1) and (2) remains a significant problem for Predicativism. (shrink)

The unification argument, usually regarded as the main argument for predicativism about proper names, has recently been attacked by Robin Jeshion. According to Jeshion, the unification argument is based on the assumption of the literality of predicative uses of proper names in statements such as “There is one Alfred in Princeton.” In such a use, a proper name ‘N’ is used predicatively to denote those, and only those, objects called N. As Jeshion argues, however, there are many other examples (...) in which a proper name ‘N’ is used predicatively to denote objects which are not called N. Based on such cases, Jeshion challenges the predicativist to provide a justification for assuming that the original predicative use of proper names, to which the predicativist appeals in the unification argument, is literal. My aim in this paper is to defend predicativism by arguing that the predicativist’s assumption is well motivated. To this end, I first present the unification argument for predicativism and Jeshion’s challenge to it. Then, I argue that the answer provided by Delia Graff Fara to Jeshion’s challenge is unsatisfactory. Finally, I meet Jeshion’s challenge by extending the phenomena highlighted in Jeshion’s examples to the referential uses of proper names. (shrink)

By combining some technical results from metamathematicalinvestigations of systems of Bounded Arithmetic, I will givean argument for the untenability of Nelson 's finitistic program,encapsulated in his book Predicative Arithmetic.

The-Predicativism is the view that names are count nouns. For example, the meaning of the name ‘Louise’ is roughly the property of being called Louise. Moreover, proponents of this view maintain that names that are ostensibly in argument position of a predicate are covert definite descriptions. In recent years, The-Predicativism has acquired a number of new supporters, mainly Elbourne (), Matushansky (), and Fara (). And while it was pointed out by Kripke () that these kinds of views (...) generally struggle with capturing the rigidity of proper names, these new views are alleged to solve this problem. In this paper I argue that the more recent versions of the view continue to struggle. In particular, I show that the views fail to provide an explanatory and/or empirically adequate analysis of rigidity. My discussions of these views are then supplemented with a general diagnosis of the problem and an explanation of why it is unlikely to be solved by The-Predicativism. (shrink)

One reason to think that names have a predicate-type semantic value is that they naturally occur in count-noun positions: ‘The Michaels in my building both lost their keys’; ‘I know one incredibly sharp Cecil and one that's incredibly dull’. Predicativism is the view that names uniformly occur as predicates. Predicativism flies in the face of the widely accepted view that names in argument position are referential, whether that be Millian Referentialism, direct-reference theories, or even Fregean Descriptivism. But names (...) are predicates in all of their occurrences; they are predicates that are true of their bearers. When a name appears as a bare singular in argument position, it really occupies the predicate position of what in this essay is called a denuded definite description: a definite description with an unpronounced definite article. Sloat provided good evidence for this. The definite article is sometimes pronounced with names in the singular: ‘The Ivan we all love doesn't feel well’. Sloat proposed a disjunctive generalization of when the definite article must be pronounced with a singular name. This essay shows that by slightly revising Sloat's generalization, we arrive at a simple, nondisjunctive, syntactic rule that governs the overt appearance of the definite article with singular names. But Ivan does not necessarily bear the name ‘Ivan’, so one might worry that the sentence “Ivan might not have had ‘Ivan’ as a name” would incorrectly be predicted false. This essay shows that Predicativism does not have this consequence by showing that incomplete definite descriptions in general and incomplete denuded descriptions, such as ‘Øthe Ivan’, in particular are rigid designators. (shrink)

Although the view that sees proper names as referential singular terms is widely considered orthodoxy, there is a growing popularity to the view that proper names are predicates. This is partly because the orthodoxy faces two anomalies that Predicativism can solve: on the one hand, proper names can have multiple bearers. But multiple bearerhood is a problem to the idea that proper names have just one individual as referent. On the other hand, as Burge noted, proper names can have (...) predicative uses. But the view that proper names are singular terms arguably does not have the resources to deal with Burge’s cases. In this paper I argue that the Predicate View of proper names is mistaken. I first argue against the syntactic evidence used to support the view and against the predicativist’s methodology of inferring a semantic account for proper names based on incomplete syntactic data. I also show that Predicativism can neither explain the behaviour of proper names in full generality, nor claim the fundamentality of predicative names. In developing my own view, however, I accept the insight that proper names in some sense express generality. Hence I propose that proper names—albeit fundamentally singular referential terms—express generality in two senses. First, by being used as predicates, since then they are true of many individuals; and second, by being referentially related to many individuals. I respond to the problem of multiple bearerhood by proposing that proper names are polyreferential, and also explain the behaviour of proper names in light of the wider phenomenon I called category change, and show how Polyreferentialism can account for all uses of proper names. (shrink)

Names are referring expressions and interact with the determiner system only exceptionally, in stark contrast with count nouns. The-predicativists like Sloat, Matushansky, and Fara claim otherwise, maintaining that syntactic data offers indicates that names belong to a special syntactic category which differs from common count nouns only in how they interact with ‘the’. I argue that the-predicativists have incorrectly discerned the syntactic facts. They have bypassed a large range of important syntactic data and misconstrued a critical data point on which (...) they ground the-predicativism. The right data offers new compelling syntactic grounds for referentialism. (shrink)

I argue that predicativism, the view that proper names are predicates, is a viable theory of the semantics of proper names given a certain hypothesis about the grammar of definiteness. Extant versions of predicativism hold that a singular name in argument position constitutes the predicative component of a covert definite description. I show that these versions cannot accommodate semantic and typological data, specifically: syntactic and semantic disparities between bare and non-bare occurrences of such names in English, the distinctive (...) modal rigidity displayed by names, as opposed to common noun definite descriptions, and cross-linguistic data that feature seemingly distinct determiners for names in argument position. I propose that predicativism needs to embrace a view of definite marking as complex, consisting of a definite article and a bindable, familiarity-tracking constituent, which I call _index_. I show that this view is empirically motivated and typologically attested. The resulting version of predicativism can accommodate elegantly the observed semantic data when coupled with language-specific morpho-phonological generalizations. I finally address criticisms of and alternatives to my version of predicativism. (shrink)

This essay is devoted to the study of proper names. Although the view that sees proper names as referential singular terms is widely considered orthodoxy, there is a growing popularity to the view that proper names are predicates. This is partly because the orthodoxy faces two anomalies that Predicativism can solve: on the one hand, proper names can have multiple bearers. But multiple bearerhood is prima facie a problem to the idea that proper names have just one individual as (...) referent. On the other hand, proper names can have predicative uses. But the view that proper names are singular terms arguably does not have the resources to deal with these uses. In this dissertation I argue that the Predicate View of proper names is mistaken. In the first part of the thesis, I analyse this view in its main contentions and offer several arguments to reject it. This critical exercise provides useful insight into the life of proper names that I incorporate in my own view as follows: I argue that the behaviour of proper names should be understood in light of the wider phenomenon I call category change. Thus, I maintain, with orthodoxy, that proper names are fundamentally referential terms, but I also argue that they also have other uses, including the predicative uses highlighted by the predicativist. I also offer a semantic theory according to which proper names are polyreferential, that is, they are terms that can have more than one referent in a way that is distinct from both plural terms and general terms. This theory resolves the problem of multiple bearerhood and provides a base to account for all other uses of proper names that are not referential, i.e., common noun, adjectival and verbal uses, as semantically derived from the more fundamental referential meaning. (shrink)

This paper is about how to interpret and evaluate purported evidence for predicativism about proper names. I aim to point out some underappreciated thorny issues and to offer both predicativists and non-predicativists some advice about how best to pursue their respective projects. I hope to establish three related claims: that non-predicativists have to posit relatively exotic, though not entirely implausible, polysemic mechanisms to capture the range of data that predicativists have introduced ; that neither referentialism nor extant versions of (...) predicativism can offer a very plausible account of the interpretive possibilities for singular unmodified definite descriptions containing names ; and that the most plausible version of predicativism would treat bare names as non-anaphoric definite descriptions. (shrink)

This contribution to the volume explains predicativism, including reasons that favour it and different versions of it. What all predicativist theories have in common is the claim that a proper name is a general, predicative term, with a hidden determiner in its single use.

Longstanding philosophical debate over the semantics of proper names has yet to examine the distinctive behavior of deadnames, names that have been rejected by their former bearers. The use of these names to deadname individuals is derogatory, but deadnaming derogates differently than other kinds of derogatory speech. This paper examines different accounts of this behavior, illustrates what going views of names will have to say to account for it, and articulates a novel version of predicativism that can give a (...) semantic explanation for this derogation. (shrink)

Reverse mathematics is a program in mathematical logic that seeks to give precise answers to the question of which axioms are necessary in order to prove theorems of "ordinary mathematics": roughly speaking, those concerning structures that are either themselves countable, or which can be represented by countable "codes". This includes many fundamental theorems of real, complex, and functional analysis, countable algebra, countable infinitary combinatorics, descriptive set theory, and mathematical logic. This entry aims to give the reader a broad introduction to (...) the history, methodology, and results of the reverse mathematics program, with a particular focus on its connections to foundational programs such as finitism, constructivism, and predicativism. (shrink)

A main selling point of predicativism is that, in addition to accounting for predicative uses of proper names, it can successfully account for their referential uses while treating them as predicates, thus providing a uniform semantics for proper names. The strategy is to postulate an unpronounced determiner that is realised with names when they appear to function as singular terms, making them effectively a concealed determiner phrase. I argue against the thesis that names are really predicates in referential uses. (...) I discuss four different environments where names do not behave like the determiner phrases that are thought to embed them. (shrink)

In this article, I explore the connections between imagination, names, and discoveries by engaging with the works of Alfred North Whitehead and Bertrand Russell. While these two thinkers had divergent philosophical perspectives, I argue that their ideas can be fruitfully integrated into the broader framework of the philosophy of scientific discovery. First, I examine Whitehead’s notion of imagination, distinguishing between two types: counterfactual reasoning within a given theoretical framework and imaginative narrative construction that reshapes the framework itself. This distinction, I (...) suggest, helps clarify how imagination contributes to scientific discoveries. Second, I revisit Russell’s theory of names, proposing a reinterpretation in light of contemporary debates. I advocate for a predicativist reading of Russell’s theory, which, I argue, provides a better account of how names function in the process of scientific discovery—particularly in the naming of newly identified species or concepts. By integrating Whitehead’s insights on imagination and Russell’s refined theory of names, I offer a systematic contribution to the philosophy of scientific discovery, highlighting the structural role of both conceptual tools in shaping scientific progress. (shrink)

PG (Plural Grundgesetze) is a predicative monadic second-order system which exploits the notion of plural quantification and a few Fregean devices, among which a formulation of the infamous Basic Law V. It is shown that second-order Peano arithmetic can be derived in PG. I also investigate the philosophical issue of predicativism connected to PG. In particular, as predicativism about concepts seems rather un-Fregean, I analyse whether there is a way to make predicativism compatible with Frege’s logicism.

This paper contributes to the debate regarding the semantic type of singular referential names. According to one view, known as referentialism, names rigidly designate individuals (Kripke 1972, Abbott 2002, Leckie 2013, Jeshion 2015, Schoubye 2017). According to another view, known as predicativism, names designate properties of individuals (Burge 1973, Geurts 1997, Bach 2002, Elbourne 2005, Matushansky 2008, Fara 2015). Most predicativist accounts claim that bare names in English occur with a phonologically null determiner, a proposal that is based on (...) languages like Greek where names require a determiner in argument position. Novel data from both English and Greek show that names can be nonrigid designators under modal operators ("Aristotle may teach Socrates") and bound variables under quantifiers ("in every set of twins, Helen is a musician"), challenging referentialism. As for rigidity, one possible source of this phenomenon is the proprial article, a name-specific determiner found in Catalan and other languages that may be null in English and homophonous with the definite article in Greek (Ghomeshi and Massam 2009, Muñoz 2019, Izumi and Erickson 2021). While much further research is needed, the data suggest that the proper analysis of names is grounded in predicativism rather than referentialism. (shrink)

From Brouwer To Hilbert: The Debate on the Foundations of Mathematics in the 1920s offers the first comprehensive introduction to the most exciting period in the foundation of mathematics in the twentieth century. The 1920s witnessed the seminal foundational work of Hilbert and Bernays in proof theory, Brouwer's refinement of intuitionistic mathematics, and Weyl's predicativist approach to the foundations of analysis. This impressive collection makes available the first English translations of twenty-five central articles by these important contributors and many others. (...) The articles have been translated for the first time from Dutch, French, and German, and the volume is divided into four sections devoted to (1) Brouwer, (2) Weyl, (3) Bernays and Hilbert, and (4) the emergence of intuitionistic logic. Each section opens with an introduction which provides the necessary historical and technical context for understanding the articles. Although most contemporary work in this field takes its start from the groundbreaking contributions of these major figures, a good, scholarly introduction to the area was not available until now. Unique and accessible, From Brouwer To Hilbert will serve as an ideal text for undergraduate and graduate courses in the philosophy of mathematics, and will also be an invaluable resource for philosophers, mathematicians, and interested non-specialists. (shrink)

A survey is made of work since 1879 on foundational problems viewed as an analysis, by reduction and formalization, of the concepts proof, feasible, number, set, and constructivity. It is suggested that there are five domains of concepts and methods, viz., anthropologism, finitism, intuitionism, predicativism, and platonism. It is also suggested that the central problem is to characterize these domains by formalization and to determine their interrelations by different forms of reduction. Finally, the range of logic in the narrower (...) sense is discussed, and applications of mathematical logic are briefly outlined.ZusammenfassungDie Entwicklung der Grundlagenforschung seit dem Jahre 1879 wird hier im Überblick dargestellt und zwar vom Standpunkt einer Analyse durch Reduktion and Formalisierung der Begriffe Beweis, Zahl, Menge und Konstruktivität aus gesehen. Fünf Bereiche von Begriffsbildungen und Methoden werden zu Grunde gelegt, nämlich: Anthropologismus, Finitismus, Intuitionismus, Prädikativismus und Platonismus. Als zentrale Aufgabenstellung wird hier die Charakterisierung dieser Bereiche durch Formalisierung betrachtet und weiterhin die Bestimmung ihrer gegenseitigen Zusammenhänge durch verschiedene Arten von Reduktionen. Schliesslich wird das Gebiet der Logik im engeren Sinne diskutiert und Anwendungen der mathematischen Logik skizziert.RésuméL'article réexamine les travaux faits depuis 1879 sur les problèmes du fondement des mathématiques, que P'on considère comme des analyses par réduction et formalisation des concepts de démonstration, de nombre, d'ensemble, et de constructivité. On suggère qu'il existe cinq domaines de concepts et de méthodes, à savoir: anthropologisme, finitisme, intuitionisme, « predicativism » et platonisme. On suggère aussi que le problème essentiel consiste à caractériser ces domaines par formalisation et à déterminer leurs relations réciproques par différentes formes de réduction. Finalement, on étudie la portée de la logique prise dans son sens le plus étroit et on esquisse rapidement les applications de la logique mathématique. (shrink)

Serious actualism is the prima facie plausible thesis that things couldn’t have been related while being nothing. The thesis plays an important role in a number of arguments in metaphysics, e.g., in Plantinga’s argument for the claim that propositions do not ontologically depend on the things that they are about and in Williamson’s argument for the claim that he, Williamson, is necessarily something. Salmon has put forward that which is, arguably, the most pressing challenge to serious actualists. Salmon’s objection is (...) based on a scenario intended to elicit the judgment that merely possible entities may nonetheless be actually referred to, and so may actually have properties. It is shown that predicativism, the thesis that names are true of their bearers, provides the resources for replying to Salmon’s objection. In addition, an argument for serious actualism based on Stephanou, 219–250 2007) is offered. Finally, it is shown that once serious actualism is conjoined with some minimal assumptions, it implies property necessitism, the thesis that necessarily all properties are necessarily something, as well as a strong comprehension principle for higher-order modal logic according to which for every condition there necessarily is the property of being a thing satisfying that condition. (shrink)

This paper takes issue with the predicativist’s identification of proper names and common count nouns. Although Predicativism emerges precisely to account for certain syntactic facts about proper names, namely, that they behave like common count nouns on occasions, it seems clear that proper names and common count nouns have different properties, and this undermines the thesis that proper names are in fact just common count nouns. The predicativist’s strategy to bridge these differences is to postulate an unpronounced determiner to (...) go with names when they appear to function as singular terms, making them effectively a concealed determiner phrase. In this paper I revisit these differences and argue that the predicativist’s strategy is not well justified and worse, it does not help make proper names and common count nouns unified; rather, it makes proper names exceptional as count nouns. I also discuss the referentialist’s take on names qua predicates and make some suggestions about how the syntactic difference between proper names and count nouns should be understood. (shrink)

The orthodox view of proper names, Millianism, provides a very simple and elegant explanation of the semantic contribution of referential uses of names–names that occur as bare singulars and as the argument of a predicate. However, one problem for Millianism is that it cannot explain the semantic contribution of predicative uses of names. In recent years, an alternative view, so-called the-predicativism, has become increasingly popular. According to the-predicativists, names are uniformly count nouns. This straightforwardly explains why names can be (...) used predicatively, but is prima facie less congenial to an analysis of referential uses. To address this issue, the-predicativists argue that referential names are in fact complex determiner phrases consisting of a covert definite determiner and a count noun—and so, a referential name is a definite description. In this paper, I will argue that despite the appearance of increased theoretical complexity, the view that names are ambiguous between predicative and referential types is in fact superior to the unitary the-predicativist view. However, I will also argue that to see why this ambiguity view is better, we need to give up the standard Millian analysis. Consequently, I will first propose an alternative analysis of referential names that retains the virtues of Millianism, but provides an important explanatory connection to the predicative uses. Once this analysis of names is adopted, the explanation for why names are systematically ambiguous between referential and predicative types is both simple and elegant. Second, I will argue that the-predicativism has the appearance of being simpler than an ambiguity view, but is in fact unable to account for certain key properties of referential names without making ad hoc stipulations. (shrink)

There are some names which cannot be spoken and others which cannot be written, at least on certain very natural ways of conceiving of them. Interestingly, this observation proves to be in tension with a wide range of views about what names are. Prima facie, this looks like a problem for predicativists. Ultima facie, it turns out to be equally problematic for Millians. For either sort of theorist, resolving this tension requires embracing a revisionary account of the metaphysics of names. (...) Revisionary Millianism, I argue, offers some important advantages over its predicativist competitor. (shrink)

This paper argues for a version of metalinguistic descriptivism, the Mill-Frege view, comparing it to a currently popular alternative, predicativism. The Mill-Frege view combines tenets of Fregean views with features of the theory of direct reference. According to it, proper names have metalinguistic senses, known by competent speakers on the basis of their competence, which figure in ancillary presuppositions. In support of the view the paper argues that the name-bearing relation—which predicativists cite to account for the properties that they (...) take names to express—depends on acts of naming with a semantic significance. Acts of naming create particular words specifically designed for referential use, which they perform whether or not the language has other words articulated with the same sound or orthography. Like other forms of metalinguistic descriptivism, the Mill-Frege view affords responses to Kripke’s semantic and epistemic arguments against descriptivism. The view is prima facie more complex than predicativism; but the additional complexity is independently attested in natural languages and well-motivated. Finally, the Mill-Frege proposal deals well with Kripke’s modal argument, and accounts for modal intuitions about names, both issues that pose serious trouble to predicativism. (shrink)

According to proponents of the continuity hypothesis, metaphors represent one end of a spectrum of linguistic phenomena, which includes various forms of loosening/broadening, such as category extensions and approximations, as well as hyperbolic interpretations. The continuity hypothesis is used to establish that the inferences derived from the set of linguistic expressions mentioned above result from the same or nearly similar pragmatic processes. In this paper, we want to challenge that particular aspect of the continuity hypothesis. We do so based on (...) considerations and analysis of an understudied linguistic phenomenon that we call the metaphorical uses of proper names (MPNs). We first explain how MPNs represent a unique linguistic class distinguishable from, for example, nicknames. In addition, we offer some remarks on how MPNs can be understood against the background of current debates between referentialists and predicativists about names. Our discussion leads us to conclude that MPNs are categorically different from literal interpretations of proper names. We spell out the consequences that the results of our analysis have for the continuity hypothesis. (shrink)

This book brings together philosophers, mathematicians and logicians to penetrate important problems in the philosophy and foundations of mathematics. In philosophy, one has been concerned with the opposition between constructivism and classical mathematics and the different ontological and epistemological views that are reflected in this opposition. The dominant foundational framework for current mathematics is classical logic and set theory with the axiom of choice (ZFC). This framework is, however, laden with philosophical difficulties. One important alternative foundational programme that is actively (...) pursued today is predicativistic constructivism based on Martin-Löf type theory. Associated philosophical foundations are meaning theories in the tradition of Wittgenstein, Dummett, Prawitz and Martin-Löf. What is the relation between proof-theoretical semantics in the tradition of Gentzen, Prawitz, and Martin-Löf and Wittgensteinian or other accounts of meaning-as-use? What can proof-theoretical analyses tell us about the scope and limits of constructive and predicative mathematics? (shrink)

It’s generally assumed that a compositional semantic theory will have to recognise a semantic category of expressions which serve simply to pick out some one object: e-type expressions. Kripke’s views about names, Kaplan’s about indexicals and demonstratives, the standard Tarskian semantics for bound variables, Heim and Kratzer’s Strawsonian view about definites, even an analysis of indefinites, assume as much. In this thesis, I argue that recent advances in the semantics of names and of quotation, and in metaphysics, give good reason (...) to doubt there is such a category. I do so in two parts. In the first part, comprising about two thirds of the thesis, I combine two recent views, one from semantics and one from metaphysics. From semantics, I take over predicativism about names, the view, as one might have guessed, that names are predicates. From metaphysics, I take over the doctrine that there are temporal parts. Putting them together, I hold that the semantic contribution of the name ’Joan’, in a sentence like ’Joan is a barrister’, is a predicate, and in particular a predicate the extension of which is Joan’s temporal parts. Names are not, as is commonly thought, e-type expressions. In the second part, building on the first, I further undermine the existence of a semantically important category of e-type expressions by arguing that a construction which might be thought to mandate such a category, namely de re attitude ascriptions, in fact, when properly analysed, does not do so. I argue this by considering the nature of transparent occurrences of expressions in opaque contexts in general, and in particular by considering the phenomenon of mixed quotation. I present a new theory of it, and show how it can be parlayed into a new Fregean theory of de re attitude ascriptions. The thesis overall, then, will provide strong evidence against the semantic importance of e-type expressions either in language, or in thought. (shrink)

This is the first installment of a two-part essay. Limitations of space prevented the publication of the full essay in present issue of the Journal. The second installment will appear in the next issue, 2021 (1). My overall goal is to outline a strategy for integrating generative linguistics with a broadly pragmatist approach to meaning and communication. Two immensely useful guides in this venture are Robert Brandom and Paul Pietroski. Squarely in the Chomskyan tradition, Pietroski’s recent book, Conjoining Meanings, offers (...) an approach to natural-language semantics that rejects foundational assumptions widely held amongst philosophers and linguists. In particular, he argues against extensionalism—the view that meanings are (or determine) truth and satisfaction conditions. Having arrived at the same conclusion by way of Brandom’s defl ationist account of truth and reference, I’ll argue that both theorists have important contributions to make to a broader anti-extensionalist approach to language. What appears here as Part 1 of the essay is largely exegetical, laying out what I see as the core aspects of Brandom’s normative inferentialism (§1) and Pietroski’s naturalistic semantics (§2). In Part 2 (next issue), I argue that there are many convergences between these two theoretical frameworks and, contrary to first appearances, very few points of substantive disagreement between them. If the integration strategy that I propose is correct, then what appear to be sharply contrasting commitments are better seen as interrelated verbal differences that come down to different—but complementary—explanatory goals. The residual disputes are, however, stubborn. I end by discussing how to square Pietroski’s commitment to predicativism with Brandom’s argument that a predicativist language is in principle incapable of expressing ordinary conditionals. (shrink)

The dominant view maintains that names are directly referring, rigid terms, the primary function of which is to designate an individual. But, as has long been noted, proper names also allow for predicative uses and combine with quantifiers and definite, indefinite, and numerical determiners. Any adequate semantic account of proper names thus must make sense not just of their referential uses but also of their seemingly predicative ones. Predicativists maintain that such uses manifest a name’s semantically encoded, predicative meaning, while (...) the directly referential theorists argue that they involve polysemic or pragmatic, metalinguistic re-interpretations. But while competing accounts differ radically in their analyses of such uses, they all, in the wake of Kripke’s attack on descriptivism, share a common feature: they interpret a predicative use of a name N as expressing (either semantically or pragmatically) the property of being called N. I argue that no such account of predicative uses currently on offer is successful. Indeed, adequately characterizing being called condition is more difficult than has been appreciated. The best attempt—on predicative and directly referential accounts alike—leaves a surprising consequence: names are ambiguous in a way unlike any other we witness with other kinds of lexical items. (shrink)

We suggest a new framework for the Weyl-Feferman predicativist program by constructing a formal predicative set theory P ZF which resembles ZF , and is suitable for mechanization. The basic idea is that the predicatively acceptable instances of the comprehension schema are those which determine the collections they define in an absolute way, independent of the extension of the “surrounding universe”. The language of P ZF is type-free, and it reflects real mathematical practice in making an extensive use of statically (...) defined abstract set terms. Another important feature of P ZF is that its underlying logic is ancestral logic (i.e. the extension of first-order logic with a transitive closure operation). (shrink)

In her recent defense of predicativism for proper names, Delia Graff Fara proposes the following non-metalinguistic being-called condition for the applicability of names as predicates: A name ‘N’ is true of a thing if and only if it is called N. The BCC is supposed to hold for names only. In this essay I criticize Fara’s BCC by arguing that the word ‘called’ is ambiguous, and that the BCC holds only for the particular sense of ‘calling’ as naming. I (...) revise accordingly Fara’s BCC and propose in its place a non-metalinguistic being-named condition. I also argue, against Fara, that being-named conditions are not unique to proper names: they hold for mass nouns, common count nouns, as well as for family names, which I distinguish from surnames. Finally, I discuss honorific titles and propose a being-entitled condition according to which a title ‘T’ is true of a thing just in case it is dubbed T. I conclude the paper with pragmatic, syntactic, as well as semantic considerations in favor of the thesis that names are a subspecies of non-hereditary, honorific titles. (shrink)

The project of this Précis de philosophie de la logique et des mathématiques (vol. 1 under the direction of F. Poggiolesi and P. Wagner, vol. 2 under the direction of A. Arana and M. Panza) aims to offer a rich, systematic and clear introduction to the main contemporary debates in the philosophy of mathematics and logic. The two volumes bring together the contributions of thirty researchers (twelve for the philosophy of logic and eighteen for the philosophy of mathematics), specialists in (...) the history or philosophy of logic or mathematics. Each volume consists of ten chapters; each chapter is about forty pages, is independent from the others and deals with a particular philosophical question about logic or mathematics. The objective is to offer to the French-speaking reader a reference book. On many of the issues addressed, this Précis offers the first clear and thorough synthesis that is available in French. -/- This book is intended for third year / master's students, but also for teachers of philosophy in secondary or higher education, for logicians and mathematicians willing to take a philosophical look at the fundamental concepts of their discipline, and for any reader interested in the basic issues discussed in the philosophy of logic and mathematics. Each chapter is self-contained, although some basic training in logic (or in mathematics, as the case may be) is required. The book should be looked at as a comprehensive framework for contemporary discussions in the philosophy of logic and mathematics, while also giving some guidance on the disciplinary content required by these discussions. -/- The first three chapters of the present volume (on the philosophy of mathematics) are devoted to the history of the philosophy of mathematics: from antiquity to the modern era, and from this period to the foundational crisis of the nineteenth century, to the twentieth century. Next, four chapters deal with the crucial questions for the philosophy of mathematics of the twentieth century: the opposition and/or comparison of set theory and category theory as foundational frameworks for mathematics; mathematical constructivism; the analysis of calculability; and Benaceraff's problem. The two following chapters are focused on the philosophy of mathematical practice, by treating the notion of ideals of proof, in particular explanation and purity, and the notion of informal proof and the use of visual artifacts in mathematical argumentation. Finally the last chapter deals with the applicability of mathematics, including the role of probability. -/- In Chapter 1, Sébastien Maronne and David Rabouin present the history of the philosophy of mathematics from antiquity to the modern era. The goal is to show that the philosophy of mathematics has a history as ancient as mathematics and philosophy itself, a history largely continuous with the latter, often by staying out of sync with respect to the former. In Chapter 2, Sébastien Gandon discusses the question of the foundations of mathematics from Kant to the end of the nineteenth century. By tying this question to Kant, he is able to show that the discussion of the foundations of mathematics that occupied a large part of these two centuries has much older roots. Accent is placed on the differences between the framework proposed by Kant for making sense of classical mathematics and the use made by Frege and then Russell of logical tools for giving a different reading of arithmetic and real analysis. The link between between these different conceptions and the evolution of mathematics itself is also underlined. -/- Chapter 3, written by Hourya Benis-Sinaceur and Mirna Džamonja, deals with the evolution of mathematics in the twentieth century, notably the structuralist turn of Dedekind, E. Noether, and Bourbaki, and certain more recent developments. They devote themselves, among other things, to explaining how these developments can be understood as responses to and extensions of questions posed during the foundational debate of the immediately preceding era. -/- In Chapter 4, Jean-Pierre Marquis and Jean-Jacques Szczeciniarz discuss the different foundational options coming from set theory and category theory. They discuss, among other things, Lawvere's program to replace ZF with an axiomatization of the category of sets, the latter judged better adapted to the needs of contemporary mathematics. Different reactions, as much philosophical as technical, raised by this program are also taken into account. -/- Constructive mathematics are the object of Chapter 5, in which Gerhard Heinzmann and Mark van Atten examine in a critical and comparative manner a variety of constructivisms, including intuitionism, constructive type theory, predicativism, and finitism. -/- In Chapter 6, Guido Gherardi and Maël Pegny present computability theory, stressing its philosophical consequences. They discuss the basic concepts of this theory, for the computability of both the natural numbers and the real numbers. They then tackle the theory of computational complexity. -/- In Chapter 7, Andrea Sereni and Fabrice Pataut present Benacerraf's problem, opposing every possible account of mathematical knowledge to the availability of a theory of truth founded on an abstract ontology of mathematical objects. They give an overview of the original problem and its reformulation by Hartry Field, and reconstruct the debate that this problem has raised, by meeting at once the major opposing positions today of the analytic affiliation of the philosophy of mathematics, as much those on the platonist side as on that of nominalism. -/- In Chapter 8, Valeria Giardino and Yacin Hamami treat certain crucial aspects of the philosophy of mathematical practice. They deal in particular with the notion of an informal proof and on the role of artifacts in mathematical reasoning. They consider how such proofs, making use of these means, can contribute to the understanding of theorems and mathematical theories, thanks also to the role of visualisation and the aid of computer tools. -/- Why do mathematics often give several proofs of the same theorem? This is the question that Andrew Arana raises in Chapter 9, introducing the notion of an epistemic ideal and discuss two such ideals, the explanatoriness and purity of proof. -/- Chapter 10 is devoted to the applicability of mathematics in the study of empirical phenomena. After summarizing the history of this question, going back to Plato and Aristotle and passing by Mill and Kant, Daniele Molinini and Marco Panza reconstruct the contemporary debate, in relation, among other things, to questions raised in the philosophy of science. -/- Two appendices complete the volume. In the first Frédéric Patras treats the French tradition in philosophy of mathematics of the 20th century. In the second, Maria Carla Galavotti discusses the notion of probability and its use in science. (shrink)

After some metatheoretic preliminaries on questions of justification and rational reconstruction, we lay out some key desiderata for foundational frameworks for mathematics, some of which reflect recent discussions of pluralism and structuralism. Next we draw out some implications (pro and con) bearing on set theory and category and topos therory. Finally, we sketch a variant of a modal-structural core system, incorporating elements of predicativism and the systems of reverse mathematics, and consider how it fares with respect to the desiderata (...) highlighted earlier. Overall, we are making a case for "foundations with modest, welltempered foundationalism". (shrink)

In these essays Geoffrey Hellman presents a strong case for a healthy pluralism in mathematics and its logics, supporting peaceful coexistence despite what appear to be contradictions between different systems, and positing different frameworks serving different legitimate purposes. The essays refine and extend Hellman's modal-structuralist account of mathematics, developing a height-potentialist view of higher set theory which recognizes indefinite extendability of models and stages at which sets occur. In the first of three new essays written for this volume, Hellman shows (...) how extendability can be deployed to derive the axiom of Infinity and that of Replacement, improving on earlier accounts; he also shows how extendability leads to attractive, novel resolutions of the set-theoretic paradoxes. Other essays explore advantages and limitations of restrictive systems - nominalist, predicativist, and constructivist. Also included are two essays, with Solomon Feferman, on predicative foundations of arithmetic. (shrink)

One of the main arguments in favor of metalinguistic predicativism is the uniformity argument. The article discusses one of its premises, according to which the Being Called Condition gives the literal meaning of proper names. First, the uniformity argument is presented. Second, the article examines a challenge by Jeshion and a recent response by Tayebi. It is then argued that Tayebi’s response is unsound. Finally, two sets of facts are discussed, which provide independent evidence against the literal meaning thesis.