George Boolos's employment of plurals to give an ontologically innocent interpretation of monadic higher‐order quantification continues and extends a minority tradition in thinking about quantification and ontological commitment. An especially prominent member of that tradition is Stanislaw Leśniewski, and shall first draw attention to this work and its relation to that of Boolos. Secondly I shall stand up briefly for plurals as logically respectable expressions, while noting their limitations in offering ontologically deflationary accounts of higher‐ (...) class='Hi'>order quantification. Thirdly I shall focus on the key idea of ontological commitment and investigate its connection with the idea of truth‐making. Fourthly I shall consider how different interpretations of quantification may sideline Boolos's work, but finally I shall largely support his analysis of quantification involving nominal expressions, while arguing, in the spirit of Arthur Prior, that non‐nominal quantification is non‐committing. (shrink)

It is a commonplace remark that the identity relation, even though not expressible in a first-order language without identity with classical set-theoretic semantics, can be defined in a language without identity, as soon as we admit second-order, set-theoretically interpreted quantifiers binding predicate variables that range over all subsets of the domain. However, there are fairly simple and intuitive higher-order languages with set-theoretic semantics in which the identity relation is not definable. The point is that the definability (...) of identity in higher-order languages not only depends on what variables range over, but also is sensitive to how predication is construed. This paper is a follow-up to , where it has been proven that no actual axiomatization of Leśniewski’s Ontology determines the standard semantics for the epsilon connective. (shrink)

This chapter provides an introduction to higher-order metaphysics as well as to the contributions to this volume. We discuss five topics, corresponding to the five parts of this volume, and summarize the contributions to each part. First, we motivate the usefulness of higher-order quantification in metaphysics using a number of examples, and discuss the question of how such quantifiers should be interpreted. We provide a brief introduction to the most common forms of higher-order (...) logics used in metaphysics, and indicate a number of questions which can be raised in such systems using logical vocabulary alone. Using a further example, we return to applications of higher-order logics in metaphysics. We also mention key developments in the history of higher-order logic as it pertains to metaphysics. Finally, we mention certain arguments which have been raised against the use of higher-order logic, and some ways of responding to them. (shrink)

Subverting a once widely held Quinean paradigm, there is a growing consensus among philosophers of logic that higher-order quantifiers (which bind variables in the syntactic position of predicates and sentences) are a perfectly legitimate and useful instrument in the logico-philosophical toolbox, while neither being reducible to nor fully explicable in terms of first-order quantifiers (which bind variables in singular term position). This article discusses the impact of this quantificational paradigm shift on metaphysics, focussing on theories of properties, (...) propositions, and identity, as well as on the metaphysics of modality. (shrink)

Prior’s problem consists in the impossibility of replacing clausal complements of most attitude verbs by ‘ordinary’ NPs; only ‘special quantifiers’ that is, quantifiers like 'something' permit a replacement, preserving grammaticality or the same reading of the verb: (1) a. John claims that he won. b. ??? John claims a proposition / some thing. c. John claims something. In my 2013 book Abstract Objects and the Semantics of Natural Language, I have shown how this generalizes to nonreferential complements of various other (...) intensional predicates and argued for a Nominalization Theory of special quantifiers. In this paper, I will review and extend the range of linguistic generalizations that motivate the Nominalization Theory and show that they pose serious problems for higher-order and substitutional analyses of special quantifiers. (shrink)

Higher-order realists about properties express their view that there are properties with the help of higher-order rather than first-order quantifiers. They claim two types of advantages for this way of formulating property realism. First, certain gridlocked debates about the nature of properties, such as the immanentism versus transcendentalism dispute, are taken to be dissolved. Second, a further such debate, the tropes versus universals dispute, is taken to be resolved. In this paper I first argue that (...) higher-order realism does not in fact resolve the tropes versus universals dispute. In a constructive spirit, I then develop higher-order realism in a way that leads to a dissolution, rather than a resolution, of this dispute too. (shrink)

This chapter offers an opinionated introduction to higher-order formal languages with an eye towards their applications in metaphysics. A simply relationally typed higher-order language is introduced in four stages: starting with first-order logic, adding first-order predicate abstraction, generalizing to higher-order predicate abstraction, and finally adding higher-order quantification. It is argued that both β-conversion and Universal Instantiation are valid on the intended interpretation of this language. Given these two principles, it (...) is then shown how we can use pure higher-order logic to ask, and begin to answer, metaphysical questions with non-trivial implications. In particular, while we must reject the popular idea that structural differences between sentences correspond to parallel distinctions in the logical structure of extra-linguistic reality, it may still be possible to give a purely logical characterization of objectual aboutness and related notions. (shrink)

Recently, some philosophers have argued that we should take quantification of any order to be a legitimate and irreducible, sui generis kind of quantification. In particular, they hold that a semantic theory for higher-order quantification must itself be couched in higher-order terms. Øystein Linnebo has criticized such views on the grounds that they are committed to general claims about the semantic values of expressions that are by their own lights inexpressible. I show (...) that Linnebo's objection rests on the assumption of a notion of semantic value or contribution which both applies to expressions of any order, and picks out, for each expression, an extra-linguistic correlate of that expression. I go on to argue that higher-orderists can plausibly reject this assumption, by means of a hierarchy of notions they can use to describe the extra-lingustic correlates of expressions of different orders. (shrink)

Although higher-order metaphysics seems prima facie to be a promising new approach to metaphysics, it is nonetheless based on a mistake. This mistake is tied to a misuse of formal languages in metaphysics in general, not just to the use of higher-order rather than lower-order languages. I hope to highlight the mistake by discussing a popular recent example of higher- order metaphysics: the argument that reality is not structured using reasoning inspired by the (...) Russell-Myhill paradox. A key issue will be the relationship between higher-order quantification in formal languages and quantification in English, in particular the questions whether such quantifiers are already to be found in English, and whether they could simply be added to English if not in order to gain expressive strength. I will conclude that little of metaphysical significance follows from this Russell-Myhill inspired argument against structure. The reason why the results of higher-order logic show little of metaphysical significance generalizes to other uses of higher-order logic in metaphysical theorizing, and with it supports that higher-order metaphysics is a flawed research program. I end with some reflections on what positive role formal tools like higher-order logic can have in metaphysics, and what the fundamental mistake is on which higher-order metaphysics is based. (shrink)

Truth predicates are widely believed to be capable of serving a certain logical or quasi-logical function. There is little consensus, however, on the exact nature of this function. We offer a series of formal results in support of the thesis that disquotational truth is a device to simulate higher-order resources in a first-order setting. More specifically, we show that any theory formulated in a higher-order language can be naturally and conservatively interpreted in a first-order (...) theory with a disquotational truth or truth-of predicate. In the first part of the paper we focus on the relation between truth and full impredicative sentential quantification. The second part is devoted to the relation between truth-of and full impredicative predicate quantification. (shrink)

W. V. Quine famously defended two theses that have fallen rather dramatically out of fashion. The first is that intensions are “creatures of darkness” that ultimately have no place in respectable philosophical circles, owing primarily to their lack of rigorous identity conditions. However, although he was thoroughly familiar with Carnap’s foundational studies in what would become known as possible world semantics, it likely wouldn’t yet have been apparent to Quine that he was fighting a losing battle against intensions, due in (...) large measure to developments stemming from Carnap’s studies and culminating in the work of Kripke, Hintikka, and Bayart. These developments undermined Quine’s crusade against intensions on two fronts. First, in the context of possible world semantics, intensions could after all be given rigorous identity conditions by defining them (in the simplest case) as functions from worlds to appropriate extensions, a fact exploited to powerful and influential effect in logic and linguistics by the likes of Kaplan, Montague, Lewis, and Cresswell. Second, the rise of possible world semantics fueled a strong resurgence of metaphysics in contemporary analytic philosophy that saw properties and propositions widely, fruitfully, and unabashedly adopted as ontological primitives in their own right. This resurgence — happily, in my view — continues into the present day. -/- For a time, at any rate, Quine experienced somewhat better success with his second thesis: that higher-order logic is, at worst, confused and, at best, a quirky notational alternative to standard first-order logic. However, Quine notwithstanding, a great deal of recent work in formal metaphysics transpires in a higher-order logical framework in which properties and propositions fall into an infinite hierarchy of types of (at least) every finite order. Initially, the most philosophically compelling reason for embracing such a framework since Russell first proposed his simple theory of types was simply that it provides a relatively natural explanation of the paradoxes. However, since the seminal work of Prior there has been a growing trend to consider higher-order logic to be the most philosophically natural framework for metaphysical inquiry, many of the contributors to this volume being among the most important and influential advocates of this view. Indeed, this is now quite arguably the dominant view among formal metaphysicians. -/- In this paper, and against the current tide, I will argue in §1 that there are still good reasons to think that Quine’s second battle is not yet lost and that the correct framework for logic is first-order and type-free — properties and propositions, logically speaking, are just individuals among others in a single domain of quantification — and that it arises naturally out of our most basic logical and semantical intuitions. The data I will draw upon are not new and are well-known to contemporary higher-order metaphysicians. However, I will try to defend my thesis in what I believe is a novel way by suggesting that these basic intuitions ground a reasonable distinction between “pure” logic and non-logical theory, and that Russell-style semantic paradoxes of truth and exemplification arise only when we move beyond the purely logical and, hence, do not of themselves provide any strong objection to a type-free conception of properties and propositions. -/- Most of my arguments in §1 are largely independent of any specific account of the nature of properties and propositions beyond their type-freedom. However, I will in addition argue that there are good reasons to take propositions, at least, to be very fine-grained. My arguments are thus bolstered significantly if it can be shown that there are in fact well-defined examples of logics that are not only type-free but which comport with such a conception of propositions. It is the purpose of §2 to lay out a logic of this sort in some detail, drawing especially upon work by George Bealer and related work of my own. With the logic in place, it will be possible to generalize the line of argument noted above regarding Russell-style paradoxes and, in §3, apply it to two propositional paradoxes — the Prior-Kaplan paradox and the Russell-Myhill paradox — that are often taken to threaten the sort of account developed here. (shrink)

In this paper I take second order-quantification to be a sui generis form of quantification, irreducible to first-order quantification, and I examine the implications of doing so for the debate over the existence of properties. Nicholas K. Jones has argued that adding sui generis second-order quantification to our ideology is enough to establish that properties exist. I argue that Jones does not settle the question of whether there are properties because—like other ontological questions—it (...) is first-order. Then I examine three of the main arguments for the existence of properties. I conclude that sui generis second-order quantification defeats the “one over many” argument and that, coupled with second-order predication, it also defeats the reference and quantification arguments. (shrink)

So-called 'dynamic' semantic theories such as Kamp's discourse representation theory and Heim's file change semantics account for such phenomena as cross-sentential anaphora, donkey anaphora, and the novelty condition on indefinites, but compare unfavorably with Montague semantics in some important respects (clarity and simplicity of mathematical foundations, compositionality, handling of quantification and coordination). Preliminary efforts have been made by Muskens and by de Groote to revise and extend Montague semantics to cover dynamic phenomena. We present a new higher-order (...) theory of discourse semantics which improves on their accounts by incorporating a more articulated notion of context inspired by ideas due to David Lewis and to Craige Roberts. On our account, a context consists of a common ground of mutually accepted propositions together with a set of discourse referents preordered by relative salience. Employing a richer notion of contexts enables us to extend our coverage beyond pronominal anaphora to a wider range of presuppositional phenomena, such as the factivity of certain sentential-complement verbs, resolution of anaphora associated with arbitrarily complex definite descriptions, presupposition 'holes' such as negation, and the independence condition on the antecedents of conditionals. Formally, our theory is expressed within a higher-order logic with natural number type, separation-style subtyping, and dependent coproducts parameterized by the natural numbers. The system of semantic types builds on proposals due to Thomason and to Pollard in which the type of propositions (static meanings of sentential utterances) is taken as basic and worlds are constructed from propositions (rather than the other way around as in standard Montague semantics). (shrink)

Although higher-order metaphysics seems prima facie to be a promising new approach to metaphysics, it is nonetheless based on a mistake. This mistake is tied to a misuse of formal languages in metaphysics in general, not just to the use of higher-order rather than lower-order languages. I hope to highlight the mistake by discussing a popular recent example of higher- order metaphysics: the argument that reality is not structured using reasoning inspired by the (...) Russell-Myhill paradox. A key issue will be the relationship between higher-order quantification in formal languages and quantification in English, in particular the questions whether such quantifiers are already to be found in English, and whether they could simply be added to English if not in order to gain expressive strength. I will conclude that little of metaphysical significance follows from this Russell-Myhill inspired argument against structure. The reason why the results of higher-order logic show little of metaphysical significance generalizes to other uses of higher-order logic in metaphysical theorizing, and with it supports that higher-order metaphysics is a flawed research program. I end with some reflections on what positive role formal tools like higher-order logic can have in metaphysics, and what the fundamental mistake is on which higher-order metaphysics is based. (shrink)

Martin-Löf's constructive type theory forms the basis of this paper. His central notions of category and set, and their relations with Russell's type theories, are discussed. It is shown that addition of an axiom - treating the category of propositions as a set and thereby enabling higher order quantification - leads to inconsistency. This theorem is a variant of Girard's paradox, which is a translation into type theory of Mirimanoff's paradox (concerning the set of all well-founded sets). (...) The occurrence of the contradiction is explained in set theoretical terms. Crucial here is the way a proof-object of an existential proposition is understood. It is shown that also Russell's paradox can be translated into type theory. The type theory extended with the axiom mentioned above contains constructive higher order logic, but even if one only adds constructive second order logic to type theory the contradictions arise. (shrink)

Using recent results in topos theory, two systems of higher-order logic are shown to be complete with respect to sheaf models over topological spaces-so-called "topological semantics". The first is classical higher-order logic, with relational quantification of finitely high type; the second system is a predicative fragment thereof with quantification over functions between types, but not over arbitrary relations. The second theorem applies to intuitionistic as well as classical logic.

Using recent results in topos theory, two systems of higher-order logic are shown to be complete with respect to sheaf models over topological spaces- so -called "topological semantics." The first is classical higher-order logic, with relational quantification of finitely high type; the second system is a predicative fragment thereof with quantification over functions between types, but not over arbitrary relations. The second theorem applies to intuitionistic as well as classical logic.

In this paper a proposal by Henkin of a nominalistic interpretation for second and higher-order logic is developed in detail and analysed. It was proposed as a response to Quine’s claim that second and higher-order logic not only are committed to the existence of sets, but also are committed to the existence of more sets than can ever be referred to in the language. Henkin’s interpretation is rarely cited in the debate on semantics and ontological commitments (...) for these logics, though it has many interesting ideas that are worth exploring. The detailed development will show that it employs an early strategy of using substitutional quantification in order to reduce ontological commitments. It will be argued that the perspective adopted for the predicate variables renders it a natural extension of Quine’s nominalistic interpretation for first-order logic. However, we will argue that, with respect to Quine’s nominalistic program and his notion of ontological commitment, still holds and thus Henkin’s interpretation is not nominalistic. Nevertheless, it will be seen that is addressed successfully and this provides further insights on the so-called “Skolem Paradox”. Moreover, the interpretation is ontologically parsimonious and, in this respect, it arguably fares better than a recent proposal by Bob Hale. (shrink)

This chapter discusses ontological commitment to properties, understood as ontological correlates of predicates. We examine the issue in four metaontological settings, beginning with an influential Quinean paradigm on which ontology concerns what there is. We argue that this naturally but not inevitably avoids ontological commitment to properties. Our remaining three settings correspond to the most prominent departures from the Quinean paradigm. Firstly, we enrich the Quinean paradigm with a primitive, non-quantificational notion of existence. Ontology then concerns what exists. We argue (...) that this strengthens the Quinean case against ontological commitment to properties while also newly distinguishing between stronger and weaker forms of nominalism. Secondly, we enrich the Quinean paradigm with the ideology of fundamentality. Ontology then centrally concerns what’s fundamental. We argue that this leaves ontological commitment to properties wide open although Bradleyan regress threatens. Thirdly, we enrich the Quinean paradigm with primitive higher-order quantifiers. Ontology then expands to concern what there higher-order is and what there first-order is. We argue that this naturally but not inevitably incurs ontological commitment to properties. (shrink)

Abstract At the time of The Logical Syntax of Language (Syntax), Quine was, in his own words, a disciple of Carnap’s who read this work page by page as it issued from Ina Carnap’s typewriter. The present paper will show that there were serious problems with how Syntax dealt with ontological claims. These problems were especially pronounced when Carnap attempted to deal with higher order quantification. Carnap, at the time, viewed all talk of reference as being part (...) of the misleading material mode of speech, and as such dismissed, rather than addressed, ontological problems. Central to the analysis in the present paper is the concept of an explication, which was seen by both Carnap and Quine as being of great philosophical importance. It will be shown that the concept of explication played a significant role in how each formulated their mature position on ontology. Both these final positions on ontology can also be seen as a evolving in reaction to Carnap’s flawed handling of ontological matters at the time of Syntax. Carnap, influenced by Tarski’s work on semantics, comes to believe that the concept of reference can be given an acceptable explication, and that by doing so we can see reference to abstract objects as unobjectionable. As a result, Carnap develops a position very different from the one presented in Syntax. Quine strongly rejected the instrumentalism of Syntax, and sought to give an explication of ontological questions that was language independent. This paper closes with a discussion of each’s understanding of the other’s position. (shrink)

Ramsey defined truth in the following way: x is true if and only if ∃p(x = [p] & p). This definition is ill-formed in standard first-order logic, so it is normally interpreted using substitutional or some kind of higher-order quantifier. I argue that these quantifiers fail to provide an adequate reading of the definition, but that, given certain adjustments, standard objectual quantification does provide an adequate reading.

Much of the ontology made in the analytic tradition of philosophy nowadays is founded on some of Quine’s proposals. His naturalism and the binding between existence and quantification are respectively two of his very influential metaphilosophical and methodological theses. Nevertheless, many of his specific claims are quite controversial and contemporaneously have few followers. Some of them are: (a) his rejection of higher-order logic; (b) his resistance in accepting the intensionality of ontological commitments; (c) his rejection of first- (...) class='Hi'>order modal logic; and (d) his rejection of the distinction between analytic and synthetic statements. I intend to argue that these controversial negative claims are just interconnected consequences of those much more accepted and apparently less harmful metaphilosophical and methodological theses, and that the glue linking all these consequences to its causes is the notion of extensionality. (shrink)

The paper presents a family of propositional epistemic logics such that languages of these logics are extended by quantification over modal operators or over agents of knowledge and extended by predicate symbols that take modal operators as arguments. Denote this family by \}\). There exist epistemic logics whose languages have the above mentioned properties :311–350, 1995; Lomuscio and Colombetti in Proceedings of ATAL 1996. Lecture Notes in Computer Science, vol 1193, pp 71–85, 1996). But these logics are obtained from (...) first-order modal logics, while a logic of \}\) can be regarded as a propositional multi-modal logic whose language includes quantifiers over modal operators and predicate symbols that take modal operators as arguments. Among the logics of \}\) there are logics with a syntactical distinction between two readings of epistemic sentences: de dicto and de re. We show the decidability of logics of \}\) with the help of the loosely guarded fragment of first-order logic. Namely, we generalize LGF to a higher-order decidable loosely guarded fragment. The latter fragment allows us to construct various decidable propositional epistemic logics with quantification over modal operators. The family of this logics coincides with \}\). There are decidable propositional logics such that these logics implicitly contain quantification over agents of knowledge, but languages of these logics are usual propositional epistemic languages without quantifiers and predicate symbols :345–378, 1993). Some logics of \}\) can be regarded as counterparts of logics defined in Grove and Halpern :345–378, 1993). We prove that the satisfiability problem for these logics of \}\) is Pspace-complete using their counterparts in Grove and Halpern :345–378, 1993). (shrink)

In the previous paper with a similar title :311–344, 2018), we presented a family of propositional epistemic logics whose languages are extended by two ingredients: by quantification over modal operators or over agents of knowledge and by predicate symbols that take modal operators as arguments. We denoted this family by \}\). The family \}\) is defined on the basis of a decidable higher-order generalization of the loosely guarded fragment of first-order logic. And since HO-LGF is decidable, (...) we obtain the decidability of logics of \}\). In this paper we construct an alternative family of decidable propositional epistemic logics whose languages include ingredients and. Denote this family by \}\). Now we will use another decidable fragment of first-order logic: the two variable fragment of first-order logic with two equivalence relations +2E) [the decidability of FO\+2E was proved in Kieroński and Otto :729–765, 2012)]. The families \}\) and \}\) differ in the expressive power. In particular, we exhibit classes of epistemic sentences considered in works on first-order modal logic demonstrating this difference. (shrink)

In this paper, I shall explore a determiner in natural language which is ambivalent as to whether it should be classified as quantificational or objectdenoting: the determiner both. Both in many ways appears to be a paradigmatic quantifier; and yet, I shall argue, it can be interpreted as having an individual—an object—as semantic value. To show the significance of this, I shall discuss two ways of thinking about quantifiers. We often think about quantifiers via intuitions about kinds of thoughts. Certain (...) terms are naturally used to express singular thoughts, and appear to do so by contributing objects to the thoughts expressed. Other terms are naturally used to express general thoughts, and appear to do so by contributing higher-order properties to the thoughts expressed. Viewed this way, the main condition on whether a term is a quantifier or not is whether its semantic value is an object or a higher-order property. At least, these provide necessary conditions. Both can be interpreted as contributing objects to thoughts, and in many cases appears to express genuine singular thoughts. Thinking about quantifiers this way, both can appear object-denoting and non-quantificational. We also often think about quantifiers in terms of a range linguistic features, including semantic value, presupposition, scope, binding, syntactic distribution, and many others. Viewed this way, I shall argue, both can appear quantificational. In particular, it displays scope behavior that is one of the hallmarks of quantification. But, I shall show, it can do so even if given a semantics on which it denotes an object. Thus, both appears quantificational by some linguistic standards, and yet appears object-denoting by standards based on intuitions about the kinds.. (shrink)

Prior’s puzzle is standardly taken to be the puzzle of why, given the assumption that that-clauses denote propositions, substitution of “the proposition that P” for “that P” within the complements of many propositional attitude verbs is invalid. I show that Prior’s puzzle is much more general than is ordinarily supposed. There are two variants on the substitutional form of the puzzle—a quantificational variant and a pronominal variant—and all three forms of the puzzle arise in a wide range of grammatical positions, (...) rather than merely in the complements of propositional attitude verbs. The generalized puzzle shows that a range of proposed solutions to the original puzzle fail, or are radically incomplete, and also reveals the connections between Prior’s puzzle and debates over the nature of semantic types and higher-order quantification. I go on to develop a novel, higher-order solution to the generalized form of the puzzle, and I argue that this higher-approach is superior to its first-order alternatives. (shrink)

Background Analysis of aphasic narratives can be a challenge for clinicians. Previous studies have mainly employed measures that categorized speech samples at the word level. They included quantification of the use and misuse of different word classes, presence and absence of narrative contents and errors, paraphasias, and perseverations, as well as morphological structures and errors within a narrative. In other words, a great amount of research has been conducted in the aphasiology literature focusing on micro-linguistic structures of oral narratives. (...) Aspects of macro- linguistic structures, such as the analysis of content information by a speaker, consistency of using cohesive devices to present information within a narrative, and order of presenting information necessary to form a coherent discourse, have not been extensively investigated. The current investigation proposes a clinical analytic system to target three aspects of macro-linguistic structures in narratives among speakers with aphasia. Specifically, (1) the presence of search events (i.e., the mentioning of key events that allow the listener to understand; Capilouto, Wright, &Wagovich, 2006) within a narrative, (2) the sequence of the mentioned events, and (3) the informativeness (i.e., the fulfillment of lexical items that allow the user to understand what the event is detailing) of the event contents, were focused in the proposed framework. Method Ten controls transcripts from were selected from the AphasiaBank (MacWhinney, Fromm, Forbes, & Holland, 2011). Three narrative tasks, including sequential picture description of ‘Refused Umbrella’, procedural narrative of making a ‘Peanut Butter and Jelly Sandwich’, and telling of ‘Cinderella’ story, were used to establish normative data for the basis of analysis. Specifically, the Search Events (e) and Informative Words (i) used by at least 70% of the speakers were listed for each genre. The sequential order of mentioning the Search Events, i.e., common order of events in 90% of the speakers, (s.total) was determined. Twelve speakers with aphasia (nine fluent and three non-fluent) were recruited and administered the Western Aphasia Battery and Object and Action Naming Battery. Their performance in the above three discourse tasks were orthographically transcribed and analyzed using the following measures: e.total, e.matched with norm, e.missed, e.irrlevant, e.extra, s.total, i.pb&j, i.umbr, i.cind, and i.total. Three samples were randomly chosen to be re-analyzed for inter- and intra-rater reliability. Results Results of an independent t-test suggested significant differences between the fluent and non-fluent subjects in sequential order of Search Events for all genres (s.total) and i.total, suggesting sensitivity of this framework to differentiate between the two fluency groups. Results of Pearson product-moment correlations revealed significant relation between Informative Words and WAB spontaneous speech scores, AQ, as well as OAB scores, for both aphasic groups. The mean value of coefficients for intra-rater reliability (0.992), with significant correlations on e.match, e.miss, and e.extra, was higher than that of inter-rater reliability (0.897). Discussion Based on our preliminary results, this objective framework allowed clinical evaluation of impairment in macro-linguistic structures present in aphasic discourse. Further extension should involve more subjects encompassing a wider range of severity with different types of aphasia. (shrink)

RESUMEN Se ha destacado que la Fórmula de Barcan -FB- y la Conversa de la Fórmula de Barcan -CFB- para lógica modal cuantificacional de orden superior parecen válidas. Si se interpreta que los cuantificadores tienen como rango propiedades, la validez de FB y CFB parece implicar la existencia de universales trascendentes, que no requieren estar instanciados para existir en un mundo posible. Se discute esta argumentación, porque la semántica, en la que los resultados de validez se siguen, no requiere que (...) las ‘intensiones' asignadas a las variables de orden superior estén instanciadas en un mundo posible para que la intensión exista ahí. En una semántica modificada, más neutral, FB y CFB de orden superior ya no son válidas. Además se sostiene que, incluso si FB y CFB de orden superior fuesen válidas, no se obtendrían resultados metafísicos sustantivos, pues diferentes formas de nominalismo y teorías de tropos las aceptarían. ABSTRACT It has been pointed out that the Barcan Formula -BF- and the Converse Barcan Formula -CBF- seem to be valid for higher-order modal quantificational logic. If quantifiers are construed as ranging over properties, the validity of BF and CBF seems to entail the existence of transcendent universals that do not require instantiation in order to exist in a possible world. The paper discusses this argument given that semantics, in which validity results follow from one another, do not require that the "intensions" assigned to higher- order variables be instantiated in a possible world in order for the intension to exist in such a world. In a modified, more neutral semantics, higher-order BF and CBF are no longer valid. The paper also argues that even if higher-order BF and CBF were valid, no substantive metaphysical results would be obtained, since different forms of nominalism and theories of tropes would accept them. (shrink)

This paper investigates the connection between two recent trends in philosophy: higher-orderism and conceptual engineering. Higher-orderists use higher-order quantifiers (in particular quantifiers binding variables that occupy the syntactic positions of predicates) to express certain key metaphysical doctrines, such as the claim that there are properties. I argue that, on a natural construal, the higher-orderist approach involves an engineering project concerning, among others, the concept of existence. I distinguish between a modest construal of this project, on (...) which it aims at engineering higher-order analogues of the familiar notion of first-order existence, and an ambitious construal, on which it additionally aims at engineering a broadened notion of existence that subsumes first-order and higher-order existence. After identifying a substantial problem for the ambitious project, I investigate a possible response which is based on adopting a cumulative type theory as the background higher-order logic. While effective against the problem at hand, this strategy turns out to undermine a major reason to embrace higher-orderism in the first place, namely the idea that higher-orderism dissolves a range of otherwise intractable debates in metaphysics. Higher-orderists are therefore best advised to pursue their engineering project on the modest variant and against the background of standard type theory. (shrink)

On at least one of its uses, ‘higher-order evidence’ refers to evidence about what opinions are rationalized by your evidence. This chapter surveys the foundational epistemological questions raised by such evidence, the methods that have proven useful for answering them, and the potential consequences and applications of such answers.

Plural Logic is an extension of First-Order Logic which has, as well as singular terms and quantifiers, their plural counterparts. Analogously, Higher-Level Plural Logic is an extension of Plural Logic which has, as well as plural terms and quantifiers, higher-level plural ones. Roughly speaking, higher-level plurals stand to plurals like plurals stand to singulars; they are pluralised plurals. Allegedly, Higher-Level Plural Logic enjoys the expressive power of a simple type theory while committing us to nothing (...) more than the austere ontology of First-Order Logic. Were this true, Higher-Level Plural Logic would be a useful tool, with various applications in philosophy and linguistics. However, while the notions of plural reference and quantification enjoy widespread acceptance today, their higher-level counterparts have been received with a lot of scepticism. In this paper, I argue for the legitimacy of Higher-Level Plural Logic by providing evidence to the effect that natural languages contain higher-level plural expressions and showing that it is likely that they do so in an indispensable manner. Since the arguments I put forward are of the same sort advocates of Plural Logic have employed to defend their position, I conclude that the commonly held view that Plural Logic is legitimate, but not so its higher-level plural extensions is untenable. (shrink)

Plural logic is widely assumed to have two important virtues: ontological innocence and determinacy. It is claimed to be innocent in the sense that it incurs no ontological commitments beyond those already incurred by the first-order quantifiers. It is claimed to be determinate in the sense that it is immune to the threat of non-standard interpretations that confronts higher-order logics on their more traditional, set-based semantics. We challenge both claims. Our challenge is based on a Henkin-style semantics (...) for plural logic that does not resort to sets or set-like objects to interpret plural variables, but adopts the view that a plural variable has many objects as its values. Using this semantics, we also articulate a generalized notion of ontological commitment which enables us to develop some ideas of earlier critics of the alleged ontological innocence of plural logic. (shrink)

Alethic pluralists often claim that accommodating certain alethic platitudes motivates rejecting deflationism in favour of a pluralist inflationism about truth. Deflationists claim that the logical role of the truth predicate, viz providing something equivalent to variables for sentence-in-use positions and quantifiers governing them, is sufficient to account for the appeal to truth in the alethic platitudes. Surprisingly, however, most deflationists face an insufficiently acknowledged problem with respect to explaining how this mode of generalizing works. The standard substitutional or higher- (...) class='Hi'>order interpretations of sentential quantifiers and variables do not meet two desiderata that we claim any adequate account of them must satisfy. To address this issue, we review and extend A. N. Prior's adverbial understanding of sentential quantification, explain how it satisfies the desiderata, and respond to some objections. This shows that deflationists can accommodate and account for the alethic platitudes by applying this non-nominal understanding of generalizing on sentence positions. (shrink)

This book develops an argument for a foundational theory of modality using higher-order logic. The use of higher-order logic in metaphysics is motivated, and a particular higher-order logic is introduced. Fine-grained theories of propositional individuation are shown to be problematic, and a course-grained theory of propositional individuation is defended. On the basis of this theory, it is argued that the metaphysical necessities can be delineated using purely logical terms; by adding an actuality operator, it (...) is shown that the logic of metaphysical necessity is S5. The theoretical role of possible worlds is articulated, and shown to be satisfied by maximal propositions if it satisfied by anything; the existence of such maximal propositions is demonstrated using plural propositional quantification. The resulting theory reduces metaphysical modal terms to higher-order logical terms, and thereby vindicates a widespread modal conception of metaphysics. (shrink)

This chapter explores the metaphysical views about higher-order logic held by two individuals responsible for introducing it to philosophy: Gottlob Frege (1848–1925) and Bertrand Russell (1872–1970). Frege understood a function at first as the remainder of the content of a proposition when one component was taken out or seen as replaceable by others, and later as a mapping between objects. His logic employed second-order quantifiers ranging over such functions, and he saw a deep division in nature between (...) objects and functions. Russell understood propositional functions as what is obtained when constituents of propositions are replaced by variables, but eventually denied that they were entities in their own right. Both encountered contradictions when supposing there to exist as many objects as functions, and both adopted views about the meaningfulness of higher-order discourse that were difficult to state from within their own strictures. (shrink)

Salmon and Soames argue against nominalism about numbers and sentence types. They employ (respectively) higher-order and first-order logic to model certain natural language inferences and claim that the natural language conclusions carry commitment to abstract objects, partially because their renderings in those formal systems seem to do that. I argue that this strategy fails because the nominalist can accept those natural language consequences, provide them with plausible and non-committing truth conditions and account for the inferences made without (...) committing themselves to abstract objects. I sketch a modal account of higher-order quantification, on which instead of ranging over sets, higher order quantifiers are used to make (logical) possibility claims about which predicate tokens can be introduced. This approach provides an alternative account of truth conditions for natural language sentences which seem to employ higher-order quantification, thus allowing the nominalist to evade Salmon’s argument. I also show how the nominalist can account for the occurrence of apparently singular abstract terms in certain true statements. I argue that the nominalist can achieve this by, first, dividing singular terms into real singular terms (referring to concrete objects) and only apparent singular terms (called onomatoids), introduced for the sake of brevity and simplicity, and then providing an account of nominalistically acceptable truth conditions of sentences containing onomatoids. I develop such an account in terms of modally interpreted abstraction principles and argue that applying this strategy to Soames’s argument allows the nominalists to defend themselves. (shrink)

The thesis that agents should calibrate their beliefs in the face of higher-order evidence—i.e., should adjust their first-order beliefs in response to evidence suggesting that the reasoning underlying those beliefs is faulty—is sometimes thought to be in tension with Bayesian approaches to belief update: in order to obey Bayesian norms, it’s claimed, agents must remain steadfast in the face of higher-order evidence. But I argue that this claim is incorrect. In particular, I motivate a (...) minimal constraint on a reasonable treatment of the evolution of self-locating beliefs over time and show that calibrationism is compatible with any generalized Bayesian approach that respects this constraint. I then use this result to argue that remaining steadfast isn’t the response to higher-order evidence that maximizes expected accuracy. (shrink)

The investigations on higher-order type theories and on the related notion of parametric polymorphism constitute the technical counterpart of the old foundational problem of the circularity of second and higher-order logic. However, the epistemological significance of such investigations has not received much attention in the contemporary foundational debate.We discuss Girard’s normalization proof for second order type theory or System F and compare it with two faulty consistency arguments: the one given by Frege for the logical (...) system of the Grundgesetze and the one given by Martin-Löf for the intuitionistic type theory with a type of all types.The comparison suggests that the question of the circularity of second order logic cannot be reduced to Russell’s and Poincaré’s 1906 “vicious circle” diagnosis. Rather, it reveals a bunch of mathematical and logical ideas hidden behind the hazardous idea of impredicative quantification, constituting a vast domain for foundational research. (shrink)

Hintikka’s semantic approach to meaning, a development of Wittgenstein’s view of meaning as use, is the general theme of this chapter. We will focus on the analysis of quantified sentences and on the scope of the principle of compositionality and compare Hintikka’s take on these issues with that of Frege. The aim of this paper is to show that Hintikka’s analysis of quantified expressions as choice functions, in spite of its obvious dissimilarities with respect to the higher-order approach, (...) is actually very close to the Fregean stance on compositionality and context dependence. In particular, we will defend that the Fregean approach to quantifiers is unavoidably linked to the idea that quantified expressions are context-dependent, and therefore should not be conceived under the traditional inside-out model for analysis. (shrink)

Recent authors have drawn attention to a new kind of defeating evidence commonly referred to as higher-order evidence. Such evidence works by inducing doubts that one’s doxastic state is the result of a flawed process – for instance, a process brought about by a reason-distorting drug. I argue that accommodating defeat by higher-order evidence requires a two-tiered theory of justification, and that the phenomenon gives rise to a puzzle. The puzzle is that at least in some (...) situations involving higher-order defeaters the correct epistemic rules issue conflicting recommendations. For instance, a subject ought to believe p, but she ought also to suspend judgment in p. I discuss three responses. The first resists the puzzle by arguing that there is only one correct epistemic rule, an Über-rule. The second accepts that there are genuine epistemic dilemmas. The third appeals to a hierarchy or ordering of correct epistemic rules. I spell out problems for all of these responses. I conclude that the right lesson to draw from the puzzle is that a state can be epistemically rational or justified even if one has what looks to be strong evidence to think that it is not. As such, the considerations put forth constitute a non question-begging argument for a kind of externalism. (shrink)

You have higher-order uncertainty iff you are uncertain of what opinions you should have. I defend three claims about it. First, the higher-order evidence debate can be helpfully reframed in terms of higher-order uncertainty. The central question becomes how your first- and higher-order opinions should relate—a precise question that can be embedded within a general, tractable framework. Second, this question is nontrivial. Rational higher-order uncertainty is pervasive, and lies at the (...) foundations of the epistemology of disagreement. Third, the answer is not obvious. The Enkratic Intuition---that your first-order opinions must “line up” with your higher-order opinions---is incorrect; epistemic akrasia can be rational. If all this is right, then it leaves us without answers---but with a clear picture of the question, and a fruitful strategy for pursuing it. (shrink)

An overview of higher-order representational theories of consciousness. Representational theories of consciousness attempt to reduce consciousness to “mental representations” rather than directly to neural or other physical states. This approach has been fairly popular over the past few decades. Examples include first-order representationalism (FOR) which attempts to explain conscious experience primarily in terms of world-directed (or first-order) intentional states (Tye 2005) as well as several versions of higher-order representationalism (HOR) which holds that what makes (...) a mental state M conscious is that it is the object of some kind of higher-order mental state directed at M. The primary focus of this entry is on HOR and especially higher-order thought (HOT) theory. The key question that should be answered by any theory of consciousness is: What makes a mental state a conscious mental state? Section 1 introduces the overall representationalist approach to consciousness and briefly discuss Tye’s FOR. Section 2 presents three major versions of HOR: higher-order thought theory, dispositional higher-order thought theory, and higher-order perception theory. In section 3, a number of common and important objections and replies are presented. Section 4 briefly outlines a close connection between HOT theory and conceptualism, that is, the claim that the representational content of a perceptual experience is entirely determined by the conceptual capacities the perceiver brings to bear in her experience. Section 5 examines several hybrid higher-order and “self-representational” theories of consciousness which all hold that conscious states are self-directed in some way. Section 6 addresses the potentially damaging claim that HOT theory requires neural activity in the prefrontal cortex (PFC) in order for one to have conscious states. (shrink)

In the contemporary epistemological literature, peer disagreement is often taken to be an instance of a more general phenomenon of “higher-order evidence.” Correspondingly, its epistemic significance is often thought to turn on the epistemic significance of higher-order evidence in general. This chapter attempts to evaluate this claim, and in doing so to clarify some points of unclarity in the current literature – both about what it is for evidence to be “higher-order,” and about the (...) relationship between disagreement and higher-order evidence. We will begin by considering some candidate definitions of “higher-order evidence,” and offering our own definition that attempts to capture the phenomenon of interest. We will then consider, in light of this definition, whether disagreement and its epistemic significance are best-understood as a kind of higher-order evidence. We’ll argue that although peer disagreement can be epistemically significant qua higher-order evidence, this role doesn’t exhaust its significance, and that it can also serve as straightforward first-order evidence. Finally, we’ll suggest that inattention to this latter point has made broadly conciliatory views about peer disagreement seem somewhat easier to resist than they in fact are. (shrink)

Higher-order defeat occurs when one loses justification for one's beliefs as a result of receiving evidence that those beliefs resulted from a cognitive malfunction. Several philosophers have identified features of higher-order defeat that distinguish it from familiar types of defeat. If higher-order defeat has these features, they are data an account of rational belief must capture. In this article, I identify a new distinguishing feature of higher-order defeat, and I argue that on (...) its own, and in conjunction with the other distinguishing features, it favors an account of higher-order defeat grounded in non-evidential, ‘state-given reasons’ for belief. (shrink)