On the Innocence and Determinacy of Plural Quantification

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 (Henkin) 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.     

The time-course of morphological constraints: evidence from eye-movements during reading

Lexical compounds in English are constrained in that the non-head noun can be an irregular but not a regular plural (e.g. mice eater vs. *rats eater), a contrast that has been argued to derive from a morphological constraint on modifiers inside compounds. In addition, bare nouns are preferred over plural forms inside compounds (e.g. mouse eater vs. mice eater), a contrast that has been ascribed to the semantics of compounds. Measuring eye-movements during reading, this study examined how morphological and semantic information become available over time during the processing of a compound. We found that the morphological constraint affected both early and late eye-movement measures, whereas the semantic constraint for singular non-heads only affected late measures of processing. These results indicate that morphological information becomes available earlier than semantic information during the processing of compounds.     

Constructing formal semantics from an ontological perspective. The case of second-order logics

In a first part, I defend that formal semantics can be used as a guide to ontological commitment. Thus, if one endorses an ontological view \(O\) and wants to interpret a formal language \(L\) , a thorough understanding of the relation between semantics and ontology will help us to construct a semantics for \(L\) in such a way that its ontological commitment will be in perfect accordance with \(O\) . Basically, that is what I call constructing formal semantics from an ontological perspective. In the rest of the paper, I develop rigorously and put into practice such a method, especially concerning the interpretation of second-order quantification. I will define the notion of ontological framework: it is a set-theoretical structure from which one can construct semantics whose ontological commitments correspond exactly to a given ontological view. I will define five ontological frameworks corresponding respectively to: (i) predicate nominalism, (ii) resemblance nominalism, (iii) armstrongian realism, (iv) platonic realism, and (v) tropism. From those different frameworks, I will construct different semantics for first-order and second-order languages. Notably I will present different kinds of nominalist semantics for second-order languages, showing thus that we can perfectly quantify over properties and relations while being ontologically committed only to individuals. I will show in what extent those semantics differ from each other; it will make clear how the disagreements between the ontological views extend from ontology to logic, and thus why endorsing an ontological view should have an impact on the kind of logic one should use.     

Quantification over Sets of Possible Worlds in Branching-Time Semantics

Temporal logic is one of the many areas in which a possible world semantics is adopted. Prior's Ockhamist and Peircean semantics for branching-time, though, depart from the genuine Kripke semantics in that they involve a quantification over histories, which is a second-order quantification over sets of possible worlds. In the paper, variants of the original Prior's semantics will be considered and it will be shown that all of them can be viewed as first-order counterparts of the original semantics.     

Indexicals in Remote Utterances

Recording devices are generally taken to present problems for the standard Kaplanian semantics for indexicals. In this paper, I argue that the remote utterance view offers the best way for the Kaplanian semantics to handle the recalcitrant data that comes from the use of recording devices. Following Sidelle (1991) I argue that recording devices allow agents to perform utterances at a distance. Using the essential, but widely ignored, distinction between tokens and utterances, I develop the view beyond the initial sketch given by Sidelle, and I answer the main objections raised against the view. The paper is structured as follows. Section 1 gives a succinct presentation of Kaplanian semantics and of the problem raised by the use recording devices, Section 2 presents the remote utterance view and Section 3 answers the objections put forward against the view and further develops it. I conclude that the remote utterance view can handle the data that comes from the use of recording devices with only modest modifications of the Kaplanian semantics.     

The Open-Endedness of the Set Concept and the Semantics of Set Theory

Some philosophers have argued that the open-endedness of the set concept has revisionary consequences for the semantics and logic of set theory. I consider (several variants of) an argument for this claim, premissed on the view that quantification in mathematics cannot outrun our conceptual abilities. The argument urges a non-standard semantics for set theory that allegedly sanctions a non-classical logic. I show that the views about quantification the argument relies on turn out to sanction a classical semantics and logic after all. More generally, this article constitutes a case study in whether the need to account for conceptual progress can ever motivate a revision of semantics or logic. I end by expressing skepticism about the prospects of a so-called non-proof-based justification for this kind of revisionism about set theory.     

Some Notes on Boolos’ Semantics: Genesis,Ontological Quests and Model-Theoretic Equivalence to Standard Semantics

The main aim of this work is to evaluate whether Boolos’ semantics for second-order languages is model-theoretically equivalent to standard model-theoretic semantics. Such an equivalence result is, actually, directly proved in the “Appendix”. I argue that Boolos’ intent in developing such a semantics is not to avoid set-theoretic notions in favor of pluralities. It is, rather, to prevent that predicates, in the sense of functions, refer to classes of classes. Boolos’ formal semantics differs from a semantics of pluralities for Boolos’ plural reading of second-order quantifiers, for the notion of plurality is much more general, not only of that set, but also of class. In fact, by showing that a plurality is equivalent to sub-sets of a power set, the notion of plurality comes to suffer a loss of generality. Despite of this equivalence result, I maintain that Boolos’ formal semantics does not committ (directly) second-order languages (theories) to second-order entities (and to set theory), contrary to standard semantics. Further, such an equivalence result provides a rationale for many criticisms to Boolos’ formal semantics, in particular those by Resnik and Parsons against its alleged ontological innocence and on its Platonistic presupposition. The key set-theoretic notion involved in the equivalence proof is that of many-valued function. But, first, I will provide a clarification of the philosophical context and theoretical grounds of the genesis of Boolos’ formal semantics.     

Necessary a Posteriori Identity Truths: Fregeanism Beats Direct Reference Theory

I argue that Fregeanism with respect to proper names—the view that modes of presentation are relevant to the contents of proper names—is able to account for the thesis that there are necessarily true a posteriori identity propositions such as the one expressed in “Hesperus is identical with Phosphorus”, whereas the Direct Reference Theory—according to which the semantic function of certain expressions, e.g., proper names, is only to pick out an object (referent)—is able to deal with only their necessary truth. Thus, at least in so far as necessarily true a posteriori identity propositions are concerned, Fregeanism should be preferred to the Direct Reference Theory.     

Logic Semantics with the Potential Infinite

A form of quantification logic referred to by the author in earlier papers as being ‘ontologically neutral’ still made use of the actual infinite in its semantics. Here it is shown that one can have, if one desires, a formal logic that refers in its semantics only to the potential infinite. Included are two new quantifiers generalizing the sentential connectives, equivalence and non-equivalence. There are thus new avenues opening up for exploration in both quantification logic and semantics of the infinite.     

The Logic and Meaning of Plurals. Part I

Contemporary accounts of logic and language cannot give proper treatments of plural constructions of natural languages. They assume that plural constructions are redundant devices used to abbreviate singular constructions. This paper and its sequel, “The logic and meaning of plurals, II”, aim to develop an account of logic and language that acknowledges limitations of singular constructions and recognizes plural constructions as their peers. To do so, the papers present natural accounts of the logic and meaning of plural constructions that result from the view that plural constructions are, by and large, devices for talking about many things (as such). The account of logic presented in the papers surpasses contemporary Fregean accounts in its scope. This extension of the scope of logic results from extending the range of languages that logic can directly relate to. Underlying the view of language that makes room for this is a perspective on reality that locates in the world what plural constructions can relate to. The papers suggest that reflections on plural constructions point to a broader framework for understanding logic, language, and reality that can replace the contemporary Fregean framework as this has replaced its Aristotelian ancestor.     

Stage theory and proper names

In the contemporary debate about the nature of persistence, stage theory is the view that ordinary objects (artefacts, animals, persons, etc.) are instantaneous and ??persist?? by being suitably related to other instantaneous objects. In this paper I focus on the issue of what stage theorists should say about the semantics of ordinary proper names, like ??Socrates?? or ??London??. I consider the remarks that stage theorists actually make about this issue, present some problems they face, and finally offer what I take to be the best alternative available for them.     

Remembering plurals: Unit of coding and form of coding during serial recall

Subjects were required to recall lists of six words which had been presented visually in sequence. One or two of the words might be plural nouns. A substantial number of errors occurred in which the plural form became detached from its original root. This is taken as evidence for a morpheme-based code as opposed to a unitary word code. A significantly high proportion of these errors maintained the form of the plural ( /S/, /Z/ or (ЪZ/) which is considered evidence for a primarily phonological coding of the plural morpheme. There is however a suggestion that on some occasions the plural is coded morphemically—i.e., in a way which does not distinguish between the various plural endings.     

Jesus loves you!

According to orthodox semantics, a given sentence as used at a given situation expresses at most one content. In the last decade, this view has been challenged with several objections. Many of them have been addressed in the literature. But one has gone almost unheeded. It stems from sentences that are used to address several people individually, like ‘Jesus loves you!’ as uttered by a priest at a sermon. Cappelen (Philos Perspect 22(1):23–46, 2008), Egan (Synthese 166(2):251–279, 2009), López de Sa (Erkenntnis 79(1):241–253, 2014), and MacFarlane (Assessment sensitivity: relative truth and its applications. Oxford University Press, Oxford, 2014, ch. 4) claim that, to account for such cases, one has to adopt a pluralist semantics, according to which the sentences in question express more than one content. In this paper, I shall counter this objection. Exploiting different so far underappreciated features of singular and plural ‘you,’ I argue, orthodox semantics can very well account for the cases in question.     

On Dependent Pronouns and Dynamic Semantics

Within natural language semantics, pronouns are often thought to correspond to variables whose values are contributed by contextual assignment functions. This paper concerns the application of this idea to cases where the antecedent of a pronoun is a plural quantifiers. The paper discusses the modelling of accessibility patterns of quantifier antecedents in a dynamic theory of interpretation. The goal is to reach a semantics of quantificational dependency which yields a fully semantic notion of pronominal accessibility. I argue that certain dependency phenomena that arise in quantificationally created contexts require a representation of context wherein the labelling of antecedents is not rigid but rather dynamic itself. I propose a stack-based alternative to classic assignment functions, along the lines of Vermeulen (1993) and van Eijck (2001), and give a dynamic semantics of quantification which correctly accommodates the problematic anaphoric phenomena.     

The Justification of the Logical Laws Revisited

The proof-theoretic analysis of logical semantics undermines the received view of proof theory as being concerned with symbols devoid of meaning, and of model theory as the sole branch of logical theory entitled to access the realm of semantics. The basic tenet of proof-theoretic semantics is that meaning is given by some rules of proofs, in terms of which all logical laws can be justified and the notion of logical consequence explained. In this paper an attempt will be made to unravel some aspects of the issue and to show that this justification as it stands is untenable, for it relies on a formalistic conception of meaning and fails to recognise the fundamental distinction between semantic definitions and rules of inference. It is also briefly suggested that the profound connection between meaning and proofs should be approached by first reconsidering our very notion of proof.     

THE CREATIVE IMPERATIVE: Religious Ethics and the Formation of Life in Common

Challenging a long‐standing assumption of the separation of ethical from poetic activity, this essay develops the basis for a theory of moral life as inherently and radically creative. A range of contemporary post‐Kantian ethicists—including Ricoeur, Nussbaum, Kearney, and Gutiérrez—are employed to make the argument that moral practice requires a fundamental capability for creative transformation, imagination, and social renewal. In addition, this poetic moral capability can finally be understood only from the primordial religious point of view of the mystery of Creation as such. Humanity as an image of its Creator is called to the endless impossible possibility of the re‐creation of its own complex, plural, and fallen social world. Such a perspective is opposed to views of moral life as the application of law‐like principles or the recovery of past moral histories. Without a better understanding of moral life's radically creative imperative, we miss a vital element of social relations' distinctive humanity.