Sentential Operators Research Articles

Paradoxes versus Contradictions in Logic of Sentential Operators

Classical logic, of first or higher order, is extended with sentential operators and quantifiers, interpreted substitutionally over unrestricted substitution class. Operators mark a single layered, consistent metalanguage. Self-reference, arising from substitutional quantification over sentences, allows to express paradoxes which, unlike contradictions, do not lead to explosion. Semantics of the resulting language, using semi-kernels of digraphs, is non-explosive yet two-valued and has classical semantics as a special case for clasically consistent theories. A complete reasoning is obtained by extending LK with two rules for sentential quantifiers. Adding (cut) yields a complete system for the explosive semantics.

Frege: A fusion of horizontals

AbstractIn Die Grundgesetze der Arithmetik (I, §48), Frege introduces his rule of the fusion of horizontals, according to which if an occurrence of the horizontal stroke is followed by another occurrence of the same stroke, either in isolation or “contained” in a propositional connective, the two occurrences can be fused with each other. However, the role of this rule, and of the horizontal sign more generally, is controversial; Michael Dummett notoriously claimed, for instance, that the horizontal is “wholly superfluous” in Frege's logical system. In this paper, we challenge Dummett's view by providing a comprehensive analysis of the significance of the horizontal stroke. After some preliminary remarks, we argue that even if Frege's connectives in some sense “contain” the horizontal, yet they are total functions. Then, we take up the question of the sense expressed by the horizontal, and we claim that, unlike other sentential operators, the horizontal is not sense‐compositional. Finally, we consider the semantic and pragmatic aspects of Frege's horizontal in connection to his judgment stroke and the double judgment stroke. Contra Dummett, we argue that the horizontal is a special and indispensable element of Frege's logic.

Clause type vs. speech act: Knowledge confirmation questions in Basque

This article analyzes Knowledge Confirmation Questions (KCQ) in Basque, an instance of non-canonical questions that has not been analyzed yet. KCQs display three characteristic elements, namely, (i) a declarative-type syntax, (ii) an interrogative-like intonation, and (iii) the discourse particle ba; and are interpreted as follows: “Do you know that p?”. Here, I propose that the meaning contribution of KCQs derives from the interaction of these three elements. More precisely, I argue that their question-like intonation, which adds interrogative interpretation, takes scope over ba, which regulates the addressee’s Doxastic State and undergoes context shift. Basque KCQs constitute an interesting case study, because they raise some interesting questions on the syntactization of discourse and the properties of discourse particles, as they seem to contradict the assumption that discourse particles do not fall under the scope of sentential operators.

Counterpossibles, story prefix and trivialism

The aim of this paper is to argue in favor of the view that some counterpossibles are false. This is done indirectly by showing that accepting the opposite view, i.e., one that ascribes truth to each and every counterpossible, results in the claim that every necessarily false theory has exactly the same consequences. Accordingly, it is shown that taking every counterpossible to be true not only undermines the value of debates over various alternative theories and their consequences, but also puts into question the very possibility of such debates. In order to explicate this thesis, the close bond between counterpossibles and the so-called story prefix (i.e., the sentential operator ‘According to fiction F, P’) is explored. A number of possible responses to this criticism are also presented, and it is argued that none of them address the main problem.

Sentential operators – their interaction (with vectors of time, causality and epistemic relevance) and their constructions

Abstract The paper starts by briefly describing the so‐called truth‐functional approach to sentential operators, typical to logic, as opposed to the more multi‐faceted approach of linguistics. The latter reflects the more complex, substantial relations between the contents of utterances, emphasizing the logico‐semantical relations and functions of sentential operators. However, as an alternative to the pragmatically inclined critique of the truth‐functional approach, the paper proposes two possible directions of explaining the specific content of sentential operators by virtue of which they transcend the role of mere truth functions. Firstly, the paper summarizes our previous investigations into the interactions between sentential operators and (1) the vector of the course of events described by a compound sentence, and (2) the direction of grammatical time captured by a compound sentence. The paper focuses on how this interaction is coordinated with the particular epistemic goal (prediction, explanation etc.) pursued when using the meaning of a complex sentence. Using the concepts of necessary and sufficient conditions, and by characterizing the vectors of condition (the if‐vector), time and relevance (dominance or the epistemic vector), the paper demarcates the rules of correspondence for conditional operators as cases of combinatorics, as described by some linguists. Secondly, based on a distinction between different constructions the same operators as truth‐functions, the paper provides a logico‐semantical explanation of the specific meaning of the else, unless and although connectives, traditionally discussed by linguists. We believe that the extensions proposed here move the camp defending a logico‐semantic approach to sentential operators at least somewhat closer to the camp of linguistic investigation.

On a Supposed Puzzle Concerning Modality and Existence

Kit Fine has proposed a new solution to what he calls ‘a familiar puzzle’ concerning modality and existence. The puzzle concerns the argument from the alleged truths ‘It is necessary that Socrates is a man’ and ‘It is possible that Socrates does not exist’ to the apparent falsehood ‘It is possible that Socrates is a man and does not exist’. We discuss in detail Fine’s setting up of the ‘puzzle’ and his rejection, with which we concur, of two mooted solutions to it. (One of these uses standard, Kripkean, notions, and the other rests on work done by Arthur Prior.) We set out, and reject, the philosophy of modality underlying Fine’s new solution, and we defend an alternative response to the alleged puzzle. Our solution follows the work of David Wiggins in distinguishing between the sentential operator ‘It is necessary that’ and the predicate modifier ‘necessarily’. We briefly provide this distinction with a possible- world semantics on which it is neither a necessary truth, in some sense, that Socrates exists nor true, in some sense, that Socrates necessarily exists.

Aspects of Aspect: Phasic and Episodic Dimensions of Verbs

The present study sets out to analyze aspectuality and coercion in Persian from a new perspective. With regard to the transcendental aspectual distinction between perfectivity, characterized by boundedness and heterogeneity, and imperfectivity, specified by uniformity and homogeneity (Langacker, 2008), it is argued that the heterogeneity of verbs may be assessed according to their phasic and episodic variables. In other words, in contrast to homogeneous verbs, which lack any kind of boundedness, heterogeneous verbs may occur either in a bounded phasic domain or in a bounded episodic domain. Concerning phasic-episodic features, this study presents a new model of lexical aspect that can differentiate five aspectual categories. The paper also scrutinizes the combinations of different verbs with different sentential operators in order to explain various kinds of type-shifting triggered by different operators. Thereby, two procedures of phasic coercion and episodic coercion are introduced which are responsible for modifying the phasic and episodic features of verbs in order to resolve the semantic conflicts between verbs and sentential operators. These procedures modify the phasic/episodic attributes of verbs according to the viewing frames evoked by interpretative operators.

The radical account of bare plural generics

Bare plural generic sentences pervade ordinary talk. And yet it is extremely controversial what semantics to assign to such sentences. In this paper, I achieve two tasks. First, I develop a novel classification of the various standard uses to which bare plurals may be put. This “variety data” is important—it gives rise to much of the difficulty in systematically theorizing about bare plurals. Second, I develop a novel account of bare plurals, the radical account. On this account, all bare plurals fail to express propositions. The content of a bare plural has to be pragmatically “completed” by a speaker in order for her to make an assertion. At least the content of a quantifier expression has to be supplied. But sometimes, the content of a sentential operator or modal verb is also supplied. The radical account straightforwardly explains the variety data: Speakers’ communicative intentions vary wildly across different contexts. The radical account should be taken seriously in the literature on generics.

Operator arguments revisited

Certain passages in Kaplan’s ‘Demonstratives’ are often taken to show that non-vacuous sentential operators associated with a certain parameter of sentential truth require a corresponding relativism concerning assertoric contents: namely, their truth values also must vary with that parameter. Thus, for example, the non-vacuity of a temporal sentential operator ‘always’ would require some of its operands to have contents that have different truth values at different times. While making no claims about Kaplan’s intentions, we provide several reconstructions of how such an argument might go, focusing on the case of time and temporal operators as an illustration. What we regard as the most plausible reconstruction of the argument establishes a conclusion similar enough to that attributed to Kaplan. However, the argument overgenerates, leading to absurd consequences. We conclude that we must distinguish assertoric contents from compositional semantic values, and argue that once they are distinguished, the argument fails to establish any substantial conclusions. We also briefly discuss a related argument commonly attributed to Lewis, and a recent variant due to Weber.

On the Systematic Inadequacy of Fictionalism about Fictional Characters

Critical statements, if true, bear ontological commitments to fictional entities. A well-known version of fictionalism about fictional characters tries to eliminate these ontological commitments by proposing that we understand critical statements as prefixed by a special sentential operator, such as ‘according to a fictional realist theory’. The aim of the present paper is to show that fictionalism about fictional characters is underdeveloped as it stands because it can be shown to be systematically inadequate. Because the fictionalist’s paraphrases of critical statements suggest that fictional realists affirm the propositions expressed by critical statements, the fictionalist mistakenly attributes to fictional realists an expertise in matters that pertain to literary criticism. Importantly, this problem of misattributed expertise paves the way to other issues that might be much more devastating to the fictionalist project. It can be shown that, because she wrongly attributes expertise to fictional realists, the fictionalist unintentionally portrays fictional realist theories in a way that renders them inconsistent and self-defeating. This undermines fictionalism about fictional characters because it leaves no workable fictional realist account in which to ground a fictionalist explanation. This is why the fictionalist about fictional characters should try to eliminate the problem of misattributed expertise and its related issues. At the end of the paper, I sketch some of the available options in this regard.

Operators vs. quantifiers: the view from linguistics

ABSTRACT In several publications, François Recanati argues that time, world, location, and similar constituents are not arguments of the verb, although they do affect truth conditions. However, he points out that this fact does not decide the debate regarding whether these notions are represented as sentential operators variables bound by quantifiers, as both approaches can be made compatible with such non-arguments. He makes these points using philosophical arguments; in this paper I use linguistic evidence from a variety of languages. Specifically, I demonstrate that time, world, location, and person behave syntactically and semantically the same across languages. Hence, either all are arguments, or neither are; and the evidence points to the latter position. The cross-linguistic data give rise to a generalization, which connects the availability of quantifying over times, worlds, locations, or persons with the availability of indexical expressions of the corresponding type. For example, a language that does not have temporal indexicals cannot have tense. I demonstrate that this generalization follows naturally from the quantifier approach, but would remain a mystery under the operator view. Therefore, the cross-linguistic evidence argues in the favor of the quantificational approach.

Complex sentential operators refute unrestricted Simplification of Disjunctive Antecedents

There is a longstanding debate about the status of the principle Simplification of Disjunctive Antecedents (SDA), according to which a counterfactual with a syntactically disjunctive antecedent [(φ ∨ ψ) > χ] entails a conjunction of counterfactuals [(φ > χ) ∧ (ψ > χ)]. This principle is highly intuitive for most examples that have been considered, but it has also been claimed to be subject to empirical counter-examples. However, there are promising pragmatic explanations for the currently known counter-examples, which have led several authors to argue in recent work that SDA is unrestrictedly valid after all. This short piece introduces new data involving sentential operators that impose both upper and lower bounds on confidence, frequency, etc., such as likely but not certain , there is an exactly n% probability , and usually but not always . These examples show clearly that SDA is not valid tout court . While SDA-supporting interpretations do exist and require an explanation, every theory of counterfactuals also requires an explanation of examples that can only be read in a way that does not support SDA. EARLY ACCESS

The syntax of yes and no by Anders Holmberg

Reviewed by: The syntax of yes and no by Anders Holmberg Satu Manninen The syntax of yes and no. By Anders Holmberg. Oxford: Oxford University Press, 2016. Pp. 250. ISBN 9780198701859. $99 (Hb). This monograph is a crosslinguistic investigation of the syntax of yes/no questions and their answers. The idea is that answers to these questions, even when they consist of a single word, are derived by ellipsis from a full sentential expression. Because the elided constituent is identical to the constituent in the preceding question, the syntax of answers turns out to be very much the same as the syntax of questions. The discussions and proposals are based on data from 136 languages, out of which a handful (English, Swedish, Finnish, Chinese, Thai, and Welsh) are selected for closer analysis. The languages have been examined in relation to two parameters of variation, namely, if answer particles (as in 1a) or echoed verbs (1b) are used, and how negative questions (2) are answered. (1) (2) The idea that verb-echo answers are derived from sentential expressions by movement and ellipsis is uncontroversial and receives support from the fact that in many languages the verb is inflected for tense and agreement. A movement-and-ellipsis analysis is also available for other questions, including alternative (Do they want tea or coffee?) and wh-questions (What do they want?). The fact that single-word answers to these questions are case-marked indicates that they are part of sentential structure. Verb-echo answers to yes/no questions may then look like 3, while single-word answers to alternative and wh-questions look like 4. (3) (4) The idea that even particle answers are derived by ellipsis from a sentential expression may seem less straightforward, and it contradicts the idea put forward by, for example, Krifka (2013) that answer particles are clause substitutes. Holmberg aims to show that the ellipsis analysis has wider coverage and more explanatory power, since it is able to capture both verb-echo and particle answers to yes/no questions, as well as answers to other types of questions. Based on Hamblin 1958, 1973, H hypothesizes that knowing the meaning of a question means knowing the set of alternative statements that can constitute its answers. In neutral yes/no questions, the set of alternative statements is restricted to p and ￢p, a positive proposition and its negation, and in negative questions to ￢p and ￢(￢p), a negative proposition and its negation. To capture the idea that a question puts a set of alternative propositions before the addressee and asks them to choose the [End Page 240] one that is the true alternative, H proposes that a question contains an open question variable in the IP. The variable moves, overtly or covertly, to the C-domain in order to take sentential scope. In direct questions, the CP is embedded under Q[uestion]-force, which contributes an invitation to the addressee to assign a value to the variable. The addressee does this by answering the question: the answer contains something that makes value assignment possible. In yes/no questions, H argues, the relevant property is polarity: answer particles like yes and no are viewed as sentential operators that can apply to a question with an open polarity variable [±Pol] and assign a value, [+Pol] or [−Pol], to it. What answers are possible in negative questions is shown to follow from the idea that a yes/no question contains a polarity variable [±Pol] and that the answer to the question assigns a value, [+Pol] or [−Pol], to the variable. The division of languages into those that follow the truth-based as opposed to the polarity-based answer system (i.e. languages where the truth of a negative alternative is confirmed by uttering Yes, and languages where it is confirmed by uttering No) is argued to be a consequence of differences in syntactic structure and, specifically, differences in the syntax of negation: truth-based answers are utilized in languages and constructions that have low negation, polarity-based answers in languages and constructions lacking low negation. Polarity and negation are viewed as two distinct properties, and the ‘wrong’ type of answer to a negative...

Japanese alternative questions are disjunctions of polar questions

We discuss the syntax and semantics of Japanese alternative questions (AltQs), and argue that they are underlyingly disjoined polar questions (PolQs). The argument is based on the following three observations: (i) the minimum syntactic size of a disjunct in a Japanese AltQ is VP or clausal, (ii) sentential operators above the disjunction in an AltQ are never interpreted in both disjuncts, and (iii) the clause-final particle in an AltQ has to be matched with the particle at the end of the first disjunct. It will be shown that these facts receive straightforward explanations under the analysis that treats Japanese AltQs as disjoined PolQs while they are problematic in a scoping analysis. We also propose a compositional semantics associated with the analysis, and address a potential problem regarding the intervention effect.

A Logic Inspired by Natural Language: Quantifiers As Subnectors

Inspired by the grammar of natural language, the paper presents a variant of first-order logic, in which quantifiers are not sentential operators, but are used as subnectors (operators forming terms from formulas). A quantified term formed by a subnector is an argument of a predicate. The logic is defined by means of a meaning-conferring natural-deduction proof-system, according to the proof-theoretic semantics program. The harmony of the I/E-rules is shown. The paper then presents a translation, called the Frege translation, from the defined logic to standard first-order logic, and shows that the proof-theoretic meanings of both logics coincide. The paper criticizes Frege’s original regimentation of quantified sentences of natural language, and argues for advantages of the proposed variant.

Apparent Generalisations about Fictional Characters

AbstractThis essay will be concerned with an evaluation, modification, and critique of van Inwagen’s famous argument for the existence of fictional characters. In the first section a reconstruction of the original argument will be provided, and three different challenges for this version of the argument will be pointed out. The first challenge concerns van Inwagen’s commitment to first-order predicate logic as a canonical language for the formal representation of truth-conditions of assertoric sentences in natural languages, and the problematic semantic complexity of van Inwagen’s original example sentences of quantifications about fictional objects. The second challenge concerns his commitment to a Quinean conception of ordinary language quantifications that conceives of first-order quantifiers as existentially loaded. The third challenge concerns van Inwagen’s tendency to interpret our ordinary intuitions about the truth-values of specific sentences as intuitions about the truth-values of the literal contents of these sentences. In the second section, a more detailed investigation of these three challenges will be provided; and a modified, and less problematic, alternative version of the argument will be proposed. It will be shown that the truth-conditions of van Inwagen’s original example sentences cannot be adequately represented on the basis of first-order predicate logic. I will propose alternative and less complex example sentences that are sufficient for the required purpose. Additionally, a reformulation of the argument will be proposed that avoids a commitment to a specific sort of formal framework. After that, it will be shown why the assumption of a Quinean conception of quantification unnecessarily increases the burden of proof. A reformulation of the argument will be proposed that avoids the commitment to a Quinean conception of quantification. Furthermore, I will make a third and final adjustment of the argument that allows us to remain neutral concerning the specific status of our truth-value intuitions concerning the proposed example sentences of generalisations about fictional objects. In the third and final section, three possible responses of an irrealist concerning fictional objects will be evaluated. The first option makes use of a recent semantic analysis of the modifying adjective ›fictional‹ proposed by Sainsbury. According to this analysis, a sentence like ›There are fictional mice that talk‹ is semantically equivalent with the claim ›There are fictional works according to which it is the case that at least one mouse talks‹. The second option additionally makes use of Sainsbury’s conception of spotty scope for ordinary language quantifiers and other related sentential operators. It will be shown why both options cannot account for the desired true readings of our example sentences. Finally, a third solution will be proposed and defended. This solution makes use of a substitutional interpretation of specific fictional generalisations based on a negative free logic to undermine the modified argument. It will be shown how this solution allows us to provide a correct analysis of the desired readings of our example sentences of generalisations about fictional characters. After that, two problems of this account will be discussed. The first problem concerns the extension of the proposed strategy to more complicated and sophisticated example sentences. The second problem concerns the independent motivation of a substitutional treatment of at least certain natural language quantificational expressions.

At-issue Proposals and Appositive Impositions in Discourse

Potts (2005) and many subsequent works have argued that the semantic content of appositive (non-restrictive) relative clauses, e.g., the underlined material in John, who nearly killed a woman with his car, visited her in the hospital, must be in some way separate from the content of the rest of the sentence, i.e., from at-issue content. At the same time, there is mounting evidence from various anaphoric processes that the two kinds of content must be integrated into a single, incrementally evolving semantic representation. The challenge is how to reconcile this informational separation with these pervasive anaphoric connections. We propose a dynamic semantic account that accomplishes this by taking appositive and at-issue content to involve two different kinds of updates to the Context Set (CS). Treating the context set as a distinguished propositional variable, p cs , we argue that appositives directly impose their content on the CS by eliminating possible values assigned to p cs . In contrast, we treat at-issue assertions as introducing a new propositional dref and proposing that p cs be updated with its content, subject to addressee’s response. In addition to capturing the behavior of appositives in discourse, we show that the account can be extended to capture the projection of appositive content past various sentential operators.

It's Not What it Seems. A Semantic Account of ‘Seems’ and Seemings

I start out by reviewing the semantics of ‘seem’. As ‘seem’ is a subject-raising verb, ‘it seems’ can be treated as a sentential operator. I look at the semantic and logical properties of ‘it seems’. I argue that ‘it seems’ is a hyperintensional and contextually flexible operator. The operator distributes over conjunction but not over disjunction, conditionals or semantic entailments. I further argue that ‘it seems’ does not commute with negation and does not agglomerate with conjunction. I then show that the mental states expressed by perceptual uses of ‘seem’ have non-conceptual, yet perspectival contents. In the final part of the paper I argue that while the content of the mental states expressed by perceptual uses of ‘seem’ are non-conceptual, having a mental state of this type requires possessing conceptual abilities corresponding to what the mental state represents.

Verb-Initial versus Subject-Initial Clauses in Greek: Eventuality Existentials versus Predication Clauses

The paper aims to describe (a) the distribution, (b) the semantic interpretation and (c) the semantic and syntactic derivation of verb-initial versus subject-initial clauses in Greek. Concerning (a), it is argued that the verb-initial and the subject-initial word orders are in complementary distribution. A particular numeration can be assembled in only one way, i.e. as a verb-initial or as a subject-initial word order. The properties of the numeration that play a role in determining the word order for that numeration include the syntactic type of the predicate, the presence or not of non-arguments, the presence or not of sentential operators, and the mode of presenting information. Concerning (b), it is proposed that the semantic interpretation of verb-initial versus subject-initial clauses can be described as a clause-type distinction between eventuality existentials versus predication clauses. Concerning (c), it is proposed that this clause-type distinction has to do with how the subject and the predicate are put together semantically/syntactically. Namely, it is proposed that in eventuality existentials (the entity denoted by) the subject saturates/is selected by (the property denoted by) the predicate, while in predication clauses it is (the property denoted by) the predicate that saturates/is ‘selected’ by (the second-order property denoted by) the subject. For the proposed analysis to be right, (a) the clause-type distinction between eventuality existentials and predication clauses, (b) the complementary distribution of the two clause types and (c) the semantic/syntactic derivation for the two clause types must be part of UG. What cannot be part of UG is the syntactic manifestation of this semantic distinction across languages.

What is Weak Ground?

Kit Fine, in The Pure Logic of Ground, has made a seminal attempt at formalizing the notion of ground. Fine ties the formal treatment of grounding to the notion of a weak ground. Formalization of this sort is supposed to bring clarity and precision to our theorizing. Unfortunately, as I will argue, it's not clear what weak ground is. I review five alternative explanations of the idea, and argue that none of them are ultimately satisfactory. I close by outlining a more complicated explanation of the notion that turns out to be more satisfactory. A number of contemporary metaphysicians are exploring the nature and uses of a phenomenon known as grounding. These thinkers link grounding to a certain kind of explanation. Philosophers and scientists are fond of asking for explanations of this kind: “In virtue of what is murder wrong?” “In virtue of what am I justified in believing that I have hands?” “What makes gravity such a weak force?” Each question sets the stage for a more or less familiar ongoing research program. Each question calls for an explanation. A correct answer to each question will tell us which are the facts in virtue of which something is the case. In general, the facts that ground a given fact are the facts in virtue of which that fact obtains. 1 Enthusiasts of grounding agree that facts may ground other facts, but they split on whether grounding relates things other than facts; Schaffer [2009] contends that it does, and Fine [2001, 2012] disagrees. If Schaffer is correct, then Fine’s formal treatment of ground may be incomplete. I take no stand on this dispute here. Fine also argues in [Fine, 2001] that, strictly speaking, we don’t need to reify facts and claim that grounding is a relation between them in order to give a theory of ground; we may instead treat talk of grounding’s being a relation between facts as a mere fa con de parler. We should formalize our theory of ground by appeal to sentential operators which do not pick out any relation, and whose arguments, semantically speaking, do not pick out some special category of entity. According to Fine, the logical Essays Philos (2013) 14:1 deRosset | 8 Though the study of grounding is still in the early stages, Kit Fine, in “The Pure Logic of Ground” [Fine, 2012], has made a seminal attempt at formalization. Formalization of this sort is supposed to bring clarity and precision to our theorizing, as it has to the study of other metaphysically important phenomena, like modality and vagueness. Unfortunately, as I will argue, Fine ties the formal treatment of grounding to the notion of a weak ground, and it is not clear what that notion comes to. Weak Ground in the Pure Logic of Ground In Fine’s system, which he calls the pure logic of ground (PLG), grounding claims vary along two independent axes: (i) a grounding claim may either be partial or full; and (ii) it may either be strict or weak. There are thus four types of grounding claim in Fine’s system. Corresponding to each type of grounding claim is an operator in the language of PLG: