Quantifier expressions like “many” and “at least” are part of a rich repository of words in language representing magnitude information. The role of numerical processing in comprehending quantifiers was studied in a semantic truth value judgment task, asking adults to quickly verify sentences about visual displays using numerical or proportional quantifiers. The visual displays were composed of systematically varied proportions of yellow and blue circles. The results demonstrated that numerical estimation and numerical reference information are fundamental in (...) encoding the meaning of quantifiers in terms of response times and acceptability judgments. However, a difference emerges in the comparison strategies when a fixed external reference numerosity is used for numerical quantifiers, whereas an internal numerical criterion is invoked for proportional quantifiers. Moreover, for both quantifier types, quantifier semantics and its polarity biased the response direction. Overall, our results indicate that quantifier comprehension involves core numerical and lexical semantic properties, demonstrating integrated processing of language and numbers. (shrink)

Abstract Proportional quantifiers have played a central role in the development of formal semantics because they set a benchmark for the expressive power needed to describe quantification in natural language (Barwise and Cooper Linguist Philos 4:159–219, 1981). The proportional quantifier most, in particular, supplied the initial motivation for adopting Generalized Quantifier Theory (GQT) because its meaning is definable as a relation between sets of individuals, which are taken to be semantic primitives in GQT. This paper proposes an (...) alternative analysis of most that does not treat it as a lexical item whose meaning is accessible without the help of compositional processes. Instead, proportional most is analyzed as the superlative of many (cf. Bresnan Linguist Inq 4(3):274–344, 1973). Two types of empirical evidence are presented in support of this view, both exploiting the fact that only a decompositional analysis of proportional quantifiers provides the means to generate different logical forms for seemingly equivalent statements of the form most A B and more than half of the A B. (shrink)

Since the time, about a century ago, when DeMorgan, Boole and Jevons, inaugurated the study of the logic of numerically definite reasoning, no one has been concerned to establish the validity rules for a very general type of numerically definite inference which is a strong analogue of the classical syllogism. The reader will readily agree that the traditional rules of syllogistic inference cannot even begin to decide whether the following proportionally quantified syllogism is a valid argument: at most 4/7 p (...) are at most 2/3 not-m and at least 3/5 s are precisely 7/8 m, hence, at most 1/3 s are p. Likely reasons, of broad methodological interest, why this readily definable type of formal inference has been neglected will presently be proposed. Among the masters of twentieth century logic, Hilbert and Bernays have, to be sure, meticulously shown how such numerically definite propositions as “at least 7 individuals have the property p” can be expressed in the predicate calculus with the use of the identity relation. They do not, since their concern with such propositions is indirect, proceed to establish a systematic calculus of classes whose “size” or extent is numerically definite. As we shall always notice, traditional logic and even ordinary Boolean algebra prefer to generalize about the laws governing the interrelationship of classes in inference systems without making any hypotheses concerning class “size” or extent except by the classical quantifier “some”, which quantifier admits the measure or extent of a class only in terms of the proposition that a given class contains or does not contain at least one member. Such a restricted admission of the relevance for inference of class size is among the fundamental reasons for the neglect of proportional quantifiers, i.e., quantifiers where numerical value is any rational number r such that 0/100 ≤ r ≤ 100/100. It can, of course, also be pointed out that the traditional syllogism and ordinary Boolean algebra do not i.e. measure, numerically define, the degree of inclusion of one class in another. Inclusion is taken either as total or partial, with no discrimination of the degree of partial inclusion. (shrink)

Most studies of the so-called proportion problem seek to understand how lexical and structural properties of sentences containing adverbial quantifiers give rise to various proportional readings. This paper explores a related but distinct problem: given a use of a particular sentence in context, why do only some of the expected proportional readings seem to be available? That is, why do some sentences allow an asymmetric reading when other, structurally similar sentences seem to require a symmetric reading? Potential (...) factors suggested in the literature include the distribution of donkey pronouns, certain uniqueness implications, and focus structures. I argue here that the use of an adverbial quantifier presupposes HOMOGENEITY: all individual situations that get lumped into a single case for the purposes of evaluating the quantification must agree on whether they satisfy the nuclear scope. For instance, in order for a token of Usually, if a farmer owns a donkey, he beats it to be felicitous when construed under a farmer-dominant asymmetric reading, the context must be consistent with the proposition that each farmer either beats all or none of his donkeys. Thus proportional sentences are indeed systematically ambiguous, but only some readings will be felicitous in a given context. (shrink)

We compared the processing of natural language quantifiers in a group of patients with schizophrenia and a healthy control group. In both groups, the difficulty of the quantifiers was consistent with computational predictions, and patients with schizophrenia took more time to solve the problems. However, they were significantly less accurate only with proportional quantifiers, like more than half. This can be explained by noting that, according to the complexity perspective, only proportional quantifiers require working (...) memory engagement. (shrink)

The paper presents a study examining the role of working<br>memory in quantifier verification. We created situations similar to the<br>span task to compare numerical quantifiers of low and high rank, parity<br>quantifiers and proportional quantifiers. The results enrich and support<br>the data obtained previously in and predictions drawn from a computational<br>model.

Proportional quantification and progressive aspect interact in English in revealing ways. This paper investigates these interactions and draws conclusions about the semantics of the progressive and telicity. In the scope of the progressive, the proportion named by a proportionality quantifier (e.g. most in The software was detecting most errors) must hold in every subevent of the event so described, indicating that a predicate in the scope of the progressive is interpreted as an internally homogeneous activity. Such an activity interpretation (...) is argued to be available for telic predicates (e.g. cross the street) because these receive a partitive interpretation except in combination with a completive operator, which asserts that the event so described has culminated. The obligatoriness of the completive operator in the preterit is shown to parametrically distinguish those languages that show completion entailments in the preterit, e.g. English, from those that do not, e.g. Malagasy, Hindi, and Japanese. (shrink)

The lack of gender parity in philosophy has garnered serious attention recently. Previous empirical work that aims to quantify what has come to be called “the gender gap” in philosophy focuses mainly on the absence of women in philosophy faculty and graduate programs. Our study looks at gender representation in philosophy among undergraduate students, undergraduate majors, graduate students, and faculty. Our findings are consistent with what other studies have found about women faculty in philosophy, but we were able to add (...) two pieces of new information. First, the biggest drop in the proportion of women in philosophy occurs between students enrolled in introductory philosophy classes and philosophy majors. Second, this drop is mitigated by the presence of more women philosophy faculty. (shrink)

This dissertation investigates the ways in which natural language restricts the domains of quantifiers. Adverbs of quantification are analyzed as quantifying over situations. The domain of quantifiers is pragmatically constrained: apparent processes of "semantic partition" are treated as pragmatic epiphenomena. The introductory Chapter 1 sketches some of the background of work on natural language quantification and begins the analysis of adverbial quantification over situations. Chapter 2 develops the central picture of "semantic partition" as a side-effect of pragmatic processes (...) of anaphora resolution. I argue that the apparent effects of topic/focus articulation and presuppositional information on the interpretation of quantifiers are not the result of a direct and local mechanism of sentence grammar. Instead, I develop an analysis where the link is established via the anaphoric dependence of quantifier domains on the discourse context. Chapter 3 discusses the analysis of conditional clauses as quantifier restrictors, concentrating on the question whether conditional clauses restrict quantifiers directly or indirectly. A treatment is explored which has if-clauses constrain the value of the hidden domain variable of the restricted quantifier. Chapter 4, on unless-clauses, and Chapter 5, on only if- and even if-clauses, present some issues in the compositional analysis of complex conditional clauses. These chapters significantly expand the data coverage of the theory of A-quantification. Building on previous work of mine on exceptives, I analyze unless-clauses as exceptive operators on A-quantifiers. The analysis of only if-clauses, treated as conditional clauses that combine if with the focus adverb only, unearthes some interesting new properties. Chapter 6, finally, examines the phenomenon of donkey-anaphora in the light of the results of the previous chapters. I show that a solution to the proportion problem may become possible once we combine the situation-semantic approach to adverbial quantification with the pragmatic theory developed in Chapter 2 and further elaborated in the analysis of donkey anaphora in complex conditionals. (shrink)

In the first half of this paper, we present a fragment of relational syllogisms named RELSYLL consisting of quantified statements with a special set of numerical quantifiers, and introduce a number of concepts that are useful for the later sections, including indirect reduction, quantifier transformations and equivalence of syllogisms. After determining the valid and invalid syllogisms in RELSYLL, we then introduce two Derivation Methods which can be used to derive valid relational syllogisms based on known valid simple syllogisms. We (...) also show that the two Methods are sound and complete for RELSYLL. In the second half of this paper, we discuss ways to extend the Derivation Methods, including the use of more valid syllogisms and the use of existential assumptions. In this way, we are able to derive more relational syllogisms that contain other types of non-classical quantifiers, including “only” and proportional quantifiers. Finally, we state and prove a proposition concerning the relationship between the two Methods. (shrink)

Words sound slightly different each time they are said, both by the same talker and across talkers. Rather than hurting learning, lab studies suggest that talker variability helps infants learn similar sounding words. However, very little is known about how much variability infants hear within a single talker or across talkers in naturalistic input. Here, we quantified these types of talker variability for highly frequent words spoken to 44 infants, from naturalistic recordings sampled longitudinally over a year of life (from (...) 6 to 17 months). We used non‐contrastive acoustic measurements (e.g., mean pitch, duration, harmonics‐to‐noise ratio) and holistic measures of sound similarity (normalized acoustic distance) to quantify acoustic variability. We find three key results. First, pitch‐based variability was generally lower for infants' top talkers than across their other talkers, but overall acoustic distance is higher for tokens from the top talker versus the others. Second, the amount of acoustic variability infants heard could not be predicted from, and thus was not redundant with, other properties of the input such as the number of talkers or tokens, or proportion of speech from particular sources (e.g., women, children, electronics). Finally, we find that patterns of pitch‐based acoustic variability heard in naturalistic input were similar to those found with in‐lab stimuli that facilitated word learning. This large‐scale quantification of talker variability in infants' everyday input sets the stage for linking naturally occurring variability “in the wild” to early word learning. (shrink)

Supporters of the autonomy of higher-level causation (or explanation) often appeal to proportionality, arguing that higher-level causes are more proportional than their lower-level realizers. Recently, measures based on information theory and causal modeling have been proposed that allow one to shed new light on proportionality and the related notion of specificity. In this paper we apply ideas from this literature to the issue of higher vs. lower-level causation (and explanation). Surprisingly, proportionality turns out to be irrelevant for the question (...) of whether higher-level causes (or explanations) can be autonomous; specificity is a much more informative notion for this purpose. (shrink)

This paper proposes a formalization of the class of sentences quantified by most, which is also interpreted as proportion of or majority of depending on the domain of discourse. We consider sentences of the form “Most A are B”, where A and B are plural nouns and the interpretations of A and B are infinite subsets of \. There are two widely used semantics for Most A are B: \ > C \) and \ > \dfrac{C}{2} \), where C denotes (...) the cardinality of a given finite set X. Although is more descriptive than, it also produces a considerable amount of insensitivity for certain sets. Since the quantifier most has a solid cardinal behaviour under the interpretation majority and has a slightly more statistical behaviour under the interpretation proportional of, we consider an alternative approach in deciding quantity-related statements regarding infinite sets. For this we introduce a new semantics using natural density for sentences in which interpretations of their nouns are infinite subsets of \, along with a list of the axiomatization of the concept of natural density. In other words, we take the standard definition of the semantics of most but define it as applying to finite approximations of infinite sets computed to the limit. (shrink)

This work presents the structure, distribution and semantic interpretation of quantificational expressions in languages from diverse language families and typological profiles. The current volume pays special attention to underrepresented languages of different status and endangerment level. Languages covered include American and Russian Sign Languages, and sixteen spoken languages from Africa, Australia, Papua, the Americas, and different parts of Asia. The articles respond to a questionnaire the editors constructed to enable detailed crosslinguistic comparison of numerous features. They offer comparable information on (...) semantic classes of quantifiers (generalized existential, generalized universal, proportional, partitive), syntactically complex quantifiers (intensive modification, Boolean compounds, exception phrases, et cetera), and several more specific issues such as quantifier scope ambiguities, floating quantifiers, and binary (type 2) quantifiers. The book is intended for semanticists, logicians interested in quantification in natural language, and general linguists as articles are meant to be descriptive and theory independent. The book continues and expands the coverage of the Handbook of Quantifiers in Natural Language (2012) by the same editors, and extends the earlier work in Matthewson (2008), Gil and others (2013) and Bach et al (1995). (shrink)

The paper presents an experimental evidence on differences in the sentence-picture verification under additional memory load between parity and proportional quantifiers. We asked subjects to memorize strings of 4 or 6 digits, then to decide whether a quantifier sentence is true at a given picture, and finally to recall the initially given string of numbers. The results show that: (a) proportional quantifiers are more difficult than parity quantifiers with respect to reaction time and accuracy; (b) (...) maintaining either 4 or 6 elements in the working memory has the same effect on the processing of parity quantifiers; (c) however, in the case of proportional quantifiers subjects performed better in the verification tasks under the 6-digit load condition, and (d) even though the strings of 4 numbers were better recalled by subjects after judging parity there is no difference between quantifiers in the case of the 6-element condition. We briefly outline two alternative explanations for the observed phenomena rooted in the computational model of quantifier verification and the different theories of working memory. (shrink)

Cognitive Science, Volume 45, Issue 11, November 2021.

Kovacs argues that honorary authorship and regarding each co-author of multi-authored papers as if they were sole authors when the performance of researchers is being evaluated by their publications mean that we should require authors to identify what proportion of each publication should be attributed to each co-author. Even if such attributions could be made reliably, such a change should not be made. Contributions to authorship cannot be validly quantified, and the relative merits of different publications are also neither equal (...) nor validly quantifiable. Research administrators need to recognise that whatever criteria they adopt to evaluate the performance of researchers, researchers will find a way to game the system in order to maximise their personal benefit. (shrink)

John Broome argues that fairness requires that claims are satisfied in proportion to their strength. Broome holds that, when distributing indivisible goods, fairness requires the use of weighted lotteries as a surrogate to satisfy proportionally each candidate's claims. In this article, we present two arguments against Broome's account of fairness. First, we argue that it is almost impossible to calculate the weights of the lotteries in accordance with the requirements of fairness. Second, we argue that Broome rules out those methods (...) whose use might provide some resolution to this problem. From these arguments, we conclude that, contra Broome, fairness does not require the proportional satisfaction of claims. (shrink)

This paper presents an extensional account of manyand few that explains data that have previously motivated intensional analyses of these quantifiers :599–620, 2000). The key insight is that their semantic arguments are themselves set intersections: the restrictor is the intersection of the predicates denoted by the N’ or the V’ and the restricted universe, U, and the scope is the intersection of the N’ and V’. Following Cohen, I assume that the universe consists of the union of alternatives to (...) the nominal and verbal predicates, where an alternative to a property ψ is one that shares a pragmatic presupposition with ψ, and a pragmatic presupposition is one that is selected by context from a set of potential presuppositions associated with the sentence. A many/few-quantified sentence is then true iff the proportion of the scope to the restrictor is greater/less than some threshold, n. In addition to explaining various problematic cases from the literature, the analysis shows how the readings of a many/few-quantified sentence can be derived from the same syntactico-semantic structure, it being unnecessary to claim lexical or structural ambiguity. The analysis also provides strong support for the idea that natural language quantification is always purely extensional. (shrink)

The verification of a sentence against a visual display in experimental conditions reveals a procedure that is driven solely by the properties of the linguistic input and not by the properties of the context (the set-up of the visual display) or extra-linguistic cognition (operations executed to obtain the truth value). This procedure, according to the Interface Transparency Thesis (ITT) (Lidz et al. in Nat Lang Semant 19(3):227–256, 2011), represents the meaning of an expression at the interface with the ‘conceptual-intentional’ system (...) (Chomsky in The minimalist program. MIT Press, Cambridge, 1995). My experiments provide support for the ITT by replicating in Polish and in Bulgarian the findings of Lidz et al. (Nat Lang Semant 19(3):227–256, 2011) for the English quantifier most. We also obtain new evidence that participants are prompted to switch between verification procedures by a change in the linguistic input (a different superlative quantifier entailed by most), but not by a change in the visual input. Thus, the motivation for the subconscious switch in procedures is not to maximize efficiency. Participants use the procedure associated with each quantifier, and in effect, the same display is verified differently depending on which information the visual system is instructed to use by the semantic representation of the sentence. (shrink)

This paper proposes that both weak and strong NPIs in English are sensitive to the downward entailingness of their licensers. It is also proposed, however, that these two types of NPIs pay attention to different aspects of the meaning of their environment. As observed by von Fintel and Chierchia, weak NPIs do not attend to the scalar implicatures of presuppositions of their licensers. Strong NPIs see both the truth-conditional and non-truth-conditional (scalar implications, presuppositions) meaning of their licensers. This theory accounts (...) for the puzzling inability, noted by Rullmann and Gajewski, of Strawson anti-additive operators to license strong NPIs, as well as for the effects of Zwarts’s hierarchy of negative strength. Additional issues concerning comparative quantifiers, few, and proportional quantifiers are addressed. (shrink)

In the study of natural language quantification, much recent attention has been devoted to the investigation of verification procedures associated with the proportional quantifier most. The aim of these studies is to go beyond the traditional characterization of the semantics of most, which is confined to explicating its truth-functional and presuppositional content as well as its combinatorial properties, as these aspects underdetermine the correct analysis of most. The present paper contributes to this effort by presenting new experimental evidence in (...) support of a decompositional analysis of most according to which it is a superlative construction built from a gradable predicate many or much and the superlative operator -est. Our evidence comes in the form of verification profiles for sentences like Most of the dots are blue which, we argue, reflect the existence of a superlative reading of most. This notably contrasts with Lidz et al.’s results. To reconcile the two sets of data, we argue, it is necessary to take important differences in task demands into account, which impose limits on the conclusions that can be drawn from these studies. (shrink)

This paper presents a generalization of the standard notions of left monotonicity (on the nominal argument of a determiner) and right monotonicity (on the VP argument of a determiner). Determiners such as “more than/at least as many as” or “fewer than/at most as many as”, which occur in so-called propositional comparison, are shown to be monotone with respect to two nominal arguments and two VP-arguments. In addition, it is argued that the standard Generalized Quantifier analysis of numerical determiners such as (...) “more than three/at least three” is a simplification which ignores the fundamental parallellism with the propositional comparatives. Furthermore, the symmetric monotonicity configurations of the existential “some” and “no” are shown to be straightforwardly related to those of numerical comparatives with the limit numeral zero, whereas the asymmetric configurations of universal “all” and “not all” involve the extra complicating mechanism of polarity reversal, which is related to Keenan's notion of co-intersectivity (as opposed to intersectivity). A second aim of the paper is to investigate some of the factors reducing the inferential potential of determiners. Different types of comparative determiners and their modification will be considered in detail. In addition, a systematic interaction will be revealed between the monotonicity properties of the determiners in propositional comparatives and the differ ent types of ellipsis in the “than”-complement. Different degrees of ellipsis are defined in terms of informational dependencies between the “than”-complement and the main clause. A general balancing mechanism is observed by virtue of which an increase in informational dependency is compensated by a reduction of the inferential potential of the comparative determiner. The structure of the paper is as follows. Part two deals with propositional comparison and introduces the two basic monotonicity configurations. Part three distinguishes three types of informational dependencies or ellipsis between the “than”-complement and the main clause. In Section 3.1 the “than”-complement only contains a VP constituent, whereas in Section 3.2. it only consists of a nominal constituent. Section 3.3 considers more complex instances of multiple dependencies. Section 3.4 then looks at the interaction of these three types with the modifier “proportionally”. Part four presents the two basic monotonicity configurations for numerical comparison, whereas part five deals with more complex numerical determiners. Bounding determiners, such as “between five and ten”, and other boolean combinations are discussed in Section 5.1, whereas Section 5.2 goes into approximative determiners involving modifiers such as “only” or “almost”. Section 5.3. is devoted to proportional determiners such as “more than two out of three”. Part six then considers the standard existential and universal quantifiers. Section 6.1 reformulates the standard Generalized Quantifier analysis in comparative terms, whereas Section 6.2 deals with exception determiners of the form “all but five”. (shrink)

According to logical theories of meaning, a meaning of an expression can be formalized and encoded in truth conditions. Vagueness of the language and individual differences between people are a challenge to incorporate into the meaning representations. In this paper, we propose a new approach to study truth-conditional representations of vague concepts. For a case study, we selected two natural language quantifiers most and more than half. We conducted two online experiments, each with 90 native English speakers. In the (...) first experiment, we tested between-subjects variability in meaning representations. In the second experiment, we tested the stability of meaning representations over time by testing the same group of participants in two experimental sessions. In both experiments, participants performed the verification task. They verified a sentence with a quantifier (e.g., “Most of the gleerbs are feezda.”) based on the numerical information provided in the second sentence, (e.g., “60% of the gleerbs are feezda”). To investigate between-subject and within-subject differences in meaning representations, we proposed an extended version of the Diffusion Decision Model with two parameters capturing truth conditions and vagueness. We fit the model to responses and reaction times data. In the first experiment, we found substantial between-subject differences in representations of most as reflected by the variability in the truth conditions. Moreover, we found that the verification of most is proportion-dependent as reflected in the reaction time effect and model parameter. In the second experiment, we showed that quantifier representations are stable over time as reflected in stable model parameters across two experimental sessions. These findings challenge semantic theories that assume the truth-conditional equivalence of most and more than half and contribute to the representational theory of vague concepts. The current study presents a promising approach to study semantic representations, which can have a wide application in experimental linguistics. (shrink)

We propose a new approach to conditional donkey sentences that allows us to face successfully the often called proportion problem. The main ingredients of the proposal are van Benthem's generalized quantifier approach to conditionals, and Barwise's situation semantics. We present some experimental data supporting our proposal.

In just proportional exchange, under Aristotle's theory of reciprocal justice, superior sharers in a community materially assist the weaker, and receive honour as a reward. Aristotle's economic thought is represented with a system of 18 formulae. Explained are: (1) What Aristotle means when he says that it is impossible for two sharers or their erga to be commensurable; (2) The extent to which the variables in Aristotle's proportions can be quantified. (3) What diagonal pairing ( ?ατ δ? ??τ?o? σ (...) ??????) is; (4) How need makes sharers and their erga ?sufficiently' commensurable; and (5) Aristotle's theory of what is just in exchange. (shrink)

Explaining the maintenance of communicative behavior in the face of incentives to deceive, conceal information, or exaggerate is an important problem in behavioral biology. When the interests of agents diverge, some form of signal cost is often seen as essential to maintaining honesty. Here, novel computational methods are used to investigate the role of common interest between the sender and receiver of messages in maintaining cost-free informative signaling in a signaling game. Two measures of common interest are defined. These quantify (...) the divergence between sender and receiver in their preference orderings over acts the receiver might perform in each state of the world. Sampling from a large space of signaling games finds that informative signaling is possible at equilibrium with zero common interest in both senses. Games of this kind are rare, however, and the proportion of games that include at least one equilibrium in which informative signals are used increases monotonically with common interest. Common interest as a predictor of informative signaling also interacts with the extent to which agents’ preferences vary with the state of the world. Our findings provide a quantitative description of the relation between common interest and informative signaling, employing exact measures of common interest, information use, and contingency of payoff under environmental variation that may be applied to a wide range of models and empirical systems. © 2013 Godfrey-Smith, Martínez. (shrink)

Cloud computing (ClC) has become a more popular computer paradigm in the preceding few years. Quality of Service (QoS) is becoming a crucial issue in service alteration because of the rapid growth in the number of cloud services. When evaluating cloud service functioning using several performance measures, the issue becomes more complex and non-trivial. It is therefore quite difficult and crucial for consumers to choose the best cloud service. The user's choices are provided in a quantifiable manner in the current (...) methods for choosing cloud services. Hence, this study attempts to achieve this objective through construction. decision-making framework so-called cloud services evaluator (CSsEv). The main indicator and its sub-indicators are formed as nodes at levels(n) in tree soft sets (TSSs). Thereafter Single Value Neutrosophic Sets (SVNSs) as branch of neutrosophic sets which conjunction with the Multi-Criteria Decision Making (MCDM) technique to facilitate analysis and evaluation process for the available Cloud services providers. Hence, entropy is employed to obtain indicators and sub_indicators weights and Complex Proportional Assessment utilizes these weights to facilitate the decision process of selecting optimal ClSPs. (shrink)

In (1b), for the most part induces a so-called Quantificational Variability Effect (QVE) on the NP the linguists from the East Coast, yielding roughly the interpretation ‘most of the linguists from the East Coast came to NELS’. We claim that the two constructions above differ in the domain where they apply, producing similar but not identical quantificational interpretations over the NP. In particular, we argue that most of the NPs applies to the nominal domain, while for the most part applies (...) to the verbal domain. Our claim is based on two sets of novel semantic data. First, we show that the distribution of most of the NPs is parallel to that of all the NPs in terms of its selective compatibility with collective predicates. To account for this data, we extend Brisson’s (1998, 2003) analysis of all the NPs to most of the NPs, concluding that most is an ∃-quantifier introducing a group of a certain proportion. Second, we show that, when for the most part gives rise to a QVE on a definite NP, the collective interpretation is not available. We develop a semantic analysis of for the most part as a verbal modifier that explains the lack of collective readings and that extends to interpretations other than QVE. The structure of the paper is as follows: in section 2, we introduce some general background on events and distributivity that are relevant to the current paper. In section 3, we propose the analysis of most of the NPs, followed by the analysis of for the most part in section 4. Section 5 concludes the paper and discusses further issues. (shrink)

Natural languages vary in their quantity expressions, but the variation seems to be constrained by general properties, so-calleduniversals. Their explanations have been sought among constraints of human cognition, communication, complexity, and pragmatics. In this article, we apply a state-of-the-art language coordination model to the semantic domain of quantities to examine whether two quantity universals—monotonicity and convexity—arise as a result of coordination. Assuming precise number perception by the agents, we evolve communicatively usable quantity terminologies in two separate conditions: a numeric-based condition (...) in which agents communicate about a number of objects and a quotient-based condition in which agents communicate about the proportions. We find out that both universals take off in all conditions but only convexity almost entirely dominates the emergent languages. Additionally, we examine whether the perceptual constraints of the agents can contribute to the further development of universals. We compare the degrees of convexity and monotonicity of languages evolving in populations of agents with precise and approximate number sense. The results suggest that approximate number sense significantly reinforces monotonicity and leads to further enhancement of convexity. Last but not least, we show that the properties of the evolved quantifiers match certain invariance properties from generalized quantifier theory. (shrink)

One of the core debates concerning equity in the response to the threat of anthropogenic climate change is how the responsibility to reduce greenhouse gas emissions should be allocated, or, correspondingly, how the right to emit greenhouse gases should be allocated. Two alternative approaches that have been widely promoted are, first, to assign obligations to the industrialized countries on the basis of both their ability to pay and their responsibility for the majority of prior emissions, or, second, to assign emissions (...) rights on a equal per capita basis. Both these proposals ignore intra-national distributional equity. Instead, we develop a policy framework we call 'Greenhouse Development Rights' which allocates obligations to pay for climate policies on the basis of an individually quantified metric of capacity and responsibility . Crucially, the GDRs framework looks at the distribution of income within countries and treats people of equal wealth similarly, whatever country they live in. Thus even poor countries have obligations proportional to the size and wealth of their middle and upper classes, defined relative to a 'development threshold'. While this method nominally identifies the 'right to development' as applying to people, not countries, as a proposal for a treaty among sovereign nations, there is no obvious way to give legal meaning to that right. In this paper, then, we raise some of the philosophical and political questions that arise in trying to quantify capacity and responsibility and to use the 'right to development' as a principle for allocating costs.*. (shrink)

Saccadic chronostasis refers to the subjective temporal lengthening of the first visual stimulus perceived after an eye movement. It has been quantified using a duration discrimination task. Most models of human duration discrimination hypothesise an internal clock. These models could explain chronostasis as a transient increase in internal clock speed due to arousal following a saccade, leading to temporal overestimation. Two experiments are described which addressed this hypothesis by parametrically varying the duration of the stimuli that are being judged. Changes (...) in internal clock speed predict chronostasis effects proportional to stimulus duration. No evidence for proportionality was found. Two further experiments assessed the appropriateness of the control conditions employed. Results indicated that the chronostasis effect is constant across a wide range of stimulus durations and does not reflect the pattern of visual stimulation experienced during a saccade, suggesting that arousal is not critical. Instead, alternative processes, such as one affecting the onset of timing are implicated. Further research is required to select between these alternatives. (shrink)

In this study meal sharing is used as a way of quantifying food transfers between households. Traditional food-sharing studies measure the flow of resources between households. Meal sharing, in contrast, measures food consumption acts according to whether one is a host or a guest in the household as well as the movement of people between households in the context of food consumption. Our goal is to test a number of evolutionary models of food transfers, but first we argue that before (...) one tests models of who should receive food one must understand the adaptiveness of food transfers. For the Ye’kwana, economies of scale in food processing and preparation appear to set the stage for the utility of meal sharing. Evolutionary models of meal sharing, such as kin selection and reciprocal altruism, are evaluated along with non-evolutionary models, such as egalitarian exchange and residential propinquity. In addition, a modified measure of exchange balance—proportional balance—is developed. Reciprocal altruism is shown to be the strongest predictor of exchange intensity and balance. (shrink)

Un de ces (syntagmes) qui… (à propos de la locution un(e) de ces […] qui) Cet article a pour objet de montrer, sur une question déjà soulevée en stylistique française, ce que nous semble pouvoir apporter la dimension des vastes corpus et des outils logiciels d’exploration assistée. La locution un(e) de ces […] qui, déjà étudiée comme stylème dix-neuviémiste (Bordas), vecteur d’exophore mémorielle (Fraser & Joly), est redéfinie comme support d’un décrochage discursif dans le cadre de la polyphonie du récit (...) (Bakhtine). Elle fait ici l’objet d’un relevé systématique dans un vaste corpus littéraire, qui permet de quantifier les proportions d’une typologie (notamment quant à la concordance aspectuo-temporelle) et d’en affiner la distribution diachronique et par auteurs. On observe alors le fonctionnement de cette locution comme filtre du vocabulaire et l’on montre que non seulement des unités isolées, mais des pôles lexico-thématiques de sa structure polycooccurrentielle (mise en évidence par l’AFC) sont significativement sur et sous-représentés dans les phrases d’emploi. On avance ainsi vers une meilleure connaissance de cette structure-frontière de la langue et du style en français. (shrink)

Motivated by advances in mass customization in business practice, explosion in the number of internet of things devices, and the lack of published research on privacy differentiation and customization, we propose a contextual information relevance model of privacy. We acknowledge the existence of individual differences with respect to unique security and privacy protection needs. We observe and argue that it is unfair and socially inefficient to treat privacy in a uniform manner whereby a large proportion of the population remain unsatisfied (...) by a common policy. Our research results provide quantifiable means to measure and evaluate the customized privacy. We show that with privacy differentiation, the social planner will observe increases in demand and overall social welfare. Our results also show that business practitioners could profit from privacy customization. (shrink)

I argue that common nouns should be analyzed as variables, rather than as predicates which take variables as arguments. This necessitates several unusual features to the analysis, such as allowing variables to be modally non-rigid, and assigning their values compositionally. However, treating common nouns as variables offers a variety of theoretical and empirical advantages over a more traditional analysis: It predicts the conservativity of nominal quantification, simplifies the analysis of articleless languages, derives the weak reading of sentences with donkey anaphora, (...) solves the proportion problem presented by quantifiers like ‘most’, improves the analysis of the temperature paradox, allows a more unified analysis of bare plurals, and regularizes the correspondence between syntactic categories and semantic types. (shrink)

In this paper we present a dynamic assignment language which extends the dynamic predicate logic of Groenendijk and Stokhof [1991: 39–100] with assignment and with generalized quantifiers. The use of this dynamic assignment language for natural language analysis, along the lines of o.c. and [Barwise, 1987: 1–29], is demonstrated by examples. We show that our representation language permits us to treat a wide variety of donkey sentences: conditionals with a donkey pronoun in their consequent and quantified sentences with donkey (...) pronouns anywhere in the scope of the quantifier. It is also demonstrated that our account does not suffer from the so-called proportion problem.Discussions about the correctness or incorrectness of proposals for dynamic interpretation of language have been hampered in the past by the difficulty of seeing through the ramifications of the dynamic semantic clauses (phrased in terms of input-output behaviour) in non-trivial cases. To remedy this, we supplement the dynamic semantics of our representation language with an axiom system in the style of Hoare. While the representation languages of barwise and Groenendijk and Stokhof were not axiomatized, the rules we propose form a deduction system for the dynamic assignment language which is proved correct and complete with respect to the semantics. (shrink)

One of the core debates concerning equity in the response to the threat of anthropogenic climate change is how the responsibility to reduce greenhouse gas emissions should be allocated, or, correspondingly, how the right to emit greenhouse gases should be allocated. Two alternative approaches that have been widely promoted are, first, to assign obligations to the industrialized countries on the basis of both their ability to pay (wealth) and their responsibility for the majority of prior emissions, or, second, to assign (...) emissions rights on a (possibly modified) equal per capita basis. Both these proposals ignore intra-national distributional equity. Instead, we develop a policy framework we call ‘Greenhouse Development Rights’ (GDRs) which allocates obligations to pay for climate policies (both mitigation and adaptation) on the basis of an individually quantified metric of capacity (ability to pay) and responsibility (prior emissions). Crucially, the GDRs framework looks at the distribution of income within countries and treats people of equal wealth similarly, whatever country they live in. Thus even poor countries have obligations proportional to the size and wealth of their middle and upper classes, defined relative to a ‘development threshold’. While this method nominally identifies the ‘right to development’ as applying to people, not countries, as a proposal for a treaty among sovereign nations, there is no obvious way to give legal meaning to that right. In this paper, then, we raise some of the philosophical and political questions that arise in trying to quantify capacity and responsibility and to use the ‘right to development’ as a principle for allocating costs.Footnote**The ‘Greenhouse Development Rights’ (GDRs) framework is a collective project. The core team includes the author, Tom Athanasiou, Sivan Kartha and Eric Kemp-Benedict; this is the ‘we’ that appears where the text refers to the project, as in ‘we intended this’, and so on. This paper, however, is primarily the author's own product and, beyond the description of GDRs, my collaborators have not read or approved it; thus much of the writing and philosophical speculation uses the first person singular. And, while credit for useful work goes to all team members, the blame for philosophical sloppiness remains with the author. (shrink)

A prefrontal control system that is less mature than the limbic reward system in adolescence is thought to impede self-regulatory abilities, which could contribute to poor dietary choices and obesity. We, therefore, aimed to examine whether structural morphology of the prefrontal cortex and the amygdala are associated with dietary decisions and obesity in children and adolescents. Seventy-one individuals between the ages of 8–22 years participated in this study; each participant completed a computer-based food choice task and a T1- and T2-weighted (...) structural brain scans. Two indices of obesity were assessed, including age- and sex-specific body mass index and waist-to-height ratio. The behavioral task included rating 60 food stimuli for tastiness, healthiness, and liking. Based on each participant’s self-ratings, 100 binary food choices were then made utilizing a computer mouse. Dietary “self-control” was calculated as the proportion of trials where the individual chose the healthier food item over the total number of trials. Cortical thickness and amygdala subnuclei volumes were quantified using FreeSurfer 6.0 and CIT168 atlas, respectively. We found that WHtR was negatively associated with the thickness of bilateral superior frontal, left superior temporal, right insula, and right inferior temporal regions. We also found WHtR to be positively associated with the volume of the central nucleus region of the amygdala, after adjusting for the hemisphere, age, sex, and intracranial volumes. A similar data pattern was observed when BMIz was used. Moreover, we found that across all participants, thinner right superior frontal cortex and larger left CEN volumes predicted lower dietary self-control. These results suggest that differential development of the PFC and amygdala relate to obesity and dietary self-control. Further longitudinal studies are merited to determine causal relationships among altered PFC to amygdala neural circuitry, dietary self-control, and obesity. (shrink)

The paper presents Property Theory with Curry Typing (PTCT) where the language of terms and well-formed formulæ are joined by a language of types. In addition to supporting fine-grained intensionality, the basic theory is essentially first-order, so that implementations using the theory can apply standard first-order theorem proving techniques. Some extensions to the type theory are discussed, type polymorphism, and enriching the system with sufficient number theory to account for quantifiers of proportion, such as “most.”.

In previous work we have developed Property Theory with Curry Typing (PTCT), an intensional first-order logic for natural language semantics. PTCT permits fine-grained specifications of meaning. It also supports polymorphic types and separation types. We develop an intensional number theory within PTCT in order to represent proportional generalized quantifiers like "most", and we suggest a dynamic type-theoretic approach to anaphora and ellipsis resolution. Here we extend the type system to include product types, and use these to define a (...) permutation function that generates underspecified scope representations within PTCT. We indicate how filters can be added to encode constraints on possible scope readings. Our account offers several important advantages over other current theories of underspecification. (shrink)

We argue for an account of chemical reactivities as chancy propensities, in accordance with the ‘complex nexus of chance’ defended by one of us in the past (Suárez, 2017, 2020). Reactivities are typically quantified as proportions, and an expression such as “A + B → C” does not entail that under the right conditions some amounts of A and B react to give the amount of C that theoretically would correspond to the stoichiometry of the reaction. Instead, what is produced (...) is a fraction α < 1 of this theoretical amount, and the corresponding percentage is usually known as the yield, which expresses the relative preponderance of its reaction. This is then routinely tested in a laboratory against the observed actual yields for the different reactions. Thus, on our account, reactivities ambiguously refer to three quantities at once. They first refer to the underlying propensities effectively acting in the reaction mechanisms, and which in ‘chemical chemistry’ (Schummer, 1998) are commonly represented by means of Lewis structures. Besides, reactivities represent the probabilities that these propensities give rise to, for any amount of the reactants to combine as prescribed. This last notion is hence best understood as a single case chance and corresponds to a theoretical stoichiometric yield. Finally, reactivities represent the actual yields observed in experimental runs, which account for and provide the requisite evidence for / against both the mechanisms and single case chances ascribed. (shrink)

We argue for an account of chemical reactivities as chancy propensities, in accordance with the ‘complex nexus of chance’ defended by one of us in the past. Reactivities are typically quantified as proportions, and an expression such as “A + B → C” does not entail that under the right conditions some given amounts of A and B react to give the mass of C that theoretically corresponds to the stoichiometry of the reaction. Instead, what is produced is a fraction (...) α < 1 of this theoretical amount, and the corresponding percentage is usually known as the yield, which expresses the relative preponderance of its reaction. This is then routinely tested in a laboratory against the observed actual yields for the different reactions. Thus, on our account, reactivities ambiguously refer to three quantities at once. They first refer to the underlying propensities effectively acting in the reaction mechanisms, which in ‘chemical chemistry’ (Schummer in Hyle 4:129–162, 1998) are commonly represented by means of Lewis structures. Besides, reactivities represent the probabilities that these propensities give rise to, for any amount of the reactants to combine as prescribed. This last notion is hence best understood as a single case chance and corresponds to a theoretical stoichiometric yield. Finally, reactivities represent the actual yields observed in experimental runs, which account for and provide the requisite evidence for/against both the mechanisms and single case chances ascribed. (shrink)

Among the reasons that Whitehead is such an interesting philosopher is that his work resonates across philosophical traditions. This collection develops connections between Whiteheadian concepts and recent European thinkers. The purpose is not simply to compare, however, but, as editor Jeremy Fackenthal suggests, to develop a Whiteheadian thinking “in tandem” with European philosophers in order to create disruptions or “dislocations” in thought that can engender creative approaches to contemporary problems.One general feature of the book deserves mention at the outset, though (...) I will return to it later in the review: although phenomenology and hermeneutics are each represented in the volume, roughly half of the essays focus on the work of Gilles Deleuze (if we group these together with essays focused on “new materialism,” which is connected with Deleuze, the proportion is more like two-thirds). This will be no surprise, since Deleuze is the European philosopher who was most appreciative of Whitehead. And yet, the result is that the conversation with “continental philosophy” is highly selective.The book is organized into three parts, each comprised of three essays. In part 1, “Technological and Systematic Dislocations,” William S. Hamrick brings Whitehead into conversation with Maurice Merleau-Ponty's concept of “the flesh” to suggest an ecological ontology capable of overcoming the instrumentalization of nature. Hamrick's strategy is to read Whitehead and Merleau-Ponty as contributing to an “ontological foundation” for a sustainable civilization (18). Bo Eberle writes about the “quantified self” suggested in new, wearable self-monitoring technologies. Drawing on Whitehead's notion of causal efficacy, Eberle argues that devices such as Fitbit give us access to bodily states that bypasses the standard ways we are aware of ourselves (i.e., through consciousness). He goes further to argue that, like all ways of knowing, wearable technologies are selective, and that the selection reflects the interests of the manufacturers and promotes a certain kind of subjectivity (in the case of Fitbit, a subjectivity that is oriented toward “getting your steps in”). Whitehead's epistemology thus enables the critic of wearable technologies to understand how contemporary experience and self-understanding is shaped not simply by recent technological mediations but by the material interests embedded in them. J.R. Hustwit and Carl Dyke take on what they call “activist” uses of Whitehead that naively (in their judgment) suggest that a non-relational substance metaphysics is to blame for most of our social ills. They employ the theory of complex adaptive systems in conversation with Whitehead and Antonio Gramsci to show that, in fact, achieving significant social change is far more difficult and even unpredictable than mere insertion of better ideas into public discourse. Dominant hegemonies have ways of adapting and absorbing attempts to undermine them. Here Hustwit and Dyke draw on the philosophy of Paul Ricoeur to suggest that resistance to the dominant hegemony is nevertheless always possible because of the vagueness of discourse, allowing a plurality of competing interpretations and thus fractures in the dominant hegemony. However, even this kind of resistance is impossible to control and its effects incapable of being entirely predicted. To the essay's titular question, “Can Whitehead save the world?” the authors answer, “No.”In part 2, “Animal/Human Dislocations,” Jeremy Fackenthal draws on the new materialism of Rosi Braidotti (and Deleuze) along with Whitehead to argue for a “process-relational” nomadism that culminates in a “becoming-imperceptible.” His reading together of Whitehead and Braidotti creates the opportunity to recast the former's concept of objective immortality in such a way that it does not refer to death so much as to being diffused into a relational network. The satisfaction of an actual occasion may be taken as its translation into its effects among its relations. Fackenthal argues that this becoming-imperceptible makes possible a sustainable presence within a fragile network of life. Deena M. Lin uses Whitehead, Braidotti, and Judith Butler to lay out a vision of human life as precarious and deserving attention, care, and solidarity. She presses this vision as a direct moral assault on US (Trump's) policy toward Syrian refugees. Going further, she draws on Braidotti's posthuman account of zoe to argue for universal connection and solidarity with all life that should foster, as the title of her essay puts it, “Welcoming of Syrian Life.” Tano Posteraro offers an intriguing essay drawing on Jakob von Uexküll's account of animal experience. Posteraro argues that Uexküll's notion of an animal's Umwelt, shaped by its distinctive perceptual apparatus, needs to be supplemented by Whitehead's notion of prehension to account for the active dimension of animal perception. Rather than a passive registering of animal environments, Posteraro argues that the latter are constructed, and that concepts (or conceptual prehensions) should be understood as tools with which such environments are constructed.In part 3, “Time, the World, and Abstraction,” three essays probe ways that Whiteheadian and Deleuzian themes may resonate critically and constructively. Kris Klotz brings the thought of Whitehead and Deleuze together to inquire about how alternatives to present social forms are envisioned. He argues that, for Whitehead, every actual occasion involves a selection of some features of the past, and, further, that every selection is also an abstraction from the concrete welter of influences impinging on it. For Whitehead, then, to envision alternatives involves a critique of abstractions, a reinstatement of the concrete plurality of possibilities. This, for Whitehead, is what rationality does: it works at restoring the concrete, and, with it, a series of alternatives that have been eclipsed. To this Whiteheadian analysis, Klotz adds Deleuze and Guattari's critique of “opinion.” For Deleuze and Guattari, opinion is not an idiosyncrasy but a consensus to which differences of experience are subjected. Philosophy, for Deleuze and Guattari, must always struggle against opinion in order to bring alternatives to light. These conceptions of reason/philosophy, Klotz argues, represent useful ways to critique inequalities and other social wrongs that are embedded in the social forms that are routinely taken for granted. Elijah Prewitt-Davis uses a scene from Buffy the Vampire Slayer, along with philosophical innovations of Foucault, Deleuze, and Whitehead, to offer a distinctive account of power. Prewitt-Davis calls attention to Deleuze's important book on Leibniz, The Fold, and to how Whitehead's concept of prehension lies at its center. The upshot is that power is not reduced to dominance but, instead, is at work wherever any occasion of experience persists amid the onslaught of the influence of other occasions. Power, as Deleuze wrote, is the capacity to be affected—and to decide how to constitute oneself anew. Keith Robinson offers a detailed account of Whitehead's epistemology along with a reading of Deleuze's analysis of temporality to suggest that there is a common trajectory that seeks to undermine what the title of the essay describes as the “Bifurcation of Nature” (i.e., the separation of natural phenomena and human experience) within the dominant Western philosophical tradition.There is much of value in the volume as a whole. Aside from staging what Spinoza might have called good encounters between Whitehead and a number of continental philosophers, enhancing the conceptual power of each, the contributors are able to make a case that these philosophical trajectories, when read together, have much to contribute to our understanding of and response to the pressing issues of the day. In addition, readers who are interested in the relationship between Whitehead and the new materialism will find this volume to be a helpful resource, stocked with fine examples of how to sharpen new materialist thinking with Whitehead and how to read contemporary contexts through these lenses. On the other hand, this book is not a handbook nor a comprehensive reference. The organizational logic behind its division into sections is murky and the amount of attention given to particular continental philosophers as opposed to others appears somewhat arbitrary: there are recent continental philosophers who get little to no attention at (Derrida, Malabou, Žižek, Agamben, Latour, Nancy, for example), several of whom might prove to be quite interesting to read “in tandem” with Whitehead. Perhaps that is just to say that there are many more essays to be written. (shrink)

This paper compares the associative system of early-learned verbs and body parts in Hebrew with previously published data on American English (Maouene, Josita, Shohei Hidaka & Linda B. Smith. 2008. Body parts and early-learned verbs. Cognitive Science 32(7). 1200–1216). Following the methodology of the former study, 51 Hebrew-speaking college students gave the first body part that came to mind for each of 103 early-learned Hebrew verbs, 81 of which were translational equivalents. Rate of convergence and divergence and underlying patterns were (...) used to make inferences about the constraints at work. Overall convergence (92.3% of the Hebrew data and 93.7% of the English data) reveal similar entropy levels, comparable semantic field shapes of verbs organized by body parts and similar general cluster patterns of verbs by body parts. Most divergence lies in the infrequent responses (offered fewer than 1% of the time) which arise around body parts that are internal, very detailed, very general categorically, used in figurative language, uniquely provided and tend to be subject to cultural taboos. This is a new contribution, as previous work has not quantified the relative proportion of convergent to divergent associations. We discuss how these findings support neural and developmental continuity and stability in the verbal system with respect to the categorization of verbs by body parts cross-culturally. (shrink)

Un de ces (syntagmes) qui… (à propos de la locution un(e) de ces […] qui) Cet article a pour objet de montrer, sur une question déjà soulevée en stylistique française, ce que nous semble pouvoir apporter la dimension des vastes corpus et des outils logiciels d’exploration assistée. La locution un(e) de ces […] qui, déjà étudiée comme stylème dix-neuviémiste (Bordas), vecteur d’exophore mémorielle (Fraser & Joly), est redéfinie comme support d’un décrochage discursif dans le cadre de la polyphonie du récit (...) (Bakhtine). Elle fait ici l’objet d’un relevé systématique dans un vaste corpus littéraire, qui permet de quantifier les proportions d’une typologie (notamment quant à la concordance aspectuo-temporelle) et d’en affiner la distribution diachronique et par auteurs. On observe alors le fonctionnement de cette locution comme filtre du vocabulaire et l’on montre que non seulement des unités isolées, mais des pôles lexico-thématiques de sa structure polycooccurrentielle (mise en évidence par l’AFC) sont significativement sur et sous-représentés dans les phrases d’emploi. On avance ainsi vers une meilleure connaissance de cette structure-frontière de la langue et du style en français. (shrink)

In three experiments, we investigated the computational complexity of German reciprocal sentences with different quantificational antecedents. Building upon the tractable cognition thesis (van Rooij, 2008) and its application to the verification of quantifiers (Szymanik, 2010) we predicted complexity differences among these sentences. Reciprocals with all-antecedents are expected to preferably receive a strong interpretation (Dalrymple et al., 1998), but reciprocals with proportional or numerical quantifier antecedents should be interpreted weakly. Experiment 1, where participants completed pictures according to their preferred (...) interpretation, provides evidence for these predictions. Experiment 2 was a picture verification task. The results show that the strong interpretation was in fact possible for tractable all but one-reciprocals, but not for exactly n. The last experiment manipulated monotonicity of the quantifier antecedents. (shrink)

When the Ottoman Empire defaulted on its public debt in 1875, British bondholders launched a campaign to win government intervention on their behalf. This article interprets the unprecedented success of this campaign as a matter of knowledge production. Mobilizing the newly established Corporation of Foreign Bondholders as a kind of ‘centre of calculation’, bondholders argued that they deserved assistance because of the unique size of the Ottoman default and the proportion of it that was held by British subjects. Yet neither (...) of these numbers was easily calculated. In fact, influential bondholders worked closely with accountants and members of the Statistical Society to devise an accurate method for quantifying the Ottoman debt – and concluded that such a method did not exist. Historians of quantification and accounting have argued that the scientific status of nineteenth-century accounting depended on its disinterestedness. In the case of the Ottoman default, however, calculation was understood to be inseparable from material interest and political debate. (shrink)

We present Property Theory with Curry Typing (PTCT), an intensional first-order logic for natural language semantics. PTCT permits fine-grained specifications of meaning. It also supports polymorphic types and separation types. We develop an intensional number theory within PTCT in order to represent proportional generalized quantifiers like “most.” We use the type system and our treatment of generalized quantifiers in natural language to construct a type-theoretic approach to pronominal anaphora that avoids some of the difficulties that undermine previous (...) type-theoretic analyses of this phenomenon. (shrink)