The Logic and Meaning of Plurals. Part II

In this sequel to “The logic and meaning of plurals. Part I”, I continue to present an account of logic and language that acknowledges limitations of singular constructions of natural languages and recognizes plural constructions as their peers. To this end, I present a non-reductive account of plural constructions that results from the conception of plurals as devices for talking about the many. In this paper, I give an informal semantics of plurals, formulate a formal characterization of truth for the regimented languages that results from augmenting elementary languages with refinements of basic plural constructions of natural languages, and account for the logic of plural constructions by characterizing the logic of those regimented languages.

Experience and grammatical agreement: Statistical learning shapes number agreement production

A robust result in research on the production of grammatical agreement is that speakers are more likely to produce an erroneous verb with phrases such as the key to the cabinets, with a singular noun followed by a plural one, than with phrases such as the keys to the cabinet, where a plural noun is followed by a singular. These asymmetries are thought to reflect core language production processes. Previous accounts have attributed error patterns to a syntactic number feature present on plurals but not singulars. An alternative approach is presented in which a process similar to structural priming contributes to the error asymmetry via speakers’ past experiences with related agreement constructions. A corpus analysis and two agreement production studies test this account. The results suggest that agreement production is shaped by statistical learning from past language experience. Implications for accounts of agreement are discussed.     

Some attractions of verb agreement

In English, words like scissors are grammatically plural but conceptually singular, while words like suds are both grammatically and conceptually plural. Words like army can be construed plurally, despite being grammatically singular. To explore whether and how congruence between grammatical and conceptual number affected the production of subject-verb number agreement in English, we elicited sentence completions for complex subject noun phrases like The advertisement for the scissors. In these phrases, singular subject nouns were followed by distractor words whose grammatical and conceptual numbers varied. The incidence of plural attraction (the use of plural verbs after plural distractors) increased only when distractors were grammatically plural, and revealed no influence from the distractors' number meanings. Companion experiments in Dutch offered converging support for this account and suggested that similar agreement processes operate in that language. The findings argue for a component of agreement that is sensitive primarily to the grammatical reflections of number. Together with other results, the evidence indicates that the implementation of agreement in languages like English and Dutch involves separable processes of number marking and number morphing, in which number meaning plays different parts.     

Applied Logic without Psychologism

Logic is a celebrated representation language because of its formal generality. But there are two senses in which a logic may be considered general, one that concerns a technical ability to discriminate between different types of individuals, and another that concerns constitutive norms for reasoning as such. This essay embraces the former, permutation-invariance conception of logic and rejects the latter, Fregean conception of logic. The question of how to apply logic under this pure invariantist view is addressed, and a methodology is given. The pure invariantist view is contrasted with logical pluralism, and a methodology for applied logic is demonstrated in remarks on a variety of issues concerning non-monotonic logic and non-monotonic inference, including Charles Morgan’s impossibility results for non-monotonic logic, David Makinson’s normative constraints for non-monotonic inference, and Igor Douven and Timothy Williamson’s proposed formal constraints on rational acceptance.     

Mass Nouns in a Logic of Classes as Many

A semantic analysis of mass nouns is given in terms of a logic of classes as many. In previous work it was shown that plural reference and predication for count nouns can be interpreted within this logic of classes as many in terms of the subclasses of the classes that are the extensions of those count nouns. A brief review of that account of plurals is given here and it is then shown how the same kind of interpretation can also be given for mass nouns.     

Numerical morphology supports early number word learning: Evidence from a comparison of young Mandarin and English learners

Previous studies showed that children learning a language with an obligatory singular/plural distinction (Russian and English) learn the meaning of the number word for one earlier than children learning Japanese, a language without obligatory number morphology (Barner, Libenson, Cheung, & Takasaki, 2009; Sarnecka, Kamenskaya, Yamana, Ogura, & Yudovina, 2007). This can be explained by differences in number morphology, but it can also be explained by many other differences between the languages and the environments of the children who were compared. The present study tests the hypothesis that the morphological singular/plural distinction supports the early acquisition of the meaning of the number word for one by comparing young English learners to age and SES matched young Mandarin Chinese learners. Mandarin does not have obligatory number morphology but is more similar to English than Japanese in many crucial respects. Corpus analyses show that, compared to English learners, Mandarin learners hear number words more frequently, are more likely to hear number words followed by a noun, and are more likely to hear number words in contexts where they denote a cardinal value. Two tasks show that, despite these advantages, Mandarin learners learn the meaning of the number word for one three to six months later than do English learners. These results provide the strongest evidence to date that prior knowledge of the numerical meaning of the distinction between singular and plural supports the acquisition of the meaning of the number word for one.     

Evidence for a non-linguistic distinction between singular and plural sets in rhesus monkeys

Set representations are explicitly expressed in natural language. For example, many languages distinguish between sets and subsets (all vs. some), as well as between singular and plural sets (a cat vs. some cats). Three experiments explored the hypothesis that these representations are language specific, and thus absent from the conceptual resources of non-linguistic animals. We found that rhesus monkeys spontaneously discriminate sets based on a conceptual singular-plural distinction. Under conditions that do not elicit comparisons based on approximate magnitudes or one-to-one correspondence, rhesus monkeys distinguished between singular and plural sets (1 vs. 2 and 1 vs. 5), but not between two plural sets (2 vs. 3, 2 vs. 4, and 2 vs. 5). These results suggest that set-relational distinctions are not a privileged part of natural language, and may have evolved in non-linguistic species to support domain general quantitative computations.     

Numbers and Relations

In this paper, I criticize John Bigelow's account of number and present my own account that results from the criticism. In doing so, I argue that proper understanding of the nature of number requires a radical departure from the standard conception of language and reality and outline the alternative conception that underlies my account of number. I argue that Bigelow's account of number rests on an incorrect analysis of the plural constructions underlying the talk of number and propound an analysis of numerical sentences, such as “Quine and Goodman are two”, that conforms to the natural understanding of the plural constructions. The analysis leads to the account of number according to which natural numbers are properties, i.e., one-place relations: the number two, for example, is the property indicated by “to be two”, which, I argue, is a one-place predicate that can combine with plural terms like “Quine and Goodman”. This revised version was published online in August 2006 with corrections to the Cover Date.     

Composition as a Kind of Identity

Composition as identity, as I understand it, is a theory of the composite structure of reality. The theory’s underlying logic is irreducibly plural; its fundamental primitive is a generalized identity relation that takes either plural or singular arguments. Strong versions of the theory that incorporate a generalized version of the indiscernibility of identicals are incompatible with the framework of plural logic, and should be rejected. Weak versions of the theory that are based on the idea that composition is merely analogous to (one-one) identity are too weak to be interesting, lacking in metaphysical consequence. I defend a moderate version according to which composition is a kind of identity, and argue that the difference is metaphysically substantial, not merely terminological. I then consider whether the notion of generalized identity, though fundamental, can be elucidated in modal terms by reverse engineering Hume’s Dictum. Unfortunately, for realists about possible worlds, such as myself, who understand Hume’s Dictum in terms of duplicates, the elucidation never gets off the ground; for modal primitivists, the elucidation may succeed in capturing some general notion of identity, but it’s characterization is too general to target the particular notion of identity, tied to classical mereology, that is the object of my theorizing. In the end, I have little to offer the skeptic who claims not to understand the relevant notion of generalized identity, or not to take it to be compulsory in providing an account of the structure of reality.     

Referential Intentions and Communicative Luck

Brian Loar [1976] observed that communicative success with singular terms requires more than correct referent assignment. For communicative success to be achieved, the audience must assign the right referent in the right way. Loar, and others since, took this to motivate Fregean accounts of the semantics of singular terms. Ray Buchanan [2014] has recently responded, maintaining that, although Loar is correct to claim that communicative success with singular terms requires more than correct referent assignment, this is compatible with direct reference approaches, as long as one also endorses an independently motivated Gricean view of communicative intentions. This paper argues that Buchanan's Gricean view cannot account for the full range of Loar cases. In doing so, it aims to explicate the structure of Loar's cases and thus to clarify the conditions that a theory must meet in order to adequately meet his challenge.     

From grammatical number to exact numbers: early meanings of 'one', 'two', and 'three' in English, Russian, and Japanese

This study examined whether singular/plural marking in a language helps children learn the meanings of the words 'one,' 'two,' and 'three.' First, CHILDES data in English, Russian (which marks singular/plural), and Japanese (which does not) were compared for frequency, variability, and contexts of number-word use. Then young children in the USA, Russia, and Japan were tested on Counting and Give-N tasks. More English and Russian learners knew the meaning of each number word than Japanese learners, regardless of whether singular/plural cues appeared in the task itself (e.g., "Give two apples" vs. "Give two"). These results suggest that the learning of "one," "two" and "three" is supported by the conceptual framework of grammatical number, rather than that of integers.     

Plural Logic and Sensitivity to Order

Sentences that exhibit sensitivity to order (e.g. John and Mary arrived at school in that order and Mary and John arrived at school in that order) present a challenge for the standard formulation of plural logic. In response, some authors have advocated new versions of plural logic based on fine-grained notions of plural reference, such as serial reference [Hewitt 2012] and articulated reference [Ben-Yami 2013]. The aim of this article is to show that sensitivity to order should be accounted for without altering the standard formulation of plural logic. In particular, sensitivity to order does not call for a fine-grained notion of plural reference. We point out that the phenomenon in question is quite broad and that current proposals are not equipped to deal with the full range of cases in which order plays a role. Then we develop an alternative and unified account, which locates the phenomenon not in the way in which plural terms can refer, but in the meaning of special expressions such as in that order and respectively.     

Formality of logic and Frege’s Begriffsschrift

This paper challenges a standard interpretation according to which Frege’s conception of logic (early and late) is at odds with the contemporary one, because on the latter’s view logic is formal, while on Frege’s view it is not, given that logic’s subject matter is reality’s most general features. I argue that Frege – in Begriffsschrift – retained the idea that logic is formal; Frege sees logic as providing the ‘logical cement’ that ties up together the contentful concepts of specific sciences, not the most general truths. Finally, I discuss how Frege conceives of the application of Begriffsschrift, and of its status as a ‘lingua characteristica’.     

Determiner selection in noun phrase production

In 3 experiments, native speakers of German named pictures of 1 or 2 objects by producing singular or plural noun phrases consisting of a definite gender-marked determiner and a noun. When singular and plural determiners differed (masculine and neuter gender), naming latencies were longer for plural utterances than for singular utterances. By contrast, when singular and plural determiners were identical (feminine gender), no such effect was obtained. When participants produced bare nouns, the Gender x Number interaction disappeared. This pattern indicates that during the production of plural definite-determiner noun phrases, singular and plural determiners compete for selection. The resulting constraints on number and gender processing in noun phrase production are discussed in the framework of models of language production.     

Moral expressivism and sentential negation

This paper advances three necessary conditions on a successful account of sentential negation. First, the ability to explain the constancy of sentential meaning across negated and unnegated contexts (the Fregean Condition). Second, the ability to explain why sentences and their negations are inconsistent, and inconsistent in virtue of the meaning of negation (the Semantic Condition). Third, the ability of the account to generalize regardless of the topic of the negated sentence (the Generality Condition). The paper discusses three accounts of negation available to moral expressivists. The first—the dominant commitment account—fails to meet the Fregean Condition. The two remaining accounts—commitment semantics and the expression account—satisfy all three conditions. A recent argument that the dominant commitment account is the only option available to expressivists is considered and rejected.     

Denoting and Disquoting

Fregeans hold that predicates denote things, albeit things different in kind from what singular terms denote. This leads to a familiar problem: it seems impossible to say what any given predicate denotes. One strategy for avoiding this problem reduces the Fregean position to form of nominalism. I develop an alternative strategy that lets the Fregean hold on to the view that predicate denote things by reconceiving the nature of singular denotation and of Fregean objects.     

The Three Quines

This paper concerns Quine's stance on the issue of meaning normativity. I argue that three distinct and not obviously compatible positions on meaning normativity can be extracted from his philosophy of language - eliminative ]naturalism (Quine I), deflationary pragmatism (Quine II), and (restricted) strong normativism (Quine III) - which result from Quine's failure to separate adequately four different questions that surround the issue: the reality, source, sense, and scope of the normative dimension. In addition to the incompatibility of the views taken together, I argue on the basis of considerations due to Wittgenstein, Dummett, and Davidson that each view taken separately has self-standing problems. The first two fail to appreciate the ineliminability of the strong normativity of logic and so face a dilemma: they either smuggle it in illicitly, or insofar as they do not, fail to give an account of anything like a language. The third position's mixture of a universalism about logical concepts with a thorough-going relativism about non-logical concepts can be challenged once a distinction is drawn between the universalist and contextualist readings of strong normativity, a distinction inspired by Wittgenstein's distinction between grammatical and empirical judgements.     

The probabilistic analysis of language acquisition: theoretical, computational, and experimental analysis

There is much debate over the degree to which language learning is governed by innate language-specific biases, or acquired through cognition-general principles. Here we examine the probabilistic language acquisition hypothesis on three levels: We outline a novel theoretical result showing that it is possible to learn the exact generative model underlying a wide class of languages, purely from observing samples of the language. We then describe a recently proposed practical framework, which quantifies natural language learnability, allowing specific learnability predictions to be made for the first time. In previous work, this framework was used to make learnability predictions for a wide variety of linguistic constructions, for which learnability has been much debated. Here, we present a new experiment which tests these learnability predictions. We find that our experimental results support the possibility that these linguistic constructions are acquired probabilistically from cognition-general principles.