Universal laziness of pronouns
Assertive graphs (AGs) modify Peirce’s Alpha part of Existential Graphs (EGs). They are used to reason about assertions without a need to resort to any ad hoc sign of assertion. The present paper presents an extension of propositional AGs to the Beta case by introducing two kinds of non-interdefinable lines. The absence of polarities in the theory of AGs necessitates Beta-AGs that resort to such two lines: standard lines that mean the presence of a certain method of asserting, and barbed lines that mean the presence of a general method of asserting. New rules of transformations for Beta-AGs are presented by which it is shown how to derive the theorems of quantificational intuitionistic logic. Generally, Beta-AGs offer a new non-classical system of quantification by which one can logically analyse complex assertions by a notation which (i) is free from a separate sign of assertion, (ii) does not involve explicit polarities, and (iii) specifies a type-referential notation for quantification. These properties stand in important contrast both to standard diagrammatic notations and to standard, occurrence-referential quantificational notations.
Quantifiers, Quantifiers, and Quantifiers: Themes in Logic, Metaphysics, and Language
In the article, I describe cases of special behavior of Russian phrases with quantifiers like neskol’ko ‘some’, mnogo ‘many, much’ and small numerals like dva ‘two’. I show that they can occur in the subject position in contexts that usually do not contain a canonical DP/NP subject (constructions with the verb xvatat’ ‘be enough’, negation contexts with the verb byt’ ‘be’ and its habitual / iterative correlate byvat’), and for neskol’ko-like quantifiers, the direct object position with intransitive predicates like na-…-sja circumfixed verbs is also available. The reason of noncanonical subject behavior is the possibility to be subjects without controlling plural verbal agreement, while the non-canonical direct object behavior is possible because neskol’ko-like quantifiers lack the category of case.
The work deals with the strategies for predicate agreement to quantified noun groups headed by nouns. In Russian, as in other Slavic languages, predicate agreement with quantified noun phrases allows singular or plural forms of the predicate. As for the sentences with quantifiers-nouns r’ad, polovina, chast’, mnozestvo, three agreement strategy are probable: predicate agrees with the head of noun phrase and takes singular masculine/feminine/neuter or agrees semantically, in plural, or takes default form – singular neuter. The last type of agreement is rare and non-standard. The most frequent is the first type, full grammatical agreement.
The study based on the National Russian Corpus showed that the strategies of predicate agreement with quantifiers-nouns are not identical. The predicate more probable agrees in plural with NP, headed by the word r’ad, than the words polovina, chast’, mnozestvo.
The reasons for the differences in strategies of predicate agreement and the factors of context that influence the choice of predicate, are analysed in the paper.
The investigation of the difference in the agreement strategy implies consideration of the semantic and grammatical properties of quantifiers.
It is shown that some quantifiers have indefinite and abstract meaning (r’ad, mnozestvo), their grammatical properties are limited (the ability to combine with a definition, to be used without dependent word). This behavior differs from usual noun behavior. The “not noun-like” properties should be the main reason for fluctuations in the choice of the form of the predicate, as Corbett has shown [Corbett 1979, Krasovitsky 2010]. The quantifiers of more specific and substantive meaning (polovina, chast’) that behave like nouns, seems to require the full grammatical agreement of predicate.
The dependence of the choice of the predicate form from grammatical gender is discussed in the paper.
The statistical analysis of the influence of the context factors is carried out. The factors of animacy, word order, conjunct subjects. conjunct predicate, the type of predicate, adjectives agreed with quantifier are considered. Some views on the influence of the factors of the context generally accepted in Russian linguistics are refined. The study has shown that a few factors can influence on the choice of the form of the predicate agreed with the words pololvina or chast’– predominantly conjunct noun phrases and animacy. The agreement with mnozestvo is influenced by more factors of context. All the factors are extremely important for the predicate agreement with r’ad