In this paper we argue, against a somewhat standard view, that pragmatic phenomena occur in mathematical language. We provide concrete examples supporting this thesis.
The study explores the acquisition of properties of the English existential quantifier any by German-speaking learners of English. The English existential quantifier is of particular theoretical ...interest, since its subtle grammatical constraints are often unobservable and thus may induce learnability difficulties, especially if parallel constructions in the L1 are scarce or entirely absent. In addition, the properties are underspecified in pedagogical materials, which renders them an apt test case for the exploration of input and taught knowledge in relation to acquisitional processes. The research question asks whether observable and/or learned grammar knowledge can shape acquired knowledge as measured by means of acceptability judgement tasks. To test this, 72 German-speaking C1 learners of English provided paced acceptability judgement ratings of sentences with any, which systematically differed according to grammatical and acquisitional constraints, partly replicating an experimental design by Marsden et al. (2018). Our results suggest sensitivity of German learners of English towards the grammatical constraints of any. This sensitivity seems to partly rest on explicit pedagogical input, with minimal L1 influence, but with some marked deviations from previous findings. Keywords: any, existential quantifier, negative polarity, L2 learning, L1 transfer
In “Kant on Existence, Predication, and the Ontological Argument” (
1981
), Hintikka argues that the so-called “Kant–Frege view” (i.e., the claim that Kant is a forerunner of Frege’s treatment of ...existence) is wrong, for its supporters erroneously assume that for Kant ‘is’ is ambiguous. In this paper, I will first critically evaluate Hintikka’s arguments against the Kant–Frege view. Then, I will attempt to prove that Kant’s claim that
existence
is not a real predicate and Frege’s claim that
existence
is a quantifier are in fact logically interdependent. Finally, I will use the Kant–Frege view in order to reconcile the various claims that Kant makes about existence.
•Cantonese pre-predicate jau5 ‘have’ and perfective marker –zo2 are not equivalents.•Borne out in its lexical semantics, jau5 is an assertive existential quantifier.•Jau5 gives two assertive ...meanings, depending on the specificity of the situation.•Endpoints of situation are differentiated between actualized and potential ones.•Stage-level stative is more like events than states in its endpoint properties.
The verb jau5 ‘have’ in Cantonese can be placed immediately before the verbal or adjectival predicate, forming “jau5+predicate” construction (henceforth pre-predicate jau5), and pervious analyses consider the pre-predicate jau5 as the preposed perfective marker –zo2. The same construction “you ‘have’+VP” renders ungrammaticality in Mandarin, with the post-verbal perfective –le being its only form. In this paper, contra previous analyses, I argue that pre-predicate jau5 and post-verbal perfective –zo2 cannot be equivalents. Following S.F. Huang's (1981) ideas on determiner quantifiers, I propose that Cantonese pre-predicate jau5 ‘have’ is an assertive existential quantifier operating in the domain of verbs and their event time, which gives rise to two assertive meanings: (i) When the situation is interpreted as non-specific, pre-predicate jau5 asserts at least one occurrence of the event; and (ii) when the situation is interpreted as specific, jau5 asserts the actualization of the natural final endpoint or the explicit bound of the situation. The existential nature of jau5 ‘have’ is inherently borne out in the lexical semantics of “have”, and the proposed analysis reveals that when assertive existential quantification performs in situations, assertions are sensitive to (i) the lexical aspect of the verbal predicates and (ii) the specificity of the situation. It leads to the theoretical implications that: (i) endpoints/boundaries of situations should be linguistically differentiated between actualized and potential ones, following Dahl's (1981) proposal; and (ii) stage-level stative patterns are more like events than states in its endpoint properties.
Some monkey devours every raisin Jacquette, Dale
Journal of applied non-classical logics,
2011, Volume:
21, Issue:
2
Journal Article
Peer reviewed
An elementary exercise in symbolizing an existential to universal relation reveals expressive limitations in standard first-order predicate-quantificational logic. Alternative translations of a ...sample some-every sentence are considered and rejected after criticism, leaving as the best choice a particular structure that demonstrably does not serve for all predicates available to the ordinary language to which the sample sentence belongs. We explain the difficulties encountered in trying to arrive at an adequate translation of the sentence in classical logic, as background to examining five alternative nonclassical logics to resolve the problem. We settle finally if only provisionally in the process on a version of intensional logic that permits reference and true predication of constitutive properties to nonexistent as well as existent objects.
Following Lauwers and Van Liedekerke (1995), this paper explores in a model-theoretic framework the relation between Arrovian aggregation rules and ultraproducts, in order to investigate a source of ...impossibility results for the case of an infinite number of individuals and an aggregation rule based on a free ultrafilter of decisive coalitions.
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