Formal semantic treatments of nominal reference have focused on natural kind nouns (Carlson 1980, Krifka et al. 1995), yet as has been widely recognized by anthropologists, cognitive scientists, philosophers, and others, artifacts (cup, furniture, chair) and natural kinds (dog, water, flower) differ critically in nature. We argue that these differences have important consequences for how artifa...

Cantor’s famous proof of the uncountability of real numbers is shown to apply to the set of natural numbers as well. Independently it is proved that the uncountability of the real numbers implies the uncountability of the rational numbers too. Finally it is shown that Cantor’s second diagonalization method is inapplicable at all because it lacks the diagonal. Hence, the conclusion that the card...

We prove a generalized version of Renault’s theorem for Cartan subalgebras. show that the original assumptions second countability and separability are not needed. This weakens assumption topological principality underlying groupoid to effectiveness.

In this article, we will be interested in the extent to which the assumption of first countability in this theorem can be weakened. Recall that a Hausdorff topological space X is Fréchet if whenever x is a limit point of A ⊆ X, there is a sequence an (n < ω) of elements of A which converges to x. This is a natural weakening of first countability which has been extensively studied in the literat...

1 Sets, Functions and Countability 2 1.1 Sets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Cartesian Products of Sets . . . . . . . . . . . . . . . . . . . . 5 1.3 Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.4 Equivalence Relations . . . . . . . . . . . . . . . . . . . . . . . 6 1.5 Functions . . . . . . . . . . . . . . . . . . . . . . . . ...

We examine the hypothesis that noun countability is consistent for a given word semantics by way of a series of experiments involving EuroWordNet and the English and Dutch languages. The basic method involves determining a default set of countabilities for each EuroWordNet synset based on countability-mapped words in that synset, and testing the match between these countabilities and those of h...

Abstract We examine three constructions across several languages in which a mass noun is embedded what appears to be count environment, but the construction as whole remains mass. argue that discussed phenomena—“Q-noun” like lots of water , bare measure kilos sugar and pluralised nouns Greek Persian—all involve portioning-out denotation. provide structural account portioning out propose structu...

Making use of Kayne’s (2005, 2010) theory light nouns, this article argues that nouns are part (simple) names and a mass/count distinction among explains the behavior certain types in German as mass rather than count. The elaborates role with new generalizations regarding their linguistic quantificational pronominal NPs, selection relative pronouns German, general difference support plural anap...

We agree with recent countability research that a satisfactory account of individuation in terms of what counts as ‘one’ unit for counting is highly relevant for characterizing a semantics of the mass/count distinction. However, we argue that an account that rests on individuation alone does not suffice to cover all the relevant mass/count data, in particular the puzzling mass/count variation d...