According to what I call the Traditional View, there is a fundamental semantic distinction between counting and measuring, which is reflected in two fundamentally different sorts of scales: discrete cardinality scales and dense measurement scales. Opposed to the Traditional View is a thesis known as the Universal Density of Measurement: there is no fundamental semantic distinction between counting and measuring, and all natural language scales are dense. This paper considers a new argument for the latter, based on a puzzle I call the Fractional Cardinalities Puzzle: if answers to ‘how many’-questions always designate cardinalities, and if cardinalities are necessarily discrete, then how can e.g. ‘2.38’ be a correct answer to the question ‘How many ounces of water are in the beaker?’? If cardinality scales are dense, then the answer is obvious: ‘2.38’ designates a fractional cardinality, contra the Traditional View. However, I provide novel evidence showing that ‘many’ is not uniformly associated with the dimension of cardinality across contexts, and so ‘how many’-questions can ask about other kinds of measures, including e.g. volume. By combining independently motivated analyses of cardinal adjectives, measure phrases, complex fractions, and degrees, I develop a semantics intended to defend the Traditional View against purported counterexamples like this and others which have received a fair amount of recent philosophical attention.

中文翻译：

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计数、测量和小数基数谜题

根据我所说的传统观点，计数和测量之间存在根本的语义区别，这体现在两种根本不同的尺度上：离散基数尺度和密集测量尺度。与传统观点相反的是一个名为“测量的普遍密度”的论文：计数和测量之间没有根本的语义区别，所有自然语言尺度都是稠密的。本文考虑了后者的一个新论点，基于我称之为分数基数谜题的一个谜题：如果“多少”问题的答案总是指定基数，并且如果基数必须是离散的，那么“2.38”怎么可能是一个问题“烧杯中有多少盎司的水？”的正确答案？如果基数尺度很密集，那么答案很明显：'2。38' 表示小数基数，与传统观点相反。然而，我提供了新的证据，表明“许多”与跨上下文的基数维度并不一致，因此“多少”问题可以询问其他类型的度量，包括例如数量。通过结合对基本形容词、量词短语、复分数和度数的独立动机分析，我开发了一种语义，旨在保护传统观点免受像这样和其他最近受到相当多的哲学关注的所谓反例。因此“多少”问题可以询问其他类型的度量，包括例如数量。通过结合对基本形容词、量词短语、复分数和度数的独立动机分析，我开发了一种语义，旨在保护传统观点免受像这样和其他最近受到相当多的哲学关注的所谓反例。因此“多少”问题可以询问其他类型的度量，包括例如数量。通过结合对基本形容词、量词短语、复分数和度数的独立动机分析，我开发了一种语义，旨在保护传统观点免受像这样和其他最近受到相当多的哲学关注的所谓反例。