厘清分数概念的模糊性，提出三种新术语明确其不同含义。
On Ambiguity: The case of fraction, its meanings and roles
- 用fracterm、fracvalue、fracsign区分分数的结构、数值与符号意义。
- 证明分数是多个概念的集合而非单一数学概念，可避免歧义。
- 适合数学教育研究者与形式化数学语言设计者阅读。
本文探讨数学话语中的模糊性问题，提出一种通用的消解模糊方法，并分析如何维持语义一致性。以初等算术中定义不清的‘分数’为例，引入新术语澄清其多重含义：用‘fracterm’指代结构层面，‘fracvalue’表示纯数值层面，‘fracsign’和‘fracsign occurrence’分别描述文本层面的符号及其出现。这些精确概念能有效解决术语混淆，并在算术话语片段中验证其有效性。论文主张‘分数’并非单一数学概念，而是一个涵盖多种概念的‘类别’。该分析进一步关联到‘数’的概念，提出一种指定数系的方法，并将其与结构主义观点进行比较。
原文摘要 · Abstract (English)
We contemplate the notion of ambiguity in mathematical discourse. We consider a general method of resolving ambiguity and semantic options for sustaining a resolution. The general discussion is applied to the case of `fraction' which is ill-defined and ambiguous in the literature of elementary arithmetic. In order to clarify the use of `fraction' we introduce several new terms to designate some of its possible meanings. For example, to distinguish structural aspects we use `fracterm', to distinguish purely numerical aspects `fracvalue' and, to distinguish purely textual aspects `fracsign' and `fracsign occurence'. These interpretations can resolve ambiguity, and we discuss the resolution by using such precise notions in fragments of arithmetical discourse. We propose that fraction does not qualify as a mathematical concept but that the term functions as a collective for several concepts, which we simply call a `category'. This analysis of fraction leads us to consider the notion of number in relation to fracvalue. We introduce a way of specifying number systems, and compare the analytical concepts with those of structuralism.
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