Journal of Humanistic Mathematics 10 (1):383-401 (2020)

Social debates, as well as discussions about certain highly charged issues, such as racism, gender identity, and sexuality, usually turn on the uses or mentions of key words. That is, the conclusions we can draw from such discussions depend on how certain terms are used or mentioned in them. Yet participants in social debates may often fail to precisely define their terms or fail to make important distinctions in terms uttered by others. Both logic and mathematics pay attention to the importance of precise definitions when it comes to engaging in discussions, arguments, or proofs. Logic also makes an important distinction between the use of words and the mention of them. This article reviews ideas from mathematics and logic about definitions, use, and mention of words by applying them to central concepts which have arisen in various social debates.
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