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In a series of recent articles, Robin Jeshion has developed a theory of singular thought which she calls ‘cognitivism’. According to Jeshion, cognitivism offers a middle path between acquaintance theories—which she takes to impose too strong a requirement on singular thought, and semantic instrumentalism—which she takes to impose too weak a requirement. In this article, I raise a series of concerns about Jeshion's theory, and suggest that the relevant data can be accommodated by a version of acquaintance theory that distinguishes unsuccessful thoughts of singular form from successful singular thoughts, and in addition allows for ‘trace-based’ acquaintance.