This paper emphasizes the complex thinking demanded by dilemmas and paradoxes. To make her case, she provides detailed analyses of the Protagoras and Euathlus dilemma as well as the librarian’s paradox. In an imagined dialogue between a supporter of Protagoras and a cross-examiner, the author unravels the increasingly detailed specifications (dependent on subjective reasoning and supposedly “required” implications) needed to clarify support for Protagoras’ case in court. Ultimately, the dilemma is best solved by noting only the language of the contract and judging against there being grounds to sue. The author next illuminates the many facets of the veridical librarian’s paradox. The author argues that the paradox as stated is not solvable given the entailed problem of self-reference. This is a problem that also crops up in the Protagoras and Euathlus dilemma, although more closely related to the liar paradox, which, as James D. Carney suggests, points toward another way of handling the Protagoras and Euathlus dilemma: introduce a “levels of language” distinction.

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