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  1. Dangerous Reference Graphs and Semantic Paradoxes.Landon Rabern, Brian Rabern & Matthew Macauley - 2013 - Journal of Philosophical Logic 42 (5):727-765.
    The semantic paradoxes are often associated with self-reference or referential circularity. Yablo (Analysis 53(4):251–252, 1993), however, has shown that there are infinitary versions of the paradoxes that do not involve this form of circularity. It remains an open question what relations of reference between collections of sentences afford the structure necessary for paradoxicality. In this essay, we lay the groundwork for a general investigation into the nature of reference structures that support the semantic paradoxes and the semantic hypodoxes. We develop (...)
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  2. A Simple Solution to the Hardest Logic Puzzle Ever.Brian Rabern & Landon Rabern - 2008 - Analysis 68 (2):105-112.
    We present the simplest solution ever to 'the hardest logic puzzle ever'. We then modify the puzzle to make it even harder and give a simple solution to the modified puzzle. The final sections investigate exploding god-heads and a two-question solution to the original puzzle.
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    Structural Fixed-Point Theorems.Brian Rabern & Landon Rabern - manuscript
    The semantic paradoxes are associated with self-reference or referential circularity. However, there are infinitary versions of the paradoxes, such as Yablo's paradox, that do not involve this form of circularity. It remains an open question what relations of reference between collections of sentences afford the structure necessary for paradoxicality -- these are the so-called "dangerous" directed graphs. Building on Rabern, et. al (2013) we reformulate this problem in terms of fixed points of certain functions, thereby boiling it down to get (...)
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