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I'm searching for "paradoxes" in classical modal logics, meaning lines of reasoning which give a counterintuitive conclusion if performed in classical logic, which can be modelled by the (semantical) possible worlds characterization of classical modal logic via Kripke-structures. Especially, a paradox of epistemic nature which relies on vagueness of accessibility of worlds is interesting for me.

While searching for epistemic and classical logic "paradoxes" on e.g. here or here and various other resources, no such example came up. Is there a common type of argument in the literature which I am not finding.

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  • It is not quite what you are looking for, but you might nevertheless be interested in the book "Vagueness, truth and paradox" by McGee – Jishin Noben Jun 7 at 15:54
  • From the way you've phrased things, it sounds more like you're interested in epistemological problems about possible worlds rather than strictly logical paradoxes in modal logic. You might read through plato.stanford.edu/entries/modality-epistemology and see if anything sticks out, especially plato.stanford.edu/entries/modality-epistemology/#CauIsoPro – transitionsynthesis Jun 7 at 16:21
  • How would lines of reasoning in modal logics be "performed" in classical logic at all? It lacks the modal operators. Since you already looked at epistemic paradoxes, and they are not it, what is "a paradox of epistemic nature" exactly? There is too little information on what "such" in "no such example" refers to. Salmon's solution to Chisholm's paradox massages the accessibility relation, the Four Worlds paradox has to do with vagueness, but I am unsure what you are asking. – Conifold Jun 7 at 19:28

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