Infinite Liar in a (Modal) Finitistic Setting
Yablo’s paradox results in a set of formulas which (with local disquotation in the background) turns out consistent, but \(\omega \)-inconsistent. Adding either uniform disquotation or the \(\omega \)-rule results in inconsistency. One might think that it doesn’t arise in finitary contexts. We study whether it does. It turns out that the issue turns on how the finitistic approach is formalized.
KeywordsAxiomatic theories of truth Paradoxes Yablo’s paradox Finitism Potential infinity
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