Priest on Set-Theoretic Paradoxes
DOI:
https://doi.org/10.47850/RL.2024.5.3.5-12Keywords:
set theoretic paradoxes, metalanguage, metatheory, PriestAbstract
Two set-theoretic paradoxes in Priest’s interpretation are considered, viz. Burali-Forti’s paradox and Koenig’s one. It is argued that Koenig’s paradox, strictly speaking, is not a set-theoretic one because it is based on some metatheoretic ideas, and is formulated in metalanguage. Priest holds that Burali-Forti’s paradox is not fully eliminated even in axiomatic set theories and that it can be seen when set theories are interpreted. In the paper, I show that this claim is not sufficiently grounded. Moreover, it is shown that even if this claim is true, it is based on some metathreoretic ideas and formulated in metalanguage (as well as Koenig’s paradox).
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