Are undecidable statements, such as the provability of the continuum hypothesis, natural examples of statements that require a multivalent logic in order for them to be adequately described and/or even properly understood? (NB: by properly I am taking this to mean that undecidable matters such as the provability of the CH are currently not fully understood)(adsbygoogle = window.adsbygoogle || []).push({});

If so, is this many-valuedness only useful trivially as in a possible trivalent description of the situation in terms of yes/no/undecidable, or can a multivalent approach to this actually contribute something much more deep and subtle, such as the direction towards another foundation of mathematics instead of ZFC set theory due to some other desirable criteria?

For example, could the ##\aleph_1##-valency of fuzzy logic possibly help map out something akin to a parameter space of possible axiomatizations wherein the truth/falsity of the continuum hypothesis is a parameter ranging in any of the infinitely many values between true and false?

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# A Undecidability and multivalent logic

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