特殊篇章玄宇宙计划原文序列部分章 (13-9)

solution template for the CH”, according to which the truth value of CH

must be decided by some new axiom for set theory, and to consider the

question whether CH holds or not as already definitively settled, as the result

of our knowledge of the different truth values it may assume in the different

universes of the multiverse. In (23), instead, the set-generic multiverse is

introduced in order to scrutinize the set-generic multiverse conception of

truth. According to the latter, a sentence formulated in the language of set

theory is true if it holds absolutely in the multiverse generated by V.ie., ifit

holds in cach universe belonging to that multiverse. Were one to adopt the AB) set-generic multiverse conception of truth, one should declare that a sentence

like CH lacks truth value. This is not Woodin's conclusion, however. In fact

he argues that the set-generic multiverse conception of truth is untenable

because it violates principles that he regards as essential for any notion of

truth for the set-theoretic universe (sce [23]).

However note that, despite Woodin's and Hamkins' different mathemati-

cal understanding of the multiverse, and their diverging positions as to the

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