tag:blogger.com,1999:blog-3891434218564545511.post4670340810985988665..comments2024-03-28T19:56:42.305-05:00Comments on Alexander Pruss's Blog: The twistAlexander R Prusshttp://www.blogger.com/profile/05989277655934827117noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-3891434218564545511.post-36337818643667376622008-02-10T14:24:00.000-06:002008-02-10T14:24:00.000-06:00Heath:I don't think so. Consider:(1) This is the ...Heath:<BR/><BR/>I don't think so. Consider:<BR/><BR/>(1) This is the first displayed sentence in the comment.<BR/><BR/>What is the negation of (1)? By your suggestion, it should be:<BR/><BR/>(2) This is not the first displayed sentence in the comment.<BR/><BR/>But (2) is not the negation of (1). In fact, both (1) and (2) are true.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-33420092367379657042008-02-08T14:48:00.000-06:002008-02-08T14:48:00.000-06:00Yes:(1) This sentence is true.Then not-(1), i.e.It...Yes:<BR/><BR/>(1) This sentence is true.<BR/><BR/>Then not-(1), i.e.<BR/><BR/>It is not the case that this sentence is true<BR/><BR/>is just<BR/><BR/>(2) It is the case that this sentence is false.<BR/><BR/>That inference assumes bivalence, but anyone who thought (1) had a meaning or truth value would be committed to that.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-18365335172022281162008-02-07T08:54:00.000-06:002008-02-07T08:54:00.000-06:00Heath,Are you assuming that (2) is the negation of...Heath,<BR/><BR/>Are you assuming that (2) is the negation of (1)? I am a bit confused.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-68543885129360289232008-02-07T08:19:00.000-06:002008-02-07T08:19:00.000-06:00I don't know if there's any general formula for do...I don't know if there's any general formula for doing this in all "twisted" cases, but you can say something about (1) and (2). Suppose you think (1) might have a meaning or truth value after all. Then consider:<BR/><BR/>(1) iff not not (1), so<BR/>(1) iff not (2).<BR/><BR/>But now suppose (1) is true. Then (2) is false, so (2) is true, so (1) is false. Mutatis mutandis for supposing (1) is false. Therefore, (1) is just as paradoxical as (2).Anonymousnoreply@blogger.com