tag:blogger.com,1999:blog-3891434218564545511.post2139224751646102786..comments2024-03-28T13:23:50.623-05:00Comments on Alexander Pruss's Blog: A modal liarAlexander R Prusshttp://www.blogger.com/profile/05989277655934827117noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-3891434218564545511.post-85983971567786679812014-08-14T09:25:42.421-05:002014-08-14T09:25:42.421-05:00See also: John F. Post
Noûs, Vol. 4, No. 4 (Nov., ...See also: John F. Post<br />Noûs, Vol. 4, No. 4 (Nov., 1970), pp. 405-409Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-32887318304130878032014-04-15T12:03:52.801-05:002014-04-15T12:03:52.801-05:00Yes, well done.
Whether we should worry about the...Yes, well done. <br />Whether we should worry about the contingency of language depends, I think, on whether 'necessarily' expresses an operator on propositions (like '~') or a predicate defined on sentences. In the latter case, Nec('a = a') seems dubious; it suggests that 'a = a' expresses a necessary proposition in every world. But I think you're safe if 'necessarily' expresses the proposition-operator (which is the standard view).Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-31133043118957701512014-04-14T11:31:59.112-05:002014-04-14T11:31:59.112-05:00Very nice. I don't know what exactly I was th...Very nice. I don't know what exactly I was thinking in my post, but I think I had some worries about self-reference that I was trying to work through. <br /><br />I guess my version was basically:<br /><br />(**) This statement is impossible.<br /><br />Suppose (**) is true at an accessible w. Then (**) is impossible at w, and hence false at w (reflexivity). So, (**) is true at every accessible w. So, (**) is necessarily true. But then it is actually true. (Reflexivity.) So, it is actually impossible, and hence it is actually both true and impossible. Contradiction.<br /><br /><br />What I was thinking in my convoluted post may be starting to come back to me now. I may have been worried that the same sentence type might express a different proposition at different worlds. <br /><br />If that's so, then one cannot go from "(*) is false at w" to "(*) is necessary at at w" (and similar inferences fail for (**)). For (*) is false at some world w iff the proposition that (*) expresses at w is false at w. But maybe the proposition that (*) expresses at w is not the proposition that (*) is not necessary?<br /><br />So I felt it necessary to rigidly fix a particular dialect to ensure that meanings can't shift between worlds. Maybe that was an unnecessary worry.Alexander R Prusshttps://www.blogger.com/profile/05989277655934827117noreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-12545373172417806382014-04-12T13:03:07.285-05:002014-04-12T13:03:07.285-05:00I was searching for "modal liar" and cam...I was searching for "modal liar" and came upon this page. I'm wondering if anyone has proposed the following as a "modal liar":<br /><br />(*) This statement is not necessary.<br /><br />It seems we can show (*) is true at @ iff (*) is false at @, assuming that accessibility is reflexive.<br /><br />Suppose first that (*) is false at @. Then, (*) is necessary--hence, at every world W accessible from here, (*) is true at W. So, if our world accesses itself, (*) is true at @. Contradiction.<br /><br />So suppose (*) is true at @. (The reductio in this case takes a tad more work.) If so, then (*) is not necessary. Hence, there is an accessible world W such that (*) is false at W. However, if (*) is false at W, then it is true at W that (*) is necessary. Hence, at every world accessible from W, (*) is true. Assuming reflexivity of access, it thus follows (*) is true at W. But ex hypothesi, W is a world where (*) is false. Contradiction.<br /><br />Do you have thoughts on this? If you prefer, please feel free to email me at parentt@vt.edu. Thanks! TedAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-3891434218564545511.post-61426724245234745042009-08-01T13:33:09.469-05:002009-08-01T13:33:09.469-05:00...therefore naturalism is false!...therefore naturalism is false!MChttps://www.blogger.com/profile/09445387965157596566noreply@blogger.com