tag:blogger.com,1999:blog-6766669393161688139.post5302459974329248726..comments2023-11-05T00:23:27.124-07:00Comments on POSSIBLE WORLDS: Grim & Plantinga on Cantorian argumentsChris Tillmanhttp://www.blogger.com/profile/07039880090804518326noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-6766669393161688139.post-69898445994878215872008-03-31T09:39:00.000-07:002008-03-31T09:39:00.000-07:00Grim's second argument bans the concept of truth i...Grim's second argument bans the concept of truth itself, for the rejected property T could just be 'being true'.<BR/><BR/>Is there a bijection from all truths to all truths? If yes, you can repeat Grim's second argument<BR/><BR/>From a set theoretic point of view a bijection, like any binary relation, is a set of ordered pairs. The obvious non existence of the set of all truths suggests there is no corresponding set of ordered pairs.<BR/><BR/>Inconsistent multiplicities are best dealt with by means of the concept of indefinite extensibility. I recommend the paper 'All Things Indefinitely Extensible' by Shapiro and Wright, in 'Absolute Generality', Rayo and Uzquiano eds. OUP, 2006.<BR/><BR/>In that book is also discussed the impossibility of unrestricted universal quantification. The thesis that we cannot speak of absolutely everything seems impossible to state, similarly to the thesis 'there is no proposition about all propositions not about themselves'.<BR/><BR/>I see a way out in the 'intensional' version of those claims:<BR/><BR/>1. The concept of universe of discourse implies the feature of being indefinitely extensible.<BR/><BR/>2. The concept of proposition about propositions not about themselves implies the feature of referring to an indefinitely extensible universe of discourse.<BR/><BR/>RegardsNueva Argentinahttps://www.blogger.com/profile/12219856503592516619noreply@blogger.com