Abstract. \;Gö\;del&rsquo\;s disjunction asserts that either &ldquo\;the mind cannot be mechanized&rdquo\; or &ldquo\;there are absolutely undecidable statements.&rdquo\; Arguments are examined for and against each disjunct in the context of precise frameworks governing the notions of absolute provability and truth. The focus is on Penrose&rsquo\;s new argument\, which interestingly involves type-free truth. In order to reconstruct Penrose&rsquo\;s argument\, a system\, DKT\, is devised for absolute provability and type-free truth. It turns out that in this setting there are actually two versions of the disjunction and its disjuncts. The first\, fully general versions end up being (provably) indeterminate. The second\, restricted versions end up being (provably) determinate\, and so\, in this case there is at least an initial prospect of success. However\, in this case it will be seen that although the disjunction itself is provable\, neither disjunct is provable nor refutable in the framework.
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\nWe will be having dinner right after the meeting at the faculty house. Please let Robby (jrf2162@columbia.edu) know if you will be joining us so that he can make an appropriate reservation (please be advised that at this point the university only agrees to cover the expenses of the speaker and the rapporteur and that the cost for all others is $25\, payable by cash or check). \; \;
ORGANIZER;CN=Robby Finley;CN=Haim Gaifman;CN=Yang Liu;CN=Rohit Parikh: METHOD:PUBLISH END:VEVENT END:VCALENDAR