tag:blogger.com,1999:blog-11295132.post2325584291136500714..comments2019-02-21T03:59:37.273-08:00Comments on A Neighborhood of Infinity: What stops us defining Truth?Dan Piponihttps://plus.google.com/107913314994758123748noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-11295132.post-36475388992107081442013-10-29T18:51:39.430-07:002013-10-29T18:51:39.430-07:00FZ I guess that comment was intended for the next ...FZ I guess that comment was intended for the next post.Dan Piponihttps://www.blogger.com/profile/08096190433222340957noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-50720145795211713982013-10-29T18:39:18.593-07:002013-10-29T18:39:18.593-07:00Whatever the input, both Alice and Box have a 0.5 ...<i>Whatever the input, both Alice and <b>Box</b> have a 0.5 chance</i> ...<br /><br />Presumably you meant "Bob"? :)FZnoreply@blogger.comtag:blogger.com,1999:blog-11295132.post-81262484162017537692013-10-21T15:05:13.296-07:002013-10-21T15:05:13.296-07:00Andrej, yes, "there is no way to put them tog...Andrej, yes, "there is no way to put them together into a single one" is usually the problem stopping us, ok, that was the premise already, no?<br /><br />I'd say that its an unrecognized problem of domains, ontology and unstable/foldable coordinate systems that stops our descent here. Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-11295132.post-11301102400687828712013-10-13T00:15:11.501-07:002013-10-13T00:15:11.501-07:00To see how recursion works here, or rather it does...To see how recursion works here, or rather it does not, it is interesting to consider a truth predicate for a limited collection of formulas. For instance, suppose we want to define the truth predicate for all formulas in which there are at most <i>n</i> occurrences of the quantifiers, for some fixed <i>n</i>. Then this can be done (because no recursion is needed). So we can in fact have a collection of truth predicates which cover all formulas, but there is no way to put them together into a single one.Andrej Bauerhttp://andrej.com/noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-69777636346401281222013-10-12T11:11:35.877-07:002013-10-12T11:11:35.877-07:00This is a very good explanation, I've never be...This is a very good explanation, I've never been able to even coherently ask the question of how truth is defined in math. I stopped at the incompleteness theorem when I learned that Provable=>True, but not necessarily the converse.Anonymousnoreply@blogger.com