tag:blogger.com,1999:blog-4987609114415205593.post985058495452244495..comments2024-03-28T13:40:26.497+00:00Comments on M-Phi: The Law of Permutation and ParacompletenessJeffrey Ketlandhttp://www.blogger.com/profile/01753975411670884721noreply@blogger.comBlogger8125tag:blogger.com,1999:blog-4987609114415205593.post-7162062511098124902011-06-27T13:17:29.038+01:002011-06-27T13:17:29.038+01:00Following up on what Dave said, there is a demonst...Following up on what Dave said, there is a demonstration of how CS plus fusion results in triviality on p. 366-367 of Relevant Logics and their Rivals vol. 1.Shawnnoreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-62537504881947055402011-06-25T13:51:09.576+01:002011-06-25T13:51:09.576+01:00Ole,
Contraposition:
[(A->B)->(~B->~A)]
...Ole,<br /><br />Contraposition:<br />[(A->B)->(~B->~A)]<br />By not negating the new antecedent, how can the two rules co-exist?<br /><br />And yes, deductively stronger. A system paraconsistent and complete can prove more true propositions true, and all true propositions can be proven with reductio ad absurdum.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-44872739429984723822011-06-24T20:19:48.674+01:002011-06-24T20:19:48.674+01:00Just a side remark on LEx and reasons you may have...Just a side remark on LEx and reasons you may have to reject it; if you want to introduce a dynamic component in your system, such that the order in which the premises make their appearance matters, then this might count as a good reason to reject LEx. The trouble with the way Field goes around is that he rejects principles whenever they 'lead you to trouble' without independent motivation.<br /><br />This is a reply to your "As far as intuitions go, I suppose that (C) is a pretty natural looking fellow too. Indeed, I'm not sure what would constitute a tie breaker between (CS) and (C)." Well, it will all depend on what you think you are up to with your logic. I don't think there is an absolute sense in which either (CS) or (C) is more/less plausible, it's going to be relative to what you want your logic to capture. One of the things that I like about linear logic is that it's very clear why they reject contraction, for example; it's just a different ball game, namely keeping track of your resources.Catarinahttps://www.blogger.com/profile/03277956118114314573noreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-41204940430557956562011-06-24T09:02:33.191+01:002011-06-24T09:02:33.191+01:00Didn't know that, Dave! Yes, definitely nice i...Didn't know that, Dave! Yes, definitely nice if multiplicative conjunction can be consistently added.Anonymoushttps://www.blogger.com/profile/08574281945279890524noreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-63790773252210071572011-06-24T01:58:45.974+01:002011-06-24T01:58:45.974+01:00Also: CS plus transparent truth plus fusion (multi...Also: CS plus transparent truth plus fusion (multiplicative/intensional conjunction) will go kaboom. (Proof is in RLR1, which I don't have handy.) I certainly wouldn't mind having fusion around; this gives another reason to avoid CS.Dave Ripleyhttp://sites.google.com/site/davewripleynoreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-24816709844647283972011-06-23T17:11:09.706+01:002011-06-23T17:11:09.706+01:00Not sure I get the questions. What do you mean by ...Not sure I get the questions. What do you mean by C violating contraposition? If the question is whether giving up C leads to giving up contraction, the answer is no (for the systems I'm considering).<br /><br />About the second question: Do you mean deductively stronger?Anonymoushttps://www.blogger.com/profile/08574281945279890524noreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-33024332667241045062011-06-20T16:50:07.415+01:002011-06-20T16:50:07.415+01:00Would C violate the rule of contraposition? Also,...Would C violate the rule of contraposition? Also, if a system can be paraconsistent and complete, wouldn't this be stronger than any system that is consistent and paracomplete?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-5864667561276359252011-06-20T16:05:38.940+01:002011-06-20T16:05:38.940+01:00wouldn't contraction violate [(A->B)->(~...wouldn't contraction violate [(A->B)->(~B->A)]?Anonymousnoreply@blogger.com