tag:blogger.com,1999:blog-4987609114415205593.post7521633943779547472..comments2021-06-19T18:51:04.369+01:00Comments on M-Phi: A dialogical analysis of structural rules - Part IJeffrey Ketlandhttp://www.blogger.com/profile/01753975411670884721noreply@blogger.comBlogger8125tag:blogger.com,1999:blog-4987609114415205593.post-53487850786693815082013-11-02T21:59:25.749+00:002013-11-02T21:59:25.749+00:00I enjoyed the possibility in this explanation of d...I enjoyed the possibility in this explanation of dialogous logic that proof-theoretic logic might have some relation to principles of exclusivity.<br /><br />For example, there is a suggestion, particularly in your statement about left-weakening, that A => C would mean an 'A exclusive for C', and likewise that 'A, B => C' would mean an A and a B exclusive for C.<br /><br />Some people may consider those to be ideal sets, which only make sense when qualia terms are used, or with simple arithmetic that is too restrictive (e.g. perhaps Pascal numbers). There is a suggestion that if exclusion were the operant principle, that then A, B => C would not follow in some cases, because the additional premise B could be the opposite of C, and thus 'A => C' would not follow. Perhaps this is a diversion, but modal realists might think that opposite are reconcilable, whereas in many actual theories and practices, opposites imply negation. Perhaps a rule to build in would be acceptance or rejection of duplicity, with even metaphysical consequences.<br /><br />The general point I am trying to get at is that sometimes a theory seems to supervene a mode or calculation (for example the concept of value, or the concept of exception). I am very interested to see what those more mathematical than myself have to say about this, or if math in general is just an ox running away with an orange cart. This could be a very large subject to address in the future, if anyone is interested. And I am interested to hear immediate responses as well, if anyone is intrigued by this concept of exclusivity.<br /><br />By the way, as a sidenote to students or those who are intrigued, I have some papers which may or may not be considered useful in relation to exclusivity or categories as a discipline, at southernct.academia.edu/NathanCoppedgeNathan Coppedgehttps://www.blogger.com/profile/13272730626911068222noreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-52936734679173949452013-11-02T21:57:10.654+00:002013-11-02T21:57:10.654+00:00This comment has been removed by the author.Nathan Coppedgehttps://www.blogger.com/profile/13272730626911068222noreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-90356528163966444582013-11-01T15:24:14.613+00:002013-11-01T15:24:14.613+00:00hi, thanks. Catarina. I think the point of LL gett...hi, thanks. Catarina. I think the point of LL getting rid of both weakening and contraction is important, because many of the mathematical arguments for naturalness and usefulness of logical systems rely on aesthetic criteria like symmetry. and relevance logic has had a very hard time trying to get itself pretty enough to be taken seriously... the picture I have in mind is that relevance logic and direct logic each remove one structural rule on the left, LL removes both and this helps to make its cut-elimination work, it makes it more symmetric, from a proof-theory point of view.<br />I'm looking forward to the next blog post on contraction, exchange and cut!Valeriahttps://www.blogger.com/profile/01336528462208811726noreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-67105554285944581182013-10-30T20:11:20.937+00:002013-10-30T20:11:20.937+00:00thanks, and thanks!thanks, and thanks!Greghttp://obscureandconfused.blogspot.comnoreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-58361806134461523742013-10-30T19:55:19.756+00:002013-10-30T19:55:19.756+00:00Hi Greg, thanks. Regarding your first point, in th...Hi Greg, thanks. Regarding your first point, in the questions and answers Aristotelian format that provides my main inspiration, proponent does not have to defend premises once they are granted by opponent; in fact, once opponent grants them *opponent* is commited to them but *not* proponent (which is the core of my dialectical explanation of reductio proofs, which I also blogged about some time ago).<br />Regarding your second point: well, first of all Hintikka and I are inspired by the same source, namely Aristotle and ancient dialectic! :) But there are many differences between his framework and mine, for example in that I am not in the business of explaining the meaning of specific logical terminology in game-theoretical terms. But perhaps the main difference (which also applies to other dialogical approaches, such as Lorenzen's) is that in the full version of the story my opponent is a built-in opponent (http://m-phi.blogspot.nl/2012/06/deductive-proofs-transferability-and.html ), a silent participant, whereas these other approaches have two active participants.Catarinahttps://www.blogger.com/profile/03277956118114314573noreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-29953802455362352982013-10-30T19:48:35.252+00:002013-10-30T19:48:35.252+00:00Hi Valeria, thanks! Yes, I had made a mess with my...Hi Valeria, thanks! Yes, I had made a mess with my variables, which seems to be fixed now :)<br />And yes, of course you are right that linear logic restricts weakening as well, for reasons very similar to those why it restricts contraction. I suppose I didn't mention this mostly so as to get a nice symmetry between contraction and linear logic on one side, and weakening and relevant logics on the other side. But you are right, from a Gricean point of view I should have mentioned both for LL :)Catarinahttps://www.blogger.com/profile/03277956118114314573noreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-8876803530834558172013-10-30T19:11:32.456+00:002013-10-30T19:11:32.456+00:00Thanks for a thought-provoking post. Two comments...Thanks for a thought-provoking post. Two comments:<br /><br />1. "So in a purely adversarial setting, weakening is in fact strategically advantageous for proponent, as it may have a confusing effect for opponent." <br />I wonder whether it might also be a strategic DISadvantage for Proponent as well (depending on the rules of the adversarial conflict): it opens up Proponent to criticisms she might not otherwise be vulnerable to. That is, if Proponent is responsible for defending all the premises she puts forward, then Opponent has many more targets to attack, if Proponent adds a bunch of unnecessary premises to the argument.<br /><br />2. You must've gotten this question a zillion times before, so feel free to just give a link to an answer you've given elsewhere. What is the relation of your view to so-called game-theoretic semantics?Greghttp://obscureandconfused.blogspot.comnoreply@blogger.comtag:blogger.com,1999:blog-4987609114415205593.post-51161401231345882332013-10-30T17:35:25.839+00:002013-10-30T17:35:25.839+00:00hi Catarina,
two trivial comments. instead of &quo...hi Catarina,<br />two trivial comments. instead of "and linear logicians pose restrictions on contraction" you should say linear logicians pose restrictions on contraction and weakening. Indeed you remove both rules in Linear Logic and moreover, it is thought that it's the removal of both, at the same time, that makes the logic well-behaved, proof-theoretically. Also I think you muddled your variables when discussing the weakening rule in the post. But I like a lot the idea of the dialogical conception of deductive proofs, it seems to make sense in many different levels.Valeriahttps://www.blogger.com/profile/01336528462208811726noreply@blogger.com