tag:blogger.com,1999:blog-6432111.post5967174416930595527..comments2018-07-09T11:10:20.727+01:00Comments on Theories 'n Things: Non-classical logics: the no interpretation accountRobbie Williamshttp://www.blogger.com/profile/02081389310232077607noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-6432111.post-61695003568507221392009-11-16T10:27:01.101+00:002009-11-16T10:27:01.101+00:00Nice post as for me. I'd like to read more abo...Nice post as for me. I'd like to read more about that matter.<br />By the way look at the design I've made myself <a href="http://www.admirableescorts.com/" rel="nofollow">Companionship in London</a>Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6432111.post-24221726798818521972008-03-17T09:37:00.000+00:002008-03-17T09:37:00.000+00:00Hi Aaron,I think you're absolutely right, I was ov...Hi Aaron,<BR/><BR/>I think you're absolutely right, I was overstating the case. I think what I should have said is that what's essential to the nonclassicist treatment is that no *classical* model is intended (even then, I think that may be too strong---I've been trying to figure out what the argument would look like over the weekend, and its not absolutely obvious). <BR/><BR/>Anyway, the point you make is that if the interpretation is nonclassical (perhaps by having a nonclassical set theory) then it's not clear why we can't have an intended interpretation. <BR/><BR/>That seems right, and seems to be Priest's view (actually, I think Field mentions it too at some points, and the idea that nonclassical models are approximating to the real, nonclassical, intended interpretation is one way of understanding some of Field's talk of wanting models that are more than a merely algebraic device). And it does seem much more natural if you think that mathematics is in the limit nonclassical anyway. I need to think about this stuff some more, and particularly whether anything he says can be dualized for the use of the paracompletist. <BR/><BR/>Hi Ole,<BR/><BR/>Hey that sounds fun! We're about to set up a reading group here on the Field book. <BR/><BR/>I think you'd need to ask someone with a prior appeciation of the subtleties of the literature about whether Field has shifted his position. I was taking it to be an elaboration of the views in the paper in JC's Liars and Heaps volume...<BR/><BR/>It'd actually be really useful for someone who knows all this stuff to blog something on what the various Field papers do and how they fit together. <BR/><BR/>See you soon!Robbiehttps://www.blogger.com/profile/02081389310232077607noreply@blogger.comtag:blogger.com,1999:blog-6432111.post-35440197511309288222008-03-17T03:16:00.000+00:002008-03-17T03:16:00.000+00:00I'm curious about your claim that the "no interpre...I'm curious about your claim that the "no interpretation" account is absolutely essential to the many-valued approach to semantic paradox. <BR/><BR/>It seems to me that Priest takes the model theory much more seriously; it's not merely a heuristic device for defining an extensionally correct consequence relation. (Actually, I think of Field and Beall's approach as more of a heuristic device for defining a T-predicate with certain target features.) <BR/><BR/>Both Beall and Field think mathematics is entirely classical, including set theory. Priest, however, doesn't. He makes much of the demand that paraconsistentist should be able to provide models in a paraconsistent meta-theory. (And he's done quite a bit of work to get it done.)<BR/><BR/>In any case, I'm with you: much of the Beall and Field's response to 'revenge' worries comes from the "no interpretation" view. But I'm not at all sure it's essential to a many-valued approach.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-6432111.post-54269407154882061932008-03-15T10:10:00.000+00:002008-03-15T10:10:00.000+00:00This would be an excellent contribution to ArchÃ©'s...This would be an excellent contribution to ArchÃ©'s philosophy of logic seminar this semester: on "Truth after Kripke", more precisely, Maudlin and Field.<BR/><BR/>Originally, the idea was to read a series of Field's articles after the Maudlin book (and perhaps the relevant chapter from JCs manuscript), but now that the book is out that is perhaps the better option. Have you had time to check if he has shifted his position from the articles (2003, 2006 especially) to the book?<BR/><BR/>Looking forward to seeing you in St Andrews.Ole Thomassen Hjortlandhttps://www.blogger.com/profile/08574281945279890524noreply@blogger.comtag:blogger.com,1999:blog-6432111.post-18392948466331761612008-03-15T10:05:00.000+00:002008-03-15T10:05:00.000+00:00Hey Shawn,Yes, I should think about how I express ...Hey Shawn,<BR/><BR/>Yes, I should think about how I express this. The background setting I was thinking of is a "general" semantics where every expression in the language gets an extension (and extensional connectives like "and" get assigned a certain function from truth-values to truth values). I see that "truth function" might then be ambiguous between the expression and the extension---I was using "truth function" for the latter. <BR/><BR/>The alternative course, as you say, is to only assign extensions to non-logical expressions, and then lay down an axiom for each connective saying how truth of compounds depends on the truth of their parts. In the setting I mention, you can get away with a single axiom. <BR/><BR/>Of course, if you allow reinterpretation of the logical particles in the models over which you generalize, then you're not going to get a sensible characterization of logical consequence. So in this setting, you have to declare some of the models logically inadmissible---and say that B follows from A if the argument is truth-preserving at all logically admissible models. <BR/><BR/>So that's the background to what I was saying. According to folklore classicism, "and" etc do get extensions on the intended interpretation---but it's just they get the same extension on this and every other admissible interpretation. <BR/><BR/>I hope nothing hangs on this framework assumption of mine---but I should definitely think about how to formulate the issues when we handle the connectives through axioms rather than through assignment of extensions. Thanks for pointing it out...<BR/><BR/>I think the Field book is really excellent. I'm no expert in the truth literature, but it surveyed and compared and contrasted loads of really important and interesting material on the semantic paradoxes. One quarter of the book is Field putting forward his own positive paracomplete view. There's only a couple of short chapters on vagueness in it---though they're pretty interesting. The papers I have in mind were "indeterminacy, degree of belief and excluded middle" from his collection Truth and the absence of fact and something called I think "the semantic paradoxes and the paradoxes of vagueness" from JC Beall's collection "Liars and Heaps". They aren't really survey pieces, but the latter in particular articulates the main things he wants to push for.Robbiehttps://www.blogger.com/profile/02081389310232077607noreply@blogger.comtag:blogger.com,1999:blog-6432111.post-68270459693777504122008-03-15T06:05:00.000+00:002008-03-15T06:05:00.000+00:00Could you explain what you mean by talking about t...Could you explain what you mean by talking about the intended interpretation of a truth function in terms of models? Usually the truth functions, which I had thought you were treating as logical vocabulary, aren't reinterpreted between models. They are fixed by the recursion clauses. The "intended interpretation" talk is something that I had thought only applied to relations, functions and constants which receive possibly different extensions in different models, so the intended interpretation is the class of models giving the intuitive extension to some non-logical symbols. <BR/><BR/>Are Field's book and articles good entry points into vagueness and the liar?Shawnhttps://www.blogger.com/profile/15244930958211791213noreply@blogger.com