tag:blogger.com,1999:blog-2631035637795172582.post3698347906627788916..comments2023-01-24T10:06:57.212-08:00Comments on (Blog&~Blog): Barwise and Etchemendy, Pt 2 (Austinian Case)Benhttp://www.blogger.com/profile/06702722560438833244noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-2631035637795172582.post-66141376396071533352008-02-26T07:55:00.000-08:002008-02-26T07:55:00.000-08:00When Sollie says "There are bats in the lavatory!"...When Sollie says "There are bats in the lavatory!", he makes an existence claim (which, arguably, the truth function hinges upon). So he says something like "it is true that there are bats in the lavatory" (which is to say, if serious, he suggests that his proposition points to some real state of affairs). <BR/><BR/><BR/>The liar sentence as stated does not really point to any real state of affairs: it's something like "it is true that this sentence is false". So regardless of Prior's solution (which seems fairly sound), what event/state of affairs does the sentence refer to? You can flip these pseudo-statements around (like the cards example), but if one grants that a assertive sentence makes an implicit existence claim about, like, objects in the world (for lack of a better term) the paradox sort of vanishes. <BR/><BR/>Russell's paradox should not be considered as part of the Liar; tho' some seem to suggest that. RP concerns sets (and the set of sets that are not members of themselves): my own view is that RP followed from Cantor's view of infinity (if not platonic accounts of mathematical objects) which are untenable.<BR/><BR/> The Paradox still can arise (say with lists, or data bases, perhaps), yet there are ways around it (including even Russell's solution via theory of types), mostly by limiting self-referentiality in ways. It's not as crucial as some in the philosophy biz make it out to be, at least for nominalists and those who question the platonic account of mathematical objects.Jhttps://www.blogger.com/profile/11567400697675996283noreply@blogger.comtag:blogger.com,1999:blog-2631035637795172582.post-28077523961722192332008-02-19T04:17:00.000-08:002008-02-19T04:17:00.000-08:00Reading back to this, I think my first reply was c...Reading back to this, I think my first reply was clear, but I'm not 100% sure, so let's try it this way:<BR/><BR/>Sentence A: Hitler won WWII.<BR/><BR/>Sentence B: "Sentence A is false."<BR/><BR/>Sentence C: "It is true that Sentence A is false."<BR/><BR/>Sentence D: "Sentence A is both true and false."<BR/><BR/>A is false, B is true, C is true and only D is a contradiction. Whatever B's truth-status was, C would necessarily have the same one. Same goes for the Liar Sentence and the version of it starting with "it is true that..."Benhttps://www.blogger.com/profile/06702722560438833244noreply@blogger.comtag:blogger.com,1999:blog-2631035637795172582.post-77748432500262369492008-02-18T14:13:00.000-08:002008-02-18T14:13:00.000-08:00One more thing about this: if instead of reading t...One more thing about this: if instead of reading the Liar by analogy with the Bat sentence as 'it is true that this sentence is false,' you want to read it as the conjunction of the Liar and the Truth-Teller , you have to go back and read the bat sentence too as a hidden conjunction of the actual bat sentence and the Truth-Teller sentence (the content-free "This sentence is false").<BR/><BR/>Since, even for those who think that the Liar Sentence is by the relevant semantic rules necessarily both true and false, it's horribly unclear what the truth value of the Truth-Teller is--Barwise and Etchemendy say that it is "up for grabs"--we'd have to do some hard and strange re-thinking of all of our existing truth-value assignments if we did see every atomic proposition as 'really' a conjunction of the atomic proposition and the Truth-Teller. (Even Graham Priest regards the Truth-Teller as a good prima facie candidate for a truth-value gap, as opposed to the Liar, which he regards as a clear truth value glut.) Fortunately, as you describe Prior's thought, it doesn't sound like Prior is suggesting this manuever. Unfortunately, what he is saying doesn't sound like it would help.Benhttps://www.blogger.com/profile/06702722560438833244noreply@blogger.comtag:blogger.com,1999:blog-2631035637795172582.post-87660621249488564692008-02-18T14:11:00.000-08:002008-02-18T14:11:00.000-08:00Prior's solution, as you describe it doesn't work....Prior's solution, as you describe it doesn't work.<BR/><BR/>Of course, even if it worked, I would still be reluctant to accept it, simply because I find it extremely implausible that every ordinary proposition its own subject. The subject of the claim there are bats in the lavatory is the bats, not the proposition that there are bats in the lavatory. It strikes me that an infinite regress problem looms here, since if 'there are bats in the lavatory' really means "it is true that 'there are bats in the lavatory,' shouldn't the embedded token also mean "it is true that 'there are bats in the lavatory'?" If so, "there are bats in the lavatory" really means 'it is true that it is true that it is true that....[on and on into infinity before we get to the original atomic proposition that] there are bats in the lavatory." There's an open question about whether this kind of infinite series of embeddings would even be coherent. At any rate, it certainly isn't plausible.<BR/><BR/>Fortunately, all this is irrelevant, because's Prior's suggestion as you describe it simply doesn't work. Here's why not:<BR/><BR/>The analogue for the Liar Sentence of reading "there are bats in the lavatory" as "it's true that there are bat's in the lavatory" is not "this sentence is true and it is false," but "it is true that this sentence is false," which is just as paradoxical as the original sentence.<BR/><BR/>Thus, this suggestion gets us nowhere.Benhttps://www.blogger.com/profile/06702722560438833244noreply@blogger.comtag:blogger.com,1999:blog-2631035637795172582.post-81648272136488455422008-02-04T07:13:00.000-08:002008-02-04T07:13:00.000-08:00Actually Prior's solution of the "Liar" seems pret...Actually Prior's solution of the "Liar" seems pretty sound. An assertive sentence already possesses an implicit truth claim: when Sollie shreiks, "there are bats in the lavatory!" He obviously means that "it's True that there are bats in the lavatory". If he said it "It is true and it is false that there are bats in the lavatory," he contradicts himself (or, as gangstas say, he's talkin' sheet). But there is no paradox. <BR/><BR/>SO the supposed paradox of the liar becomes "this sentence is true and it is false," which is just contradiction, not a paradox (I think this can be applied to other situtations as well). Kripke said something similar, it appears (see Wiki).<BR/><BR/>The ZFC stuff (and Russ. paradox) is another, more difficult matter (I have yet to read--even from a set theory guru like Suppes, a detailed proof of Zermelo's "separation" axiom), but I think with most set theorists (even Frege and Lord Bertie) they start from platonic assumptions (about sets, universals, number, infinity, functions, etc.) which are themselves questionable. In the "game" of set theory, OK, that's understandable, but some of the peeps often seem like they are discussing some abstract, platonic forms ("Set world") which have little to do with how mathematics functions in the real worldJhttps://www.blogger.com/profile/11567400697675996283noreply@blogger.comtag:blogger.com,1999:blog-2631035637795172582.post-69770661985675470602008-02-04T07:11:00.000-08:002008-02-04T07:11:00.000-08:00This comment has been removed by the author.Jhttps://www.blogger.com/profile/11567400697675996283noreply@blogger.com