tag:blogger.com,1999:blog-2631035637795172582.post8089583551399063333..comments2023-01-24T10:06:57.212-08:00Comments on (Blog&~Blog): Quantum Logic, Part II of IVBenhttp://www.blogger.com/profile/06702722560438833244noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-2631035637795172582.post-77759568428053301102010-09-17T09:42:45.910-07:002010-09-17T09:42:45.910-07:00One possible way to analyze them is to regard them...One possible way to analyze them is to regard them as having truth values conditionally linked to each other, so that the truth value of (1) is [T if (2) is F and F if (2) is T] and of (2) is [T if (1) is F and F if (1) is T]. Only one possible way, of course, although if you give people the statements as a true/false quiz the conjoined conditional truth value assignment tends to capture their initial response fairly well.Brandonhttps://www.blogger.com/profile/06698839146562734910noreply@blogger.comtag:blogger.com,1999:blog-2631035637795172582.post-2888944414672960112010-09-17T03:01:20.948-07:002010-09-17T03:01:20.948-07:00Fair enough.
Could you say a bit more about your ...Fair enough.<br /><br />Could you say a bit more about your analysis of the inter-referring sentences? I'm not sure I follow.Benhttps://www.blogger.com/profile/06702722560438833244noreply@blogger.comtag:blogger.com,1999:blog-2631035637795172582.post-2173497232555518822010-09-16T22:06:12.259-07:002010-09-16T22:06:12.259-07:00It's not an intuition I have at all, but you&#...It's not an intuition I have at all, but you're right that it certainly does seem to be common. It's much the same intuition, I suppose, that wants to rule out inter-referring statement pairs like<br /><br />(1) Statement (2) is false.<br />(2) Statement (1) is false.<br /><br />(Since a natural way to assign truth values, if they are allowed to be assigned, is as conjoined conditional truth values.) <br /><br />In any case, it was just an attempt to rise to the challenge and show that there is at least one deviant truth value that preserves the classical structure but breaks Distribution.Brandonhttps://www.blogger.com/profile/06698839146562734910noreply@blogger.comtag:blogger.com,1999:blog-2631035637795172582.post-26314087862703693892010-09-16T21:40:39.800-07:002010-09-16T21:40:39.800-07:00Brandon,
Interesting thought, but of course, intu...Brandon,<br /><br />Interesting thought, but of course, intuitively, whether a statement is true or false should be determined by whatever it is the statement refers to, rather than depending on why we are uttering it--if we're saying that it's true, if we're embedding it in a disjunction, or whatever. I'd definitely be interested, though, to see what the more sophisticated versions of the proposal would look like.Benhttps://www.blogger.com/profile/06702722560438833244noreply@blogger.comtag:blogger.com,1999:blog-2631035637795172582.post-17935100609594264722010-09-16T20:08:16.599-07:002010-09-16T20:08:16.599-07:00Suppose you allow conditional truth values, just a...Suppose you allow conditional truth values, just as we can allow conjunctive or nondisjunctive truth values. Then you could have a truth table for disjunction that's something like:<br /><br />[p][q] = [p v q]<br />[T][T] = [T]<br />[T][F] = [T]<br />[F][T] = [T]<br />[F][F] = [F]<br />[cT][T] = [T]<br />[cT][F] = [T]<br />[T][cT] = [T]<br />[F][cT] = [T]<br />[cT][cT] = [T]<br /><br />where cT is that particular conditional truth value that means 'true if disjoined with only false fellow disjuncts'. Here we have a truth table in which all the classical lines correspond, disjunction can still be understood as 'at least one of these is true', and, if it were properly expanded, [P & (Q v R)] could be true without [(P & Q) v (P & R)] being true. That is, substituting the truth values for the propositions:<br /><br />[T] & ([cT] v (cT)]<br /><br />won't preserve truth if reordered to:<br /><br />([T] & [cT]) v ([T] & [cT])<br /><br />unless [cT] doesn't just mean 'true if disjoined with only false fellow disjuncts' but also has meaning in a conjunction.<br /><br />This is a pretty crude way of doing it, since [cT] as defined here guarantees the truth of any disjunction to which it is assigned; I'm sure more sophisticated ways are possible.<br /><br />Of course, I could be missing something.Brandonhttps://www.blogger.com/profile/06698839146562734910noreply@blogger.com