tag:blogger.com,1999:blog-2631035637795172582.post6074527115206761092..comments2015-09-13T21:38:32.218-07:00Comments on (Blog&~Blog): One Truth Or Two?Benhttp://www.blogger.com/profile/06702722560438833244noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-2631035637795172582.post-77880934412968561342007-12-31T07:36:00.000-08:002007-12-31T07:36:00.000-08:00Sorry to be responding to a post you wrote last mo...Sorry to be responding to a post you wrote last month, but I can't help myself. I don't see how dialtheism faces any problems on the basis of the multi-valued model theory used to give, i.e. models for LP. Put the issue this way. Suppose you believe in the non-triviality of truth.<BR/><BR/><B>NT:</B> not everything is true.<BR/><BR/>And suppose you believe that the semantic paradoxes are significant, as opposed to being meaningless sentences.<BR/><BR/><B>MS:</B> the semantic paradoxes, such as the Liar, are meaningful sentences.<BR/><BR/>Now, suppose you believe the correct account of consequence is given by classical logic. This seems to get you into trouble. Take a sentence like L below and run the following argument.<BR/><BR/>(L) This sentence is not true.<BR/><BR/><BR/>1) L or ~L (LEM)<BR/>2) suppose L<BR/>3) then ~L<BR/>4) so from 2,3 we have L and ~L<BR/>5) suppose ~L<BR/>6) then L<BR/>7) so from 5,6 we have L and ~L<BR/>8) by either disjunct in (1), L and ~L<BR/>9) so, L and ~L<BR/>10) therefore, everything is true (EFQ)<BR/><BR/><BR/>Now you face a problem. It looks like classical logic is incompatible with the assumptions of NT and MS. You could deny one of these assumptions as a potential solution, probably MS, but that is no easy case to make either.<BR/><BR/>All of this is entirely independent of any details of model theory. It is simply a matter of the inferential rules condoned by one or another logic. Now, even if we accept the impetus to revise our logic, I've highlighted at least two places that revision might take place.<BR/><BR/>If, like the dialetheist, you think the implication to (9) is tolerable and something we want to understand better, then you need to deny EFQ. So you need a paraconsistent logic. So you need a model theory that involved either truth value relations in place of functions, or some kind of third truth value, etc. But at this stage, the model theory can be seen as instrumental to all the goals I have outlined.<BR/><BR/>On the other hand, you might take the route of Hartry Field and others who deny LEM. This would block the above inference at the first premise, but as is well known, it seems to raise further similar paradoxes. It remains to be seen who has the better solution here, but the motives are clear enough.<BR/><BR/>The main point is that the dialetheist needn't have a funny conception of truth and falsity, of there being more than one 'kind' of truth. The model theory which invokes a third truth value can just be an instrument to giving an account of consequence that is appropriate to their aims: to wit, taking NT and MS as fixed and figuring out how to resolve the problematic argument sketched above.Colinhttps://www.blogger.com/profile/11764726376012276409noreply@blogger.comtag:blogger.com,1999:blog-2631035637795172582.post-60917180210974266032007-11-30T10:42:00.000-08:002007-11-30T10:42:00.000-08:00Well, as I read him, Priest strongly favors the co...Well, as I read him, Priest strongly favors the conception of philosophy of logic whereby we have pre-formal notions of truth, falsity, negation, conjunction, disjunction, etc., etc., etc., and different logics are just different theories of those pre-existing notions--Quine saying that anyone who thinks statements of the form (P&~P) might be true is changing the meaning of negation operator is like a Newtonian saying anyone who thinks space is relative is just changing the meaning of the word "space"--so there's an extent to which it's quite reasonable (if you think that's the right way to think about it) to talk about the forms of inference as if they were the same.<BR/><BR/>In any case, it's somewhat orthogonal to the main open question here--this might just make matters worse for the LP if you're right--but I will note that if we do read these as four truth values, rather than as four combinations of the two truth values, this is even more counter-intuitive when it comes to the "neither" than it is for the "both."<BR/><BR/>"Not having a truth value" really shouldn't be its own truth value.Benhttps://www.blogger.com/profile/06702722560438833244noreply@blogger.comtag:blogger.com,1999:blog-2631035637795172582.post-42012005666085083992007-11-29T13:40:00.000-08:002007-11-29T13:40:00.000-08:00In the LP, truth value is thought of as a relation...<I>In the LP, truth value is thought of as a relation, such that any given proposition can be related either to 1 (True), to 0 (False), to both 1 and 0 (True/False) or to neither.</I><BR/><BR/>I need to re-read LP; but when Priest discusses the matter elsewhere (e.g., Beyond the Limits of Thought), he often puts it in terms of multivalence, i.e., there are four truth values: true (true simpliciter, as he sometimes calls it), false (false simpliciter), neither true or false, and then both true and false. The problem with this is that, since connectives are usually understood truth-functionally, adding new truth values changes how the connectives are understood, and you can no longer talk about the inference rules as if they were the same (which Priest tends to do). New connectives, therefore new rules governing them, and therefore a different logical subject entirely. Of course, this could be treated as just a loose way of talking. This brings us to the option that there are only two truth values, 0 and 1, which may be given to propositions in the following ways: 0, 1, both 0 and 1, neither 0 and 1. <BR/><BR/>This gets us out of the problem of additional truth values; but it gets us right into the problem you note at the end of the post. Because classical logic really does mean by 1 or T, true to the exclusion of false, and it really does mean by 0 or F, false to the exclusion of true, so that you could just substitute those descriptions in without any change; and the dialetheist is introducing a new way of looking at truth and falsity, where true can be <I>either</I> classical logic's T or true-and-false, and ditto with false. And then the dialetheist still seems to be changing the subject. (And equivocating; although I'm not quite sure if equivocation is an accusation that has quite so much bite with dialetheists!)Brandonhttps://www.blogger.com/profile/06698839146562734910noreply@blogger.com