tag:blogger.com,1999:blog-15005476.post8195211829939229493..comments2023-10-10T08:02:18.073-04:00Comments on Rationally Speaking: Rationally Speaking podcast: Graham Priest on Paradoxes and Paraconsistent LogicUnknownnoreply@blogger.comBlogger83125tag:blogger.com,1999:blog-15005476.post-29598346702744892692012-12-18T06:37:32.296-05:002012-12-18T06:37:32.296-05:00At 33:12, Massimo said:
"It took us 1500 year...At 33:12, Massimo said:<br />"It took us 1500 years to question the idea that the earth is flat."<br /><br /><a href="http://en.wikipedia.org/wiki/Myth_of_the_Flat_Earth" rel="nofollow">Article</a>: Wikipedia - Myth of the Flat Earth<br /><br />"During the early Middle Ages, virtually all scholars maintained the spherical viewpoint first expressed by the Ancient Greeks. By the 14th century, belief in a flat earth among the educated was nearly nonexistent."<br />CompulsoryAcount7746https://www.blogger.com/profile/15741746042938454172noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-42434803049123999872012-11-30T02:45:41.659-05:002012-11-30T02:45:41.659-05:00Wrong again Richard, and every occasion I have res...Wrong again Richard, and every occasion I have responded to you, to the extent I have responded (I like to avoid most of the abstracts). This is the Baron quote, and you will need to read your own explanations to me referred to by Baron to understand it. You have apprently again completely misunderstood the reference and concluded I must have no relevant quote by Baron to refer to. It is serious overstepping once again, and similar to massino, eamon and others who cannot stay with the argument.<br /><br />"I'm not avoiding the issue with Cantor, just saying it was irrelevant to the efforts you made to explain the paradox to Dave. Because a paradox is a logical illusion, and when you explained it, you found ourself explaining the illusion instead of the logic. Which in effect destroyed the illusion. Which I don't think was your purpose."<br /><br />Im not going to revisit your explanations, Baron's problem with them, my problem with them, Cantor, or the rest. That's why this is all pointless, it reduces to that. Just remember, you can't pass the logical buck onto this axiom or that, and their failings at making a self-consistent whole. If they fail, they fail, like turtles, its logic all the way down.DaveKhttps://www.blogger.com/profile/10588445807090485179noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-51499722694974694882012-11-30T02:26:46.178-05:002012-11-30T02:26:46.178-05:00I don't care if you understand their frustrati...I don't care if you understand their frustrations, I have a clear argument based entirely on logical self-consistency which none of you have answered by various illogical arrangements of terms as staements. There is no excuse for personal attacks, keep the attacks to the argument, call the argument ridiculous if you like, but don't call me preening, egotistical etc. as they do, that would be a mistake.<br /><br />So as I have some time, let me explain how to interpret my clear statement. Priest argues that there is a true and false status to paradoxes, when in fact every single paradox is based on self-contradiction, its the deifiniton of a paradox. If a real theory has contradicting elements, or two theories contradict, it doesn't mean they are both true, it means the truth is uncertain until falsification. I write in brief, but surely you read my brief statement as having that meaning in the context of prior posts and discussion in general. It should not require me to lay it out chapter and verse like this, between reasonable people.<br /><br />DaveKhttps://www.blogger.com/profile/10588445807090485179noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-56143992375907290302012-11-22T01:43:07.268-05:002012-11-22T01:43:07.268-05:00PS You aren't even reading the thread correctl...PS You aren't even reading the thread correctly. Baron never responded to me, except when he mistook me for Eamon, and that reply was not at all along the lines of what you just claimed above. At any rate he was presenting a rhetorical argument (like yours) and not a logical one, so it hardly changes anything. (I'm being generous with "hardly"). Richardhttps://www.blogger.com/profile/10042619745483254124noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-44005654841762287652012-11-22T01:24:29.693-05:002012-11-22T01:24:29.693-05:00Okay DaveK. Steep yourself in denial. It's you...Okay DaveK. Steep yourself in denial. It's your choice. I am done here. Richardhttps://www.blogger.com/profile/10042619745483254124noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-12621301196090340812012-11-21T16:42:44.250-05:002012-11-21T16:42:44.250-05:00A final effort to see if I can bring Baron's c...A final effort to see if I can bring Baron's correction to bear. Take a statement as a whole of various statements (axioms) that might in themselves have self-consistency or application to reality, but together they make a self-contradictory whole. Perhaps reality is warped, or the statement as a whole is simply self-contradictory (as in your abstract paradox cases).<br /><br />You can replace or re-arrange the axioms (and any assumed realities on which they are based) to make it self-consistent, or you can dwell on how (un)special it is that they form a self-contradictory whole. Either reality is warped or your logic is warped, depending how abstract your analysis might be. I prefer the former. In fact, you literally dig a hole by shifting the issue to axioms that themselves should be logical or empirical. Like turtles, it's logic all the way up and down - just logic (or lack of it), and preferably applied to reality. I'm done with this head banging repetition.DaveKhttps://www.blogger.com/profile/10588445807090485179noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-60326128371577588592012-11-21T16:22:41.816-05:002012-11-21T16:22:41.816-05:00Then in response I can only say that I am not bein...Then in response I can only say that I am not being argumentative, and by claiming I am, you are being argumentative. But that does not advance the discussion. Nor does the rest of the post because you did not read Baron's correction of your attempt to define as lack of logic as having logic, nor my correction of it. Empriicism is entriely relevant because if an axiom does not apply to reality, what use is it other than as as self-consistent statement? <br /><br />The 'hole' you hope exists simply does not, and no amount of rhetoric on your part can change that. The abiding rule is self-consistentcy, read any definition of 'paradox' and it will offend self-consistentcy and therefore it is not logical. It's a pity you opt for the rhetoric of Eamon and Massimo, so I will bow out of this pointless argument. It's better not to inflate, conflate, uselessly redefine, rely on contradicitory statements, and raise nonsense to being special (such as paradoxes and emergence). DaveKhttps://www.blogger.com/profile/10588445807090485179noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-6585576801637931672012-11-21T10:50:27.550-05:002012-11-21T10:50:27.550-05:00You are wrong and you are just being argumentative...You are wrong and you are just being argumentative. Paradoxes arise from faulty axioms or premises, not from faulty logic. If the latter were the case, a paradox would be of no interest. As it is, when seemingly consistent axioms, through sound logic, yield contradictions, we are forced to reexamine the premises. And that *is* interesting.<br /><br />The reference to empiricism is irrelevant. If we encounter contradiction in a physical experiment, and the result is repeatable, it is our assumptions about the physical world that are to be questioned, not the logic. That is why physicists no longer believe in the aether. <br /><br />I know you have a lot invested in your point of view, but you should step back and reexamine, instead of continuing to dig deeper into that hole. Richardhttps://www.blogger.com/profile/10042619745483254124noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-55561131582606608782012-11-20T17:37:37.405-05:002012-11-20T17:37:37.405-05:00Reading this thread, and in response to the filthy...Reading this thread, and in response to the filthy ad hominems at the beginning of the thread, I do have an argument, and it succeeds. QEDDaveKhttps://www.blogger.com/profile/10588445807090485179noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-82849531673184409492012-11-20T17:29:18.263-05:002012-11-20T17:29:18.263-05:00Of course its ad hominem to say someone is ignoran...Of course its ad hominem to say someone is ignorant, pompus, preening, egotistical etc (read the above). Don't try to redfine reality as you do with useless conundrums about emergence and paradoxes. Deal with what I say. If I have said something ad hominem or directly offensive and you and Eamon have done, point it out specifically. This is a dsigrace as a public blog. Establish any of the ad hominem claims if you can: you cannot beacuse they are filthy lies.DaveKhttps://www.blogger.com/profile/10588445807090485179noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-5313071595722318822012-11-19T16:59:53.748-05:002012-11-19T16:59:53.748-05:00Reading your set theory example, and others here, ...Reading your set theory example, and others here, and the equations, is is just another definitional conundrum. You can chase any rabbit into any maze, propose this and that logical conundrum based on the terms you imagine, and try to figure why those terms should produce that illogicality. Best of luck, but apply it to empirical results, preferably, that's all I'm saying, as that might straighten out the terms. DaveKhttps://www.blogger.com/profile/10588445807090485179noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-2937043975901133022012-11-19T16:50:01.872-05:002012-11-19T16:50:01.872-05:00It is a matter of defining the terms in any way yo...It is a matter of defining the terms in any way you choose, but you require those terms to be logical, whether it in physics, liar cases, set theory, or whatever. If they are paradoxical they are by definition illogical. The terms fail to follow an unbroken logical thread, and thus a 'paradox' arises, and so the terms need revision to straighten them out. You are just restating what I have said and somehow concluded that to break logic requires logic, thus a paradox is logical. If your paradox is logical, where is the paradox? DaveKhttps://www.blogger.com/profile/10588445807090485179noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-47447156026151928582012-11-15T02:17:51.625-05:002012-11-15T02:17:51.625-05:00DaveK, you kept talking about "conflating&quo...DaveK, you kept talking about "conflating" before, but you are conflating science and logic. Logic is a tool for partitioning statements (ideally in some formal language, but not always) into true, false, and indeterminate, based on assumptions. Science is the technique of finding theories that concur with observations. The assumptions in logic need not be empirical at all.<br /><br />Paradox is not "lack of logic". Russell's paradox exists in the presence of logic. Another good example is the Burali-Forti paradox: The set of all ordinal numbers has all the properties of an ordinal number, and therefore must be an ordinal number, therefore it must have a successor which is an ordinal, therefore it must include that successor, therefore it must be greater than its own successor, therefore it must be greater than itself. It's perfectly logical from the premises of naive set theory, as is the Russell paradox.<br /><br />What's missing in these cases is not logic. If you throw out logic, you have no paradox, because you cannot infer the paradoxical conclusions. What's missing is a sufficiently limiting axiom to prevent the paradox from occurring.<br />Richardhttps://www.blogger.com/profile/10042619745483254124noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-21184404723408601992012-11-14T18:30:28.237-05:002012-11-14T18:30:28.237-05:00Thanks, I started working through the articles.
S...Thanks, I started working through the articles.<br /><br />Sooo much more to understand... :)<br /><br />I might come back at some point in the future to discuss the point further, if I have some better grasp of Logics.SKhttps://www.blogger.com/profile/00829924212975839045noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-27392239514447611062012-11-13T03:04:45.069-05:002012-11-13T03:04:45.069-05:00Didn't mean to confuse the situation, just bei...Didn't mean to confuse the situation, just being brief. I did a post just now above to answer some of this. A paradox is just a lack of logic, and as physics is reasonably self-consistent as far as we know, it is logical to that extent. So a paradox is as much a matter pf physics as it is of logic. Science is comprised of physics and stamp collecting, and logic is just abstract waffle if it offends physics.DaveKhttps://www.blogger.com/profile/10588445807090485179noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-76041585575978338302012-11-13T02:57:04.099-05:002012-11-13T02:57:04.099-05:00I didn't mean to write unclear sentences, just...I didn't mean to write unclear sentences, just obvious ones. I was only saying that self-consistency rules both in logic and in reality. Whether a statement is grammatically or mathematically logical, it must be self-consistent or it remains inconclusive. In the Scientific Method, theories are inconclusive if they are inconsistent in a point of overlap, and that's how any inference should be viewed if it offends self-consistency. It is not both true and false, it is conditionally either/neither until the illogicality and unreality is resolved.<br /><br />I realize you have a technical approach to the general problem of paradoxes, with Russell and other references, but it boils down to self-consistency. Perhaps you are trying to penetrate Cantor to determine whether set theory is or is not logically self-consistent. That just returns to the task of penetrating any 'statement' presented on given terms to be assessed by logic applied to those terms. The more complicated the terms (or the paradigm in general if it goes that far), the more difficult the assessment of the illogicality. Endless fun for the young at heart.DaveKhttps://www.blogger.com/profile/10588445807090485179noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-25062491774315846672012-11-13T01:45:54.292-05:002012-11-13T01:45:54.292-05:00SK,
One place to start might be here: http://en.w...SK,<br /><br />One place to start might be here: http://en.wikipedia.org/wiki/Three-valued_logic<br />or here:<br />http://en.wikipedia.org/wiki/Many-valued_logic<br /><br />In particular, look at the sections on Kleene (K3) and Priest (P3) three-valued logics. We can determine by examination whether these logics meet the usual rules of inference. For example (and I'm getting out of my comfort zone so take this with a grain of salt) I think Priest's logic (the same logic discussed in the podcast) probably does not support deduction by means of reductio ad absurdum or modus tollens. Reductio ad absurdum fails because if A implies B, and A implies not B, we can't conclude that A is false, since B could be a dialetheia (both true and false). Modus tollens fails because if A implies B, and B is false, we can't conclude that A is false, because B could be a dialetheia and therefore true at the same time. As I said in an earlier post, paraconsistent logic would have to be weaker (able to prove less from a given set of premises) than classical logic, to avoid explosion, and not having these two rules to work with is a manifestation of that weakening.<br /><br />I think that Kleene logic, on the other hand, supports most if not all of the classical rules of inference. It does require that law of excluded middle is not valid in the logic. The middle value of K3 logic has the semantics of "either true or false, but we don't know which".<br /><br />I know this doesn't really answer your question, but it might help to know that, while not all logics are the same, there is a common basis in the rules of inference (or appropriate subsets thereof) which makes them useful.<br />Richardhttps://www.blogger.com/profile/10042619745483254124noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-3987241612715976452012-11-12T03:49:58.559-05:002012-11-12T03:49:58.559-05:00Thanks for your answer Ian. At first glance I thou...Thanks for your answer Ian. At first glance I thought I had understood it. :)<br /><br />On second thought however I have some doubts. Such statements as the one you provided are similar to what I guess logical explosion can do. But since explosion seems to be up for debate the statement "this can't be right" does not necessarily follow for me (at least not in this discussion. If we were talking in any other context I would completely agree with you). I guess there is some subtle difference I am missing.<br /><br />Again my problem is with the term "can't be right". I don't know how to assess that for a logical statement without using some form of logic.<br /><br />I came up with some analogy to science which might be useful, but I am not sure if it holds. In science we establish facts with our current best measurement methods. We use these to test theories, which in turn might allow us to improve our measurements. Then it might turn out that some facts we used were wrong. So we build new theories on the basis of the new facts.<br />In Logic that would probably mean we start from a logic build on our intuition and test it against common sense. As we progress with the development of our logic we hit paradoxes and need to improve our logics to accommodate these. When we have trained enough on such paradoxes we might end up with an improved common sense to test our logics against.<br /><br />This feels weird to me, because logic always was kind of an absolute thing to me...<br />But I don't see an obvious reason why it should be.SKhttps://www.blogger.com/profile/00829924212975839045noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-35850101298365770202012-11-09T21:55:38.171-05:002012-11-09T21:55:38.171-05:00I am not all that knowledgeable either, but it see...I am not all that knowledgeable either, but it seems that what we check a given logic against is what inferences it would permit about various kinds of facts (metaphysical, physical, mathematical...).<br /><br />For example, take the logical statement "If A then B; A, therefore C." This can't be right because it would license inferences like "If I have a sister then she is female; I have a sister, therefore JFK was a manatee." So the set of all logics that contain "If A then B; A, therefore C" as a theorem must be wrong.ianpollockhttps://www.blogger.com/profile/15579140807988796286noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-50361341286742570682012-11-09T07:27:21.383-05:002012-11-09T07:27:21.383-05:00Hi Everyone,
I have to say this podcast was very ...Hi Everyone,<br /><br />I have to say this podcast was very thought provoking. It gave me kind of the same experience that Massimo mentioned on the show: I have a full science training in physics but have never heard of Logics in the plural. So understandably I was quite confused a lot of the time. <br />What bothered me most are the logical facts that were mentioned as things against which a particular logic can be checked. As Julia said in most other endeavours we actually have some "reality" against we can check our theory but I don't see how that works in logic.<br />The grammar example mentioned works as follows in my mind: We come up with a grammar, construct some sentences from it and then show it to a native speaker who will tell us if they are intelligible and correct. (If that is not how it works please correct me.) <br />My problem now is that I don't know what would be the equivalent of a native speaker in the case of logical facts. As Julia mentioned we can not just go out and ask people if statements such as "sth. can be true and false" are correct, because, well, intuition doesn't serve us very well as graham priest mentioned, as we are not used to such examples. What we then could do is do some reasoning to see if the sentence is correct. But to check if the reasoning is correct we presumably have to subscribe to some logic.<br />In my mind this is a catch-22, because you end up checking a theory against facts that were determined on the basis of the theory. In that case you have checked if the theory is self consistent (or consistent with another logic), but I don't see how this can discriminate between theories.<br /><br />As I said I don't know anything about logics, so any help in understanding this is appreciatedSKhttps://www.blogger.com/profile/00829924212975839045noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-21269496301700280932012-11-09T04:26:23.717-05:002012-11-09T04:26:23.717-05:00Pete,
Exactly.
/dlk.Pete,<br /><br />Exactly.<br /><br />/dlk.denlillekemistenhttps://www.blogger.com/profile/00335313520929777417noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-32511538718515701382012-11-09T04:25:31.556-05:002012-11-09T04:25:31.556-05:00Massimo,
I do understand that bayesianism isn'...Massimo,<br /><br />I do understand that bayesianism isn't primarily a logical tool. However, people like Colin Howson of have been trying to do push these ideas in a more "non-subjective" direction, so to speak:<br /><br />http://www2.lse.ac.uk/researchAndExpertise/Experts/profile.aspx?KeyValue=c.howson@lse.ac.uk<br /><br />Any thoughts on that? <br /><br />(I know what to little to say anything on HOW Mr Dawson deals with the above paradoxes, but I know he does address them.)<br />denlillekemistenhttps://www.blogger.com/profile/00335313520929777417noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-53759880817147639202012-11-08T20:45:23.237-05:002012-11-08T20:45:23.237-05:00Hello Massimo,
I think this is what denlillekemis...Hello Massimo,<br /><br />I think this is what denlillekemisten might be talking about:<br /><br />http://en.wikipedia.org/wiki/Paraconsistent_logic#Alternatives<br /><br />In the alternatives section of the PL wiki page there is discussion of how these problems can be avoided without getting rid of the classical logic rules. I think this is a much more intuitive approach to the problem as well.petehttps://www.blogger.com/profile/12969621709127674152noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-79144973866760342002012-11-08T03:04:56.424-05:002012-11-08T03:04:56.424-05:00Yes, one may reject LEM, as did the intuitionists,...Yes, one may reject LEM, as did the intuitionists, ending up with a limited mathematics. It was a price the intuitionists were willing to pay on meta-mathematical grounds, by claiming that even in a mathematical system assumed to be consistent such as ZF, not every infinite set the mind constructs can be said to exist or not exist. This rejects AC, which explains why intuitionists have remained a negligible minority among mathematicians. The acceptance of AC, and hence LEM, by most mathematicians implies a meta-mathematical affirmation of the legitimacy of asserting existence (or non-existence) of well-defined mathematical objects. <br /><br />Our discussion is off-topic and better belongs, perhaps, on an earlier thread on Platonism. But I can say nothing about dialetheism in the context of set theory because it speaks about language, not mathematics. I do not think contradictions are true even in ordinary language, and if dialetheists are happy with the idea, itâ€™s their problem.<br />Zalhttps://www.blogger.com/profile/12014580581375983716noreply@blogger.comtag:blogger.com,1999:blog-15005476.post-13887443504834160962012-11-07T23:06:33.032-05:002012-11-07T23:06:33.032-05:00Yes, I thought I was responding to Eamon.
Yes, I thought I was responding to Eamon.<br />Baron Phttps://www.blogger.com/profile/04138430918331887648noreply@blogger.com