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Consensus in the math WikiProject is strongly against nav templates. I can't see any purpose for this one at all; there doesn't seem to be any content to it. Do you want to explain what you had in mind with it? --Trovatore04:12, 27 June 2007 (UTC)[reply]
Oh, I found the "show" button. Fairly slick, I have to admit, but I'm not sure it's enough to overcome the strong position against nav templates. A curiosity: Why do you have "sets" under "first-order logic" but "type theory" under "second-order logic"? That doesn't make much sense to me; sets as modernly conceived are basically just like types except that you can mix different levels (which then allows you to iterate further; it's hard to see how you can push types past a limit ordinal without allowing mixing). --Trovatore04:24, 27 June 2007 (UTC)[reply]
That a wikipedia subculture should have an aversion to nav templates I find facinating. The wikipedia isn't just for the use of whatever subculture was fascinated enough to make the article. It's for people who are trying to learn. I would think that math pages would have a greater need for such a device...
Mathematics is a subset of logic, not the other way around. We have a math-centric wikipedia (rather than logic-centric) because there are more math people working on it. However, many of the overlapping articles would be better off if they were organized under logic primarily. I don't actually see this becoming the case, however.
Since this is the case, and since an encyclopedia should be organized around the concepts (with the category or subject as a lesser organizational priority) there should be an effort to include sections on the logical applications, and mathematical applications as well. There are some articles that have two or more pages for the same concept. I propose that many of them should be united. This would be a huge undertaking. I am concentrating mainly on the logical connectives. There is a project proposal on the matter. I invite your participation.
In the case of this nav template I have no objection to your re-organization. However, I think a link to set should be include somewhere. You tell me? Be well,
Well, first of all I disagree that "mathematics is a subset of logic". That sounds to me like the mostly discredited logicist view. I see mathematics as "synthetic a priori", in Kant's categories, and its study as an empirical natural science. (And by the way, "mathematical logic" isn't really "logic" in the strict sense; it's a collection of mathematical topics that have historically been associated with logic. The use of the word "logic" to describe these fields is completely standard, but whether that linguistic and historical association is a good enough reason to include them in the logic template is less clear.)
I raised the issue of the nav templates on WT:WPM and there seems to be no great outcry about this one, mainly because of its "collapsible collapsed" state. I think the most important objection has always been aesthetic, and the unobtrusiveness of the newer version may obviate that. However the necessary arbitrariness of the content of such templates is also a problem.
I had discovered that the entry for theorem had a math-centric view throughout so as to completely miss the essential point of theoremhood. After I corrected the problem, it was reverted back (somewhat) to the math-pov version. But look more closely. The theorem as conceived in math is contained within the concept from logic. It would have been a good way to demonstrate my larger point about the math v logic situation I am trying to make here. But it seems to have been over some heads or whatever.
An encyclopedia entry should be organized from general to specific. The logical perspective should come first because it leads into the math perspective (not really the other way around.) I don't really know what you are talking about 'discredited logicism.' I think you have misinterpreted some criticism so as to throw out the baby with the bath water.
You say you don't believe that 'mathematical logic' isn't really logic, so that's pretty math-centric. I suppose we should call it Logical mathematics? That would be pretty silly wouldn't it? There is more going on here than linguistic and historical association. It's the concepts themselves that matter. In that regard logic is more fundamental than mathematics. What is going on at the theorem page should have made it clear. Oh well. Be well, Gregbard12:42, 6 July 2007 (UTC)[reply]
Greg, frankly it feels like you're pushing a POV here, though I'm not exactly sure which one. From your earlier remarks I thought you were saying that mathematics could be reduced to logic, that it has no content outside of logic. That view is indeed logicism, and is mostly discredited, though there are a few lonely souls who call themselves "neo-logicist" or some such.
On your question about what to call mathematical logic, of course I call it "mathematical logic", because that's the standard name, and it's useful to demarcate certain branches of mathematics that share some common concerns. I see no reason to change the terminology. But that doesn't make them logic in the older sense of "the science of making valid inferences". --Trovatore19:33, 6 July 2007 (UTC)[reply]
I think the compromise is a subtle wording change. I will make it now to present it to all for consideration (philosophy of logic line) Jok2000 (talk) 13:16, 12 May 2008 (UTC)[reply]
The problem is that several items listed as "logic" are in fact philosophy but not logic, including the unfortunately named logical positivism, which on its own page is discredited by Popper. It was a movement in the philosophy of science, in fact [Okasa: A Very Short Introduction to the Philosophy of Science] that has passed. The other offending members are: Finitism, Empiricism, Platonism, Fictionalism and Nominalism which are epistemlogical pursuits, as for example you can gain knowledge without logic, by, for example, reading a book. The other recently added items are things like mathematical logic, and that sounds close enough to the meaning of "logic" for me. Anyway, I have now cited a book on philosophy and an example meaning of epistemlogical from dictionary.com. Please kindly cite your sources for the categorization of these philosophical topics listed here. Jok2000 (talk) 00:21, 7 May 2008 (UTC)[reply]
Just because a philosophical tradition influences science, or epistemology, as the case may be, does not mean it doesn't influence other fields as well. So this is a false dilemma you have accepted. Furthermore all of the traditions listed are major traditions in the history of logic. There are others such as Psychologism which are not included because they are minor. Perhaps we should include them. I'm not inclined to go the other way deleting them. The ones included currently are the major traditions in logic. Pontiff Greg Bard (talk) 00:45, 7 May 2008 (UTC)[reply]
Would you give us the pleasure of a citation? A category on logic should be tied closely to symbolic logic (as per Encyclopaedia Britanica). Logical Positivism is not an influence on other fields, it is a *rejection* of them. (Encyclopaedia Britanica, again). Jok2000 (talk) 01:45, 7 May 2008 (UTC)[reply]
Plato's dialog Phaedo talks about "the forms", among them the laws of logic.
No, a "category" on logic need not be closely tied to "symbolic" (called mathematical logic these days). There is a world of logic beyond what is formalized, Reasoning, and critical thinking among them.
Logical positivism is a philosophy that is not only applied to the laws of the empirical sciences, but also to the laws of logic. Logic is sometimes seen as quasi-empirical. Be well.
I know we're actually waiting for someone else to weigh in, but you have this a bit backwards, you need to cite a definition of logic that encompasses the things you have added based on your WP:OR. Phaedo, this is the first time I read it, is about the afterlife, which I'm sorry to say, does not exist. Anyway, argument is pointless, this "world of logic" you refer to is called Reasoning and should not appear on the logic template. You are again writing mounds of WP:OR about logical positivism without a single citation. You are concerned about the effort you are expending with me doing my research, save your fingers man, I am not going to read uncited stuff you write here, as I absolutely reject your reasoning system outright (mostly on the grounds that you will not cite relevant definitions for your writing). I do not have to research finitism just because you added it out of the blue to this template with no citation. I want it reverted -- I did the minimum necessary, which was to read the pages you linked to to see that they are about reasoning and definitely not about logic, in fact most are *discredited* lines of reasoning (as cited above). Jok2000 (talk) 20:26, 8 May 2008 (UTC)[reply]
Fortunately, the wikipedia doesn't stand in justification to you alone. I'm not going to have any problem getting sources if it becomes a real priority. You don't think reasoning belongs in the template eh? Yeah, that's not going to fly. You still also seem to be harping on how these philosophies have been discredited. Guess what? I agree. They still were prevailing views on logic in their time. That is the standard. You've really missed the point. Be well, Pontiff Greg Bard (talk) 20:39, 8 May 2008 (UTC)[reply]
These are from only the first page of google search:
12 -- this guy thinks mathematicians should be Platonists
3 Stanford E.P.
4a book title Logic with Platonismanother
and Penelope Maddy, 'The Roots of Contemporary Platonism', Journal of Symbolic Logic, 54/4 (December 1989): 1121-1144
It amazes me that someone who has taught correct lines of reasoning continuously employs invalid forms of reasoning and promotes outdated discredited ones, however in this case it was just to create a personal attack on me, and I'm 100% sure no one cares about my opinions in particular. Fortunately, you did employ a valid line of reasoning to show that my suspicions were wrong about Platonism, but I will remind you that the platonism page here only has the word logic once, and that is your recent addition. Is it so hard to provide a fellow editor who has to regularly revert vandalism from these logic pages with a valid citation as you have now done? Anyway, although an unimportant opinion, I do need to point out that when I click on a logic template, I wouldn't personally be looking for a bunch of crap about soul and ethics, it appears to me that only the dialectic part of platonism would need to be on the logic template. This however, as you point out harshly, is not for me to decide, but I already knew this, hence the rFc. Jok2000 (talk) 01:39, 9 May 2008 (UTC)[reply]
You still really do not understand the basic wikipedia concept of WP:NPOV. It isn't "promot[ing] outdated discredited" schools of thought just to list them among philosophies of logic. All of these philosophies have been discredited in academia. They are there for historical purposes. I suppose you are totally capable of giving an example of an "invalid form of reasoning" I have made, since you make the accusation. Apparently your view is really motivated by this idea that you don't want to see stuff about "soul and ethics." Please observe, the wikipedia is in a continuous state of change. What matters is that the topic is correct, and that the appropriate material would be found there in principle. You need to tone down all the snipiness. If you are correct, it shouldn't matter if I'm ignorant, or an idiot or whatever. Right? Pontiff Greg Bard (talk) 02:06, 9 May 2008 (UTC)[reply]
If I understand correctly, the articles at issue are: Platonism, Scholasticism, Empiricism, Logical atomism, Logical positivism, Logicism, Formalism, Nominalism, Fictionalism, Realism, Intuitionism, Constructivism, and Finitism. The section itself, philosophy of logic, does not seem to be at issue. To be redundant, then, the question is which articles to include in the section. According to the Wikipedia article on philosophy of logic, and verified by the Routledge Encyclopedia's article on the same, the philosophy of logic regards those philosophical issues that arise within logic and about logic. That is, issues within modal logic (such as the debate over S5) and arguments about logic (such as how we can know/trust it or its structure) are part of the philosophy of logic (and in the later case, metalogic—which may in fact be a subset of the philosophy of logic). Whether something is an issue within or about logic will not always be clear, of course, but so long as both are appropriate this is not a substantive problem. Finally, as Wikipedia strives for a global view, rather than ethnocentrism, and the long historical view, rather than recentism, the issue is also not about which theories are correct (imagine an analogous situation in ethics: would we include realism or anti-realism? utilitarianism or deontology?), but rather which have been influential to philosophical movements.
With this understanding, two of the articles should become almost immediately uncontroversial. The first is Logicism, which positions logic as the foundation of mathematics and thus all a priori reasoning (see Russell and Whitehead, Principia Mathematica and A.D. Irvine's article on that book). The second is logical atomism, which is fundamental to Russell's early belief that the entire world could be described in purely logical terms. (Principia Mathematica is again relevant here, but see volume eight of Russell's collected papers, The Philosophy of Logical Atomism and Other Essays, his book Logic and Knowledge, and of course, his article "Analytic Realism." Russell was not the only logical atomist, however, so we should not ignore Wittgenstein's Tractatus Logico-Philosophicus. I am not familiar enough with Carnap to suggest something of his, but I suspect the given sources are sufficient.)
I am rather skeptical about including logical positivism in that it is an approach not to logic, but to philosophy. That is, while there is a philosophy of logic behind logical positivism, the movement is not defined by that philosophy. Rather, logical positivism is defined by the way it combines the competing principles of empiricism and rationalism, insisting on strictly phenomenalistic descriptions of the world. I have a similar problem with empiricism, which is really a position in epistemology.
Formalism is a more difficult case. Formalism is certainly relevant to logic, but the Wikipedia article does not even broach the topic. Indeed, the article's full name is Formalism (philosophy) and yet it is barely recognizable as a philosophy article. If we spruce it up with information from sources such as Schiller's Formal Logic (and his "Formalism in Logic," a response to Hoernlé's review of Schiller's book) then we might have an article worth including. But until then, it is more confusing to include the link than to delete it.
Platonism is another tricky one. Really what should be included is Platonic realism, as this where Plato's rationalism and his views on the a priori come out (as seen in The Republic and the Phaedo, which is about much more than the afterlife). The emphasis on universals in Platonic realism is opposed by nominalism, which again rests on an issue within logic—namely, how it should treat set theory (see Goodman's The Structure of Appearance but also Peter Abelard's Tractatus de intellectibus, which can be found in translation in Peter King's Peter Abailard and the Problem of Universals in the Twelfth Century). One might take Abelard's nominalism as a reason to then include Scholasticism, but this becomes a bit of stretch for me. Scholasticism is typically taken as period in the history of philosophy. And while its emphasis on dialectic (in the pre-Hegelian sense) might seem to make it about logic, I remain unconvinced.
Mercifully, this is all I have to say about the matter for now. Perhaps I will address fictionalism, realism, intuitionism, constructivism, and finitism at some other time, but I have at least given some framework within which others can consider these articles. Or, of course, they can come up with their own framework. If I may make one last suggestion, it is that we include some of the issues within logic (e.g. counterfactuals or vagueness) under philosophy of logic section, rather than insisting only on larger scale movements or positions. Postmodern Beatnik (talk) 15:13, 9 May 2008 (UTC)[reply]
Surprisingly, i have somewhat understood about a half of what Beatnik wrote, and it agrees with my views and my intuition. Seems that i can make sense of some philosophy (as long as it is written not by Gregbard). --Cokaban (talk) 16:28, 9 May 2008 (UTC)[reply]
Quite frankly, I'm impressed anyone even read half of what I wrote, let alone understood it. :p But I must concur with the Pontiff that your last comment was a bit uncivil. I don't need complements that come in the form of a backhanded insult to someone else. Postmodern Beatnik (talk) 12:20, 12 May 2008 (UTC)[reply]
There should be some degree of correspondence between (a) the contents of the section titled Philosophy of logic with (b) the contents of the article philosophy of logic--Philogo 11:29, 10 May 2008 (UTC)
Well that would be ideal, wouldn't it? ; ) Unfortunately, that article seems rather under construction at the moment. Still, you are quite correct that we should keep an eye on both of them to ensure they remain in agreement. Postmodern Beatnik (talk) 12:22, 12 May 2008 (UTC)[reply]
Agreed--Philogo 12:35, 12 May 2008 (UTC)
GregBard, by noting that "Epistemology" was nonsensical, did you mean you were unable to find the word in the dictionary to make sense of it (this seems unlikely to me), that others would fail to do same, or that you wanted it to say "theory of knowledge", but were not in the mood for it (you're making me guess), or do you dispute the fact that the individual article pages are about epistemology? Most of these possible interpretations don't lead anywhere, by the way. I recommend you elucidate your "revert" reason in the log in the future. Jok2000 (talk) 01:23, 12 May 2008 (UTC)[reply]
I want to move on and edit other articles, but I do need to point out that my edit comment generally holds true, as for example finitism's page says it is in the philosophy of mathematics (i.e. not philosophy of logic). I did make an effort to buy a philosophy of logic book so I could snatch its list of topics in philosophy it covers, but the store did not carry the title, so I officially give up trying to find your or an equivalent source for this stuff, noting again that wikipedia is no longer self-consistent on this topic. And besides, there was a hilarious book on "The Daily Show and Philosophy" so I bought it instead. Jok2000 (talk) 03:15, 12 May 2008 (UTC)[reply]
Yes, The Daily Show and Philosophy is an amusing book. I particularly like the essay about Jon's status as a public intellectual (something I find sorely missing from society these days). On a more serious topic, however, it is the unfortunate case that there is not always a clear division between the philosophy of logic and the philosophy of mathematics. Set theory is one clear instance of the problems we face trying to separate the two. It gets murkier when we consider the philosophy done under the aegis of logicism. This is not to say that Finitism definitely is philosophy of logic, nor to say that it definitely is not. I am simply trying to warn against one mistaken way of making the decision (that is, thinking that philosophical categories are all mutually exclusive).
As for your comment about the contents of a philosophy of logic book, I rather suspect that no one book will cover all the possible topics. Here, though, is the publisher's description of one such book:
The papers presented in this volume examine topics of central interest in contemporary philosophy of logic. They include reflections on the nature of logic and its relevance for philosophy today, and explore in depth developments in informal logic and the relation of informal to symbolic logic, mathematical metatheory and the limiting metatheorems, modal logic, many-valued logic, relevance and paraconsistent logic, free logics, extensional v. intensional logics, the logic of fiction, epistemic logic, formal logical and semantic paradoxes, the concept of truth, the formal theory of entailment, objectual and substitutional interpretation of the quantifiers, infinity and domain constraints, the Lowenheim-Skolem theorem and Skolem paradox, vagueness, modal realism v. actualism, counterfactuals and the logic of causation, applications of logic and mathematics to the physical sciences, logically possible worlds and counterpart semantics, and the legacy of Hilbert's program and logicism. The handbook is meant to be both a compendium of new work in symbolic logic and an authoritative resource for students and researchers, a book to be consulted for specific information about recent developments in logic and to be read with pleasure for its technical acumen and philosophical insights.
Not all of the topics listed above should be in the template, of course, and not all of the topics that should be listed in the template are necessarily in this book description. But it does seem to be what you were looking for. On a related note, I see that my earlier comment resulted in some changes to the template. Unless I have missed something about why we are focusing on "-isms", I might reiterate my request that we consider putting some issues into the template and not just focus on movements. Postmodern Beatnik (talk) 12:36, 12 May 2008 (UTC)[reply]
Until today we had a link to formula (mathematical logic) and one to well-formed formula. The first was actually a redirect to the second, and it was removed (correctly) today by an anonymous user. I changed it to appear as formula, with the following edit summary:
well-formed formula -> formula for brevity; also, in modern mathematical usage there is no such thing as a non-well-formed formula[1]
In more detail:
The same notion is sometimes called "formula" and sometimes "well-formed formula". Space considerations in a template suggest a bias towards the shorter term.
The fact that this is under the heading "Mathematical" suggests a bias towards up-to-date mathematical terminology, rather than philosophical or obsolescent mathematical terminology.
Mathematical usage is overwhelmingly to drop the redundant "well-formed". E.g. I made some searches in Mathematical Reviews, restricted to the MSC category 03 (Mathematical Logic and Foundations) to get rid of spurious results. Here are the results:
Anywhere: "well-formed" or "well formed": 104 hits
Anywhere: "wellformed": 0 hits
Anywhere: "wff": 78 hits
Anywhere: "formula": 5817 hits
I do not know a single source that would define some kind of more general formulas that are not "well-formed". This absurd artifact of terminology probably makes no sense since at least half a century ago. All my books agree: neither "well-formed" nor "wff" makes it into the index. This includes Chang & Keisler (1973) and Bell & Slomson (1969). Note that Bell & Slomson use the term "string of symbols" for what may at some time in the past have been called a not necessarily well-formed formula. Then they say: "We single out a subset of the strings. The elements of this subset are called formulas. Intuitively these are those strings which can be interpreted meaningfully and unambiguously when we interpret […]." They continue with a parenthetical remark to "philosophically minded readers", but even that doesn't note the "wff"/"well-formed" terminology. Modern mathematics students who specialise in logic will not normally be exposed to this terminology.
Before this background I was a bit surprised to be reverted with an edit comment of "term wff well established". Is it OK if I revert back? --Hans Adler (talk) 15:34, 9 December 2008 (UTC)[reply]
I'll look into this. So far as I know the term well formed formula is in current use. Perhaps "Modern mathematics students who specialise in logic" read different texts to "students who study logic" and some readers may not be any kind of student of logic. As an enclopedia we should be writing for a wide audience.--Philogo 13:16, 10 December 2008 (UTC)
I am not at all sure it is the right way to go about things looking for hits but as a matter of fact Google retunrs 15,200 hits for '"Well formed formula" logic', 19,500 hits for "Well formed formula" and 57,400 for "wff". The issue is not what is a better term, or what term certain specialist use, but what term has the widest comprehension. I think, for comparison, I would expect to find an articles on "Aspirin", "Vitamin C" and "Shin bone" "ME" rather than under their chemical, bichemical or medical proper names (which I would expect to find in parantheses). --Philogo 13:32, 10 December 2008 (UTC)
Never mind; I misread the category it's in. However, the template should probably be split into mathematical logic and philosophical logic, which have very little in common. — Arthur Rubin(talk)21:34, 19 August 2009 (UTC)[reply]
I agree with the math/philosophy split. Templates are there to help people reading one page read other related pages. If I'm reading logical fallacy, there's really no reason to believe that I would be interested in reading about the compactness theorem of first order logic, and the other way around. --Robin (talk) 13:46, 24 August 2009 (UTC)[reply]
Actually, I think a certain degree of uniformity is a good thing for such templates. Currently this one is very special. We could try to reorganise it so that it becomes simultaneously more similar to the templates used in philosophy and those used in mathematics. It's not clear to me how to do this, so I will think a bit more about it. Hans Adler08:49, 1 March 2010 (UTC)[reply]
That's a personal attack Arthur, with no comment on the actual content that a good faith collaborator can work with. You should be ashamed of yourself. Is your complaint that math is being labeled as philosophy? How terrible for you. I'm sure there is a way we can satisfy everybody.. if you drop the attitude. Greg Bard 19:29, 1 March 2010 (UTC)
I misspoke, to some extent. I object to the miscategorization you (and only you, among active editors) made. That you are the only one who has ever (at least since I've been monitoring the articles) so miscategorized and/or redefined mathematical logic concepts as philosphical logic concepts is not entirely relevant. — Arthur Rubin(talk)09:18, 2 March 2010 (UTC)[reply]
I not the one interested in labeling in the first place Arthur. That is an invention of yourself and the others. Like I have said before, "philosophical logic" is only meaningful to you guys. We don't have "philosophical ethics" or "philosophical aesthetics" because that would be silly. Perhaps we should misplace the isms under metalogic, so as to avoid the territory issues that you and your friends have created. Greg Bard21:54, 2 March 2010 (UTC)[reply]
You are the only one interested in the topics you have been misattributing into the Category:Logic; I apologize for attributing the name to you, only the fact that you conflate other-than-mathematical logic into mathematical logic articles. — Arthur Rubin(talk)03:18, 3 March 2010 (UTC)[reply]
(to Trovatore) Well, perhaps you're right, but, if a redirect is to a section of the page, it's probably better to replace it with [[X#S|S]]. He's still removing redirects he doesn't like (or possibly doesn't understand), even if they are there. — Arthur Rubin(talk)02:43, 19 June 2010 (UTC)[reply]
More often the proper thing to do is to leave the redirect as a redirect. That way, if at some later date the redirect becomes a separate article on its aspect of the subject, the link will still go to the right place. —David Eppstein (talk) 05:18, 19 June 2010 (UTC)[reply]
You can see as plainly as I can, that I made a number of changes at the same time. If you disagree with 1% of it and revert the whole thing on that basis, then you are not a good faith collaborator. I am perfectly willing to discuss any concerns you have AFTER the cleanup. That is just basic politeness Arthur. You are jumping to conclusions again, because of your disposition. Greg Bard02:45, 19 June 2010 (UTC)[reply]
I don't have a bot that will distinguish "following redirects" from removing redirects and/or incorrectly following redirects. As you previously damaged Model (logic), I don't think you're the best choice of deciding which redirects are correct. — Arthur Rubin(talk)02:52, 19 June 2010 (UTC)[reply]
Fortunately, it is an openly editable medium, and we are able to change it, and have civil discussion about it. At least some of are. I don't think you are a good choice to be editing this for the next 24 hours quite frankly.Greg Bard03:06, 19 June 2010 (UTC)[reply]
You're probably right. You're still damaging the template. I can see it's not vandalizing; you just don't understand mathematical logic well enough to understand which concepts are different. — Arthur Rubin(talk)03:10, 19 June 2010 (UTC)[reply]
Try this version. I've followed those which make sense to follow. I left Church's theorem and Church's thesis as a parallel construction within that section, but I did pipe the latter. I also sorted a few alphabetical. I unsorted the model theory section as "model" should probably come first. In set theory, I followed "decidable set" to "recursive set", although the concept of constructible set, definable set and ordinal definable set may also belong there.
Edit summary in "unexplained" edit #1: "rm non-article project & changes links per WP:SELF"
Edit summary in "unexplained" edit #2: "rv unexplained addition of self-reference on WP templates"
It appears Philogo is incorrect in his description of the edits, even though his edit summaries do not explain his restorations other than "Revert unexplained edit by an anon editor" after I clearly explained in the edit summary.
Nevertheless, please read the guideline WP:SELF; no references to wikiprojects, etc., on the article, transcluded or otherwise. Links to wikiprojects are appropriate on the article talk page, but not on the article itself. A link to recent changes is appropriate as a "noinclude" on the template, but not as part of the transclusion. If Philogo disagrees with this, he may wish to initiate a discussion at Wikipedia talk:Manual of Style (self-references to avoid). (These 3 IP edits are the same person as I apparently have a dynamic address.) 64.85.220.131 (talk) 16:50, 24 February 2011 (UTC)[reply]