Talk:Metamathematics
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[edit] obsolete term?
The term 'metamathematics' is obsolete? Hmm... Maybe I've been reading way too many old texts on math, but I've certainly come across it more often than this article seems to state. Just because mathematical logic has more google hits means nothing in this circumstance. Anyway, metamathematics does not have to be mathematical, does it? But mathematical logic does. I would think this means that mathematical logic is actually a subset of metamathematics. Eric Herboso 02:00, 18 Feb 2005 (UTC)
[edit] Googlefight
Is using Googlefight in the way the article does really necessary and/or encyclopedic? --Aioth 15:21, 13 January 2006 (UTC)
[edit] Proposed merge
There seems to be no difference between metalogic and metamathematics. At least, all the examples in metalogic are or should be in metamathematics, and everything in metamathematics fits the definitions in metalogic. If metalogic were to discuss the meta-theory of non-mathematical logic, that could be different, but that would seem to require a formal theory of non-mathematical logic — which would make that aspect mathematical logic. — Arthur Rubin | (talk) 19:55, 14 January 2008 (UTC)
- The people I know who are doing what is described as "metalogic" consider themselves (and are called by others) logicians, not metalogicians – as for example those in Category:American logicians – and the field they are working in is known as "(mathematical) logic", not "metalogic". The latter term does not even occur in the AMS Mathematics Subject Classification. I don't think these logicians are particularly concerned with the "truths-of-logic", whatever that may be. (The term is not explained.) --Lambiam 23:26, 14 January 2008 (UTC)
- Metalogic and metamathematics do not seem to be the same subject, though there appears to be some overlap in the matters considered and studied. Metamathematics appears to study many of the foundational problems in formal logic and seems geared towards system analysis. Metalogic seems much more narrowly focused on the advantages and shortcomings of formal language, rather than taking the systemic approach. Vassyana (talk) 15:03, 15 January 2008 (UTC)
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- Thinking about it, metalogic seems just to be what is commonly known in mathematical circles as model theory and proof theory. Although Britannica (online) has an article on it, the article metalogic has no secondary sources (the current reference being a primary source), and the article at present has nothing distinguishing it from other better known concepts in mathematical logic. I think, perhaps, I should withdraw the merge request in favor of changing it to a quasi-disambiguation page, unless sources can be provided that people doing it use the term. — Arthur Rubin | (talk) 17:38, 15 January 2008 (UTC)
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- Assuming (I can't find an explicit statement to the effect) that the author of Metalogic: An Introduction to the Metatheory of Standard First-Order Logic equates metalogic with "the metatheory of logic", the definition offered is:
- "The metatheory of logic is the theory of those formal languages and systems that for one reason or another matter to the logician."
- There is a chapter with the title "Metalogic" in Hao Wang's From Mathematics to Philosophy, p. 166.[1] It defines the notion as follows:
- "Metalogic may be defined as the study of the syntax and the semantics of formal languages and formal systems."
- I agree that this covers the areas of model theory and proof theory within mathematical logic, and the article should indeed point that out. --Lambiam 21:06, 15 January 2008 (UTC)
- Assuming (I can't find an explicit statement to the effect) that the author of Metalogic: An Introduction to the Metatheory of Standard First-Order Logic equates metalogic with "the metatheory of logic", the definition offered is:
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Oppose. Metalogic straddles mathematics and philosophy. Just doing a quick Google search, UC Berkeley offers Metalogic as a course in the Philosophy Dept. UC Irvine offers it as a joint course of the Logic & Philosophy of Science and the Philosophy Departments. Compare Philosophy with Metaphilosophy. Chet Ubetcha (talk) 02:42, 23 January 2008 (UTC)
- Comment. Well, UCI is not really known for having a first-class logic or philosophy department, but that's beside the point. I attempted to withdraw the merge request above, but others have said it should be merged somewhere, so it seems improper just to delete the request. — Arthur Rubin | (talk) 02:51, 23 January 2008 (UTC)
- Comment. Both those courses are based on the book Metalogic, not necessarily on the subject. Odd, isn't it. — Arthur Rubin | (talk) 02:54, 23 January 2008 (UTC)
We are not the first to argue this. The players were Tarski versus Carnap, who were so important that I don't have to pipe their names to get the links to work. Chet Ubetcha (talk) 03:10, 23 January 2008 (UTC)
- off-topic remark I have to take exception to Arthur's comment about UCI. I don't know about their philosophy department in general, but in philosophy of math specifically it is extremely strong (that's where Penelope Maddy is), and they have a whole department of "Logic and Philosphy of Science", which I believe is the first of its kind. In math logic, on the other hand, they have Matthew Foreman, so not hurting on that score either. --Trovatore (talk) 03:17, 24 January 2008 (UTC)
Oppose. Metamathematics is not the same as metalogic. Furthermore, metamathematics is different enough (and important in its own right by enough) to warrant its own article in wikipedia. By the way, how many official votes do we need before we can take that merge tag down? — Eric Herboso 09:41, 6 February 2008 (UTC)
Question If the two topics are different enough to warrant distinct articles why is the distinction not made clear?
- Comment Neither article is very long, detailed or clear. They seem to refer to each other, I'd say that the topic is almost circular. I have no doubt that the two subjects are different and that if you had two experts, one from each field, they could tell you how the subjects are related but that they look at different ASPECTS of the theory. I'm a math person myself, and it seems to me that 'metamathematics' is a specific field of study within the larger on context of 'metalogic'. I think that if you want to keep the two articles disjoint then you should probably ADD enough context in both articles to warrant a distinction and disjoint articles; otherwise they should be merged and put into correct context of one another. Jka02 (talk) 15:50, 22 March 2008 (UTC)
