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Metalogic

Metalogic is the metatheory of logic. Whereas logic studies how logical systems can be used to construct valid and sound arguments, metalogic studies the properties of logical systems. Logic concerns the truths that may be derived using a logical system; metalogic concerns the truths that may be derived about the languages and systems that are used to express truths.

The basic objects of metalogical study are formal languages, formal systems, and their interpretations. The study of interpretation of formal systems is the branch of mathematical logic that is known as model theory, and the study of deductive systems is the branch that is known as proof theory.

Formal language
A formal language is an organized set of symbols, the symbols of which precisely define it by shape and place. Such a language therefore can be defined without reference to the meanings of its expressions; it can exist before any interpretation is assigned to it—that is, before it has any meaning. First-order logic is expressed in some formal language. A formal grammar determines which symbols and sets of symbols are formulas in a formal language.

A formal language can be formally defined as a set A of strings (finite sequences) on a fixed alphabet α. Some authors, including Rudolf Carnap, define the language as the ordered pair <α, A>. Carnap also requires that each element of α must occur in at least one string in A.

Formation rules
Formation rules (also called formal grammar) are a precise description of the well-formed formulas of a formal language. They are synonymous with the set of strings over the alphabet of the formal language that constitute well formed formulas. However, it does not describe their semantics (i.e. what they mean).

Formal systems
A formal system (also called a logical calculus, or a logical system) consists of a formal language together with a deductive apparatus (also called a deductive system). The deductive apparatus may consist of a set of transformation rules (also called inference rules) or a set of axioms, or have both. A formal system is used to derive one expression from one or more other expressions.

A formal system can be formally defined as an ordered triple <α,$$\mathcal{I}$$,$$\mathcal{D}$$d>, where $$\mathcal{D}$$d is the relation of direct derivability. This relation is understood in a comprehensive sense such that the primitive sentences of the formal system are taken as directly derivable from the empty set of sentences. Direct derivability is a relation between a sentence and a finite, possibly empty set of sentences. Axioms are so chosen that every first place member of $$\mathcal{D}$$d is a member of $$\mathcal{I}$$ and every second place member is a finite subset of $$\mathcal{I}$$.

A formal system can also be defined with only the relation $$\mathcal{D}$$d. Thereby can be omitted $$\mathcal{I}$$ and α in the definitions of interpreted formal language, and interpreted formal system. However, this method can be more difficult to understand and use.

Formal proofs
A formal proof is a sequence of well-formed formulas of a formal language, the last of which is a theorem of a formal system. The theorem is a syntactic consequence of all the well formed formulae that precede it in the proof system. For a well formed formula to qualify as part of a proof, it must result from applying a rule of the deductive apparatus of some formal system to the previous well formed formulae in the proof sequence.

Interpretations
An interpretation of a formal system is the assignment of meanings to the symbols and truth-values to the sentences of the formal system. The study of interpretations is called Formal semantics. Giving an interpretation is synonymous with constructing a model.

Metalanguage–object language
In metalogic, formal languages are sometimes called object languages. The language used to make statements about an object language is called a metalanguage. This distinction is a key difference between logic and metalogic. While logic deals with proofs in a formal system, expressed in some formal language, metalogic deals with proofs about a formal system which are expressed in a metalanguage about some object language.

Syntax–semantics
In metalogic, 'syntax' has to do with formal languages or formal systems without regard to any interpretation of them, whereas, 'semantics' has to do with interpretations of formal languages. The term 'syntactic' has a slightly wider scope than 'proof-theoretic', since it may be applied to properties of formal languages without any deductive systems, as well as to formal systems. 'Semantic' is synonymous with 'model-theoretic'.

Use–mention
In metalogic, the words 'use' and 'mention', in both their noun and verb forms, take on a technical sense in order to identify an important distinction. The use–mention distinction (sometimes referred to as the words-as-words distinction) is the distinction between using a word (or phrase) and mentioning it. Usually it is indicated that an expression is being mentioned rather than used by enclosing it in quotation marks, printing it in italics, or setting the expression by itself on a line. The enclosing in quotes of an expression gives us the name of an expression, for example:

 * 'Metalogic' is the name of this article.
 * This article is about metalogic.

Type–token
The type-token distinction is a distinction in metalogic, that separates an abstract concept from the objects which are particular instances of the concept. For example, the particular bicycle in your garage is a token of the type of thing known as "The bicycle." Whereas, the bicycle in your garage is in a particular place at a particular time, that is not true of "the bicycle" as used in the sentence: "The bicycle has become more popular recently." This distinction is used to clarify the meaning of symbols of formal languages.

History
Metalogical questions have been asked since the time of Aristotle. However, it was only with the rise of formal languages in the late 19th and early 20th century that investigations into the foundations of logic began to flourish. In 1904, David Hilbert observed that in investigating the foundations of mathematics that logical notions are presupposed, and therefore a simultaneous account of metalogical and metamathematical principles was required. Today, metalogic and metamathematics are largely synonymous with each other, and both have been substantially subsumed by mathematical logic in academia. A possible alternate, less mathematical model may be found in the writings of Charles Sanders Peirce and other semioticians.

Results
Results in metalogic consist of such things as formal proofs demonstrating the consistency, completeness, and decidability of particular formal systems.

Major results in metalogic include:

 * Proof of the uncountability of the power set of the natural numbers (Cantor's theorem 1891)
 * Löwenheim–Skolem theorem (Leopold Löwenheim 1915 and Thoralf Skolem 1919)
 * Proof of the consistency of truth-functional propositional logic (Emil Post 1920)
 * Proof of the semantic completeness of truth-functional propositional logic (Paul Bernays 1918), (Emil Post 1920)
 * Proof of the syntactic completeness of truth-functional propositional logic (Emil Post 1920)
 * Proof of the decidability of truth-functional propositional logic (Emil Post 1920)
 * Proof of the consistency of first-order monadic predicate logic (Leopold Löwenheim 1915)
 * Proof of the semantic completeness of first-order monadic predicate logic (Leopold Löwenheim 1915)
 * Proof of the decidability of first-order monadic predicate logic (Leopold Löwenheim 1915)
 * Proof of the consistency of first-order predicate logic (David Hilbert and Wilhelm Ackermann 1928)
 * Proof of the semantic completeness of first-order predicate logic (Gödel's completeness theorem 1930)
 * Proof of the cut-elimination theorem for the sequent calculus (Gentzen's Hauptsatz 1934)
 * Proof of the undecidability of first-order predicate logic (Church's theorem 1936)
 * Gödel's first incompleteness theorem 1931
 * Gödel's second incompleteness theorem 1931
 * Tarski's undefinability theorem (Gödel and Tarski in the 1930s)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Metalogic


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Tsugaru Strait

The Tsugaru Strait (津軽海峡) is a strait between Honshu and Hokkaido in northern Japan connecting the Sea of Japan with the Pacific Ocean. It was named after the western part of Aomori Prefecture. The Seikan Tunnel passes under it at its narrowest point 12.1 miles (19.5 km) between Tappi Misaki on the Tsugaru Peninsula in Aomori Prefecture, Honshu, and Shirakami Misaki on the Matsumae Peninsula in Hokkaido.

Western maps made prior to the 20th century also referred to this waterway as the Strait of Sangar.

Japan's territorial waters extend to three nautical miles (5.6 km) into the strait instead of the usual twelve, reportedly to allow nuclear-armed United States Navy warships and submarines to transit the strait without violating Japan's prohibition against nuclear weapons in its territory. Despite this, the part of the Tsugaru Strait considered to be in international waters is still within Japan's exclusive economic zone, and the Seikan Tunnel remains entirely under Japanese jurisdiction even though part of it is technically outside Japan's territorial waters.

The Tsugaru Strait has eastern and western necks, both approximately 20 km across with maximum depths of 200 m and 140 m respectively.

There are also ferry services that operate across the strait, including the Tsugaru Kaikyō Ferry and the Seikan ferry.

On September 26, 1954, 1,172 people died when the ferry Tōya Maru sank in the strait.

Thomas Blakiston, an English explorer and naturalist, noticed that animals in Hokkaido were related to northern Asian species, whereas those on Honshu to the south were related to those from southern Asia. The Tsugaru Strait was therefore established as a major zoogeographical boundary, and became known as Blakiston's Line or the "Blakiston Line".

title: Tsugaru Strait


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User:HammerTime

It's = HammerTime = baby!

title: User:HammerTime


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Cantor distribution

The Cantor distribution is the probability distribution whose cumulative distribution function is the Cantor function.

This distribution has neither a probability density function nor a probability mass function, since although its cumulative distribution function is a continuous function, the distribution is not absolutely continuous with respect to Lebesgue measure, nor does it have any point-masses. It is thus neither a discrete nor an absolutely continuous probability distribution, nor is it a mixture of these. Rather it is an example of a singular distribution.

Its cumulative distribution function is continuous everywhere but horizontal almost everywhere, so is sometimes referred to as the Devil's staircase, although that term has a more general meaning.

Characterization
The support of the Cantor distribution is the Cantor set, itself the intersection of the (countably infinitely many) sets:

\begin{align} C_0 = {} & [0,1] \\[8pt] C_1 = {} & [0,1/3]\cup[2/3,1] \\[8pt] C_2 = {} & [0,1/9]\cup[2/9,1/3]\cup[2/3,7/9]\cup[8/9,1] \\[8pt] C_3 = {} & [0,1/27]\cup[2/27,1/9]\cup[2/9,7/27]\cup[8/27,1/3]\cup \\[4pt] {} & [2/3,19/27]\cup[20/27,7/9]\cup[8/9,25/27]\cup[26/27,1] \\[8pt] C_4 = {} & [0,1/81]\cup[2/81,1/27]\cup[2/27,7/81]\cup[8/81,1/9]\cup[2/9,19/81]\cup[20/81,7/27]\cup \\[4pt] & [8/27,25/81]\cup[26/81,1/3]\cup[2/3,55/81]\cup[56/81,19/27]\cup[20/27,61/81]\cup \\[4pt] & [62/81,21/27]\cup[8/9,73/81]\cup[74/81,25/27]\cup[26/27,79/81]\cup[80/81,1] \\[8pt] C_5 = {} & \cdots \end{align} $$

The Cantor distribution is the unique probability distribution for which for any Ct (t ∈ { 0, 1, 2, 3, ... }), the probability of a particular interval in Ct containing the Cantor-distributed random variable is identically 2−t on each one of the 2t intervals.

Moments
It is easy to see by symmetry and being bounded that for a random variable X having this distribution, its expected value E(X) = 1/2, and that all odd central moments of X are 0.

The law of total variance can be used to find the variance var(X), as follows. For the above set C1, let Y = 0 if X ∈ [0,1/3], and 1 if X ∈ [2/3,1]. Then:

\begin{align} \operatorname{var}(X) & = \operatorname{E}(\operatorname{var}(X\mid Y)) + \operatorname{var}(\operatorname{E}(X\mid Y)) \\ & = \frac{1}{9}\operatorname{var}(X) + \operatorname{var} \left\{ \begin{matrix} 1/6 & \mbox{with probability}\ 1/2 \\ 5/6 & \mbox{with probability}\ 1/2 \end{matrix} \right\} \\ & = \frac{1}{9}\operatorname{var}(X) + \frac{1}{9} \end{align} $$

From this we get:

 * $$\operatorname{var}(X)=\frac{1}{8}.$$

A closed-form expression for any even central moment can be found by first obtaining the even cumulants

\kappa_{2n} = \frac{2^{2n-1} (2^{2n}-1) B_{2n}} {n\, (3^{2n}-1)}, \,\! $$

where B2n is the 2nth Bernoulli number, and then expressing the moments as functions of the cumulants.

title: Cantor distribution


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2001 bomb plot in Europe

In 2001, a network of interconnected terrorist cells in France, Belgium, and the Netherlands was uncovered by law enforcement. The network had connections to al-Qaeda and was planning to commit one or more bombings.

Plot
Three cells were involved: one in Rotterdam, one in Brussels, and one in a suburb of Paris. According to Djamel Beghal, Nizar Trabelsi planned to strap a bomb onto himself, cover it up with a business suit, and then detonate the bomb along with himself in the U.S. Embassy in Paris. Concurrently, a van packed with explosives would be detonated outside a U.S. cultural centre at the nearby Place de la Madeleine. Trabelsi denied this, but admitted that he had planned to commit a suicide bombing by detonating a car bomb next to the canteen at Kleine Brogel Air Base in Belgium. Trabelsi also said that he had met Osama bin Laden and personally requested to become a suicide bomber.

Investigation
Beghal was arrested on 28 July 2001 in Dubai as he was attempting to travel back to Europe on a false French passport after visiting an al-Qaeda camp in Afghanistan. During interrogation, Beghal said that there was a plan to attack the U.S. Embassy in Paris and told investigators of terrorist cells in Rotterdam and Paris. He also said that Abu Zubaydah, a close associate of Osama bin Laden, had ordered the attack. After being extradited from the United Arab Emirates to France on 1 October 2001, Beghal retracted his confession, saying that it had been extracted using torture.

Surveillance of a suspected terrorist cell led by Kamel Daoudi in Corbeil-Essonnes near Paris started on 10 September. Following surveillance officers overhearing discussion of destroying evidence, French police moved in and arrested seven men on 21 September. Daoudi was not among the arrested, but he was shortly thereafter arrested in Leicester and extradited from the United Kingdom to France on 29 September 2001.

Dutch police started surveilling the Rotterdam cell in August. The four members of the cell were arrested on 13 September.

Police became aware of a connection between the Rotterdam cell and one led by Trabelsi in Brussels. Trabelsi and a Belgian Moroccan were arrested in two different areas of the Brussels metropolitan area on 13 September in an operation coordinated with the arrests in the Netherlands on the same day. At Trabelsi's apartment, police found machine pistols, chemical formulas for bomb-making, detailed maps of the U.S. embassy in Paris, and a business suit. In a restaurant run by one of Trabelsi's associates, police found materials that could have been used to make a bomb capable of blowing up a building.

Legal proceedings
In December 2002, four men were found not guilty of charges relating to the plot by a Dutch court, citing insufficient and improperly obtained evidence. Two of them, Jérôme Courtailler and Abdelghani Rabia, were convicted in absentia of belonging to a terrorist organization by an appellate court on 21 June 2004, and Courtailler turned himself in on 24 June.

Nizar Trabelsi was sentenced to ten years in prison by a Belgian court on 30 September 2003 for the attempted destruction of public property, illegal arms possession, and membership in a private militia, reflecting Belgium's lack of specific anti-terrorism laws at the time. It was the largest terrorism trial the country had held up to that point; seventeen others were convicted of lesser offences and another five were acquitted. Trabelsi was extradited to the United States in 2013.

Six men were convicted of criminal association in relation with a terrorist enterprise by a French court on 15 March 2005; Djamel Beghal and Kamel Daoudi were sentenced to ten and nine years in prison, respectively, and the other four received sentences ranging from one to six years in prison. Beghal was released in 2010. Daoudi was released from prison in 2008, whereupon he was to be deported to Algeria. However, the European Court of Human Rights blocked the order, and he was instead placed under house arrest.

title: 2001 bomb plot in Europe


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Talk:Aylesbury Vale

Untitled
Apologies to all for the jiggery-pokery, but the area is known as Aylesbury Vale first, Vale of Aylesbury second. Therefore, by whatever naming conventions, Aylesbury Vale should be the main article, Vale of Aylesbury the redirect. Graham :) 01:02, 5 Dec 2003 (UTC)

Ranking lists?
I read about this Admiral Ross, he spent his final years in Aylesbury Vale. As a man of prestige, he could retire where he wanted, and he ended up there. Are there any statistics confirming that A-Vale is a place to live in? --83.108.31.191 (talk) 22:06, 14 June 2011 (UTC)

External links modified
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Name and subject of article
It seems that this article is attempting to describe two different though overlapping areas - one is the Vale of Aylebsury, a physical feature and named as such on Ordnance Survey mapping and secondly the Aylesbury Vale local government unit. There would be merit in teasing these two things apart. cheers Geopersona (talk) 18:57, 5 January 2022 (UTC)

title: Talk:Aylesbury Vale


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User talk:Bc expert

Hello Bc expert,

A very warm welcome to Wikipedia! If you need editing help, visit How does one edit a page or how to format them visit our manual of style. Experiment at Sandbox. If you need pointers on how we title pages visit Naming conventions. You can sign posts on talk pages by entering four tildes. If you have any other questions about the project, check out Help, add a question to the Village pump, or leave a message on my Talk page.

BTW, Nice work on the birth control topics. IMO, we could use a good history of the subject. What do you think?

Enjoy, -- Viajero 01:02, 5 Dec 2003 (UTC)

title: User talk:Bc expert


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Iga Province

Iga Province (伊賀国) was a province of Japan located in what is today part of western Mie Prefecture. Its abbreviated name was Ishū (伊州). Iga is classified as one of the provinces of the Tōkaidō. Under the Engishiki classification system, Iga was ranked as an "inferior country" (下国 gekoku) and a "near country" (近国 kingoku).

Iga was bordered by Ise to the east and south, Ōmi to the north, Yamato to the west and south, and Yamashiro Province to the northwest. It roughly coincides with the modern municipalities of Iga and Nabari in Mie Prefecture as well as Yagyu in Nara Prefecture. Surrounded by mountains, historically, Iga Province was rather inaccessible due to extremely poor road conditions. However, the area is now relatively easy to access from nearby Nara and Kyoto, as well as the larger cities of Osaka and Nagoya.

Asuka period
Iga was separated from Ise Province during the Asuka period, around 680 AD. The provincial capital was located in what is now part of the city of Iga, along with the ruins of the Iga Kokubun-ji. The Ichinomiya of the province is the Aekuni Shrine, which is also located in what is now part of the city of Iga.

Heian, Kamakura and Muromachi periods
Little is known of the subsequent history of the province during the Heian and Kamakura periods. However, by the middle of the Muromachi period, Iga became effectively independent from its nominal feudal rulers and established a confederacy, Iga Sokoku Ikki. During this period, Iga came to be known as a center for ninja activity. This serves that basis of its claim, along with Kōka in what is now Shiga Prefecture, to be one of the birthplaces of the ninja clans and ninjutsu.

In 1581, two years after a failed invasion led by his son, the warlord Oda Nobunaga launched a massive invasion of Iga, attacking from six directions with a force of 40,000 to 60,000 men which effectively destroyed the political power of the ninja (see the Tenshō Iga War).

Tokugawa shogunate
With the establishment of the Tokugawa shogunate, Iga was briefly (1600–1608) under the control of Iga-Ueno Domain, a 200,000-koku han during the rule of Tsutsui Sadatsugu, a former retainer of Toyotomi Hideyoshi. However, the Tsutsui clan was dispossessed in 1608, and the territory of the domain was given to Tōdō Takatora, the daimyō of Tsu Domain. It remained a part of Tsu Domain until the Meiji Restoration.

Edo period
Notable Edo-period people from Iga included the famous samurai Hattori Hanzō and the haiku poet Matsuo Bashō. Iga Ueno Castle was retained by Tsu Domain as a secondary administrative center for the western portion of the domain.

Mie Prefecture
After the abolition of the han system in July 1871, Tsu Domain became "Tsu Prefecture", which later became part of Mie Prefecture.

Historical districts
Iga was divided into 4 Districts (郡), which were further subdivided into 197 villages. The total assessed value of the province in terms of kokudaka was 110,843 koku.
 * Ahai District (阿拝郡) – merged with Yamada District to become Ayama District (阿山郡) on March 29, 1896
 * Iga District (伊賀郡) – merged with Nabari District to become Naga District (名賀郡) on March 29, 1896
 * Nabari District (名張郡) – merged with Iga District to become Naga District on March 29, 1896
 * Yamada District (山田郡) – merged with Ahai District to become Ayama District on March 29, 1896

title: Iga Province


text:
Talk:List of Latter Day Saint movement topics

Purpose of article
Not all of these articles are about mormonism, such as the years. they mention Mormonism.. this article should be renamed (moved). Noldoaran 01:12, Dec 5, 2003 (UTC)

 * perhaps a sub-page or sub-section with a heading: "Articles that Mention Mormonism"? The page has already been re-named since it's inception once, but I think a better name would be "List of Articles that reference Mormonism." Similar pages are in the works for Catholicism and Orthodoxy, etc. Visorstuff 16:32, 5 Dec 2003 (UTC)

Desciptions not requests
I appreciate the work done on this article. However, I have a few pointers to mention that could help prevent it from winding up on Votes for Deletion.

The intro of this article needs to be changed. It should ONLY describe the purpose and lay out of this article. It should NOT make requests of users.

Furthermore, quick work needs to be done refining the list. It is lengthy and unruly. Too many things listed don't belong here. Categories within the article need to be laid out more specifically. Kingturtle 01:13, 5 Dec 2003 (UTC)

 * Sounds good. Feedback is good, and I've only started with the refining of the lists and categories. This has taken a lot of time - perhaps I posted the page prematurely. Visorstuff 16:32, 5 Dec 2003 (UTC)

 * I commend the workers on this article. In a month and a half it has really taken shape. Kingturtle 21:54, 25 Jan 2004 (UTC)

Miscellany Pages
such sub-pages should not be listed in an article. I've placed them here to preserve them. Kingturtle 01:16, 5 Dec 2003 (UTC)

Wikipedia topics
Wikipedia talk:Naming conventions (aircraft), Wikipedia talk:Naming conventions (Mormon), Wikipedia talk:Naming conventions (Mormonism), Arab-Israeli conflict editing project/Pages related to Israel or Palestine, Naming conventions, Naming conventions (common names), Naming conventions (Mormon), Naming conventions (Mormonism), Orphan talk pages, Reference Desk archive 1, Six degrees of Wikipedia, Vandalism in progress, Village pump, Wikipedia commentary/Folklore, Myth, and Religion,

Talk Pages
Talk:Abstract Zionism, Talk:Adamic language, Talk:Book of Mormon, Talk:Christianity and the Church of Jesus Christ of Latter-day Saints, Talk:Church of Jesus Christ of Latter-day Saints (archive), Talk:Creationism/Archive 4, Talk:Evolution/Misc, Talk:God, Talk:God/archive 1, Talk:Hell, Talk:Images of Rachel Corrie, Talk:Jehovah's Witnesses/archive 2, Talk:Linguistics, Talk:Melchizedek Priesthood, Talk:Mormon, Talk:Mormon (Mormon's record), Talk:Mormonism, Talk:Oxymoron, Talk:Polytheism, Talk:Priesthood (LDS)/archive 1, Talk:Saint, Talk:The problem of evil/Archive 1,

Users
User talk:Frecklefoot, User talk:Mkweise, User talk:Netesq, User talk:Peter Chamberlain, User talk:Quintessent, User talk:Rob Hooft/page4, User talk:The Anome, User talk:Zandperl/archive, User talk:Zulugrid, User talk:Zundark, User:Anthere/Soupente, User:BoNoMoJo, User:Daniel Quinlan/redirects6h, User:David Merrill, User:Dori/Queries, User:Eloquence/Watchlist, User:Frecklefoot, User:Hank Ramsey, User:Maveric149, User:Quintessent, User:Stokerm, User:Visorstuff, User:Wik/Articles, User:Zulugrid,

 * I think the lists can be helpful - any other thoughts? I agree with the removal of talk pages and users. Visorstuff 16:32, 5 Dec 2003 (UTC)

-

Page History
Comments on overall feedback thus far: I've spent a considerable amount of time compiling pages that deal with various religious organizations, (Mormonism, Scientology, Catholicism, Orthodoxy, etc., to make it easier for those who have specific interest in these subjects to find and edit them, helping the Wikipedia community as a whole. However, I also don't want this to be controversial, as it is solely a tool since the search feature is pretty flimsy though Google (see Village pump). My academic interests is in religions (more specifically studies in American religion), and I would like to see a better way to track these religions. Maybe I should delete myself and add to a subpage of my own page? However, I'd like the page to stay as it's own. Please let me know what you all think. It's not as easy as it seems to compile such a list. Visorstuff 16:32, 5 Dec 2003 (UTC)~

 * Done with major clean up Visorstuff 00:47, 6 Dec 2003 (UTC)

I made some significant (provisional) changes. In particular, as per its title, I think this article needs to reflect Mormonism in general, and not just the Church of Jesus Christ of Latter-day Saints. Second, I rearranged the outline a bit. The way that articles on Mormonism have been progressing, some parts of the outline have been overfilled, and some of the articles seemed out of place. I'm still not sure the way I arranged things is the best way, but I think it's a little better. Please take a look and see if the new organization makes sense. (No articles have been deleted.) COGDEN 08:39, 23 Dec 2003 (UTC)

Can't add Nibley!
I've tried half a dozen times now and I can't add Hugh Nibley to the list...Wikipedia keeps giving me a "search error"! Can someone else add him, please. —B|Talk 01:46, May 19, 2004 (UTC)
 * Nevermind I finally got it to work.  —B|Talk 04:26, May 19, 2004 (UTC)

Incorporation into the new Wikipedia categorization system
The information on this page should probably be incorporated into the new Wikipedia categorization system. I'm going to try to use a Mormonism categorization system that roughly follows the outline of this page. COGDEN 19:22, 8 Jun 2004 (UTC)

Notable Latter Day Saints Category
I'm very pleased that COGDEN seperated "Notable people in Latter Day Saint history" from "Notable Latter Day Saints". I'll certainly be much less hesitent to add people to this list now.

However, I'd like to get some consensus about what the criteria for being "Notable people in Latter Day Saint history" ought to be. I think that the distinction should be marked on whether their primary contributions were related to the LDS faith or not, not necessarily how significant they were to Mormonism. Thus, Leonard J. Arrington belongs firmly in LDS history while Jewel should be moved even though she and several others on the list are not exactly Mormon. Some cases are more difficult (for example, Mark Hoffman--probably history), but most notable Mormons should be easy to seperate based on this criteria. CHL 22:21, 25 Jul 2004 (UTC)

 * That was what I was thinking as well. People would be in the Category:Notable people in Later Day Saint history if their notability was primarily related to LDS history or their connection to Mormonism, as opposed to people whose primary notability is independent of their connection to Mormonism. COGDEN 18:47, 26 Jul 2004 (UTC)

 * I really don't think Jewel is LDS. She's stated that she and her father used to attend the LDS church (and one can assume he was a member), but stopped attending shortly before she turned eight, when her father was excommunicated (for adultry or fornication, but that is OT).  Since they stopped attending before she turned eight, one can assume she was never baptized and, therefore, not even a formal member.  I think it'd be great if she were LDS, but she's not and certainly doesn't seem to lead an LDS lifestyle.

 * As for who should be on the list, people like Orson Scott Card should be on the list. Even though he would be famous even if he weren't LDS, he is a strong member of the Church and sometimes even an outspoken apologist.  So, even though he is not known because he is Mormon, he is known as being Mormon.  I hope that was clear. :-S   — Frecklefoot | Talk 21:41, Sep 8, 2004 (UTC)

 * My head keeps trying to make this Latter Day Saint Historians - probably because Arrington leads the list. Should we have such a category in this list?  See existing category:  Latter Day Saint Historians. WBardwin 02:59, 15 April 2006 (UTC)

 * Note that Latter Day Saint Historians, and two related categories, are being considered for deletion or renaming. Please express any opinions.   Attention:  Categories up for deletion or movement
 * 5.2.22 Category:Latter Day Saint history to Category:History of Mormonism
 * 5.2.23 Category:Latter Day Saint History Books to Category:History books about Mormonism
 * 5.2.24 Category:Latter Day Saint Historians to Category:Historians of Mormonism
 * Thanks. WBardwin 10:14, 18 April 2006 (UTC)

Relief Society Presidents
I'm slowly working on articles for each of the LDS Relief Society Presidents. Would a category by that name be appropriate or should they go into "Leaders?" WBardwin 23:00, 7 November 2005 (UTC)

 * I personally would suggest leaders. -Visorstuff 00:15, 8 November 2005 (UTC)

 * will do. WBardwin 07:10, 9 November 2005 (UTC)

Alphabetizing Names and Topics
I started alphabetizing the leaders section/creating two subsections in each group. Do you think this is worthwhile? Placing entries in "order" should make it easier to find items/names and might make it easier for new articles to be inserted. WBardwin 07:10, 9 November 2005 (UTC)

 * I think alphabetizing is a useful action.--andersonpd 17:41, 9 November 2005 (UTC)

Name Tag
It's hard to rename a list. In light of the self-reference tag, how about ---
 * List of topics about Mormonism
 * List of Mormon related topics
 * Mormon subjects by category
 * Mormon topics by category
 * Index of topics about Mormonism
 * Resource index about Mormonism

or should we move the page into the LDS project pages and keep the present name? WBardwin 00:47, 12 November 2005 (UTC)

I don't see where the self-reference is. The Jade Knight 23:30, 26 December 2005 (UTC)

Cleanup - please adopt the Root page concept
The Root page concept is now taking shape with forward and backward linking. Properly used it would reduce this page to just ten or twenty branch links, each themselves root pages for a further ten or twenty branches. This eliminates the need for complete listing, and facilitates easy navigation backwards or forwards. --Lindosland 18:41, 27 February 2006 (UTC)

New Joseph Smith articles
What would be the appropriate placement for the new sub-articles on Joseph Smith, Jr.? Under his name, under Presidents of the Church, or should we have a new subcategory Origins of the Latter Day Saint Movement? Ideas? WBardwin 02:56, 15 April 2006 (UTC)

post-mortem baptisms
There's long been talk of a ritual of the Mormons in which the dead are 'converted' to Mormonism. It's reputed to be one of the reasons for their genealogical works. From what I've heard, it's got somethign to do with 'sealing them to the church'. Where's the relevant article on it? thanks. ThuranX 06:24, 25 November 2006 (UTC)

 * Check out Baptism for the dead. :) -Porlob 18:18, 25 November 2006 (UTC)

Why does this article exist?
Shouldn't this be a category? Bytebear 19:44, 10 January 2007 (UTC)
 * Actually, I think it would be better as being added to the WikiProject Latter Day Saint movement/Articles page, as that also would allow people to use it to monitor recent changes. I am in the process of adding the most narrow-range banner to all sorts of religion articles, including LDS (though not in the past few days), and will eventually (I hope) have all the articles mentioned on that list. But, right now, there are a couple of projects which don't have as clearly defined a scope, at least in terms of categories, and I'm working on them now, so as to know get the narrowest-scope, most directly relevant, banner on all the religion pages. Badbilltucker 19:52, 10 January 2007 (UTC)

 * This was the front-runner of the current project, and I have to admit a bit of a pet project that took a lot of my time in creating and gathering the articles. It contains (or should contain) a list of all LDS/Mormonism categories. It has been highlighted as a decent list for navigation, and was one of the main examples in the ill-fated root page project for navigation. It is still a great example of navigation on wikipedia and I disagree with it being moved for many reasons, but will accept a consensus if that's what it comes down to.

 * I can agree that it could be a sub-page of the project, however, I do not like the sub-page strategy (nor do many others), and at one time early in the project, nearly all sub-pages were destroyed - certainly sought out and re-directed if possible, aside from user sub pages. Now they are on the rise again, and I think they'll meet the same fate again. I think the loss of this content would be a great loss to those of us in the project who use it regularly. Rather we should have the sub-page redirect here, rather than having this be a sub-page. Make sense? In any case, it is listed on the WP:LDS project page. Hope this helps give context. -Visorstuff 20:43, 10 January 2007 (UTC)

 * PS: this is a list not an "article," which are quite standard on Wikipedia to exist. -Visorstuff 20:43, 10 January 2007 (UTC)

Tree of Life
I was editing the First Book of Nephi and noticed that there is no article about Lehi's dream of the Tree of Life. Or am I just missing it? Val42 03:32, 3 February 2007 (UTC)

Avoid self references
This page does not belong in article space as it is. It should either be stripped of its self-references (ie, name it "List of LDS topics", remove references to "Wikipedia" and "articles") or it should be moved to WP: space. --B (talk) 04:31, 9 January 2008 (UTC)

 * Self-references were removed. -- œ ™ 05:58, 13 July 2010 (UTC)


text:
Copying

Copying is the duplication of information or an artifact based on an instance of that information or artifact, and not using the process that originally generated it. With analog forms of information, copying is only possible to a limited degree of accuracy, which depends on the quality of the equipment used and the skill of the operator. There is some inevitable generation loss, deterioration and accumulation of "noise" (random small changes) from original to copy when copies are made. This deterioration accumulates with each generation. With digital forms of information, copying is perfect. Copy and paste is frequently used by a computer user when they select and copy an area of text or content.

In art
In visual art, copying the works of the masters is a standard way that students learn to paint and sculpt. Often, artists will use the term after to credit the original artist in the title of the copy (regardless of how similar the two works appear) such as in Vincent van Gogh's "First Steps (after Millet)" and Pablo Picasso's "Luncheon on the Grass, after Manet" (based on Manet's well-known work). In sculpture, copies have often been made using devices such as the pointing machine, the pantograph or, more recently, computer guided router systems that scan a model and can produce it in a variety of materials and in any desired size. Another way of copying three-dimensional works is by lost-wax casting and other forms of molding and casting.

In literature
Prior to the invention of the printing press, the only way to obtain a copy of a book was to copy it out by hand (see scrivener). Throughout the Middle Ages, monks copied entire texts as a way of disseminating and preserving literary, philosophical and religious texts.

In office work
Offices need more than one copy of a document in a number of situations. They usually need a copy of outgoing correspondence for their records. Sometimes they want to circulate copies of documents they create to several interested parties.

Until the late 18th century, if an office wanted to keep a copy of an outgoing letter, a clerk had to write out the copy by hand. This technology continued to be prevalent through most of the 19th century. For these purposes, offices employed copy clerks, also known as copyists, scribes, and scriveners.

A few alternatives to hand copying were invented between the mid-17th century and the late 18th century, but none had a significant impact on offices. In 1780 James Watt obtained a patent for letter copying presses, which James Watt & Co. produced beginning in that year. Letter copying presses were used by the early 1780s by people like Benjamin Franklin, George Washington, and Thomas Jefferson. In 1785, Jefferson was using both stationary and portable presses made by James Watt & Co.

During the 19th century, a host of competing technologies were introduced to meet office copying needs. The technologies that were most commonly used in 1895 are identified in an 1895 description of the New York Business College's course program: "All important letters or documents are copied in a letter-book or carbon copies [are] made, and instruction is also given in the use of the mimeograph and other labor-saving office devices."

Biological copying
Organically, copying of genetic information can take place using DNA replication, which is able to copy and replicate the data with a high degree of accuracy, but mistakes are common, and occur in the form of mutations. However, in the process of DNA repair, many of the mistakes are corrected by checking the copied data against the original data.

Digital copying
The same principle is applied digitally, in devices such as in hard disks, but in a different form. The magnetised data on the disk consists of 1s and 0s. Unlike DNA, it only has two types of information, rather than four types, however, it still has a polar concept of transfer. In this case, the read-write head acts as an intermediary. A data section reading "1", can only trigger one type of response, and "0" for the other. These responses from reading are converted into an electrical form that gets carried through the circuits. Although this can be later converted and processed for other ways of using the data, which can be modified, if a file was being copied from one hard disk to another, the principle ensures that the data is transferred with high fidelity, because only each type of signal can only trigger one type of data write, in this case, a 1 or a 0. This excludes exceptions where the data was written incorrectly or the existing data has been corrupted while on the disk such that no distinction can be made, but usually the hard disk returns the area as unreadable. The other concept that using digital copying is website copy, digital copying has more interpretation than just the basic concept of disk read and write itself. Digital Copy is a sample of interpretation of digital copying.

Copying rights
The concept of copying has a particular significance in certain areas of law. In each of the primary areas of intellectual property law, a number of cases have refined the question of what exactly constitutes the kind of copying prohibited by law, especially in areas such as copyright law.

A related concept is plagiarism, copying others' work and passing it off as one's own. Many schools will take plagiarism to academic suspension, or even the failure of a course.

title: Copying


text:
Cutting

Cutting is the separation or opening of a physical object, into two or more portions, through the application of an acutely directed force.

Implements commonly used for cutting are the knife and saw, or in medicine and science the scalpel and microtome. However, any sufficiently sharp object is capable of cutting if it has a hardness sufficiently larger than the object being cut, and if it is applied with sufficient force. Even liquids can be used to cut things when applied with sufficient force (see water jet cutter).

Cutting is a compressive and shearing phenomenon, and occurs only when the total stress generated by the cutting implement exceeds the ultimate strength of the material of the object being cut. The simplest applicable equation is:

$$\text{stress} = {\text{force} \over \text{area}}$$  or   $$\tau=\frac{F}{A}$$

The stress generated by a cutting implement is directly proportional to the force with which it is applied, and inversely proportional to the area of contact. Hence, the smaller the area (i.e., the sharper the cutting implement), the less force is needed to cut something. It is generally seen that cutting edges are thinner for cutting soft materials and thicker for harder materials. This progression is seen from kitchen knife, to cleaver, to axe, and is a balance between the easy cutting action of a thin blade vs strength and edge durability of a thicker blade.

Metal cutting
Cutting has been at the core of manufacturing throughout history. For metals many methods are used and can be grouped by the physical phenomenon used. It is the process of producing a work piece by removing unwanted material from a block of metal, in the form of chips.
 * Chip forming (material removal processes) – sawing, drilling, milling, turning etc.
 * Shearing – punching, stamping, scissoring, blanking
 * Abrasive material removal – grinding, lapping, polishing, water-jet
 * Heat – flame cutting, plasma cutting, laser cutting
 * Electrochemical – etching, electrical discharge machining (EDM), electrochemical machining (ECM)

Every method has its limitations in accuracy, cost, and effect on the material. For example, heat may damage the quality of heat treated alloys, and laser cutting is less suitable for highly reflective materials such as aluminum. Laser cutting sheet metal produces flat parts and etches and engraves parts from complex or simple designs. It is used over other cutting options for its quick process and customizable abilities.

title: Cutting