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Bludenz

Bludenz (Alemannic: Bludaz) is a town in the westernmost Austrian state of Vorarlberg with around 15.000 inhabitants. It is the administrative seat of the Bludenz District, which encompasses about half of Vorarlberg's territory.

Geography
The town is located on the Ill River, a direct tributary of the Rhine. It is surrounded by the ranges of the Bregenz Forest Mountains in the north, and by the Rätikon and Silvretta ranges in the south. Bludenz lies at the meeting point of five valleys: Walgau and Montafon (Ill), Brandnertal, Klostertal up to Arlberg Pass, and Großes Walsertal.

Bludenz is a popular starting point for hiking and mountain-biking in spring, summer, and autumn. It is located not far from many skiing resorts (e.g., Brand and Lech ).

Major companies are Mondelēz International (Milka chocolate) and the Fohrenburg brewery which was established in 1881.

History
Archaeological finds indicate that settlement in the area of Bludenz began in the Bronze Age, and continued throughout the La Tène era.

Bludenz itself was first mentioned in the year 830 CE in an urbarium of the Raetian estates within the Carolingian Empire. The town was established by the comital Werdenberg dynasty; town privileges were granted in 1274. A stay by the Habsburg Duke Frederick IV of Austria, who had just received an imperial ban at the Council of Constance, is documented from 30 March 1416. Four years later, Bludenz passed into the Further Austrian possessions of the Habsburg dynasty.

The Bludenz district headquarters are situated in the Castle of Gayenhofen, built in the 18th century.

Education
High schools in Blundenz include Bundesgymnasium und Bundesrealgymnasium Bludenz.

Culture
The Alpinale Short Film Festival was founded in 1985 in Bludenz. In August, around 40 international short films are shown to a crowd of 1,000 visitors. Related events are the Alpinale Ländle Tour, the Vorarlberger Short Film Night, and the Horror Short Film Night in autumn. The festival has taken place in Bludenz from 1985 to 2002, and from 2020 onwards. Between 2003 and 2019, it was held in Nenzing.

The Brewery Museum Fohrenburg displays the development of the Fohrenburg brewery and beer brewing in Bludenz in general. Historical photographs, old beer bottles and labels, earlier advertising motifs and equipment for beer production allow a look back at more than 130 years of Fohrenburg's brewing history. The Bludenzer Tage zeitgemäßer Musik is an international contemporary music festival annually held in autumn/winter. It was founded by Hans Peter Frick, later artistic directors were Georg Friedrich Haas, Wolfram Schurig and Alexander Moosbrugger and the young Italian composer, Clara Iannotta, who been responsible for the programme since 2014. Over the years, more than 100 world premieres have been performed in Bludenz.

Notable people

 * Bertram Batlogg (born 1950), an Austrian physicist, researches high-temperature superconductivity
 * Herbert Willi (born 1956), an Austrian composer of classical music
 * Robert Rollinger (born 1964), an ancient historian and Assyriologist, worked on Herodotus
 * Markus Wallner (born 1967), an Austrian politician (ÖVP) and governor of Vorarlberg.

Sport

 * Dietmar Berchtold (born 1974), an Austrian football midfielder, played over 370 games
 * Dursun Karatay (born 1984), an Austrian football player who has played over 250 games
 * Johannes Strolz (born 1992), alpine ski racer, won two gold and one silver medal at the 2022 Winter Olympics
 * Seifedin Chabbi (born 1993), an Austrian footballer who has played over 260 games
 * Marco Stark (born 1993), an Austrian former footballer who played over 290 games

title: Bludenz


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Vito Antuofermo

Vito Antuofermo (born February 9, 1953) is an Italian American actor and retired professional boxer. He is a former undisputed World Middleweight Champion.

Background
Antuofermo was born in Italy, in the town of Palo del Colle, about 15 km inland from the city of Bari. His family moved to the United States when he was 17 years old. Antuofermo learned how to fight in the tough areas of New York City. By his teens, he had made up his mind that he wanted to be a professional boxer.

He has lived in Howard Beach, Queens.

Amateur career
Antuofermo won the 1970 147 lb New York Golden Gloves Championship, defeating Thomas Chestnut in the finals. In 1971, Antuofermo was defeated by future Light Heavyweight Champion Eddie Gregory in the finals of the 147 lb Open division. Antuofermo trained at the Police Athletic Leagues Sweeney Center in Brooklyn, New York.

Professional career
Antuofermo had a propensity to cut easily, especially around the eyebrows. In between rounds in his fights, as much attention (if not more) was given to Vito patching up cuts on his face as it was giving him advice and instructions.

In 1979, Antuofermo became World Middleweight Champion by beating defending champion Hugo Corro by a decision in 15 rounds at Monte Carlo. According to an article in The Ring, Howard Cosell, who was working on that fight's live broadcast to the US, was telling viewers that Corro was, in his opinion, way ahead on the judges' cards. When someone on the American television crew found out it was Antuofermo who was actually leading on the cards, Cosell then began to say he had Antuofermo ahead. All three judges' scorecards were very close, each showing a tight, one-point margin: 143–142, 146–145 in Antuofermo's favor, and 146–145 in Corro's favor.

On the morning after winning the title, Antuofermo and his crew were driving to a small vacation in Italy, when he saw a car fly off a bridge under which they were passing. The car landed right in front of him, but luckily the accident did not injure any occupants in Antuofermo's car. He was so shocked that he kept driving and never found out what happened to the occupants of that car. He came back to his senses about 20 minutes later.

On November 30, 1979, Antuofermo defended his title against Marvelous Marvin Hagler in Las Vegas, Nevada, the fight resulting in a controversial 15-round draw. Judge Duane Ford scored the bout in Hagler's favor, 145–141. Judge Dalby Shirley scored it for Antuofermo, 144–142. Judge Hal Miller had it even at 143–143. The draw enabled Antuofermo to retain his title. In his next defense, against Alan Minter, also in Las Vegas, he lost the title by a 15-round split decision. The bout featured a wild disparity in scoring with a Venezuelan judge scoring the fight for Antuofermo while a British judge had Minter winning 13 of the 15 rounds. They had a rematch in London on June 28, 1980. Minter retained the crown by a TKO (on cuts) in eight rounds.

Antuofermo kept fighting and winning and, after Hagler won the title from Minter in 1980, Antuofermo was given another chance to regain the World Middleweight Championship. In front of an HBO Boxing audience and a full house at Hagler's native Boston's Boston Garden, Antuofermo this time lost by a TKO on cuts in the fourth round.

After several attempts at becoming a top middleweight again, Antuofermo retired from boxing in 1985.

Apart from Corro, other boxers he beat included world champions Eckhard Dagge, Denny Moyer and Emile Griffith.

In 1992, Michael Franzese, a Caporegime of the Colombo crime family, testified that Antoufermo had been under the control of mobsters including Andy Russo. Franzese stated that the outcome of many of Antuofermo's fights was pre-determined so that organized crime figures could safely bet, but that the fights with Marvelous Marvin Hagler were not fixed.

Life after boxing
After retirement, Antuofermo began to pursue an acting career. In 1990, he landed a small role in The Godfather Part III as the chief bodyguard of gangster Joey Zasa. He has landed several small speaking roles in movies and television shows since, including the critically acclaimed television show The Sopranos as a mobster. He has also done many theater plays.

Antuofermo also made television commercials for Old Spice deodorant.

Antuofermo's record reads 50 wins, 7 losses and 2 draws, with 21 wins by knockout. Vito Antuofermo's second oldest son, Pasquale Antuofermo, boxed as an amateur, but never turned pro. He now owns a successful landscaping company that operates in Long Island, New York.

Filmography

 * 1990: Goodfellas – Prizefighter
 * 1990: The Godfather Part III – Anthony 'The Ant' Squigliaro
 * 1991: Loser – Homeless Man
 * 1993: New York Undercover – Jimmy
 * 1996: The Mouse – Trainer
 * 1998: Hell's Kitchen – Boyle's Thug
 * 1999: La bomba – Pippo Messina
 * 2000: The Boys Behind the Desk

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

title: Vito Antuofermo


text:
Talk:1983 in music

Correct Year for "She's So Unusual
She's So Unusual - Cyndi Lauper - listed here as 1983, but in its own entry as 1981. Which is right? Nevilley 08:37 Jan 10, 2003 (UTC)
 * Apparently, 1984 in music is correct. I'll fix them both. Tuf-Kat
 * Thanks. Nevilley 08:03 Feb 19, 2003 (UTC)

Cocteau Twins?
Seems a bit POV and original research to claim that particular Cocteau Twins album is the most influential thing in 1983. Admittedly I am not yet a Cocteau fan but I read all sorts of indie music sites, I am well aware of their importance, I know people who like them and I have NEVER heard such a major claim made before. The Cocteau Twins' influence has also been probably just as much on the new age genre as on rock.

1983 a Good Year
1983 was a pretty damn good year for pop music (Synchronicity!) but still not a patch on 80-82 overall. the most mainstream stuff from 80-82 really sucked though except Michael Jackson and Duran Duran and Soft Cell and synth-bands like that, whereas the pop hits were slightly more decent in 83. The rest of the '80s until 1989 are pretty much horrible for mainstream pop hits because the original coolness of the synth pop sound wore off and got tired and compromised with horrible bands who didn't know how to use it. With the exception of U2, virtually all the chart toppers from 84-88 are awful, but that period is also more brilliant and influential than any other period for alternative stuff. whatever.

Disambiguation link repair
Just did a disambiguation link repair for the name Grandmaster:

 * 1) "White Lines (Don't Don't Do It)" - Grandmaster and Melle Mel

from the "Top hits on record" section. I changed the link from Grandmaster to Grandmaster Flash. I'm not sure if this is correct, though... If anyone know, please change it to the correct location. --Christie 14:45, 21 February 2006 (UTC)

Page Needs Help
Compared to other "year in music" pages, this one is pretty sad. I tried to do what I could with my limited time, but if someone could bring this page up to snuff in terms of format (timeline and all), that would be great. Moonroe

title: Talk:1983 in music


text:
Talk:Mind uploading

Wiki Education Foundation-supported course assignment
This article was the subject of a Wiki Education Foundation-supported course assignment, between 25 January 2021 and 16 May 2021. Further details are available on the course page. Student editor(s): Nhugnu.

Above undated message substituted from Template:Dashboard.wikiedu.org assignment by PrimeBOT (talk) 04:13, 17 January 2022 (UTC)

Pop-culture
Is a section specifically discussing the topic in popular culture and/or media suitable or appropriate for inclusion in this article? -- dsprc   [talk]  20:36, 2 June 2016 (UTC)

 * Well there already is Mind uploading in fiction so I'm not sure what that section would feature? (Note that if "Mind uploading in fiction" isn't large enough in scope it could be moved to "Mind uploading in popular culture".) --Fixuture (talk) 22:11, 2 June 2016 (UTC)

Speedup
In the section "Speedup" it is stated that in the future, transistors will have reached sub-atomic size. It is impossible for a transistor to be sub-atomic. The effects of an electron moving from one type of atom to another is what make transistors and other semiconductor components work. 71.29.14.207 (talk) 11:01, 2 September 2016 (UTC)

 * I've cut the entire section as blatant OR. Subatomic transistors, what on earth ... - David Gerard (talk) 13:56, 2 September 2016 (UTC)

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The problem of immortality
Should this section be removed? There are no citations and is an opinion yet frames that opinion using factual terminology.

It also contradictes the overview section's sources re: a mind follows biological laws and does not arise from some magical or otherworldly quality.

I'm unsure how to proceed as I personally disagree with the opinion and 'two wrongs don't make a right'.

Paul (talk) 02:46, 10 December 2017 (UTC)

 * yes. moved here, below Jytdog (talk) 03:28, 10 December 2017 (UTC)

Cyborg Immortality
A more realistic possibility but far from fiction would be the use of cyborg brains that help and learn from the biological brain, its function is to preserve the brain's memories and other mental information, however the cyborg brain would always be dependent on a new biological brain, to 'visualize' your content, it is not a file container but a brain that, when connecting with the person, becomes part of them, a single mind, but it would be the most realistic conception of mind upload, and when better the fidelity of the brain cyborg with a real brain, better the preservation of the mind, however its objective is to preserve the memory and feeling of continuity is not the same person, the new 'user' could still refuse or accept something, but now learning from the inside point of view.

There is no very realistic reference to this idea, it is 100% invasive to the point of opening the brain and placing a 3rd part completely connected to the volunteer, but in a vague way this concept of immortality is addressed in the series Altered Carbon (TV series) and Avatar (2009 film), however, the connection between the mind and the computer is still very distant and we are unable to transmit and receive thoughts directly from the computer to produce essential technologies in this concept such as Deep_Oniric_Reality referring to the machine from the film Inception 2010 (video game dream), a connected Cyborg_Brain, reference Positronic brain and Bicentennial Man (film), remotely with a Cyborg-Telepresent, reference Surrogates, and needless to say more studies on the biological brain.

The upload would not be instantaneous or in a few hours, having an interface with maximum connection, 10k neurons is basic, and maximum time (to replicated learning) would be ideal, Between 200 and 10 thousand years based on current R&D pace and research focused on this methodology and double experts could reduce the estimate to around 20 to 100 years, expert as in general, Biomedical engineering and Neuroscience, and several necessary subspecializations such as Computer engineering, Computer science, Neuromorphic engineering, neurocomputing, cyborg Mechatronics, etc..., a premature technology of this type could be the size of entire buildings, as these years pass, the technology can be updated to smaller, more resistant versions, in a cyborg-brain cloud and more resistant to the destruction of bodies.

current technology still looks like a calculator from the stone age trying to trap consciousness in a gear, we still haven't learned how to make 3d circuits, they are printed like a sheet, I'm not that expert to define the criteria but when at least we get a technology that can moving consciousness from a real brain to a computer dream Black Museum (Black Mirror) before that is just an improved memory store, that is if the philosopher doesn't worry that there is no real immortality just how much information is preserved, then the displacement of consciousness would just be a gentler, more continuous tranzition; More realistic than that, one must seek biological immortality for longevity, but this results will take longer than the computerized one and only for the person to have a more comfortable old age, and believe me, the pain will only accumulate, and extend a century's life, but health and Longevity would be your true body, these needs are maintained in a cyborg brain, the difference is that there is a legacy, but it is no different from leaving a book or film, but it is a clone of you, but works that address another side of the philosophical issue are The 6th Day and Soma (video game) from the point of view of copying.

I did not insert it in the main article as it is more of an insight question than a reference to ongoing research. — Preceding unsigned comment added by 177.101.40.143 (talk) 18:26, 28 March 2024 (UTC)

unsourced section on immortality
moved here per WP:PRESERVE. Though, in theory, an uploaded, or copied version of an individual's brain would have the same memory and personality, the use of this process for eternal life (see Immortality) is in theory impossible for the simple reason that one would not be prolonging one's life, but simply creating another with the same experience. The creator, or original would feel no difference, and would still die of natural cause. In fact, the idea of mind uploading is likeable to cloning, and in the same way as a clone, the "copied" mind would not be the same as the origin, just a copy.
 * The problem of immortality

-- Jytdog (talk) 03:28, 10 December 2017 (UTC)

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New sensors and 22Na/40K enhancement
Hi, did some research and using both sodium-22 and potassium-40 it may be possible to image the actual neural firing patterns. In this case standard APD arrays (SiPM) would be utilized and this can be tested on a small scale with conventional sensors. The tricky part would be to calibrate each sensor so they are optimized for annihilation gamma rays eg 460-570keV.

I invented a way to actually concentrate potassium-40 which is the subject of a patent search. — Preceding unsigned comment added by 185.3.100.9 (talk) 08:06, 15 March 2019 (UTC)

Article title
I think that whole brain emulation is more generic than mind uploading (for example, I could in principle imagine an emulated brain which is "grown" from a "seed", similar as the human brain, but which isn't initialized by an uploaded copy of an actually existing human brain). Thus, it seems inaccurate that WBE is redirected to MU. If there is a redirection, then it should be the other way round. Any thoughts on this? Notyetborn (talk) 16:58, 4 December 2020 (UTC)
 * As far as I know, all the sources on WBE are about "scanning" an existing brain and emulating it in a computer. Growing a generally intelligent mind in a computer just regular AI. Titles are decided by WP:COMMONNAME, which "mind uploading" appears to be. Crossroads -talk- 20:09, 4 December 2020 (UTC)
 * Thanks for this! OK, let's stick to the community concensus. :-) Notyetborn (talk) 13:25, 11 December 2020 (UTC)

Updated?
Is the article updated to cover recent developments or progress towards mind uploading? CoffeeEnergy (talk) 11:18, 13 July 2022 (UTC)

Possibly useful article mentioning practical difficulties

This article is by a neuroscientist and assistant professor of biology, and could be useful as a source regarding practical difficulties that might keep the technology from ever coming to pass. Crossroads -talk- 00:52, 2 February 2023 (UTC)

Outdated section?
The section "Political and economic implications" does not look so relevant anymore. Even if mind uploading already existed, it likely wouldn't be competitive with large multimodal models, that require much less compute and are already around human-level in many tasks. As it turns out, mind uploading is unlikely to really play a role in the economy. I propose to remove the section. Alenoach (talk) 17:48, 2 June 2024 (UTC)

 * @Alenoach The first paragraph has a speculative tone that could be improved, but I don't agree with your case for removal. The paragraph apparently mentions possibilities identified by two journal articles.  Are you aware of comparable new sources dismissing them because of LLMs? WeyerStudentOfAgrippa (talk) 18:39, 2 June 2024 (UTC)
 * What I think is most outdated is the aspect on the economy. Nowadays, mind uploading is rarely mentioned in the context of AGI. The political aspect can actually be still relevant though, so the section can arguably be kept. The 2022 source was added to support the idea that mind uploading could lead to more "inequalities and power struggles", not as a sign that it would "be preceded by a technological arms race driven by first-strike advantages". The book The Age of Em seems to talk about an economy of mind uploads, but it predates large language models. But if you think it's good to keep it, I won't insist. Alenoach (talk) 19:15, 2 June 2024 (UTC)

title: Talk:Mind uploading


text:
Talk:Proof by contradiction

Please help add sources
This is a decent article, though it is lacks any source.. Luckily, there seem to be several good web sites which can be cited for the majority of this article's content. Here's what a quick google search yielded:, , Jellocube27 20:25, 11 March 2007 (UTC)
 * Hello User:Jellocube; I have just added the IEP link, thanks. — Gamall Wednesday Ida (t · c) 16:52, 19 December 2016 (UTC)

Use of tilda (~) for logical NOT
Is the tilda symbol ~ in common use to mean logical NOT? I have never seen its usage before. I am more familiar with ¬, if others agree then I think it should be changed.

The ¬ symbol is used later on in the article, so either ~ or ¬ should be used throughout (not both) for consistency.Bah23 12:51, 5 March 2007 (UTC)

 * It is extremely common. It was introduced by Giuseppe Peano, and is widely used, for example in Principia Mathematica.  I agree with you that the usage in the article should be consistent. -- Dominus 16:48, 5 March 2007 (UTC)

One will also find ` and ! through the literature, as well as the bar.
 * I have replaced all instances of ~ by $$\lnot$$, which seems to me to be the standard symbol. cf Negation. I work in CS fields related to logic (though I'm not a logician), and I cannot recall having seen ~ in a paper. (Though it would still be clear enough in context that I may have seen it and not been shocked enough to commit such instances to memory.)  — Gamall Wednesday Ida (t · c) 17:05, 19 December 2016 (UTC)

contraposition
I notice that there is a detailed discussion of contraposition in one of the comments above, but none of it seems to have made it into the article Reductio ad absurdum itself. It may be helpful to have a simple-minded comparison of the two as part of the article. Also, if anybody cares to explain the difference between "proof by contradiction" and ''law of excluded middle", I would be much obliged. Katzmik (talk) 12:43, 26 October 2008 (UTC)
 * Hello Katzmik; I have just added a paragraph Proof by contradiction. Is it helpful? — Gamall Wednesday Ida (t · c) 19:46, 19 December 2016 (UTC)

Is it really contradiction?
I just made a minor edit to make statement names consistent. In the main part of the article, P was the name of the statement to be proven, and Q was the name of the statement that was contradicted to prove P. The section "Relationship with other proof techniques" in one place used both the name Q, and the compound statement "If P, then Q" as the statement to be proven. I changed the former to P, and the latter to "If A, then B" to show that A and B were components of P, not the P and Q in the main part.

And that distinction is related to what I think is a common misapplication; that is, confusing elements of the proof method, with elements of the statement to be proven. And it points to a problem with many claimed proofs-by-contradiction in general. The section describes how you can prove P="If A, then B" by proving the contrapositive "If ~B, then ~A". But that is not the only form of a proof that uses contraposition.

The section "Principle" lists two forms of proof by contradiction, but many claimed examples I've seen fit neither. They (1) assume that P is false, (2) show that a statement ~Q follows from ~P where (3) Q is a known truth that is independent of P. In a proof by contradiction, both Q and ~Q have to follow from ~Q.

In the Pythagorean example of proof by contradiction, the claimed contradiction is "a^2+b^2=c^2, then a+b>c. Since we know that a^2+b^2=c^2, we can conclude that a+b>c.

And not only is Cantor's proof not a proof by contradiction, he never claimed it was one. JeffJor (talk) 22:16, 9 January 2018 (UTC)

Is it really contradiction? PART II
For the section "No least positive rational number", the proof is technically not a contradiction. In fact the statement itself is negative, so assuming its affirmation is just regular constructive practice. — Preceding unsigned comment added by Matteo.Ferrari95 (talk • contribs) 08:28, 6 May 2019 (UTC)

 * You're right in raising this issue. It's important!   This issue - the difference between proof by contradiction and refutation by contradiction - has been dealt with now.   John Baez (talk) 10:51, 3 October 2022 (UTC)

Is it really contradiction? PART III (NO! well, ok, yes, but very artificially)
"No least positive rational number" is technically a proof by contradiction as it is stated, but only artificially. Let me elaborate. Denote by R the claim that there is a smallest positive rational number. Then we wish to prove ~R. For that, we assume R (!). By double-negation (which as it happens is the logical axiom used in proofs-by-contradiction) this implies R. Then we derive False as in the article. Thus R is false, so R is false.

In fact, the proof that sqrt(2) is irrational is just as bad, because the property of being irrational is a negative property (not rational).

The hypotenuse example, though not as bad, is also not great because again one can quite easily avoid using proof-by-contradiction. In this case, once could directly use the trichotomy property, and have a+bc, and derive a+b>c by cases - in the first two cases, one could derive false as explained in the example; and in the third derive a+b>c trivially.

This is really quite amazing. Better examples should be provided, preferably one that cannot be proven constructively, and one that can but where it is considerably more difficult. It might be educational to keep some of the current examples and explain why they are artificial (better than I did just now), but in an appropriate section dedicated to that objective. TheFountainOfLamneth (talk) 14:11, 19 June 2019 (UTC)

 * This is really quite amazing.
 * Yes, most of the supposed proofs by contradiction in this article were really not examples of that technique. I think the article is better now.  John Baez (talk) 10:54, 3 October 2022 (UTC)

Necessity of law of excluded middle is not shown
In the section 'law of excluded middle' https://en.wikipedia.org/wiki/Proof_by_contradiction#Law_of_the_excluded_middle, the claim is made that a proof by contradiction requires the law of excluded middle. This isn't shown nor referenced, and I couldn't find a statement resulting to this claim on the page Law of excluded middle either ShearedLizard (talk) 17:19, 20 February 2018 (UTC) Although it is shown how the law of excluded middle is used, it necessity is not shown. I suppose this has been proven by someone? ShearedLizard (talk) 17:21, 20 February 2018 (UTC)

Some proofs that people often *call* "proofs by contradiction" - including some examples on this page - are in fact "refutations by contradiction", and those do not require the law of excluded middle. This issue has been dealt with now. John Baez (talk) 10:49, 3 October 2022 (UTC)

Same as other article
isn't this the same as the article reductio ad absurdum? Yelly314 (talk) 18:56, 1 June 2020 (UTC)

I mean, like, it's not actually the same content, but it means the same thing? 18:57, 1 June 2020 (UTC) — Preceding unsigned comment added by Yelly314 (talk • contribs)

 * Seems like it. There may be a case for making a distinction, but usage overlaps sufficiently that the two topics should be merged. Paradoctor (talk) 19:20, 1 June 2020 (UTC)
 * Oh me oh my.
 * Talk:Proof by contradiction/Archive 1 (2010)
 * Talk:Reductio ad absurdum (2017)
 * Slightly less sure about the merge now. Even if contradiction is a "mere" subtopic of reductio, merging might make sense, especially in light of the frequent conflation of the two. I'll propose a merger to see what others think, unless you tell me you've change your mind. Paradoctor (talk) 19:31, 1 June 2020 (UTC)

about Q.E.A.
Gauss seems to have written Q.E.A. sometimes.--SilverMatsu (talk) 15:43, 5 January 2022 (UTC)

Help of an expert
Hello. The page stated that the help of an expert was needed, and rightfully so. It was full of false statements and inaccuracies. I took the liberty of editing it, as I am an expert. Please note however, that I do not know various Wikipedia policies and rules, and that I do not have time to fight random Wikipedia administrators. So I kindly ask that you take these edits in good faith and improve on them (this is how Wikipedia used to be), rather than to revert them based on some random policy. Reverting is really, really bad, because the previous content was downright false. Thanks! AndrejBauer (talk) 19:54, 2 October 2022 (UTC)

 * Let me also say this: I am quite willing to conform the edits to the gazillion Wikipedia policies, if someone would be so kind to tell me precisely what needs to be done. I can probably come up with external references for most of the material, just let me know which bits you think should be properly cited. 19:56, 2 October 2022 (UTC) AndrejBauer (talk) 19:56, 2 October 2022 (UTC)

I'll just add that yes, Andrej Bauer is an expert on logic in general, and proof by contradiction in particular. His changes are a vast improvement. In particular, the article now explains - as various people in this talk page had requested - that some proofs often called "proofs by contradiction" are in fact "refutations by contradiction". These have a different logical status: even intuitionists accept them, because they don't require using the rule "not(not(P)) implies P". John Baez (talk) 10:48, 3 October 2022 (UTC)

 * Thanks for your recent improvement of the article! I'd like to ask for two additional improvements:
 * (1) I feel that a proof method (like Proof by contradiction) is something quite different from a logical axiom (like law of excluded middle). However, your text can be misread to confuse both kinds, viz. in section "Principle" ("Formally, the principle may be written as the implication ¬¬P ⇒ P"), and "Law of the excluded middle" ("Proof by contradiction is equivalent to the law of the excluded middle"). I'd prefer something like "Proof by contradiction is essentially based on the law of the excluded middle", etc.
 * (2) In section "Proof by contradiction in intuitionistic logic", I suggest to start with a 1-sentence introduction of the intuitionistic notion of (constructive) proof, which requires, in order to prove "∃x ...", an algorithm (i.e. constructive method) to obtain a value for x. This would also prepare the reader to understand the paragraph on Turing machines and the halting problem. However, as I'm not an expert in intuitionism, I feel unable to come up with such a sentence. - Jochen Burghardt (talk) 17:36, 3 October 2022 (UTC)
 * Thanks for your suggestions!
 * Regarding (1): the correct distinction here is that of a Hilbert-style system with axioms, or a natural deduction-style with inference rules. So if we want to be precise, then we have to choose one option or mention both. I think I'd prefer the latter and say something like: "In a Hilbert-style system we write it as .... As a reference rule it is writen as ..." (and I would of course link to these concepts). Saying that one law is "essentially based" on another is imprecise and devoid of content. What does "based on" mean? Is derivable from? Is admissible? But I'll see how to improve the text.
 * Regarding (2): It is not correct to say that intuitionistic logic requires an algorithm to obtain a value of x. It asks for a proof, just like any other kind of logic. Again, I'll think about an acceptable improvement that is more explanatory for the casual reader.
 * AndrejBauer (talk) 07:25, 4 October 2022 (UTC)

Not actually a proof by contradiction, again
The infinitude of primes is stated as being proved by contradiction when Euclid's proof wasn't by contradiction, and as clearly stated at Euclid%27s_theorem. One might argue that the article never claims this, just that "the usual proof" is by contradiction. But the lead-up and theorem statement are clearly about Euclid's version:

Euclid's theorem states that there are infinitely many primes. In Euclid's Elements the theorem is stated in Book IX, Proposition 20:[4]

Prime numbers are more than any assigned multitude of prime numbers.

At the very least, a comment about the fact *Euclid's original proof* was not by contradiction should be included, or else this example could go in the non-example section. — Preceding unsigned comment added by 118.210.42.219 (talk) 06:07, 5 October 2022 (UTC)

The argument that is currently there on the page, that a contradiction is arrived at—that 1 should be divisible by a prime, but cannot be—is actually almost in Euclid (see eg http://aleph0.clarku.edu/%7Edjoyce/java/elements/bookIX/propIX20.html). But Euclid's version is a refutation by contradiction, namely that it is used to conclude that the prime divisor of the newly constructed number is **not** equal to one of the original primes, hence a negative statement. This is only a subpart of the argument, based on cases (the new number is prime or not), and is only used to lead to the actual, positive, conclusion: that you have constructed a larger collection of primes than you started with. — Preceding unsigned comment added by 118.210.42.219 (talk) 06:23, 5 October 2022 (UTC)

 * I find it diffuclt to judge what precisely is in Euclid's proof becuause the theorem statement is not formally written down there. What is the precise statement that we are proving there? Is it "there does not exist a finite list of primes such that every prime is in that list"? In that case, yes, it is a refutation by contradiction. But if the theorem is "for every number there is a prime larger than it" or "for every list of primes there is one that is not in the list" (which I think is a reasonable interpretation of what Euclid stated) then the argument takes the form of proof by contradiction. I think this is all very interesting, but I am not sure an extended discussion belongs on this page. Maybe on Euclid's theorem? In any case, I explicitly stated how I formally interpreted Euclid's statement. Also, I am not sure whether you're suggesting that any changes be made, or just chatting :-) 07:40, 5 October 2022 (UTC) AndrejBauer (talk) 07:40, 5 October 2022 (UTC)
 * Here is a thought. We could use Euclid's theorem to illustrate how a proof may take the form of a proof by contradiction or refutation by contradiction, depending on how the statement is formalized. What do you think? 07:49, 5 October 2022 (UTC) AndrejBauer (talk) 07:49, 5 October 2022 (UTC)

 * I have edited the section (moving it to the non-examples) and included the refutation by contradiction proof, cleaned up both so you can see how the structure of the assumption/conclusion is different. At the translation http://aleph0.clarku.edu/%7Edjoyce/java/elements/bookIX/propIX20.html we have

 * "I say that G is not the same with any of the numbers A, B, and C. If possible, let it be so. ..... which is absurd."

 * which to me clearly flags the start of a refutation by contradiction ("I claim a negative statement. Suppose the statement were in fact true... thus we arrive at an absurdity"). I think having both arguments side by side is useful to really hammer home the distinction, and pointing out the quite fine differences in where and what is assumed in order to arrive at a contradiction. — Preceding unsigned comment added by 118.210.42.219 (talk) 07:56, 5 October 2022 (UTC)
 * Thanks for writing up the refutation by contradiction. I split the section into two, each in its own section (but adjacent to each other). I think it works well. I dared reduce the verbosity of the refutation by contradiction a little bit, and I used the mathematical notation. By the way, I wouldn't be to hung up with what Euclid actually said. This is not a historical article, I would give priority to clarity of explanation. AndrejBauer (talk) 11:12, 5 October 2022 (UTC)
 * Thanks, the new version is good, and clearly flags the difference between the two proofs. 118.210.42.219 (talk) 23:14, 5 October 2022 (UTC)

Contradiction vs negation: treading carefully…
Let me begin by acknowledging that I’m no expert, and I have never delved into intuitionistic vs classical. Perhaps for that reason, I have not, to my knowledge, previously encountered the idea that these are not the same thing:
 * Assume ¬P; ¬P ⇒ contradiction; hence P.
 * Assume Q; Q ⇒ contradiction; hence ¬Q.

Since October, the article has been reorganised to distinguish these as "proof by contradiction" and "refutation by contradiction". This has me confused. And while my understanding (or lack thereof) is not material to the content of the article, it does mean that I had a second look (and a third, and…) at what has been going on. And there are two things that trouble me.

Firstly, it appears to be taking sides in what, to my outsider's perspective, seem like two creditable schools of mathematical–logical thought: intuitionistic logic and classical logic. ("Creditable" in the sense that neither appears to be considered discredited or fringe; I'm not saying we need to give equal weight to phlogiston theory!) This is both an NPOV issue and confusing to the average reader—who probably knows nothing about the debate, and can't grasp why the article is so emphatic about "refutation by contradiction" being something totally different.

Secondly, and I think more importantly, the sources cited for the difference have raised my eyebrows. On the one hand, we have a wiki article. On the other hand, we have a blog post and a paper by one Andrej Bauer, whom I dare to guess is the same person as Wikipedia editor. (The title of that paper seems again to be taking a side on classical vs intuitionistic.) I hear alarm bells, and they sound like WP:SPS, WP:COI, and probably some other policies with three-letter acronyms.

I'm aware that I'm veering into "experts are scum" territory here by questioning the contributions by Andrej Bauer, whom asserted is "an expert on logic in general, and proof by contradiction in particular". But I'm going to lean into it and say that if Albert Einstein rocked up to edit the Wikipedia article on mass–energy equivalence, we would be right to politely point him to policy pages and ask him to take a step back! -- Perey (talk) 14:06, 11 January 2023 (UTC)

 * I can confirm that the distinction "proof vs refutation by contradiction" is an important issue in intuitionistic logic, and is far more than just a hobby of some Andrej Bauer. As far as I know, intuitionistic logic aim at constructive proofs, that is, from an intuitionstic proof of "there exists some x that has property P", one can obtain a "witness", i.e. a "value" that indeed satisfies P (see Constructive_proof for existence proofs without witness in classical logic). The price for this property of intuitionstic proofs is (among others) that from "not not Q" one cannot infer "Q". For this reason, intuitionists have to distinguish refutation by contradiction and proof by contradiction, and admit the former, but forbid the latter. In classical logic, the latter follows from the former and the law "if not not Q, then Q". - Maybe the article becomes less confusing if we move the subsection "Refutation by contradiction" into the section "Proof by contradiction in intuitionistic logic"; this way, all intuitionstic stuff would be encapsulated there. - Jochen Burghardt (talk) 15:00, 11 January 2023 (UTC)
 * I think that's a good idea, collecting info on the intuitionistic view in one place. I think we should also avoid wording like "confused with", which implies those who take the classical logic view are confused. As for the sourcing issue, I certainly don't mean to imply that this is "just a hobby of some Andrej Bauer"! As a non-expert, I'm working under the presumption that everything Bauer has written is entirely factually correct. But correctness is orthogonal to propriety: we have rules that say we need to be careful with self-citing and self-published sources. "Careful" in my understanding here means we need to have more, independent, sources to go along with the existing ones. -- Perey (talk) 03:46, 12 January 2023 (UTC)

 * Let us distinguish here several issues.

 * The first is a matter of logic. The discussion about "proof by contradiction" and "refutation by contradiction" is prior to the distinction between classical and intuitionistic logic. It makes no sense to say that "proof by contradiction is different in intuitionistic logic than in classical logic". It's exactly the same. The difference is one of acceptance of it as true. It would be a bad idea to rewrite the page so that somehow we give the impression that "proof by contradiction" is a different animal in classical and intuitionistic logic. That would be like saying that the equation "x * y = y * x" stated for a general group is different from the equation "x * y = y * x" stated for a commutative group. It's the same equation, which happens to be true in one of the cases.

 * Whether "proof by contradiction" and "refutation by contradiction" are "the same" is also prior to any distinction between classical and intuitionistic logic. They are different simply because they have different syntactic forms throught which they receive different meanings. Obviously so, because in some situations one of the rules can be applied whereas the other cannot (irrespective of which kind of logic we are in since applicability of a rule is just about syntax and not about what is valid). To reiterate, the distinction in the meaning of the two rules is exactly the same in intuitionistic and classical lgoic. However, it is the case that in classical logic both rules are valid – but that does not cause the distinction to disappear! You would not say "2 * 2 = 4 and 2 + 2 = 4 are the same statement" even though they are logically equivalent (both are true), would you?

 * Perhaps a good plan would be to take "Proof by refutation" out of the page and make it into a separate one. The present page would then speak only of "Proof by contradiction", with two short remarks, namely: that proof by contradiction is not generally accepted in intuitionistic mathematics (this can be properly discussed ona page about intuitionistic mathematics), and that there is a related notion of "refutation by contradiction" which is not the same as "proof by contradiction" (but "refutation by contradiction" would be discussed on a separate page, I am not sure where the difference is to be discussed).

 * The second matter is one of terminology. You will notice that early versions of the page said "proof of negation" instead of "refutation by contradiction". After some discussions on Twitter, in particular with Noam Zeilberger and Joel Hamkins, the phrase "refutation by contradiction" was suggested as a better one (see here and here). The advantage is that "proof by contradiction" and "refutation by contradiction" nicely reflect the symmetry between the two principles. Of course, we need good external citation. I am indeed no expert on Wikipedia policies, and I have had very negative experiences with Wikipedia, so I am hesitant to contribute. I was advised that it was ok to quote my own work as a source. If I erred, well then, I shouldn't take advice from Twitter. I have tried to find some further sources, in particular for "refutation by contradiction", of which the nLab reference seemed most promising (notice that the nLab reference further points to my writing, but not with regards to "refutation by contradiction"). I shall ask Noam Zeilberger for some further references, as he knows this particular topic better than I do.

 * The third matter is how to apply various Wikipedia policies. I think that the "neutral point of view" is irrelevant, as I understand it. There may be a host of other policies that apply (as there usually are), but not NPOV. There is no matter of opinion here, nor are there different valid views. There may be differences in opinion on what terminology to use, where to provide more references, or which things to mention and which ones should go elsewhere – but those are editorial issues.

 * I am happy to continue helping with the page, and I appreciate the comments. Please bare with me, I am not a Wikipedia policy expert. I would appreciate some concrete suggestions on what needs to be done. AndrejBauer (talk) 14:45, 12 January 2023 (UTC)
 * TL;DR: I have two suggestions. ① Call the different usages of "proof of contradiction" broad and narrow, not confused. ② Find some citations from people who use the broad/confused sense, preferably addressing the distinction between them.
 * Here's the thing: I didn't come here to comment because when I read the article, I saw policies being violated. It was because I felt confronted by the way the article's written.
 * The reason I cited policies is that I didn't want to be the idiot who comes in here, saying we should be nicer about the whole "all these people are wrong" thing, and gets told to sit down and shut up because these are the facts. So I went and found policies to try and shore up my position, hoping that they would explain better than I could why something needs to change.
 * Instead, that makes me the idiot who comes in here waving a bunch of policies and makes you go, "See? I was right! Except it's not an administrator throwing policies in my face, it's just some random nobody." So I'll try and explain my position anyway, without reference to policies.
 * Roughly speaking, there are three kinds of people here. There are those who are completely unfamiliar with the topic, who don't know an excluded middle from a bare midriff. There are those (like me) who know something about it, and who probably learned that the proof that $$\sqrt{2}$$ is irrational is a great example of proof by contradiction! And then there are the actual experts.
 * Right now, the article is very dismissive of the second group. It says that they're confused, that they're wrong. Maybe that's so. But as someone in that group, it put me on the defensive. That's relevant for two reasons. One is that I think not alienating the audience is a worthy goal. (Assuming, of course, that I'm not alone in reading the article as confrontational.) Pedagogically, I think that moving people from the first group into the second is a good outcome, and a step on the road to expanding the third group.
 * The second reason it's relevant is that when I get defensive, I read. So I went digging further. This article, and my associated reading around it, has led me to the following understandings:
 * "Classical logic" and "intuitionistic logic" are two schools of thought that disagree with each other. Both have adherents, and the debate is ongoing.
 * The distinction is sort of like Euclidean versus hyperbolic geometry, in that they accept different sets of definitions or axioms. It's quite unlike that, in that the thing being described is the very notion of truth: what constitutes valid reasoning about whether or not something is true?
 * Classical logic accepts ¬¬P ⇒ P (the law of the excluded middle). Intuitionistic logic does not (not as a general principle; it needs to be shown to hold in a specific case).
 * There are two things referred to as "proof by contradiction":
 * Properly speaking, it means affirming P by showing that ¬P leads to a contradiction (both logics accept the law of noncontradiction). It then needs ¬¬P ⇒ P to transform this into an affirmative statement of P.
 * The alternative—denying P by showing that P leads to a contradiction—is "refutation by contradiction" or "proof by negation". (This is acceptable in both logics.) The article asserts that calling this "proof by contradiction" is wrong.
 * Given LEM, the one can be turned into the other by a trivial substitution of ¬Q for P. Hence, they are equivalent in classical logic.
 * Now, you wanted concrete suggestions. My first is to change how we describe the use of "proof by contradiction" to mean "refutation by contradiction". I think that the article should not call the usage "confused". It seems to me that you're fighting the same fight as prescriptivists in language: if a usage is common, at what point does it stop being wrong and become a part of a broader definition? Given that it is common, given the ongoing debate between logic camps, and given the simplicity of their equivalence when LEM is allowed, I contend that we're not able to call it wrong. Instead, I propose describing it in terms of a broad and a narrow definition. I don't support moving refutation to its own article.
 * My second is that we need citations that give a broader cross-section of views on these fine distinctions. This is where I appealed to policy earlier, and I do think those policies exist for good reasons, but I'm making the case myself now. When there's a disagreement, I want to know (= I want Wikipedia to address) what each side says about the other. Right now it seems like the citations all come from a handful of people who reference each other. When I see that, it doesn't matter whether they're the leading lights of the field or three cranks in a pub; I want to know what someone else thinks about what they're saying. Someone who might be expected to disagree with them. Can we cite someone whose work uses "proof by contradiction" in its broad ("confused") sense? Someone from the classical logic camp, maybe?
 * Those are my suggestions, anyway. I think we can restructure this article so that it's both accessible and accurate. The absolute last thing I want to do is to drive you away or make you feel that your expertise is not valued. -- Perey (talk) 05:52, 14 January 2023 (UTC)
 * I much appreciate your explanation of what you feel is wrong with the article (rather than citing policies), as I can actually act on that. I think we can easily incorporate your suggestion about broad/narrow distinction, and it's a good one. There is just one (technical) point which I disagree with. Stating that "assuming LEM, we can turn one of the principles into the other" is at best misleading. That is because "proof by refutation" is already valid in first-order logic (with or without LEM), and so all you are saying is "a principle which everybody already accepts can be re-rederived from LEM and proof by contradiction", and that's not very illuminating. Let me make the broad/narrow change, which I like very much, and then we see where we stand with the rest. AndrejBauer (talk) 09:39, 16 January 2023 (UTC)
 * Regarding better citations, I called for help, so we should be getting some soon. I am familiar with constructive logic literature, but less with philosophically slanted one, where this sort of thing is probably discussed. AndrejBauer (talk) 09:43, 16 January 2023 (UTC)
 * Thanks very much for your response. I think the article's looking better already.
 * "that's not very illuminating"—no, probably not! My thought wasn't to derive p.b.negation from p.b.contradiction. That'd be like deriving  from  . All I meant was that, given LEM (or in this analogy,  ), you can freely switch back and forth between the two forms.
 * Which is why I think the broad usage comes about: people just take this freedom for granted. ("So we've proven the assertion that sqrt(2) is irrational…" "No, you’ve refuted the assertion that it’s rational." "But that's the same thing!") -- Perey (talk) 15:17, 16 January 2023 (UTC)
 * I have added a bit more text explaining that under $$P = \neg\neg P$$ (which is what everyone knows in pracrice) the difference betweeen the two principles is obscured. However, I will die on the hill of "they are not the same" :-) 07:08, 24 January 2023 (UTC) AndrejBauer (talk) 07:08, 24 January 2023 (UTC)
 * As somewhat of a side note to all of the above, let me say that, although I am hardly an expert on this topic, I do have a PhD in mathematics (my dissertation was on categorical topology), and used to believe, at least, that I had a nodding acquaintance with this topic, and that I find myself sharing some of the concerns being expressed by, and would like to thank him for expressing those concerns here ;-) Paul August ☎ 13:50, 16 January 2023 (UTC)

Clarification of BHK interpretation of proof by contradiction.
Jochen Burghardt asks for clarification regarding the passage about the BHK interpretation of proof by contradiction. I think this is a fair point, and he remarks that such clarification is not available in on the BHK page (the passage about absurdity comes close). I am not sure how to proceed. The BHK page has a fairly narrow explanation of what the BHK interpretation is, namely it claims to be about proofs, whereas the present page takes the BHK interpretation in its wider (and more acurate) sense explaining what the intuitionistic conditions for validity are. So until the BHK page is fixed, we cannot link to a reasonable explanation there. Any ideas what to do, apart from going after a major edit of the BHK page? AndrejBauer (talk) 18:56, 27 May 2024 (UTC)

 * No. A major edit of the BHK article to me seems to be the right way to go. --Daniel5Ko (talk) 22:35, 14 June 2024 (UTC)
 * Ugh, I am still a bit afraid of major edits around here, because I invariably hit some weird Wikipedia policy that I am not aware of. 14:47, 17 June 2024 (UTC) 193.77.148.136 (talk) 14:47, 17 June 2024 (UTC)
 * Don't be afraid. In my experience, WP is still very much anarchy-like in general. "Policies" were and are made up on the spot, but of course, always up to discussion. --Daniel5Ko (talk) 01:34, 18 June 2024 (UTC)

title: Talk:Proof by contradiction