Talk:Axiom

message: "As the word axiom is understood in mathematics, an axiom is not a proposition that is self-evident."
The Liddell and Scott entry for (axioma) says the exact opposite
--Dwight 15:36, 12 Apr 2004 (UTC)
replies: text: That remark seems very silly.  The only "Liddell and Scott" I've been able to find is a lexicon translating ancient Greek words into English.  They would therefore be expected to write about what the word meant in Ancient Greek, not about what it means in the usage of modern mathematicians.  Liddell and Scott are probably right, and the statement you quote above about use in mathematics is also right.  They do not contradict each other; they are about two different things.  Liddell and Scott do not appear to be mathematicians and cannot be supposed to have expertise in that area.  I, on the other hand, am a mathematician, and I am quite familiar with both usages.  I suggest you read the whole Wikipedia article, and you will see that there is no contradiction between these points. Michael Hardy 22:33, 12 Apr 2004 (UTC)

text: Nor with the trivial and obvious, which are theorems =) 142.177.126.230 21:19, 4 Aug 2004 (UTC)

text: ...except that there is are technical definitions of self-evident in epistemology.  See self-evidence. Michael Hardy 01:41, 5 Aug 2004 (UTC)

text: I'm a layman in logic, but from what I read in other aricles, treating axioms as self-evident is an outdated approach, they are rather considered starting points of theories. In fact, there are many different logics (classical logic, intuitionist logic etc.) so treating axioms as self-evident becomes philosophically moot. — Kallikanzaridtalk 08:54, 6 March 2011 (UTC)
thread_title: Self-evident?

message: Gödel's completeness theorem establishes that every deductive system with a consistent set of non-logical axioms is complete
Does it?  Doesn't it apply to a certain set of logical axioms and rules of deduction?  Take a typical deductive system and remove a logical axiom schema or modus ponens.  You still have a deductive system with a consistent set of non-logical axioms--albeit one that would not ordinarily be used (except perhaps by an intuitionist)--but it's not complete. Josh Cherry 02:07, 24 Oct 2004 (UTC)
thread_title: Completeness?

message: We are fortunate enough to have that the standard model of "real analysis", described by the axioms of a complete ordered commutative field, is unique up to isomorphism.
This seems to say that there is a set of axioms that picks out the reals uniquely (up to isomorphism).  What about the Löwenheim-Skolem theorem and such?  I presume that although the reals are the unique complete ordered commutative field, completeness can not be expressed axiomatically, at least in systems to which the L-S theorems apply. Josh Cherry 02:58, 24 Oct 2004 (UTC)
replies: text: L-S is about first-order theories, and this axiomization isn't one. You can come up with a first-order theory of all first-order sentences true of the real numbers using the ring functions of addition and multiplication, as well as the order relation, and then L-S would apply, and would tell us it has a countable model. We get the theory of formally real fields in this way, but not the real numbers uniquely. Gene Ward Smith 08:01, 1 Dec 2004 (UTC)
thread_title: Uniqueness of the reals?

message: An automated Wikipedia link suggester has some possible wiki link suggestions for the Axiom article, and they have been placed on this page for your convenience.Tip: Some people find it helpful if these suggestions are shown on this talk page, rather than on another page. To do this, just add  to this page. — LinkBot 10:39, 17 Dec 2004 (UTC)
thread_title:  [[User:LinkBot/suggestions/Axiom|Link suggestions]] 

message: The article now claims:
*Basic theories, such as arithmetic, real analysis (sometimes referred to as the theory of functions of one real variable), linear algebra, and complex analysis (a.k.a. complex variables), are often introduced non-axiomatically in mostly technical studies, but any rigorous course in these subjects always begins by presenting its axioms.
It seems to me this just isn't true. Most often, what is done instead is to present definitions inside of set theory, and the set theory used is normally naive set theory.  Linear algebra uses axioms when it wants to talk about vector spaces over arbitary fields, but that is quite different than using axioms to define the integers, real numbers, or complex numbers. If this sentence isn't given a good defense I'll remove it. Gene Ward Smith 19:34, 29 April 2006 (UTC)
thread_title:  When are axioms used? 

message: While Galois theory was successfully applied to classic questions of geometry, the names here should be Gauss and Pierre Wantzel, not Galois. Gene Ward Smith 02:02, 2 May 2006 (UTC)
thread_title:  Galois and geometry 

message: I probably shouldn't be saying this.  And this maybe should be deleted.  But I'm a little annoyed how every equation in wiki makes absolutely no sense.  I would think there should be easy and hard ones to demonstrate how it works. —The preceding unsigned comment was added by 208.186.255.18 (talk • contribs)  05:54, June 3, 2006 (UTC)
:Firstly, could you identify yourself by user name so we don't need to do detective work with the edit history to find out who wrote this?
:Secondly, your complaint is horribly vague.  Please explain what in the world you mean and cite examples. Michael Hardy 00:31, 5 June 2006 (UTC)
thread_title:  I have a complaint.  

message: Sorry, I forgot to post here after adding . There's not a single reference in the entire article, so I think the tag is warranted until the problem can be addressed. Simões (talk/contribs) 01:17, 22 October 2006 (UTC)
thread_title:  Lack of sources 

message: Assuming it is not controversial to make the point that an 'axiom' does not necessarily connote a notion of "truth" or actuality, (except perhaps in the realms of epistemology, deontology, etc.) and therefore axioms are subject to whatever motivation is deemed appropriate under the circumstances, intro paragraph should reflect this. drefty.mac 07:00, 28 October 2006 (UTC)
thread_title:  abstracted 'truth' out of introductory paragraph 

message: The article states that 
"...for nearly two millennia the fifth (parallel) postulate ("through a point outside a line there is exactly one parallel") was suspected of being derivable from the first four. Ultimately, the fifth postulate was found to be independent of the first four. Indeed, one can assume that no parallels through a point outside a line exist, that exactly one exists, or that infinitely many exist."
I think it might be a good idea to change part of this statement.  It is true that the fifth postulate is independent of the first four, but the assumption that no parallels exist is not - it is a much stronger statement than the negation of Euclid's fifth and is inconsistent with the first four postulates.  The difference between the two kinds of geometry with the first four postulates already given is that in non-euclidean geometry parallels are not unique, whereas in euclidean geometry they are.  See "Euclidean and non-euclidean geometries" by Greenberg.  Stephen Thompson 01:14, 29 April 2007 (UTC)
thread_title:  Misleading Statement 

message: Under "Mathematical logic" the article says: "...φ, ψ, and χ can be any formulae of the language...". Are these letters in the correct order? The article "Greek alphabet" says the alphabetical order of these letters is φ, χ, ψ. (Complex Buttons 20:03, 4 July 2007 (UTC)
thread_title:  φ, ψ, χ or φ, χ, ψ? 

message: Is this a word???
maybe Bush wrote it?  —Preceding unsigned comment added by 128.232.238.250 (talk) 22:58, 24 November 2007 (UTC)
replies: text: Snork Mardiste! :) 85.210.15.219 (talk) 23:29, 6 May 2011 (UTC)
thread_title:  acceptation? 

message: I added a link to http://www.allmathwords.org/axiom.html to this article. It was removed.
Wikipedia guidelines allow links to sites that provide something the Wikipedia article does not. The Wikipedia article 'Axiom' is written at a college level. The All Math Words Encyclopedia is written at a level for grades 7-10 (U.S.). It is much more accessable to middle school and high school students than the Wikipedia article. I feel this is sufficient reason to include the link to All Math Words Encyclopedia.  —Preceding unsigned comment added by DEMcAdams (talk • contribs) 15:22, 8 October 2008 (UTC)
replies: text: I don't think this external link should be included. According to WP:LINKSTOAVOID, links that duplicate content that the article would contain if it were a featured article should be avoided. The allmathwords page has very little content, and apart from different choice of examples its content is already included in the present article. — Carl (CBM · talk) 16:04, 8 October 2008 (UTC)
replies: text: I'm not familiar with the EL guidelines for simple.wikipedia.com, but it may be more appropriate there.  — Arthur Rubin  (talk) 16:07, 8 October 2008 (UTC)
thread_title:  External Links 

message: Both 'Axiom Schema' and 'Axiom Scheme' are used in this article. Are they both correct? Passingtramp (talk) 09:45, 21 May 2009 (UTC)
thread_title:  Scheme / schema 

message: On the first line of the third paragraph there is an example given in the first set of parentheses 'e.g., A and B implies A'. This appears to be mis-written. Then again, what do I know. I will leave it up to editors of these types of pages. If I am wrong, please disregard. 220.255.1.30 (talk) 03:49, 16 January 2011 (UTC)
thread_title:  An error? 

message: The distinction between axoims and postulates is never explicitly stated, which is regrettable since Postulate redirectes here. Anybody up for rectifying this? --93.206.135.188 (talk) 08:02, 13 September 2011 (UTC)
thread_title:  Axiom / Postulate 

message: This example axiom is unclear; what does taken mean?
I can see only two interpretations:
1) Subtracting equal amounts from equals produces equal amounts; then the quote should be revised to read "equal amounts result", as there are two quantities being compared
2) Subtracting equal amounts from two quantities and adding each to a third produces an amount equal to the first two; this is plainly false
So perhaps the quote should be revised.Anaxiomatic (talk) 10:57, 12 February 2013 (UTC)
thread_title:  Unclear: "When an equal amount is taken from equals, an equal amount results." 

message: The third formula in 3.2.1.1 Arithmetic seems to have mismatching parenteses, there is 1 unnecessary opening parentesis. Could someone who understands the formula well repair it?213.125.95.58 (talk) 14:36, 7 May 2017 (UTC)
replies: text: --Bill Cherowitzo  (talk) 14:52, 7 May 2017 (UTC)
thread_title:  Mismatching parentheses in formula 

message: One of the discoveries since the ancient Greeks is that there are incorrect proofs in Euclid's Elements and that, in fact, some of the stated theorems do not follow from the stated axioms and postulates. Should this not be discussed when mentioning the Elements?. In that context, a reference to, e.g., Hilbert's Grundlagen der Geometrie, may be appropriate, Shmuel (Seymour J.) Metz Username:Chatul (talk) 02:07, 8 July 2020 (UTC)
replies: text: It seems to me more about the Elements than it is about axioms, so I would tend to think it does not really belong in this article.  However I wouldn't dig in my heels to prevent a passing mention, if you can word it so it doesn't sound out of place. --Trovatore (talk) 05:55, 8 July 2020 (UTC)
replies: text: To clarify, the article already mentions the Elements in Axiom#Early Greeks; I'm concerned that the existing text promises more than the Elements can deliver. Shmuel (Seymour J.) Metz Username:Chatul (talk) 12:26, 8 July 2020 (UTC)
replies: text: Of course we should mention the Elements, as an early (maybe the earliest?) explicit example of the axiomatic method.  That's about axioms.  When you start talking about whether all the specific results in the Elements follow from the axioms in the Elements, then it seems to me that maybe you've left off talking about axioms, and started talking about the Elements.  --Trovatore (talk) 15:02, 8 July 2020 (UTC)
replies: text: Well, would you object to a short footnote, e.g., , and to a brief mention in #Modern development of adding axioms? Shmuel (Seymour J.) Metz Username:Chatul (talk) 15:30, 8 July 2020 (UTC)
thread_title:  Flaws in ''The Elements'' 

message: Hello Community🙂❤️
Here below my edit aproach:
"In historical sciences/context you can see axiomata perhaps as more inclusive as it, for example the third reich here, is satisfying enough if it fully encovers the empathic aspekt abeling one with permission to go on with further assumptions. Inclusive in this way, that it is possible to work with prezise statements regarding empathic ideas without necessarly having great knowledge of formally required information normally required in this topic. So for example: "If ones an ex nationalsocialist it is appropriate for him as a way of caesura in his further life to go on with maybe dramatically social ideas maybe in a slightly risky kontext at least in generating this ideas mentally". So this axiomata is more inclusive as through fully satisfying every aspekt (at that point not yet formally) regarding empathy and through this at least this specific phrase in this specific context, if satisfying the empathic site enough automatically creates valid statements to work with. It is also inclusive in that way that in its origin, the messenger is able to collect information and knowledge for this specific case without explicit formal reputation/education so it enables the working with this discipline to a broader number of people."
So first my provided sources https://www.linkedin.com/pulse/hard-maths-empathy-sophie-carr#:~:text=The%20truth%20is%20that%20mathematical,considered%20relate%20to%20one%20another.
The autor of this article says that the ability to work with statistical math requires the same way of thinking as with connecting to someones feelings.
https://psychologic.science/social/logic/12.html The autor of this article works with our core sozial values as mathematical axioma and how society changes if changing this values.
https://www.mdpi.com/2076-3417/13/2/1163
This (also a bit more Professional) source says that with an AI, working with empathy and with this training it in social complex situations outperformes other AIs in methodological learning.
Also I tried writing down some context below, first in case of reposting my edit, but because I love wikipedia too much to get blocked, I switched to the Talk section so Here it is:
"First, I want to say, I love Wikipedia and sometimes I Love editing. Also english is not my native language and I know I make grammatical and orthographically mistakes. Second, I provided some Sources which stated that empathy have significantly Impact on mathematics. But thats just a Part of what I wanted to say. As said before I Love wikipedia and this article. Im not an expert, but first, I tried Just writing about things, that, as far as I guess am able to understand. So second I tried to say that when you, in the process of working with axiomatas, switch the things referred to in this process, to themes you are more familiar with, maybe for this parts of the process Its easier to work with making this Part of mathematics maybe more inclusive. So with this said maybe I can work on this edit to Point this Out more clearly. Second, I guess that, If just regarding the improved performance when work with themes, one is more familiar with, and, regarding my explicit example of working with the third reich in this context, which, is from a science aspect one of the few themes, that, are finished in some way completely and almost every statement  is true working With an anti fascist View, maybe this theme gives somehow an extra boost. To be honest, surely, I don't know if the parts I describe in the process with axiomatas, even when performance is better, wether it is possible to get outcomes which are satisfying enough for this mathematical aspect even with, as it is with me also, little lackings of full knowledge of this aspect. To the critiques regarding non dictionary language I want to say that the people I wanted to reach are nonexperts explicitly so I wanted to decrease the limitations for gaining more safety in performing this theme a bit, mostly just as I do in thinking of this theme relatively correct, so it isn't even my aproach to reach people working, regarding this theme, in expressing their workings down to sheets of paper or professionals."
So if you read all this, I would love to hear your critiques, improving ideas, and, if you think all this is pure trash, let me hear your opinion, don't worry Im not THAT emotional unstable😁❤️ Materie34 (talk) 03:00, 20 November 2023 (UTC)
replies: text: Wikipedia is not a forum for discussion and not a platform for publishing your own ideas.  If any of the material above is somehow being proposed as something to include in our article at Axiom, I have to observe that it is not proper English, even in a single clause of it, and it appears to desire to dwell on Nazism, which would be very undue. If the term "axiom" has something to do with the Nazi doctrine, that could perhaps be covered somewhere in the article, but only if there are reliable sources that show it to be central to that doctrine, and an important historical aspect of the meaning of axiom. The material you've provided has no clear purpose, direction, or theme, and seems to be a bunch of quasi-philosophical rambling, veering from Nazis, to empathy, to statement precision, to messengers of some kind, to reputation, to AI, and it makes no sense at all, much less to the average encyclopedia reader. There's nothing for us to work with here. Your "sources" are a self-published opinion piece at a social media site (which doesn't mention axioms); psychologic.science, which is obviously just a bunch of self-published material on pseudo-scientific nonsense like "alpha males"; and a paper published by MDPI which is listed at WP:Reliable_sources/Perennial_sources#MDPI as "questionable" to "predatory", and the paper has no mention of "axiom" at all any way, so it is not any kind of source for this topic.  Please do not waste Wikipedia editors' time with more material of this sort.  If you are actually interested in working on an encyclopedia, which means working with  sources and summarizing what they say without engaging in any form of original research of your own on any topic, then you would do well to focus on whichever edition of Wikipedia is in your native language.  — SMcCandlish ☏ ¢ 😼  04:36, 20 November 2023 (UTC)
thread_title:  Aproach Edit