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One of the 500 most frequently viewed mathematics articles.

Archive 1 to end may 2007

definitions in mathematics[edit]

Maybe see also Gowers: Two definitions of `definition' Boris Tsirelson 09:43, 12 March 2007 (UTC)

I've been asked to comment on definitions in mathematics by Jtir.
Definitions are a major part of mathematics. Indeed, good definitions can be more important than theorems (think of the definition of a group for example). The article by Gowers contains useful information which could be used to flesh out a section on the topic. However, I would caution against making any sort of dichotomy explicit: there is only one notion of a definition in mathematics, even if some are intuitive, some pragmatic, some foundational. One person's definition is another person's theorem. Indeed, sometimes a definition will be preceded by a theorem stating "The following n properties of a gadget X are equivalent"; after the proof, the definition will be given "A gadget X is said to be pseudo-tame if the above properties hold"! There is also the concept of a Definition/Proposition, in which one needs to prove that something exists or is makes sense as part of its definition.
I hope this provides some helpful information. Geometry guy 12:37, 3 June 2007 (UTC)
Further to this, I would like to thank Jtir for adding a Philosophy rating to the article, to clarify that this is within the scope of both projects. I am now going to lower the class on the maths rating scale to Start, because although this is a nice article overall, there is some work to do before it covers the mathematical concept. The maths ratings and comments are copied over to tables at WikiProject Mathematics, so I hope this will attract a maths editor to contribute to the article. Geometry guy 18:28, 3 June 2007 (UTC)

The web page cited above seems to this lay reader to do no more than draw the distinction, already mentioned in the article, between stipulative and descriptive definitions. Banno 23:13, 23 June 2007 (UTC)


Scientific classification of living things uses definition by genus and differentia

This article needs a picture or two. Any ideas? Banno 21:07, 4 May 2007 (UTC)

Good idea.
Portraits are common (Philosophy, Mathematics).
Dictionary has several apt images.
Ostensive definition could be illustrated with, for example, a picture of a parent pointing out a dog or a rainbow to a child.
Genetic definition could be illustrated with an animation of someone drawing a circle. Bézier curve has some nice animations.
Wikipedia:Featured_pictures might suggest other ideas.
--Jtir 15:46, 5 May 2007 (UTC)
I was going to add a portrait of Locke with a caption quoting him (re "where should we stop?"), until I
The cover of How Children Learn the Meanings of Words by Paul Bloom shows a painting by Titian.[1]
While searching for images of rainbows, I came across this painting by a seven year old.
I rather like this one. It will need a good caption, though. Banno 22:53, 23 June 2007 (UTC)
Since the article mentions hobbits, maybe a "portrait" of one could be used.
Tying any of these into the article would, of course, require a well-written caption.
--Jtir 22:20, 23 June 2007 (UTC)

What about using Biological classification - but for some reason the caption will not show. Banno 22:51, 23 June 2007 (UTC)

Nice. Banno 09:24, 24 June 2007 (UTC)

A definition is a concise statement explaining the meaning of a term, word or phrase.[edit]

user:BMF81 has requested that a citation be found for this. By all means, do so if an appropriate source can be found - but I wonder that anyone might actual question this definition? Is there a problem with this wording? See the criteria for requesting citations set out at Wikipedia:Citing sources#When to cite sources Banno 22:29, 11 June 2007 (UTC)

The first sentence is essentially a dictionary definition of definition. I have added a link to Wiktionary. --Jtir 23:01, 11 June 2007 (UTC)
ISTM that "concision" is not a necessity. Indeed, whole books have been devoted to the definition of a single concept. (e.g. What is Mathematics? by Courant and Robbins) --Jtir 23:28, 11 June 2007 (UTC)
The lead section is supposed to summarize the article. Further, if the article is sourced, the lead may not need to be explicitly sourced. --Jtir 23:38, 11 June 2007 (UTC)

Cool. unless BMF81 provides some explanation, I will remove the request for citation - give it a day or so. Banno 23:39, 11 June 2007 (UTC)


I changed the link to point to Oneness, b/c the link to Unity points to a disambiguation page, which to my noobie understanding is against standards. Banno pointed out that 'Oneness' is a new-age and not a philosophical concept. So maybe you should find a link target that is more appropriate, or get rid of the link altogether? --Rog 21:42, 10 September 2007 (UTC)

Is this unity as in the number 1? If that is the case then the link could go to 1 (number).--Rog 22:13, 10 September 2007 (UTC)

WikiProject class rating[edit]

This article was automatically assessed because at least one WikiProject had rated the article as start, and the rating on other projects was brought up to start class. BetacommandBot 03:55, 10 November 2007 (UTC)

Extensive vs. Ostensive definitions[edit]

There appears to be a contradiction in the article: extensive definitions are defined as "a list naming every object that is a member of a specific set" but ostensive definitions, while said to be "one important form of extensional definition" are also said to give "the meaning of a term by pointing ... in the case of a class, to examples of the right kind". The question is: if a definition gives the meaning of a term by pointing to a proper subset (i.e. not all) of a class, can it be an ostensive definition? If it is not, the last quotation is strongly misleading. If it is (and Wittgenstein's interest suggests that this is so) then either the definition of "extensive definitions" is incorrect, or ostensive definitions are not a form of extensional definition. I don't know the answer - anyone?(Mountain Goat (talk) 00:07, 30 January 2008 (UTC))


The article is a high-frequency target for IP vandalism. It is also frequently viewed. I'm semi-protecting for three month, as per the policy. Vandalism is well over the 5% average. Banno (talk) 23:30, 3 March 2009 (UTC)

Approaching the last month of this semi-protection. Are there any objections to my making this permanent? I think the value of protection has been demonstrated. Banno (talk) 01:01, 24 April 2009 (UTC)
Banno, please make it permanent. Thank you, --Ancheta Wis (talk) 01:24, 24 April 2009 (UTC)
I suppose we should try unprotecting it again, to see how it goes. Protection in itself is never a good thing. Velho (talk) 23:52, 26 April 2009 (UTC)

Definition of a definition[edit]

I remember a speech a while back, and the speaker, giving a talk on marketing basics, offered this:

  • Subject is a category that point of difference.

He said this definition of a definition was from Socrates, and illustrated it with marketing examples:

  • Crest (subject) is a toothpaste (category) that prevents cavities (point of difference).

The idea is that the category is something everybody knows, and the point of difference is how the subject differs from others in the category, and it moves from the known to the unknown, logically. He said this format can be used to define most things, not just marketing stuff:

  • A horse (subject) is an animal (category) that has four legs, runs fast, and can be ridden by humans (point of difference).
  • A tree (subject) is a large plant (category) that grows several stories tall, has leaves & roots (point of difference).
  • Bill Cunliffe (subject) is a jazz pianist (category) who won a Grammy Award (point of difference).

(subject) is a (category) that (point of difference).

Wondering if anybody else has come across something similar in philosophy, about this, and if it should be here in this article?--Tomwsulcer (talk) 00:55, 14 June 2010 (UTC)


Is there a term for definitions which say what something is not (i.e., that work by excluding everything other than the thing in question)? Cesiumfrog (talk) 03:28, 21 December 2010 (UTC)

It is revealing that googling for "exclusionary definition" yields nothing that Cesiumfrog would have sought above. Apparently just adding a qualifier fools the search software that the qualifier is the concept being sought. So, Cesiumfrog you have a different POV than most. Keep it up and you will discover something for the rest of us. --Ancheta Wis (talk) 13:46, 21 December 2010 (UTC)

Definition as knowledge[edit]

Even natural languages are supposed to consist of words (phrases, etc.) that are known to the community in a recursive fashion. Thus what is not known is explained by connecting it to something known. No word is possible to remember for long without any association to anything at all, and most words are learnt by associating them according to the triangle of term, concept and referent. Thus a term is defined in relation to a referent, and a referent is tagged or labelled by a term. Knowing this relationship is the simplest form of making a definition. Thus if nothing is known about the referent of a noun (term), then it is used with an indefinite article, but when it is already known, it is used with a definite article. Knowledge is specific, hence generic terms need to be specified, i.e. defined in order to make sense, or to learn something useful about them. The specific-generic continuum is the illustration of progress of inquiry and knowledge, each time giving another definition of something in the form of topic and comment. Topic is the known part of the compound structure and comment is the new information about the topic. Topic and comment may come in the form of a description or in the form of an explanation. If we are listening and reading we begin with Description and proceed to Explanation. If we are speaking and writing, we begin with Explanation and proceed to Description. This is called the DEED paradigm created by David Crystal.

Genezistan (talk) 23:55, 22 January 2011 (UTC)

Definition of definition criticised[edit]

In a lengthy exercise on definition by Professor Norman Swartz [2], Simon Fraser University the author says (Under 2.1, near the end) “For example, the term, "pain", is defined, but pain itself is not defined. We define only terms, never their referents.”

The rest of the discussion is moved to my homepage Genezistan

Genezistan (talk) 11:12, 24 January 2011 (UTC) — Preceding unsigned comment added by Genezistan (talkcontribs) 11:58, 23 January 2011 (UTC)

This stuff should not be on a talk-page. I suggest you enter into a dialog with Swartz directly, but if you insist on having it in Wikipedia, why not keep it on your user-page or write an essay? Hpvpp (talk) 00:01, 24 January 2011 (UTC)

Good point (brownie point)

Genezistan (talk) 11:26, 24 January 2011 (UTC)

Definitions as a choice[edit]

Some definitions are simply chosen for practical purposes, notably conciseveness. These definitions can't be right or wrong, they only differ in practical value. Being generally accepted is a plus, but not a need.

A typical example are legal definitions, often listed in an initial section in a statute. The legal defintion may be more precise than the collquial definition, or more restricted, or even wider. For instance, in common parlance an invention is something new, but an "invention" in patent law is not necessarily new.

Perhaps this type of definition is covered by the paragraph "working definitions", but I guess the practical importance requires a better description. Also, a "working definition" suggests that it is preliminary, while for instacne legal definitions definitely are final. Rbakels (talk) 14:05, 15 February 2012 (UTC)

list of future prime ministers?[edit]

I very much appreciate this article and thank the editor for the time dedicated to it.

Regarding the following quote from it: "An extensional definition would be a list of all past, present and future prime ministers."

With very few exceptions a list of future prime ministers is not doable.

FactotumGeek (talk) 18:54, 21 October 2012 (UTC)

Much appreciation, definition and distinction[edit]

Just to say -- that I find this stuff stunningly interesting. The caliber of interconnected comments foments a major revolution in the science of clear and parsimonious thinking. "Who are these guys, anyway?" We start connecting classical philosophical questions with computer science models and issues regarding classes and taxonomy -- and for me, the nature of distinction and dimensionality, from which imho all this stuff can be constructed -- and we are pushing for something astonishingly simple in the amazing forest of complexity. This is my first post/comment on Wikipedia, and I just gotta thank somebody for how brilliant this all is. And maybe "definition" for me, gets right to the heart of it all. My instinct is -- construct all semantic space from the single primitive element "distinction". In other words -- build all definition as something like "composite dimensional assemblies of distinctions" -- such that every object in the system is constructed from ("defined in terms of") that primitive element (and maybe that ultimate primitive is something like the Dedekind Cut in the real number line?). This review of definition -- particularly stipulative definition -- is so helpful, and the examples so resonant with my own instincts. Thank you.

Bruceschuman (talk) 23:48, 29 July 2013 (UTC) Bruce Schuman, July 29, 2013, Santa Barbara,

The golden rule of definitions[edit]

I do know that the definiendum is not supposed to be in the definition itself. What is the name of this rule? (talk) 17:31, 5 May 2014 (UTC)