Talk:Definition

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Archive 1 to end may 2007

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[edit] definitions in mathematics

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)

[edit] Image

Scientific classification of living things uses definition by genus and differentia
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 looked at one.
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)

[edit] proposed addition to lead paragraph

I moved this from the lead section for discussion:

  • "A definition could also be defined as statement that holds true irrespective of time and circumstance."

--Jtir 22:10, 8 May 2007 (UTC)

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

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)

[edit] Unity

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)

[edit] WikiProject class rating

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)

[edit] Extensive vs. Ostensive definitions

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))