Talk:Definition

Archive 1 to end may 2007

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)

' 50.240.174.93 (talk) 11:44, 21 June 2023 (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)

@'''' 50.240.174.93 (talk) 11:43, 21 June 2023 (UTC)

Image

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.

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 fqor citation - give it a day or so. Banno 23:39, 11 June 2007 (UTC)

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)

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)

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))

Semi-protection

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

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)

negative

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

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

In a lengthy exercise on definition by Professor Norman Swartz [2], Simon Fraser University http://www.sfu.ca/philosophy/ 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 (talk • contribs) 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

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?

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

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, http://originresearch.com

The golden rule of definitions

I do know that the definiendum is not supposed to be in the definition itself. What is the name of this rule? 189.226.211.250 (talk) 17:31, 5 May 2014 (UTC)

Definiens & definiendum

This article would be a good place to define 'definiens' and 'definiendum'. 'Definiens' is used without explanation. 86.164.173.122 (talk) 19:05, 3 May 2015 (UTC)

Classes of intensional definitions

I just corrected a few minor mistakes in the above-mentioned subsection. But I think the entire paragraph is a bit shaky in respect of its content. In particular, the explanation "An existing definition that serves as a portion of the new definition" for "genus" seems a bit idiosyncratic to me. To my mind it would be more classical to say that the genus is something (a notion, concept, idea, or whatever you want to call it and whatever it turns out to be) that is already defined, that is: for which a definition already exists. Though I'm not even sure about that: Does it need to be defined. Is it not often the case that it is simply assumed that its meaning is clear?

Futhermore: "Bussler, Christoph, and Dieter Fensel, eds. Artificial Intelligence: Methodology, Systems and Applications: 11th International Conference, AIMSA 2004: Proceedings. Springer-Verlag, 2004. p.6" is hardly the best reference we can find. This is taken from conference proceedings in AI, surely we can find a logic-textbook.--TheseusX (talk) 22:02, 29 June 2015 (UTC)

The title suggests that there are several classes of intensional definitions but only one is given, namely genus–differentia definition. — Preceding unsigned comment added by Kaelltee (talk • contribs) 10:36, 8 December 2021 (UTC)

Convention

It means diverting buying thoughts. Rnbmbaml (talk) 16:19, 31 October 2016 (UTC)

Etymology of 'Definition'

Do you think we should add a section on the etymology of the word 'definition'? It's a bit fascinating and to me, and a misnomer. The root latin word is 'finis' - which in Latin means "end." However, defintions have changed, so they are not really "bound" or "brought to an end."

Any thoughts? RyanDanielst (talk) 22:04, 20 October 2017 (UTC)

Antonyms

In the fallacies of definition section, it states that 'antecedent' clearly cannot be defined without the use of 'consequent', and conversely. This does not seem clear to me at all - it seems not only unnecessary, but circular. Dictionary.com defines antecedent as "a preceding circumstance, event, object, style, phenomenon, etc." and consequent as "following as an effect or result; resulting (often followed by on, upon, or to)". Neither of these definitions make use of the antonym. Nautilus 06:08, 6 December 2017 (UTC)

The sequent article defines the case of a standalone 'consequent', without 'antecedent'. You could use this as a counterexample for the statement that " 'consequent' clearly cannot be defined without the use of 'antecedent'. " --Ancheta Wis   (talk | contribs) 10:58, 6 December 2017 (UTC)

What if we were to strike 'nor conversely' in #2 of the 'fallacies of definition' section? --Ancheta Wis   (talk | contribs) 13:07, 6 December 2017 (UTC)

Nominal definitions vs real definitions

Why can't there be a quid rei of "hobbit"? That is (to say much the same in different ways):

• Does the possibility of a quid rei depend upon actual existence or only upon suggested existence, even if actual existence is denied (fiction)?

• Why should there be a quid rei of "horse" but not of "unicorn"?

• If the possibility of a quid rei depends upon actual existence, how can there ever be a hypothesis?

• Was there no quid rei of "black swan" before one was found? Errantius (talk) 22:13, 29 January 2020 (UTC)

Semi-protected edit request on 9 August 2021

In the "Problems" section:

Change: "For this reason, Locking adds ..."

To: "For this reason, Locke adds ..."

That reverts this edit, which changed "Locke" to "Locking".

--50.53.35.207 (talk) 00:33, 9 August 2021 (UTC)

 Done RudolfRed (talk) 01:39, 9 August 2021 (UTC)

what's the definition of "recession"

lol User:Muboshgu what is the definition of recession?

105.160.91.231 (talk) 05:38, 30 July 2022 (UTC)lollollollollollol

You can participate in the discussion at Talk:Recession. Schazjmd (talk) 14:01, 30 July 2022 (UTC)

Background note for other editors: Jack Posobiec, among others, has been tweeting a faked version of this article, in which the lead has been changed to A definition is a fluid statement..., possibly to poke fun at the edit storm on Recession. Hundreds of other twitter users have taken the hoax as fact. Schazjmd (talk) 14:05, 30 July 2022 (UTC)

Discussed today by the USA Today fact-checking team. —scs (talk) 18:27, 26 August 2022 (UTC)

Need a separate article about definitions in formal logic

We need a separate article about definitions in formal logic (such as first-order predicate logic, lambda calculi, etc.) VictorPorton (talk) 02:41, 7 August 2022 (UTC)

Agree 👍 This article might also benefits to include under a section close to the top an overview of formal perspectives on definitions.

Two heads better than one. Interested in starting the page together and augment with the essential matter a section of this article? Mathias Hoffnung (talk) 12:59, 14 November 2022 (UTC)

Semi-protected edit request on 17 March 2023

The definition of definition is basically meaning the meaning of a word. For example, the definition of tall means a suggestively high person,thing or object and so on.

 Not done: it's not clear what changes you want to be made. Please mention the specific changes in a "change X to Y" format and provide a reliable source if appropriate. Cannolis (talk) 08:21, 17 March 2023 (UTC)

AvaSci

Motion capture collects a large volume of accurate data on a subject's movement and then creates an Avatar. If you analyze this data with the best Science has to offer, you can make advancements for the betterment of the world. Hence the portmanteau AvaSci. Mocapforbetter (talk) 21:07, 24 October 2023 (UTC)

Here's a definition of definition

A definition is a carefully crafted statement that reveals the inherent nature of a subject. It pinpoints the intrinsic qualities that distinguish the subject, whether it is abstract or tangible. For abstract concepts, a definition aids in understanding. For tangible entities, it permits identification GPC (talk) 19:25, 18 December 2023 (UTC)

And in an ostensive definition which is worked-through by participants in a mutual process, the participants can reach an agreement among themselves, by treaty. One advantage of such a process is that unspoken assumptions by the respective participants can be unearthed. See Penrose triangle, in which ground truth is exposed as a projection, or perspective, or model. -- Ancheta Wis   (talk | contribs) 09:11, 21 May 2024 (UTC)

Definitions as logic programs

User D.Lizard has deleted the logic programming section, without a proper discussion. I do not want to engage in an editing war. But such major changes should not be made without adequate justification. Robert Kowalski (talk) 08:39, 21 May 2024 (UTC)

The reasons for deleting the section are the following:

• A large part of it is a copy of a detailed example given in the article Logic programming. This has nothing to do here.
• The linked article uses 13 times the word "definition", but always with the common meaning of the word (nothing specific to logic programming). There is no evidence that there is a specific notion of a definition in logic programming
• Logic programming is a programming paradigm that seems to not be commonly used nowadays. In any case it is a niche research subject that must not appear here per WP:UNDUE.
• Definitions appear in many areas of computer science (definition of a function or subprogram, of a data type etc. Mentioning logic programming, and logic programing only, gives clearly a WP:UNDUE weight to this minor subarea of computer science.

In summary, this section does not contain anything that is relevant to this article. D.Lazard (talk) 17:45, 21 May 2024 (UTC)

• There are two examples in the deleted subsection. The first example shows how the definition of ancestor in the previous subsection can be represented as a logic program. The fact that this example is also used in the logic programming article does not affect its relevance to this article. The second example is not in the logic programming article.
• There is detailed evidence that logic programs can be viewed as definitions and definitions can be formalised by logic programs in many papers, two of which are cited in the deleted subsection. The two papers are: (1) Denecker, M., Ternovska, E.: A logic of nonmonotone inductive definitions. ACM Trans. Comput. Log. 9(2), 14:1–14:52 (2008) and (2) Warren, D.S. and Denecker, M., 2023. A better logical semantics for prolog. In Prolog: The Next 50 Years (pp. 82-92). Cham: Springer Nature Switzerland.
• The view that logic programming is a niche research subject is a subjective opinion, and not a neutral point of view.
• The point of the deleted logic programming section is to show that definitions (when viewed as logic programs) are a Turing complete model of computation. The same point can (and should) be made about functional programs.

The fact that definitions are a Turing complete model of computation is an important property of definitions, which should be represented in the article. Robert Kowalski (talk) 12:41, 22 May 2024 (UTC)

If definitions are important in logic programming, the article Logic programming must be edited for making this clear. You wrote "the fact that definitions are a Turing complete model of computation is an important property of definitions". In logic programming I read "Horn clause logic programs are Turing complete". I deduce that, for you, "definition" is an alternate name for a Horn clause. There is nothing in Horn clause and Logic programming that suggests this equivalence. You assert that definitions and logic programs are equivalent concept, and you cite several WP:primary sources to support this assertion. For such a fundamental assertion, primary sources are no sufficient. This must be discuted in WP:secondary sources; that is, in this case, textbooks on logical programming.

The article Definition is is intended for a general audience, and therefore must be a summary of the different variants of the concept. So, it must refer to other Wikipedia articles for the technical details. Direct references to WP:primary sources are not suitable since they are generally not understandable by a general audience. So, for WP:Verification, interested readers must pass through specialized Wikipedia articles. It results that, with the current state of the specialized articles, the concept of a definition in logic programming cannot be mentioned here. D.Lazard (talk) 13:53, 22 May 2024 (UTC)

The recent textbook by Poole and Mackworth 2023 puts it like this: "clauses with the atom as the head cover all the cases when the atom is true. In particular, an atom with no clauses is false. Under this assumption, an agent can conclude that an atom is false if it cannot derive that the atom is true. This is also called the closed-world assumption. It can be contrasted with the open world assumption, which is that the agent does not know everything and so cannot make any conclusions from a lack of knowledge. The closed-world assumption requires that everything relevant about the world is known to the agent. This assumption that there is a definition of each atom in terms of clauses is the basis of logic programming." Robert Kowalski (talk) 15:08, 22 May 2024 (UTC)

This must be discussed in the relevant article before it may be included here in a comprehensible way. Moreover WP:UNDUE must be considered. In particular, the definition of types in type theory and of functions in functional programming seem to be at least as important as the definitions of atoms in logic programming. So, I am in favor of a section that present a balanced view of the different sort of definitions considered in computer science, but I am strongly against giving such a undue weight to logic programming. D.Lazard (talk) 16:18, 22 May 2024 (UTC)

Presumably, by "relevant article" you mean the logic programming article, and I agree with that. But then someone should explain the relationship between definitions and functional programs, and between definitions and type theories. Robert Kowalski (talk) 09:25, 23 May 2024 (UTC)