What are some methods of defining things?

Question

In my experience, many definitions define an object/idea by merely listing it's characteristics. For example:

• Avocado
  
  • a large, usually pear-shaped fruit having green to blackish skin, a single large seed, and a soft, light-green pulp
• Sweet
  
  • having the taste or flavor characteristic of sugar, honey, etc.
  • producing the one of the four basic taste sensations that is not bitter, sour, or salt

These definitions list characteristics of the object/idea. But suppose I were to use an avocado to hold down some papers, and my friend asked me what the object on the papers was. I would tell him that it is a paper weight.

It occurred to me that definitions need not be solely defined by their physical characteristics, but perhaps through other methods, such as the purpose of the object/idea. What are some of the other ways one can define a thing?

Thanks in advance!

Answer 1

The classification of a definition might refer to

1. What is defined (an entity, a tangible thing, a word etc...)
2. How is it defined

In terms of what, in brief (since it's not directly relevant to the question but it's important in order to understand what follows) a definition may be:

1. Realistic: When it defines a tangible being in the sense that the definition refers to the object rather that to the word we use to describe it or its reflection in our mind (conception).
2. Conceptualistic: When the defined being is a concept or our concept about a being.
3. Nominalistic: When the defined being is a word and the focus is on the e explanation of the word (etymology, meaning etc)

A definition, regarding how we define things/entities/words etc... can be:

1. By Recursion: Well known in mathematics. For example the Fibonacci sequence is defined recursively. It is a sequence whose first and second elements equal 1 (x1 = x2 = 1) and all other elements are retrieved from the formula x(k+2)=x(k+1)+x(k) for k=1,2,... Constructively, we say that a recursive definition consists of the following:

   1. Determination of a number of elements that belong to the set we define
   2. A recursive rule or formula using which all other elements of the set emerge
   3. An explicit or tacit assumption that the set contains no other elements.

2. Analytical: A definition in which we plumb the logical depth and the essential characteristics of the underlying entity are analyzed. For example Euclid, provides the definition of surface as (Euclid, Elements, Book I)

   A surface is that which has length and breadth only.

3. By Enumeration: This kind of definition examines the logical width rather than the logical length of the underlying entity to be defined. The definition is carried out by referring to the elements of the defined set one by one. For example, we say that one-digit numbers are the numbers {1,2,3,4,5,6,7,8,9,0}.

4. Interpretational: A definition is interpretational when it analyses the semantics of the entity to be defined. For example from the free online dictionary, one definition of weight is

   "A measure of the heaviness of an object".

5. Etymological: The root of the word is analyzed and explained. For example the etymological definition of "etymology" from Wikipedia is

   The word "etymology" (pronounced /ɛtɨˈmɒlədʒi/) derives from Greek ἐτυμολογία (etumologíā); from ἔτυμον (étumon), meaning "true sense", and -λογία (-logía), meaning "study"; from λόγος (lógos), meaning "speech, account, reason".

6. Demonstrational: Definition by providing example. For example

   Red is the colour of this pen (pointing at the pen at the same time). This is an avocado

7. Constructive: A definition that provides a way to generate the defined object.

8. Implicit: The singleton {0} is implicitly defined as {x|x^2 + 10*x^4 = 0 and x is real}.

9. Operational(ist): The defined entity is what accrues from a measuring procedure, either physically and practically or merely mentally and only that. An operational(ist) definition runs something like that (hypothetical quotation):

   Length of an object is the result of placing a ruler along this object and we read the measurement on the ruler. This number accompanied by the units of the ruler is the length of the object.

10. GPDS definition (Genus Proximum and Differentia specifica): Is a definition that outlines the key differences (Differentia specifica) between the entity to be defined and a proximal genre (Genus Proximum) in whose logical width the defined entity is included. For example:

    In Euclidian Geometry a square is a surface (Genus Proximum) which is both equilateral and right-angled (Differentia specifica).

11. By convention: A definition that intentionally restricts the range of the defined notion to a particular field of application. There are numerous such examples in science. For example in mathematics an in particular in Finite-Dimensional Analysis one can find the definition that inner product is the binary relation:

    In finite-dimensional Euclidean spaces (Re^n where n is a non-zero integer) we call inner product the binary relation <.,.>:Re^n x Re^n -> Re, such that =SUM x(i)*y(i)

    This is fine for finite-dimensional vectors (as it is mentioned in the definition). Sometimes such assumptions are not mentioned and the reader has to wary.

12. By connotation: Definition by connotation outline the main and most important characteristics (this is subjective of course) of the entity to be defined and intentionally omit other attributes. An example is the definition of lizard from thefreedictionary.com:

    Any of numerous reptiles of the suborder Sauria or Lacertilia, characteristically having a scaly elongated body, movable eyelids, four legs, and a tapering tail.

13. Usage-driven: A definition explaining the context, conditions or situations when the defined entity is used. For example:

    Oh! :Used to express strong emotion, such as surprise, fear, anger, or pain.
    Screwdriver: A tool used for turning screws.

14. Tautological: A mapping between a notion to be defined and another well-defined one. For example:

    Fiddle := Violin

15. Contextual: A definition from the context, formally having the structure "Def(Q): Not P Then Q" (Definition of Q). Example:

    Unstable System: If a dynamical system is not stable then it is called unstable.

All these kinds of definitions appear in Science. Some of them are employed for merely pedagogical purposes. For example it is not easy to explain temperature to a primary school child as the partial Legendre transform on Internal Energy with respect to Entropy so you will concoct some less strict definition like "Temperature is the measure of hotness of a body" (Interpretational). Later on, one learns that "Temperature is the measure of mobility of the molecules of a body" (No different that the previous one - an interpretational definition).

Important: It is important to understand that there in not a single way to draw definitions. Some classes of definitions might not look not Scientifically valid.

Relations between classes of definitions: The provided classification of definitions covers a wide range of definition one finds in all fields of science (from mathematics and chemistry to social sciences and history) but does not necessarily cover all kinds of definitions. Moreover, this classification is overlapping in the sense that a particular definition might lie in more that a single class. As a conclusion... it's hard to give or understand a definition.

References:

K. Masavetas, "Introduction to Philosophy of Thermodynamic Method", Athens, 1999, pp. 22-42, NTUA Press (in Greek).

Answer 2

What are we doing when we ask for the "definition" of a word? What are we looking for? —Often we’re looking to “make sense” of a sentence that contains an unknown word in it. So we might ask, “what does this word mean?” But, with a word like “hammer,” (something that seems simple to define), we get a plethora of different uses. It’s used in a sentence as a noun. It’s used in a sentence as a verb. It’s used in a sentence as a phrasal verb (with another element). It is implicit that the question, “what is the general meaning of the word ‘hammer’?” is nonsense—we search for what connects its different uses and we find only the different circumstances in which the word is used; we could say the noun “hammer” is the same word, in terms of its construction of letters, as the verb “hammer”; but is this different from saying that the word “sun” sounds the same as the word “son?” If someone unfamiliar with English were to ask me, in speech, what “sun/son” meant, I’d ask him what sense of the sound “son/sun” he meant. If he didn’t know what sense he meant, I’d give a few examples either by demonstrating the different semantics of the two words (by getting him to see how the two suns might be used correctly in different situations—i.e. a fiery ball in the sky / a male offspring) or I’d try to explain the syntactics of the two words (by using sentences that included the word “sun” and others that included the word “son”).

Similarly, we could say that a word such as “good” has the same visual-sound but different meanings. The different meanings depend on the circumstances in which the word is used. We can grasp a meaning only through a certain use of a word. To look for the essential characteristic of “good” (or any word) is to look for the general meaning of the word. But the meaning of a word depends on its use in a specific circumstance. To look for the “good” in general is to look for the same [sən] sound in the words “sun” and “son.” But what about the “concept” of the word “good?” Don’t we use phrases like “a good runner,” a “good person,” “a good day,” etc., as though “good” has the same meaning in each case (it does have the same syntactics). But, as Wittgenstein points out in his “Lecture on Ethics,” “good” is used relatively, and its semantics depend upon its use. What makes a “good runner” is exactly what does not make a “good swimmer” (and these are analogous examples of athletes). Try to abstract the general “good” from what makes a “good horse” and a “good cook.” What is left?

So we have to see how a word is used in the circumstances in which we wish to derive its meaning (or definition). The problem is that our language is insufficient: we use the same word differently in different situations, and what connects one of its meanings to another is, essentially, its appearance, or what Wittgenstein calls “family resemblances.” (Sometimes siblings look strikingly similar, other times it’s hard to imagine that they’re related; and sometimes the unrelated look identical.) But don’t we say that a “good something” points to a “best” of something, perhaps an “ideal something?” To this Wittgenstein’s “Lecture on Ethics” is also informative: what happens if we ask what the “best road to take to town is?” Well, it depends if we want the quickest path to town, or the most scenic, or the least busy, and so on. The circumstances determine what we would call the “best.”

So a definition of a word might mislead us, if we don’t know the sense in which a word or phrase has meaning? But, as J.L. Austin points out in his illuminating essay, “The Meaning of a Word” (1940),

“The sense in which a word or a phrase ‘has a meaning’ is derivative from the sense in which a sentence ‘has a meaning’: to say a word or a phrase ‘has a meaning’ is to say that there are sentences in which it occurs which ‘have meanings’: and to know the meaning which the word or phrase has, is to know the meaning of sentences in which it occurs” (p.56, Philosophical Papers, 1961).

His statement above should be consistent with our everyday experiences: when we encounter unfamiliar words in sentences, we either intuit the unknown word’s meaning in the sentence—from the sentence (if we can)—or look up the definition of the word in a dictionary to make sense of the sentence (if we can’t make sense of the sentence without knowing that word). Only after this step can you ask your question."All the dictionary can do when we "look up the meaning of a word" is to suggest aids to the understanding of sentences in which it occurs" ("The Meaning of a Word").

Answer 3

The key distinction between a definition and a simple list of characteristics seems to me to be that the latter would include accidental and contingent properties, and the former is more concerned with the essential properties.

So, while the ability to hold down papers in the wind is a property of an avocado, it is not an essential property; on the other hand, it is the essential property of a paperweight. And, as you indicate, if the avocado is functioning as a paperweight, any definition will have to be contextual-- are you being asked about the avocado qua avocado or the avocado qua paperweight?

Answer 4

I just added an explanation of how to define basically and through a dependency.

Dynamic & Consistent

The definition should be consistent and if necessary it can be developed. The definition of something may not be fixed but dynamic, which is an expansion of undertanding (deepening), but still consistent.

Definition is dynamic. It can be developed further, as long as it has consistency. A definition may be developed with different consistency or with previous consistency along with further additional consistencies (found later).

Complete Definition

A complete definition may be provided by opposed to all the elements of the realities and still have resistance that can be configured to point at the same existence.

For example: defining the "four books" as "two books" plus "another two books", is not an exact (complete) definition. Defining the proper approach to this is, "four books" are "not five books", "instead of ten pieces of cake", "not a plant", "not a type of drink", "not a four of the fact that there are many planets in the solar system ", and further must be opposed to everything that exist. This is in order to achieve the proper (complete) definition. Can this be achieved?, Surely no!

There is no standardization whether our definition is 10% percent complete or 95% complete.

• There is no way for us to judge whether a definition is at 10%, or at any percent closer to completeness. Unless we know everything.

Dependency within Definition

• Definition must be constructed with consistencies (these consistencies may be called as nodes)

  Definition that is constructed with consistencies is equal to: a function (definition) with subfunctions (consistencies).

• In between subfunction (consistency) to another subfunction (another consistency) there must be dependencies. A consistency leads to another consistency again and again for a purpose which is to provide a definition.

  • Asserting "John is a male being" must be understood that there must be a "being" as a function may cause something that known as "male characteristic". Asserting that there is being "with" male characteristic is fallacy (unless "with" must be understood as dependency).

  Because a definition must be treated as single of something, where consistencies are part of a definition. Stating consistencies for a definition without dependencies is equal to asserting consistencies for several areas (several definitions).

Comparison in between Definitions

Two definitions may be compared each other following rules:

1. whether there is dependency from one to another definition

   • (Horse is ...) ; (Animal is ...) ; horse is part of animal, or

   • Further from two definitions may be constructed as one definition.

   (Animal is ...), where one of them is (Horse is ...)

2. whether there is intersection with dependencies from one to another definition

   • Something is: (1..., 2..., 3...), Something else is : (2..., 3..., 4...)

   Then (2..., 3...) is another conclusion (it's intersection with dependency)

3. whether there is no dependency one to another definition

   • Running Horse is ..... ; Uranium is ..... ; Running Horse is not Uranium

   • But for definitions that have no dependencies may be in the future known as there are dependencies

Rules on Reducing Definition

Reducing a definition must be provided by:

1. All consistencies from previous definition may be replaced with new consistencies with less than previous, as long as there are dependencies in between previous consistencies and the new (current, latest) consistencies,

   1. "Philosophy is ...", may be reduced to "philosophy is knowing as it is to lead us to do as it should be relevantly". We may unpack it "knowing as it is" as "any possible ways whether reasonable thinking with any additional method and from any field of knowledge" may lead us to "do properly, wisely, correctly, relevantly"

      • Understanding "what philosophy is" through reduction "philosophy is knowing as it is to lead us to do as it should be relevantly" can be accepted because this reduction implies dependencies (continuation) to any consistency within defining "what philosophy is".

   2. Another clear example: "Living human is conscious being" has relational with possibility that "Living human is being with awareness" and possibility that "Living human is being with emotions".

      • These three definitions may be used separately on different case, relevantly, because one to another definition implies dependencies (continuation). If there is consciousness then further there will be our awareness, and if there is consciousness then further we may find emotions.

      • By using one of them, it doesn't mean narrowing definition improperly about "human" (UNLESS, someone asserts that ALL human are only beings with emotions without consciousness)

      • But this reduction may not be the one and only version to define something, but it's just to focus our understanding related to specific case, to make a clear distinction.

      • If somehow we are dealing with different case where this reduction is needed to be unpacked (expanded), then we must expand this reduction to capture the problem area.

2. On discussion, a definition may be reduced by choosing only several of all consistencies from a definition and skip for the rest of available consistencies, because only several of consistencies are needed on discussion.

   1. It's provide as needed. Unless other side on discussion clearly assert the boundaries then several consistencies may be expanded wider to capture the problem

      • For example: someone asking "whether there is a car that can transport someone to another place", and we may respond by answering "i have a car for your purposes". But if we said "i have a car with four wheel drive from a specific country, already tested and no one need it at this time, and can be loaded with 5 passengers ....., ....., ....", it's inefficient (improper).

      • Unless someone asking additional assertion "that the car must have functional air conditioning, ...., ...." then at this point, we may expand more complete understanding about available car.

      • This part may be used if we aren't so sure working area of definition, or at least to provide as needed.

   2. Another example: the first law of thermodynamics

      • "Energy is neither created nor destroyed. It can only change form."

      • We can use only a part of it "Energy is neither created nor destroyed, ..." to assert for someone trying to create an energy, that someone wasn't creating energy. But if somehow someone was trying to repeat again and again creating energy and someone believe energy will be created, perhaps we could expand the definition with additional assertion "...., It can only change form".

      • This can be worked only within directional conversation. From A with B making conversation. But when A defining something to B, and C made a claim, then there is no accurate way to determine whether a definition must be expanded to a specific direction as needed by B. Unless for C only. A limited definition from A for B is still valid until (unless) B state an exception that oblige A to expand a definition to capture the problem.

The use of dependency within definition

• The essence is: that definition is dynamic. A definition may be adjusted to support any different point of view without changing consistencies that assert dependency outside boundaries. It's not twisting a definition. It's using definition within boundaries. It's within relevant relational. AND,

• A definition may be applied completely or a portion of it (relatively), but implementation must follow the direction of dependency within a definition.

  • An example: Something is 1..., 2..., 3... etc. We may use from 1 to 3, or from 2 to 3, but not from 3 to 1 (In the sense that we know the sequence represent priorities for consistencies)

The points are:

• Defining must involve consistencies,

• Definition is dynamic and adjustable by reducing or expanding within available (limited) boundaries.

• There is no exact position to "what percent" (whether 10% or 95% or at any percent) for a definition closer to completeness.

• The closer way to provide a proper definition is, by providing definition with consistencies as needed relevant to different point of view without changing consistencies that assert dependency outside boundaries.

• Definition can be reduced to provide comparison as long as

  • There is no consistency being replaced with another consistency that assert dependency outside boundaries.

  • After reduction, a definition still can capture the problem area relevantly (within scope).

This is just small part of huge methods available out there on defining something, further, we should learn about syllogism, particular and universal proposition and anything related to these.

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For implementation of dependency, Please refer to these examples, Is Kurt Gödel's Incompleteness Theorem a “cheap trick”? & Are omniscience and omnipotence mutually inconsistent?.