Defining ``definition'' - a summary

All definitions have two parts:

Definiendum:

that which is to be defined, i.e. a word (or other lexical item such as an idiom) or an object (or concept).

Definiens:

that which defines, i.e. a complex of other words or concepts.

While there are just two main kinds of definiendum, there are many kindsw of definiens.

1. The popular understanding of definition is the ``dictionary definition'', known as a definition by genus proximum et differentia specifica, as in ``a poodle is a dog with a haircut'':
   1. definiendum: poodle
   2. definiens:
      1. genus proximum (nearest kind): dog
      2. differens specificum (specific difference): with a haircut
2. A contextual definition is in general taken from a text corpus and gives examples of the use of a term:
   1. definiendum: dog
   2. definiens: a dog barks, is sometimes called a man's best friend, an accolade which I find incomprehensible.
      1. genus proximum (nearest kind): dog
      2. differens specificum (specific difference): with a haircut
   or
   1. definiendum: moo
   2. definiens: Well, a cow moos.
3. An ostensive definition involves showing the object or objects to be defined:
   • What is an ampersand? - &
   • What does `moo' mean? - [demonstrate a mooing sound]
   • What is a web page? - What you are looking at right now.
   • What is a letter? - One of the set {a, b, c, ..., z}.
4. A recursive or inductive definition is a combination of the genus proximum et differentia specifica type and the contextual type, and it is used to define infinite sets of objects such as the set of words of a language or the set of sentences of a language (new words and sentences can always be invented ad infinitum). An inductive definition always has 3 parts: The base, the recursion, and the exclusion (you will also find other terms used in different disciplines). For example:
   1. Defining a word (in English):
      1. Base: A word is a stem. (This defines an uninflected word.).
      2. Recursion: A word is a word with an inflection. (This sounds circular, but it is not, because the simplest case is a word with a stem which is a root, and maybe an inflection; inflections just make the word grow longer - in English, the ``depth of recursion'' is highly restricted, but this is not the case for many so-called ``agglutinative'' languages.
      3. Exclusion: Nothing else is a word.
      and
      1. Base: A stem is a root.
      2. Recursion: A stem is a stem with a derivational affix.
      3. Nothing else is a stem.
      and finally, to ensure a complete chain of definitions:
      1. A root is the smallest semantically interpretable constituent of a lexical item (i.e. a lexical morpheme).
         Note: roots and lexical items are ostensively defined by listing them in dictionaries!

Note that a special combination of ostensive and contextual definition occurs with deictic expressions, i.e. expressions which involve reference to the person or persons, time and place concerned in the utterance:

1. Deictic pro-forms: I, you, he, she, it, we, they; here, there, yonder; now, then; this, that.
2. Implicitly deictic lexical items as in the pairs: come, go; give, take; bring, take.

Tasks:

1. What is the difference between a definition and an explanation?
2. Construct other examples for all definition types.
3. Define the meanings of the deictic words listed above, incorporating references to the context of utterance.