To: |
Pat Hayes <phayes@xxxxxxx>, "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx> |
---|---|

From: |
"Barkmeyer, Edward J" <edward.barkmeyer@xxxxxxxx> |

Date: |
Mon, 23 Jun 2014 20:43:51 +0000 |

Message-id: |
<df323e6f6fb14cc097b47b1eb6e16792@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx> |

Pat, (01) Now that you put it that way, I suppose there are two other approaches: (02) (3) There is the mathematical approach: axiomatic definition. You specify a set of axioms involving Xs and every thing t that satisfies all of those axioms is an X. The concept is exactly: "things that obey this set of axioms, regardless of what other properties they may have." This is also called the "if it walks like a duck" approach. But the predicates that are used in the axioms other than is-a-X must also have been previously defined. (In mathematics, the best known examples of pure axiomatic definition are 'equivalence relation' and 'ordering relation'.) (03) (4) There is the special case of (3) that is "co-definition". The set of axioms that defines X uses the undefined symbol Y, but what is happening is the simultaneous definitions of two kinds of things (X and Y) by their interrelationships. (The familiar example in mathematics is 'group' and 'operator'.) (04) To start the process, there must somewhere be 'primitive concepts' -- things you can't formally "define". In ISO 1087 terms, such things have 'descriptions', by which a human might be able to figure out what you are talking about, as opposed to 'definitions', which are clear as to how to make the determination. In an ontology, the primitive predicates/concepts are the ones you elect not to define explicitly (via iff) or axiomatically, whether you could have or not. When I construct ontologies, I try to at least be aware of the 'primitive concepts' that it introduces. Note also that a theory may intentionally leave some fundamental concepts undefined, so as to enable the theory to be applied to a variety of things; each application then assumes that some class of things is a subclass of the fundamental theoretical concept. (05) Dictionaries ultimately avoid 'turtles all the way down', either by ultimately becoming descriptive rather than definitive, or by ultimately becoming circular. (06) -Ed (07) > -----Original Message----- > |

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