User:Marshallsumter/Dominant group/Rigorous definition
What is a rigorous definition of "dominant group"?
Notation: let the symbol Def. indicate that a definition is following.
To help with definitions, their meanings and intents, there is the learning resource theory of definition.
The rigorous definition fulfills the axioms that define a metadefinition so that a generalized definition can be defined using an appropriate function that fulfills the axioms. Having met these axioms as a criteria of a general definition, the definition is said to be a rigorous definition.
An axiomatic definition is a rigorous definition: "the definition must clearly state the rules that are considered as binding, and on the other hand give the implementor enough freedom to achieve efficiency by leaving certain less important aspects undefined."
The term "dominant group" appears to be used to identify entities of importance. The genera differentia for possible relative synonyms of "dominant group" fall into the following set of orderable pairs:
|Synonym for "dominant"||Category Number||Category Title||Synonym for "group"||Category Number||Catgeory Title|
|-----||---||-------||"sect"||1018||RELIGIONS, CULTS, SECTS|
'Orderable' means that any synonym from within the first category can be ordered with any synonym from the second category to form an alternate term for "dominant group"; for example, "superior class", "influential sect", "master assembly", "most important group", and "dominant painting". "Dominant" falls into category 171. "Group" is in category 61. Further, any word which has its most or much more common usage within these categories may also form an alternate term, such as "ruling group", where "ruling" has its most common usage in category 739, or "dominant party", where "party" is in category 74. "Taxon" or "taxa" are like "species" in category 61. "Society" is in category 786 so there is a "dominant society".
When one or two orderable pairs are produced, the results are
- one pair - relative synonym,
- one pair in which the first or second category has each of two from a category - definition, and
- two pairs from two to four categories - definition.
Meaningless dominant group
Each subject area within which the term "dominant group" is used has the same problem: "unless and until a rigorous definition of the term 'dominant group' is rendered, the argument fails to establish its conclusion due to the fact that one of its premises is meaningless."
Def. a category synonym for "group", including "group", and a category synonym for "dominant", including "dominant", that as one or two orderable pairs has only the properties of two pairs: i.e., from two to four categories [exclusive], or one pair in which the first or second category has up to each of two from a category is called a rigorous definition of dominant group.
Def. "the duration of a neuron's spike train assumed to correspond to a single symbol in the neural code" is called "an encoding time window".
Theorem: "[t]he duration of the encoding time window is dictated by the time scale of the information being encoded."
- C. A. R. Hoare and N. Wirth (1973). "An axiomatic definition of the programming language PASCAL". Acta Informatica 2 (4): 335-55. doi:10.1007/BF00289504. Retrieved on 2011-09-16.
- Peter Mark Roget (1969). Lester V. Berrey and Gorton Carruth. ed. Roget's International Thesaurus, third edition. New York: Thomas Y. Crowell Company. pp. 1258.
- Janet L. Travis (September 1971). "A Criticism of the Use of the Concept of "Dominant Group" in Arguments for Evolutionary Progressivism". Philosophy of Science 38 (3): 369-75. Retrieved on 2011-07-27.
- Frédéric Theunissen and John P. Miller (1995). "Temporal Encoding in Nervous Systems: A Rigorous Definition". Journal of Computational Neuroscienc 2 (2): 149-62. doi:10.1007/BF00961885. Retrieved on 2011-09-17.