Wednesday, 23 May 2018
Halliday (1961: Section 2.2):
... I have used the terms 'hierarchy', taxonomy', and 'cline' as general scale types.
A hierarchy is taken to mean a system of terms related along a single dimension which must be one involving some form of logical precedence (such as inclusion).
A taxonomy is taken to mean a special type of hierarchy, one with two additional characteristics:
(i) there is a constant relation of each term to the term immediately following it, and a constant reciprocal relation of each to that immediately preceding it; and
(ii) degree is significant, so that the place in order of each one of the terms, statable as the distance in number of steps from either end, is a defining characteristic of that term.
A cline resembles a hierarchy in that it involves relation along a single dimension; but instead of being made up of a number of discrete terms a cline is a continuum carrying potentially infinite gradation.
Monday, 21 May 2018
Saturday, 19 May 2018
Lemke (unpublished, undated):
A topology, in mathematical terms, is A SET OF CRITERIA FOR ESTABLISHING DEGREES OF NEARNESS OR PROXIMITY AMONG THE MEMBERS OF SOME CATEGORY. It turns a 'collection' or set of objects into a space defined by the relations of those objects. Objects which are more alike by the criteria are represented in this space as being closer together; those which are less alike are further apart. There can be multiple criteria, which may be more or less independent of one another, so that two texts, for instance may be closer together in one dimension (say horizontal distance), but further apart in another (vertical distance). What is essential, obviously, is our choice of the criteria, the parameters, that define similarity and difference on each dimension.