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Revision as of 18:52, 16 January 2008
, 18:52, 16 January 2008→2.3.3. Pragmatic Roles: format display as table
The part of the analogy that carries propositions into functions combines with the characteristic relation between functions and sets to generate a multitude of different ways to describe essentially the same conceptual objects. From an information-theoretic point of view "essentially the same" means that the objects in comparison are equivalent pieces of information, parameterized or coded by the same number of bits and falling under isomorphic types. When assigning characters to individual examples of these entities, I think it helps to avoid drawing too fine a distinction between the logical, functional, and set-theoretic roles that have just been put in correspondence. Thus, I avoid usages that rigidify the pragmatic dimensions of variation within the columns below:
The part of the analogy that carries propositions into functions combines with the characteristic relation between functions and sets to generate a multitude of different ways to describe essentially the same conceptual objects. From an information-theoretic point of view "essentially the same" means that the objects in comparison are equivalent pieces of information, parameterized or coded by the same number of bits and falling under isomorphic types. When assigning characters to individual examples of these entities, I think it helps to avoid drawing too fine a distinction between the logical, functional, and set-theoretic roles that have just been put in correspondence. Thus, I avoid usages that rigidify the pragmatic dimensions of variation within the columns below:
:{| cellpadding="4"
| Proposition
| ''':'''
| Interpretation
| '''→'''
| Boolean
| '''{'''
| False
| ''','''
| True
| '''}'''
|-
| Function
| ''':'''
| Vector
| '''→'''
| Binary
| '''{'''
| 0
| ''','''
| 1
| '''}'''
|-
| Region
| ''':'''
| Cell
| '''→'''
| Content
| '''{'''
| Out
| ''','''
| In
| '''}'''
|-
| Subset
| ''':'''
| Point
| '''→'''
| Content
| '''{'''
| Out
| ''','''
| In
| '''}'''
|}
Though it may be advisable not to reify the practical distinctions among these roles, this is not the same thing as failing to see them or denying their use. Obviously, these differences may vary in relative importance with the purpose at hand or context of use. However, the mere fact that a distinction can generally be made is not a sufficient argument that it has any useful bearing on a particular purpose.
Though it may be advisable not to reify the practical distinctions among these roles, this is not the same thing as failing to see them or denying their use. Obviously, these differences may vary in relative importance with the purpose at hand or context of use. However, the mere fact that a distinction can generally be made is not a sufficient argument that it has any useful bearing on a particular purpose.
