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Revision as of 21:32, 25 May 2007
, 21:32, 25 May 2007→1.3.4.2. Sign Relations : A Primer: note on notation
In the present example, ''S'' = ''I'' = syntactic domain.
In the present example, ''S'' = ''I'' = syntactic domain.
The sign relation associated with a given interpreter ''J'' may be denoted ''L''<sub>''J'' </sub> or ''L''(''J''). Tables 1 and 2 give the sign relations associated with the interpreters ''A'' and ''B'', respectively, putting them in the form of ''[[relational database]]s''. Thus, the rows of each Table list the ordered triples of the form ‹''o'', ''s'', ''i''› that make up the corresponding sign relations, ''L''<sub>''A'' </sub>, ''L''<sub>''B'' </sub> ⊆ ''O'' × ''S'' × ''I''. It is often tempting to use the same names for objects and for relations involving these objects, but it is best to avoid this in a first approach, taking up the issues that this practice raises after the less problematic features of these relations have been treated.
The sign relation associated with a given interpreter ''J'' is denoted ''L''<sub>''J'' </sub> or ''L''(''J''). Tables 1 and 2 give the sign relations associated with the interpreters ''A'' and ''B'', respectively, putting them in the form of ''[[relational database]]s''. Thus, the rows of each Table list the ordered triples of the form ‹''o'', ''s'', ''i''› that make up the corresponding sign relations, ''L''<sub>''A'' </sub>, ''L''<sub>''B'' </sub> ⊆ ''O'' × ''S'' × ''I''. It is often tempting to use the same names for objects and for relations involving these objects, but it is best to avoid this in a first approach, taking up the issues that this practice raises after the less problematic features of these relations have been treated.
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:60%"
{| align="center" border="1" cellpadding="8" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:60%"
As it happens, the sign relations ''L''<sub>''A''</sub> and ''L''<sub>''B''</sub> in the present example are fully symmetric with respect to exchanging signs and interpretants, so all of the structure of (''L''<sub>''A''</sub>)<sub>''OS'' </sub> and (''L''<sub>''B''</sub>)<sub>''OS'' </sub> is merely echoed in (''L''<sub>''A''</sub>)<sub>''OI'' </sub> and (''L''<sub>''B''</sub>)<sub>''OI'' </sub>, respectively.
As it happens, the sign relations ''L''<sub>''A''</sub> and ''L''<sub>''B''</sub> in the present example are fully symmetric with respect to exchanging signs and interpretants, so all of the structure of (''L''<sub>''A''</sub>)<sub>''OS'' </sub> and (''L''<sub>''B''</sub>)<sub>''OS'' </sub> is merely echoed in (''L''<sub>''A''</sub>)<sub>''OI'' </sub> and (''L''<sub>''B''</sub>)<sub>''OI'' </sub>, respectively.
'''Note on notation.''' When there is only one sign relation ''L''<sub>''J'' </sub> = ''L''(''J'') associated with a given interpreter ''J'', it is convenient to use the following forms of abbreviation:
:{| cellpadding=4
| ''J''<sub>''OS''</sub>
| = || ''Proj''<sub>''OS'' </sub>''L''<sub>''J''</sub>
| = || (''L''<sub>''J'' </sub>)<sub>''OS''</sub>
| = || ''L''(''J'')<sub>''OS''</sub>
|-
| ''J''<sub>''SI''</sub>
| = || ''Proj''<sub>''SI'' </sub>''L''<sub>''J''</sub>
| = || (''L''<sub>''J'' </sub>)<sub>''SI''</sub>
| = || ''L''(''J'')<sub>''SI''</sub>
|-
| ''J''<sub>''OI''</sub>
| = || ''Proj''<sub>''OI'' </sub>''L''<sub>''J''</sub>
| = || (''L''<sub>''J'' </sub>)<sub>''OI''</sub>
| = || ''L''(''J'')<sub>''OI''</sub>
|}
The principal concern of this project is not with every conceivable sign relation but chiefly with those that are capable of supporting inquiry processes. In these, the relationship between the connotational and the denotational aspects of meaning is not wholly arbitrary. Instead, this relationship must be naturally constrained or deliberately designed in such a way that it:
The principal concern of this project is not with every conceivable sign relation but chiefly with those that are capable of supporting inquiry processes. In these, the relationship between the connotational and the denotational aspects of meaning is not wholly arbitrary. Instead, this relationship must be naturally constrained or deliberately designed in such a way that it: