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Directory:Jon Awbrey/Papers/Inquiry Driven Systems (view source)
Revision as of 19:11, 1 September 2007
, 19:11, 1 September 2007→1.3.4.14. Application of OF : Generic Level: markup
A symbol like "''x'' <font face="system"><s><</s></font>" or "''x'' <font face="system"><s>></s></font>", with extra spaces or dots being optional, is called a ''catenation'', where "''x''" is the ''catenand'' and "<font face="system"><s><</s></font>" or "<font face="system"><s>></s></font>" is the ''catenator''. Due to the fact that "<font face="system"><s><</s></font>" and "<font face="system"><s>></s></font>" indicate dyadic relations, the significance of these so-called ''unsaturated'' catenations can be rationalized as follows:
A symbol like "''x'' <font face="system"><s><</s></font>" or "''x'' <font face="system"><s>></s></font>", with extra spaces or dots being optional, is called a ''catenation'', where "''x''" is the ''catenand'' and "<font face="system"><s><</s></font>" or "<font face="system"><s>></s></font>" is the ''catenator''. Due to the fact that "<font face="system"><s><</s></font>" and "<font face="system"><s>></s></font>" indicate dyadic relations, the significance of these so-called ''unsaturated'' catenations can be rationalized as follows:
: "''x'' <font face="system"><s><</s></font>" = "''x'' is the Instance of what?" = "''x''’s Property",
: "''x'' <font face="system"><s><</s></font>" = "''x'' is the Instance of what?" = "''x''’s Property" ,
: "''x'' <font face="system"><s>></s></font>" = "''x'' is the Property of what?" = "''x''’s Instance".
: "''x'' <font face="system"><s>></s></font>" = "''x'' is the Property of what?" = "''x''’s Instance" .
In this fashion, the definitions of icons and indices can be reformulated:
In this fashion, the definitions of icons and indices can be reformulated:
: ''x''’s Icon = ''x''’s Property's Instance = ''x'' <math>\cdot</math> <font face="system"><s><</s></font><font face="system"><s>></s></font>,
: ''x''’s Icon = ''x''’s Property's Instance = ''x'' <math>\cdot</math> <font face="system"><s><</s></font><font face="system"><s>></s></font> ,
: ''x''’s Index = ''x''’s Instance's Property = ''x'' <math>\cdot</math> <font face="system"><s>></s></font><font face="system"><s><</s></font>.
: ''x''’s Index = ''x''’s Instance's Property = ''x'' <math>\cdot</math> <font face="system"><s>></s></font><font face="system"><s><</s></font> .
According to the definitions of the homogeneous sign relations ''M'' and ''N'', we have:
According to the definitions of the homogeneous sign relations ''M'' and ''N'', we have:
: ''x''’s Icon = ''x'' <math>\cdot</math> ''M''<sub>''OS''</sub>,
: ''x''’s Icon = ''x'' <math>\cdot</math> ''M''<sub>''OS''</sub> ,
: ''x''’s Index = ''x'' <math>\cdot</math> ''N''<sub>''OS''</sub>.
: ''x''’s Index = ''x'' <math>\cdot</math> ''N''<sub>''OS''</sub> .
Equating the results of these equations yields the analysis of M and N as forms of composition within the genre of properties and instances:
Equating the results of these equations yields the analysis of ''M'' and ''N'' as forms of composition within the genre of properties and instances:
: ''x''’s Icon = ''x'' <math>\cdot</math> ''M''<sub>''OS''</sub> = ''x'' <math>\cdot</math> <>,
: ''x''’s Icon = ''x'' <math>\cdot</math> ''M''<sub>''OS''</sub> = ''x'' <math>\cdot</math> <font face="system"><s><</s></font><font face="system"><s>></s></font> ,
: ''x''’s Index = ''x'' <math>\cdot</math> ''N''<sub>''OS''</sub> = ''x'' <math>\cdot</math> ><.
: ''x''’s Index = ''x'' <math>\cdot</math> ''N''<sub>''OS''</sub> = ''x'' <math>\cdot</math> <font face="system"><s>></s></font><font face="system"><s><</s></font> .
On the assumption (to be examined more closely later) that any object x can be taken as a sign, the converse relations appear to be manifestly identical to the originals:
On the assumption (to be examined more closely later) that any object ''x'' can be taken as a sign, the converse relations appear to be manifestly identical to the originals:
: For Icons: ''x''’s Object = ''x'' <math>\cdot</math> ''M''<sub>''SO''</sub> = ''x'' <math>\cdot</math> <>,
: For Icons: ''x''’s Object = ''x'' <math>\cdot</math> ''M''<sub>''SO''</sub> = ''x'' <math>\cdot</math> <font face="system"><s><</s></font><font face="system"><s>></s></font> ,
: For Indices: ''x''’s Object = ''x'' <math>\cdot</math> ''N''<sub>''SO''</sub> = ''x'' <math>\cdot</math> ><.
: For Indices: ''x''’s Object = ''x'' <math>\cdot</math> ''N''<sub>''SO''</sub> = ''x'' <math>\cdot</math> <font face="system"><s>></s></font><font face="system"><s><</s></font> .
Abstracting from the applications to an otiose x delivers the results:
Abstracting from the applications to an otiose ''x'' delivers the results:
: For Icons: ''M''<sub>''OS''</sub> = ''M''<sub>''SO''</sub> = <>,
: For Icons: ''M''<sub>''OS''</sub> = ''M''<sub>''SO''</sub> = <font face="system"><s><</s></font><font face="system"><s>></s></font> ,
: For Indices: ''N''<sub>''OS''</sub> = ''N''<sub>''SO''</sub> = ><.
: For Indices: ''N''<sub>''OS''</sub> = ''N''<sub>''SO''</sub> = <font face="system"><s>></s></font><font face="system"><s><</s></font> .
This appears to suggest that icons and their objects are icons of each other, and that indices and their objects are indices of each other. Are the results of these symbolic manipulations really to be trusted? Given that there is no mention of the interpretive agent to whom these sign relations are supposed to appear, one might well suspect that these results can only amount to approximate truths or potential verities.
This appears to suggest that icons and their objects are icons of each other, and that indices and their objects are indices of each other. Are the results of these symbolic manipulations really to be trusted? Given that there is no mention of the interpretive agent to whom these sign relations are supposed to appear, one might well suspect that these results can only amount to approximate truths or potential verities.