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Revision as of 18:06, 17 November 2008
, 18:06, 17 November 2008renumber figures & tables
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Intuitively, the ''L''<sub>''uv''</sub> operators may be thought of as qualifying propositions according to the elements of the universe of discourse that each proposition positively values. Taken together, these measures provide us with the means to express many useful observations about the propositions in ''X''° = [''x'', ''y''], and so they mediate a subtext [''L''<sub>00</sub>, ''L''<sub>01</sub>, ''L''<sub>10</sub>, ''L''<sub>11</sub>] that takes place within the higher order universe of discourse ''X''°2 = [''X''°] = <nowiki>[[</nowiki>''x'', ''y''<nowiki>]]</nowiki>. Figure 12 summarizes the action of the ''L''<sub>''uv''</sub> on the ''f''<sub>''i''</sub> within ''X''°2.
Intuitively, the ''L''<sub>''uv''</sub> operators may be thought of as qualifying propositions according to the elements of the universe of discourse that each proposition positively values. Taken together, these measures provide us with the means to express many useful observations about the propositions in ''X''° = [''x'', ''y''], and so they mediate a subtext [''L''<sub>00</sub>, ''L''<sub>01</sub>, ''L''<sub>10</sub>, ''L''<sub>11</sub>] that takes place within the higher order universe of discourse ''X''°2 = [''X''°] = <nowiki>[[</nowiki>''x'', ''y''<nowiki>]]</nowiki>. Figure 6 summarizes the action of the ''L''<sub>''uv''</sub> on the ''f''<sub>''i''</sub> within ''X''°2.
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Figure 12. Higher Order Universe of Discourse [L_uv] c [[x, y]]
Figure 6. Higher Order Universe of Discourse [L_uv] c [[x, y]]
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{| align="center" border="1" cellpadding="6" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:90%"
{| align="center" border="1" cellpadding="6" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:90%"
|+ '''Table 13. Syllogistic Premisses as Higher Order Indicator Functions'''
|+ '''Table 7. Syllogistic Premisses as Higher Order Indicator Functions'''
| A
| A
| align=left | Universal Affirmative
| align=left | Universal Affirmative
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Tables 14 and 15 develop these ideas in more detail.
Tables 8 and 9 develop these ideas in more detail.
{| align="center" border="1" cellpadding="6" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:90%"
{| align="center" border="1" cellpadding="6" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:90%"
|+ '''Table 14. Relation of Quantifiers to Higher Order Propositions'''
|+ '''Table 8. Relation of Quantifiers to Higher Order Propositions'''
|- style="background:paleturquoise"
|- style="background:paleturquoise"
|Mnemonic||Category||Classical Form||Alternate Form||Symmetric Form||Operator
|Mnemonic||Category||Classical Form||Alternate Form||Symmetric Form||Operator
{| align="center" border="1" cellpadding="4" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:90%"
{| align="center" border="1" cellpadding="4" cellspacing="0" style="background:lightcyan; font-weight:bold; text-align:center; width:90%"
|+ '''Table 15. Simple Qualifiers of Propositions (n = 2)'''
|+ '''Table 9. Simple Qualifiers of Propositions (''n'' = 2)'''
|- style="background:paleturquoise"
|- style="background:paleturquoise"
| align=right | ''x'' : || 1100 || ''f''
| align=right | ''x'' : || 1100 || ''f''
