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MyWikiBiz, Author Your Legacy — Tuesday November 26, 2024
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With this interpretation in mind we note the following correspondences between classical quantifications and higher order indicator functions:
 
With this interpretation in mind we note the following correspondences between classical quantifications and higher order indicator functions:
   −
{| 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="font-weight:bold; text-align:center; width:90%"
 
|+ '''Table 7.  Syllogistic Premisses as Higher Order Indicator Functions'''
 
|+ '''Table 7.  Syllogistic Premisses as Higher Order Indicator Functions'''
 
| <math>\mathrm{A}\!</math>
 
| <math>\mathrm{A}\!</math>
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Tables&nbsp;8 and 9 develop these ideas in more detail.
 
Tables&nbsp;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="font-weight:bold; text-align:center; width:90%"
 
|+ '''Table 8.  Relation of Quantifiers to Higher Order Propositions'''
 
|+ '''Table 8.  Relation of Quantifiers to Higher Order Propositions'''
|- style="background:paleturquoise"
+
|- style="background:ghostwhite"
 
|Mnemonic||Category||Classical Form||Alternate Form||Symmetric Form||Operator
 
|Mnemonic||Category||Classical Form||Alternate Form||Symmetric Form||Operator
 
|-
 
|-
| E<br>Exclusive
+
| <math>\mathrm{E}\!</math><br>Exclusive
 
| Universal<br>Negative
 
| Universal<br>Negative
 
| align=left | All x is (y)
 
| align=left | All x is (y)
 
| align=left | &nbsp;
 
| align=left | &nbsp;
 
| align=left | No x is y
 
| align=left | No x is y
| (''L''<sub>11</sub>)
+
| <math>(\!| L_{11} |\!)</math>
 
|-
 
|-
| A<br>Absolute
+
| <math>\mathrm{A}\!</math><br>Absolute
 
| Universal<br>Affirmative
 
| Universal<br>Affirmative
 
| align=left | All x is y
 
| align=left | All x is y
 
| align=left | &nbsp;
 
| align=left | &nbsp;
 
| align=left | No x is (y)
 
| align=left | No x is (y)
| (''L''<sub>10</sub>)
+
| <math>(\!| L_{10} |\!)</math>
 
|-
 
|-
 
| &nbsp;
 
| &nbsp;
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| align=left | No y is (x)
 
| align=left | No y is (x)
 
| align=left | No (x) is y
 
| align=left | No (x) is y
| (''L''<sub>01</sub>)
+
| <math>(\!| L_{01} |\!)</math>
 
|-
 
|-
 
| &nbsp;
 
| &nbsp;
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| align=left | No (y) is (x)
 
| align=left | No (y) is (x)
 
| align=left | No (x) is (y)
 
| align=left | No (x) is (y)
| (''L''<sub>00</sub>)
+
| <math>(\!| L_{00} |\!)</math>
 
|-
 
|-
 
| &nbsp;
 
| &nbsp;
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| align=left | &nbsp;
 
| align=left | &nbsp;
 
| align=left | Some (x) is (y)
 
| align=left | Some (x) is (y)
| ''L''<sub>00</sub>
+
| <math>L_{00}\!</math>
 
|-
 
|-
 
| &nbsp;
 
| &nbsp;
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| align=left | &nbsp;
 
| align=left | &nbsp;
 
| align=left | Some (x) is y
 
| align=left | Some (x) is y
| ''L''<sub>01</sub>
+
| <math>L_{01}\!</math>
 
|-
 
|-
| O<br>Obtrusive
+
| <math>\mathrm{O}\!</math><br>Obtrusive
 
| Particular<br>Negative
 
| Particular<br>Negative
 
| align=left | Some x is (y)
 
| align=left | Some x is (y)
 
| align=left | &nbsp;
 
| align=left | &nbsp;
 
| align=left | Some x is (y)
 
| align=left | Some x is (y)
| ''L''<sub>10</sub>
+
| <math>L_{10}\!</math>
 
|-
 
|-
| I<br>Indefinite
+
| <math>\mathrm{I}\!</math><br>Indefinite
 
| Particular<br>Affirmative
 
| Particular<br>Affirmative
 
| align=left | Some x is y
 
| align=left | Some x is y
 
| align=left | &nbsp;
 
| align=left | &nbsp;
 
| align=left | Some x is y
 
| align=left | Some x is y
| ''L''<sub>11</sub>
+
| <math>L_{11}\!</math>
 
|}<br>
 
|}<br>
  
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