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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: |
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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="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 8 and 9 develop these ideas in more detail. | | Tables 8 and 9 develop these ideas in more detail. |
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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="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 | | | | align=left | |
| | 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 | | | | align=left | |
| | align=left | No x is (y) | | | align=left | No x is (y) |
− | | (''L''<sub>10</sub>) | + | | <math>(\!| L_{10} |\!)</math> |
| |- | | |- |
| | | | | |
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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> |
| |- | | |- |
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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> |
| |- | | |- |
| | | | | |
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| | align=left | | | | align=left | |
| | align=left | Some (x) is (y) | | | align=left | Some (x) is (y) |
− | | ''L''<sub>00</sub> | + | | <math>L_{00}\!</math> |
| |- | | |- |
| | | | | |
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| | align=left | | | | align=left | |
| | 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 | | | | align=left | |
| | 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 | | | | align=left | |
| | align=left | Some x is y | | | align=left | Some x is y |
− | | ''L''<sub>11</sub> | + | | <math>L_{11}\!</math> |
| |}<br> | | |}<br> |
| | | |