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, 16:14, 22 November 2009
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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="8" cellspacing="0" style="text-align:center; width:90%" | | {| align="center" border="1" cellpadding="8" cellspacing="0" style="text-align:center; width:90%" |
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| | <pre> | | <pre> |
| − | <table align="center" border="1" cellpadding="8" cellspacing="0" width="80%">
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| − | <caption><font size="+2"><math>\text{Table 7.} ~~ \text{Syllogistic Premisses as Higher Order Indicator Functions}</math></font></caption>
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| − | <td align="center"><math>\operatorname{A}</math></td>
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| − | <td><math>\text{Absolute}</math></td>
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| − | <td><math>\text{Universal Affirmative}</math></td>
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| − | <td align="center"><math>All ~ u ~ is ~ v</math></td>
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| − | <td><math>Indicator of u ~ \texttt{(} v \texttt{)} = 0</math></td></tr>
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| − | <td align="center"><math>\operatorname{E}</math></td>
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| − | <td><math>Exclusive</math></td>
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| − | <td><math>Universal Negative</math></td>
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| − | <td align="center"><math>All ~ u ~ is ~ \texttt{(} v \texttt{)}</math></td>
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| − | <td><math>Indicator of ~ u ~ \cdot ~ v = 0</math></td></tr>
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| − | <td align="center"><math>\operatorname{I}</math></td>
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| − | <td><math>Indefinite</math></td>
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| − | <td><math>Particular Affirmative</math></td>
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| − | <td align="center"><math>Some ~ u ~ is ~ v</math></td>
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| − | <td><math>Indicator of ~ u ~ \cdot ~ v = 1</math></td></tr>
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| − | <td align="center"><math>\operatorname{O}</math></td>
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| − | <td><math>Obtrusive</math></td>
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| − | <td><math>Particular Negative</math></td>
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| − | <td align="center"><math>Some ~ u ~ is ~ \texttt{(} v \texttt{)}</math></td>
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| − | <td><math>Indicator of ~ u ~ \texttt{(} v \texttt{)} = 1</math></td></tr>
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| − | </table></font>
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| − | <br>
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| | The following Tables develop these ideas in more detail. | | The following Tables develop these ideas in more detail. |
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