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