Changes

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="font-weight:bold; text-align:center; width:90%"

{| align="center" border="1" cellpadding="8" cellspacing="0" style="font-weight:bold; width:90%"

|+ '''Table 7.  Syllogistic Premisses as Higher Order Indicator Functions'''

|+ '''Table 7.  Syllogistic Premisses as Higher Order Indicator Functions'''

| <math>\mathrm{A}\!</math>

|

| align=left | Universal Affirmative

<math>\begin{array}{clcl}

| align=left | All

\mathrm{A}                           &

| <math>x\!</math> || is || <math>y\!</math>

\mathrm{Universal~Affirmative}      &

| align=left | Indicator of <math>x (\!| y |\!) = 0</math>

\mathrm{All}\ x\ \mathrm{is}\ y     &

\mathrm{Indicator~of}\ x (y) = 0     \\

| <math>\mathrm{E}\!</math>

\mathrm{E}                           &

| align=left | Universal Negative

\mathrm{Universal~Negative}          &

| align=left | All

\mathrm{All}\ x\ \mathrm{is}\ (y)   &

| <math>x\!</math> || is || <math>(\!| y |\!)</math>

\mathrm{Indicator~of}\ x \cdot y = 0 \\

| align=left | Indicator of <math>x\ y = 0\!</math>

\mathrm{I}                           &

\mathrm{Particular~Affirmative}      &

| <math>\mathrm{I}\!</math>

\mathrm{Some}\ x\ \mathrm{is}\ y     &

| align=left | Particular Affirmative

\mathrm{Indicator~of}\ x \cdot y = 1 \\

| align=left | Some

\mathrm{O}                           &

| <math>x\!</math> || is || <math>y\!</math>

\mathrm{Particular~Negative}        &

| align=left | Indicator of <math>x\ y = 1\!</math>

\mathrm{Some}\ x\ \mathrm{is}\ (y)   &

\mathrm{Indicator~of}\ x (y) = 1     \\

| <math>\mathrm{O}\!</math>

\end{array}</math>

| align=left | Particular Negative

|}<br>

| align=left | Some

| <math>x\!</math> || is || <math>(\!| y |\!)</math>

| align=left | Indicator of <math>x (\!| y |\!) = 1</math>

|}

Tables&nbsp;8 and 9 develop these ideas in more detail.

Tables&nbsp;8 and 9 develop these ideas in more detail.