Changes

As always, it is probably best to begin with a concrete example.  So let us initiate a discourse, whose universe <math>X\!</math> may remind us a little of the cast of characters in Shakespeare's ''Othello''.

As always, it is probably best to begin with a concrete example.  So let us initiate a discourse, whose universe <math>X\!</math> may remind us a little of the cast of characters in Shakespeare's ''Othello''.

{| align="center" cellspacing="6" width="90%"

{| align="center" cellspacing="6" style="text-align:center" width="90%"

| <math>X ~=~ \{ \mathrm{Bianca}, \mathrm{Cassio}, \mathrm{Clown}, \mathrm{Desdemona}, \mathrm{Emilia}, \mathrm{Iago}, \mathrm{Othello} \}.</math>

| <math>X ~=~ \{ \mathrm{Bianca}, \mathrm{Cassio}, \mathrm{Clown}, \mathrm{Desdemona}, \mathrm{Emilia}, \mathrm{Iago}, \mathrm{Othello} \}.</math>

|}

|}

In order to provide ourselves with the convenience of abbreviated terms, while preserving Peirce's conventions about capitalization, we may use the alternate names <math>^{\backprime\backprime}\mathrm{u}^{\prime\prime}</math> for the universe <math>X\!</math> and <math>^{\backprime\backprime}\mathrm{Jeste}^{\prime\prime}</math> for the character <math>\mathrm{Clown}.\!</math>  This permits the above description of the universe of discourse to be rewritten in the following fashion:

In order to provide ourselves with the convenience of abbreviated terms, while preserving Peirce's conventions about capitalization, we may use the alternate names <math>^{\backprime\backprime}\mathrm{u}^{\prime\prime}</math> for the universe <math>X\!</math> and <math>^{\backprime\backprime}\mathrm{Jeste}^{\prime\prime}</math> for the character <math>\mathrm{Clown}.\!</math>  This permits the above description of the universe of discourse to be rewritten in the following fashion:

{| align="center" cellspacing="6" width="90%"

{| align="center" cellspacing="6" style="text-align:center" width="90%"

| <math>\mathrm{u} ~=~ \{ \mathrm{B}, \mathrm{C}, \mathrm{D}, \mathrm{E}, \mathrm{I}, \mathrm{J}, \mathrm{O} \}</math>

| <math>\mathrm{u} ~=~ \{ \mathrm{B}, \mathrm{C}, \mathrm{D}, \mathrm{E}, \mathrm{I}, \mathrm{J}, \mathrm{O} \}</math>

|}

|}

This specification of the universe of discourse could be summed up in Peirce's notation by the following equation:

This specification of the universe of discourse could be summed up in Peirce's notation by the following equation:

{| align="center" cellspacing="6" width="90%"

{| align="center" cellspacing="6" style="text-align:center" width="90%"

| <math>1 ~=~ \mathrm{B} ~+\!\!,~ \mathrm{C} ~+\!\!,~ \mathrm{D} ~+\!\!,~ \mathrm{E} ~+\!\!,~ \mathrm{I} ~+\!\!,~ \mathrm{J} ~+\!\!,~ \mathrm{O}</math>

| <math>1 ~=~ \mathrm{B} ~+\!\!,~ \mathrm{C} ~+\!\!,~ \mathrm{D} ~+\!\!,~ \mathrm{E} ~+\!\!,~ \mathrm{I} ~+\!\!,~ \mathrm{J} ~+\!\!,~ \mathrm{O}</math>

|}

|}

Within this discussion, then, the ''individual terms'' are as follows:

Within this discussion, then, the ''individual terms'' are as follows:

{| align="center" cellspacing="6" width="90%"

{| align="center" cellspacing="6" style="text-align:center" width="90%"

|

|

<math>\begin{matrix}

<math>\begin{matrix}

Each of these terms denotes in a singular fashion the corresponding individual in <math>X.\!</math>

Each of these terms denotes in a singular fashion the corresponding individual in <math>X.\!</math>

As "general terms" of this discussion, we might begin with the following set:

As the ''general terms'' of this discussion, we may begin with the following set:

: "b" = "black"

{| align="center" cellspacing="6" style="text-align:center" width="90%"

 

: "m" = "man"

 

^{\backprime\backprime}\mathrm{b}^{\prime\prime}

: "w" = "woman"

& = &

^{\backprime\backprime}\mathrm{black}^{\prime\prime}

^{\backprime\backprime}\mathrm{m}^{\prime\prime}

& = &

^{\backprime\backprime}\mathrm{man}^{\prime\prime}

^{\backprime\backprime}\mathrm{w}^{\prime\prime}

& = &

^{\backprime\backprime}\mathrm{woman}^{\prime\prime}

In Peirce's notation, the denotation of a general term can be expressed by means of an equation between terms:

In Peirce's notation, the denotation of a general term can be expressed by means of an equation between terms: