Changes

As a temporary notation, let the relationship between a particular sign <math>s\!</math> and a particular object <math>o\!</math>, namely, the fact that <math>s\!</math> denotes <math>o\!</math> or the fact that <math>o\!</math> is denoted by <math>s\!</math>, be symbolized in one of the following two ways:

As a temporary notation, let the relationship between a particular sign <math>s\!</math> and a particular object <math>o\!</math>, namely, the fact that <math>s\!</math> denotes <math>o\!</math> or the fact that <math>o\!</math> is denoted by <math>s\!</math>, be symbolized in one of the following two ways:

: <math>s \rightarrow o.</math>

 

: <math>o \leftarrow s.</math>

<math>\begin{matrix}

s & \rightarrow & o. \\

o & \leftarrow & s. \\

\end{matrix}</math>

Now consider the following paradigm:

Now consider the following paradigm:

:{| cellpadding="4"

{| align="center" cellpadding="8"

| 1.

|

| If

| "A"

1. &

| <math>\rightarrow</math>

\text{If} &

| Ann,

^{\backprime\backprime}\operatorname{A}^{\prime\prime} &

\rightarrow &

| &nbsp;

\operatorname{Ann}, \\

| that is,

&

| "A"

\text{that is}, &

| denotes

^{\backprime\backprime}\operatorname{A}^{\prime\prime} &

| Ann,

\operatorname{denotes} &

\operatorname{Ann}, \\

| &nbsp;

&

| then

\text{then} &

| A

A &

| <math>=\!</math>

= &

| Ann,

\operatorname{Ann}, \\

&

| &nbsp;

\text{and} &

| &nbsp;

\operatorname{Ann} &

| Ann

= &

| <math>=\!</math>

A. \\

| A

\text{Thus} &

| &nbsp;

^{\backprime\backprime}\operatorname{Ann}^{\prime\prime} &

\rightarrow &

| "Ann"

A, \\

| <math>\rightarrow</math>

&

| A,

\text{that is}, &

^{\backprime\backprime}\operatorname{Ann}^{\prime\prime} &

| &nbsp;

\operatorname{denotes} &

| that is,

A. \\

| "Ann"

| denotes

| A.

|}

|}