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:

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<math>\begin{array}{lccc}

<math>\begin{array}{lccc}

Now consider the following paradigm:

Now consider the following paradigm:

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<math>\begin{array}{llccc}

<math>\begin{array}{llccc}

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<math>\begin{array}{llccc}

<math>\begin{array}{llccc}

When I say that the sign "blank" denotes the sign "&nbsp;", it means that the string of characters inside the first pair of quotation marks can be used as another name for the string of characters inside the second pair of quotes.  In other words, "blank" is a higher order sign whose object is "&nbsp;", and the string of five characters inside the first pair of quotation marks is a sign at a higher level of signification than the string of one character inside the second pair of quotation marks.  This relationship can be abbreviated in either one of the following ways:

When I say that the sign "blank" denotes the sign "&nbsp;", it means that the string of characters inside the first pair of quotation marks can be used as another name for the string of characters inside the second pair of quotes.  In other words, "blank" is a higher order sign whose object is "&nbsp;", and the string of five characters inside the first pair of quotation marks is a sign at a higher level of signification than the string of one character inside the second pair of quotation marks.  This relationship can be abbreviated in either one of the following ways:

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<math>\begin{matrix}

<math>\begin{array}{lll}

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

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

\leftarrow &

\leftarrow &

\rightarrow &

\rightarrow &

^{\backprime\backprime}\operatorname{~}^{\prime\prime} \\

^{\backprime\backprime}\operatorname{~}^{\prime\prime} \\

\end{matrix}</math>

\end{array}</math>

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Using the raised dot "<math>\cdot</math>" as a sign to mark the articulation of a quoted string into a sequence of possibly shorter quoted strings, and thus to mark the concatenation of a sequence of quoted strings into a possibly larger quoted string, one can write:

Using the raised dot "<math>\cdot</math>" as a sign to mark the articulation of a quoted string into a sequence of possibly shorter quoted strings, and thus to mark the concatenation of a sequence of quoted strings into a possibly larger quoted string, one can write:

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<math>\begin{matrix}

<math>\begin{array}{lllll}

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

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

\leftarrow &

\leftarrow &

^{\backprime\backprime}\operatorname{n}^{\prime\prime} \cdot\,

^{\backprime\backprime}\operatorname{n}^{\prime\prime} \cdot\,

^{\backprime\backprime}\operatorname{k}^{\prime\prime} \\

^{\backprime\backprime}\operatorname{k}^{\prime\prime} \\

\end{matrix}</math>

\end{array}</math>

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