Changes

==Proof as semiosis==

==Proof as semiosis==

We have been looking at several different ways of proving one particular example of a propositional equation, and along the way we have been exemplifying the species of sign transforming process that is commonly known as a ''proof'', more specifically, an equational proof of the propositional equation at issue.

We have been looking at several different ways of proving one particular example of a propositional equation, and along the way we have been exemplifying the species of sign transforming process that is commonly known as a ''proof'', more specifically, an equational proof of the propositional equation at issue. Let us now draw out these semiotic features of the business of proof and place them in relief.

 

Let us now draw out these semiotic features of the business of proof and place them in relief.

Our syntactic domain <math>S\!</math> contains an infinite number of signs or expressions, which we may choose to view in either their text or their graphic forms, glossing over for now the many details of their parsicular correspondence.

Our syntactic domain <math>S\!</math> contains an infinite number of signs or expressions, which we may choose to view in either their text or their graphic forms, glossing over for now the many details of their parsicular correspondence.

{| align="center" cellpadding="8" width="90%"

{| align="center" cellpadding="8" width="90%"

|

|

<math>\begin{array}{lcc}

<math>\begin{array}{lll}

e_0 & = & {}^{\backprime\backprime} \texttt{(~)} {}^{\prime\prime}

e_0 & = &

{}^{\backprime\backprime}

\texttt{(~)}

{}^{\prime\prime}

\\[4pt]

\\[4pt]

e_1 & = & {}^{\backprime\backprime} \texttt{~} {}^{\prime\prime}

e_1 & = &

{}^{\backprime\backprime}

\texttt{~}

{}^{\prime\prime}

\end{array}</math>

\end{array}</math>

|}

|}

Under <math>\operatorname{Ex}</math> we have the following interpretations:

Under <math>\operatorname{Ex}</math> we have the following interpretations: