Changes

But a working maxim of information theory says that “Partial information is your ordinary information.”  Applied to the principle regulating the sign-theoretic convention this means that the adjective ''partial'' is swallowed up by the substantive ''information'', so that the ostensibly more general case is always already subsumed within the ordinary case.  Because partiality is part and parcel to the usual nature of information, it is a perfectly typical feature of the signs and expressions bearing it to provide normally only partial information about ordinary objects.

But a working maxim of information theory says that “Partial information is your ordinary information.”  Applied to the principle regulating the sign-theoretic convention this means that the adjective ''partial'' is swallowed up by the substantive ''information'', so that the ostensibly more general case is always already subsumed within the ordinary case.  Because partiality is part and parcel to the usual nature of information, it is a perfectly typical feature of the signs and expressions bearing it to provide normally only partial information about ordinary objects.

The only time when a finite sign or expression can give the appearance of determining a perfectly precise content or a post finite amount of information, for example, when the symbol <math>{}^{\backprime\backprime} e {}^{\prime\prime}\!</math> is used to denote the number also known as &ldquo;the unique base of the natural logarithms&rdquo; &mdash; this can only happen when interpreters are prepared, by dint of the information embodied in their prior design and preliminary training, to accept as meaningful and be terminally satisfied with what is still only a finite content, syntactically speaking.  Every remaining impression that a perfectly determinate object, an ''individual'' in the original sense of the word, has nevertheless been successfully specified &mdash; this can only be the aftermath of some prestidigitation, that is, the effect of some pre-arranged consensus, for example, of accepting a finite system of definitions and axioms that are supposed to define the space <math>\mathbb{R}\!</math> and the element <math>e\!</math> within it, and of remembering or imagining that an effective proof system has once been able or will yet be able to convince one of its demonstrations.

The only time when a finite sign or expression can give the appearance of determining a perfectly precise content or a post-finite amount of information, for example, when the symbol <math>{}^{\backprime\backprime} e {}^{\prime\prime}\!</math> is used to denote the number also known as &ldquo;the unique base of the natural logarithms&rdquo; &mdash; this can only happen when interpreters are prepared, by dint of the information embodied in their prior design and preliminary training, to accept as meaningful and be terminally satisfied with what is still only a finite content, syntactically speaking.  Every remaining impression that a perfectly determinate object, an ''individual'' in the original sense of the word, has nevertheless been successfully specified &mdash; this can only be the aftermath of some prestidigitation, that is, the effect of some pre-arranged consensus, for example, of accepting a finite system of definitions and axioms that are supposed to define the space <math>\mathbb{R}\!</math> and the element <math>e\!</math> within it, and of remembering or imagining that an effective proof system has once been able or will yet be able to convince one of its demonstrations.

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