Changes

This construction is often useful in situations where has to deal with a set of signs <math>\{ {}^{\backprime\backprime} s_1 {}^{\prime\prime}, \ldots, {}^{\backprime\backprime} s_n {}^{\prime\prime} \}\!</math> with a fixed or a faulty interpretation.  Here one needs a fresh set of signs <math>\{ \underline{\underline{x_1}}, \ldots, \underline{\underline{x_n}} \}\!</math> that can be used in ways analogous to the original, but free enough to be controlled and flexible enough to be repaired.  In other words, the interpretation of the new list is subject to experimental variation, freely controllable in such a way that it can follow or assimilate the original interpretation whenever it makes sense to do so, but critically reflected and flexible enough to have its interpretation amended whenever necessary.

This construction is often useful in situations where has to deal with a set of signs <math>\{ {}^{\backprime\backprime} s_1 {}^{\prime\prime}, \ldots, {}^{\backprime\backprime} s_n {}^{\prime\prime} \}\!</math> with a fixed or a faulty interpretation.  Here one needs a fresh set of signs <math>\{ \underline{\underline{x_1}}, \ldots, \underline{\underline{x_n}} \}\!</math> that can be used in ways analogous to the original, but free enough to be controlled and flexible enough to be repaired.  In other words, the interpretation of the new list is subject to experimental variation, freely controllable in such a way that it can follow or assimilate the original interpretation whenever it makes sense to do so, but critically reflected and flexible enough to have its interpretation amended whenever necessary.

Interpreted on a casual basis, the set <math>\underline{\underline{X}}\!</math> can be treated as a list of ''boolean variables'', or, according to another reading, as a list of ''boolean variable names'', but both of these choices are subject to the eventual requirement of saying exactly what a &ldquo;variable&rdquo; is.

Interpreted on a casual basis, the set X can be treated as a list of "boolean variables", or, according to another reading, as a list of "boolean variable names", but both of these choices are subject to the eventual requirement of saying exactly what a "variable" is.

The overall problem about the "ontological status" of variables will also be the subject of an extended study at a later point in this project, but for now I am forced to side step the whole issue, merely giving notice of a signal distinction that promises to yield a measure of effective advantage in finally disposing of the problem.

The overall problem about the &ldquo;ontological status&rdquo; of variables will also be the subject of an extended study at a later point in this project, but for now I am forced to side-step the whole issue, merely giving notice of a signal distinction that promises to yield a measure of effective advantage in finally disposing of the problem.

If a sign, as accepted and interpreted in a particular setting, has an "existentially unique" (EU) denotation, that is, if there exists a unique object that the sign denotes under the operative sign relation, then the sign is said to possess a "EU denotation", or to have a "EU object".  When this is so, the sign is said to be "eudenotational", otherwise it is said to be "dysdenotational".

If a sign, as accepted and interpreted in a particular setting, has an ''existentially unique'' denotation, that is, if there exists a unique object that the sign denotes under the operative sign relation, then the sign is said to possess a ''EU-denotation'', or to have a ''EU-object''.  When this is so, the sign is said to be ''eudenotational'', otherwise it is said to be ''dysdenotational''.

Using the distinction accorded to eudenotational signs, the issue about the ontological status of variables can be illustrated as turning on two different "acceptations" of the list X = {x1, ..., xn}.

Using the distinction accorded to eudenotational signs, the issue about the ontological status of variables can be illustrated as turning on two different acceptations of the list X = {x1, ..., xn}.

1. The natural (or naive) acceptation is for a reader to interpret the list as referring to a set of objects, in effect, to pass without hesitation from impressions of the characters "x1", ..., "xn" to thoughts of their respective EU objects x1, ..., xn, all taken for granted to exist uniquely.  The whole set of interpretive assumptions that go into this acceptation will be referred to as the "object convention".

1. The natural (or naive) acceptation is for a reader to interpret the list as referring to a set of objects, in effect, to pass without hesitation from impressions of the characters "x1", ..., "xn" to thoughts of their respective EU objects x1, ..., xn, all taken for granted to exist uniquely.  The whole set of interpretive assumptions that go into this acceptation will be referred to as the "object convention".