Changes

To emphasize the empirical contingency of this definition, one can say that a sentence is any sign that is interpreted as naming a proposition, any sign that is taken to denote an indicator function, or any sign whose object happens to be a function of the form <math>f : X \to \underline\mathbb{B}.</math>

To emphasize the empirical contingency of this definition, one can say that a sentence is any sign that is interpreted as naming a proposition, any sign that is taken to denote an indicator function, or any sign whose object happens to be a function of the form <math>f : X \to \underline\mathbb{B}.</math>

An ''expression'' is a type of sign, for instance, a term or a sentence, that has a value.  In this conception of an expression, I am deliberately leaving a number of options open, like whether it amounts to a term or to a sentence and whether it ought to be accounted as denoting a value or as connoting a value.  Perhaps the expression has different values under different lights, and perhaps it relates to them differently in different respects.  In the end, what one calls an expression matters less than where its value lies.  Of course, no matter whether one calls an expression a ''term'' or a ''sentence'', if the value is an element in <math>\underline\mathbb{B},</math> then the expression affords the option of being treated as a sentence, meaning that it is subject to assertion and composition in the same way that any sentence is, having its value figure into the values of larger expressions through the linkages of sentential connectives, and allowing the consideration of what things in what universe the corresponding proposition indicates.

An ''expression'' is a type of sign, for instance, a term or a sentence, that has a value.  In forming this conception of an expression, I am deliberately leaving a number of options open, for example, whether the expression amounts to a term or to a sentence and whether it ought to be accounted as denoting a value or as connoting a value.  Perhaps the expression has different values under different lights, and perhaps it relates to them differently in different respects.  In the end, what one calls an expression matters less than where its value lies.  Of course, no matter whether one chooses to call an expression a ''term'' or a ''sentence'', if the value is an element of <math>\underline\mathbb{B},</math> then the expression affords the option of being treated as a sentence, meaning that it is subject to assertion and composition in the same way that any sentence is, having its value figure into the values of larger expressions through the linkages of sentential connectives, and affording the consideration of what things in what universe the corresponding proposition happens to indicate.

Expressions with this degree of flexibility in the types under which they can be interpreted are difficult to translate from their formal settings into more natural contexts.  Indeed, the whole issue can be difficult to talk about, or even to think about, since the grammatical categories of sentences and noun phrases are not so fluid in natural language settings are they can made in artificial arenas.

Expressions with this degree of flexibility in the types under which they can be interpreted are difficult to translate from their formal settings into more natural contexts.  Indeed, the whole issue can be difficult to talk about, or even to think about, since the grammatical categories of sentential clauses and noun phrases are rarely so fluid in natural language settings are they can be rendered in artificially contrived arenas.

To finesse the issue of whether an expression denotes or connotes its value, or else to create general term that covers what both possibilities have in common, one can say that an expression ''evalues'' its value.

To finesse the issue of whether an expression denotes or connotes its value, or else to create a general term that covers what both possibilities have in common, one can say that an expression ''evalues'' its value.

An ''assertion'' is just a sentence that is being used in a certain way, namely, to indicate the indication of the indicator function that the sentence is usually used to denote.  In other words, an assertion is a sentence that is being converted to a certain use or being interpreted in a certain role, and one whose immediate denotation is being pursued to its substantive indication, specifically, the fiber of truth of the proposition that the sentence potentially denotes.  Thus, an assertion is a sentence that is held to denote the set of things in the universe of which the sentence is true.

An ''assertion'' is just a sentence that is being used in a certain way, namely, to indicate the indication of the indicator function that the sentence is usually used to denote.  In other words, an assertion is a sentence that is being converted to a certain use or being interpreted in a certain role, and one whose immediate denotation is being pursued to its substantive indication, specifically, the fiber of truth of the proposition that the sentence potentially denotes.  Thus, an assertion is a sentence that is held to denote the set of things in the universe of which the sentence is true.