Changes

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.

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 discourse for which the sentence is held to be true.

Taken in a context of communication, an assertion is basically a request that the interpreter consider the things for which the sentence is true, in other words, to find the fiber of truth in the associated proposition, or to invert the indicator function that is denoted by the sentence with respect to its possible value of truth.

Taken in a context of communication, an assertion invites the interpreter to consider the things for which the sentence is true, in other words, to find the fiber of truth in the associated proposition, or yet again, to invert the indicator function denoted by the sentence with respect to its possible value of truth.

A ''denial'' of a sentence <math>s\!</math> is an assertion of its negation <math>^{\backprime\backprime} \, \underline{(} s \underline{)} \, ^{\prime\prime}.</math>  It acts as a request to think about the things for which the sentence is false, in other words, to find the fiber of falsity in the indicted proposition, or to invert the indicator function that is denoted by the sentence with respect to its possible value of falsity.

A ''denial'' of a sentence <math>s\!</math> is an assertion of its negation <math>^{\backprime\backprime} \, \underline{(} s \underline{)} \, ^{\prime\prime}.</math>  The denial acts as a request to think about the things for which the sentence is false, in other words, to find the fiber of falsity in the indicted proposition, or to invert the indicator function denoted by the sentence with respect to its possible value of falsity.

According to this manner of definition, any sign that happens to denote a proposition, any sign that is taken as denoting an indicator function, by that very fact alone successfully qualifies as a sentence.  That is, a sentence is any sign that actually succeeds in denoting a proposition, any sign that one way or another brings to mind, as its actual object, a function of the form <math>f : X \to \underline\mathbb{B}.</math>

According to this manner of definition, any sign that happens to denote a proposition, any sign that is taken as denoting an indicator function, by that very fact alone successfully qualifies as a sentence.  That is, a sentence is any sign that actually succeeds in denoting a proposition, any sign that one way or another brings to mind, as its actual object, a function of the form <math>f : X \to \underline\mathbb{B}.</math>

There are several features of this definition that need be understood.  Indeed, there are problems involved in this whole style of definition that need to be discussed, and this requires a slight digression.

There are many features of this definition that need to be understood.  Indeed, there are problems involved in this whole style of definition that need to be discussed, and doing this requires a slight excursion.

=====1.3.10.3.  Propositions and Sentences=====

=====1.3.10.3.  Propositions and Sentences=====