Changes

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 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.

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 S is an assertion of its negation (S).  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.

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 f : U �> B.

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 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.

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

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