Changes

Viewed in this light, an intentional proposition <math>q\!</math> may be rephrased as a map <math>q : X \times X' \to \mathbb{B},</math> which judges the juxtaposition of states in <math>X\!</math> from one moment to the next.  Alternatively, <math>q\!</math> may be parsed in two stages in two different ways, as <math>q : X \to (X' \to \mathbb{B})</math> and as <math>q : X' \to (X \to \mathbb{B}),</math> which associate to each point of <math>X\!</math> or <math>X'\!</math> a proposition about states in <math>X'\!</math> or <math>X,\!</math> respectively.  In this way, an intentional proposition embodies a type of value system, in effect, a proposal that places a value on a collection of ends-in-view, or a project that evaluates a set of goals as regarded from each point of view in the state space of a system.

Viewed in this light, an intentional proposition <math>q\!</math> may be rephrased as a map <math>q : X \times X' \to \mathbb{B},</math> which judges the juxtaposition of states in <math>X\!</math> from one moment to the next.  Alternatively, <math>q\!</math> may be parsed in two stages in two different ways, as <math>q : X \to (X' \to \mathbb{B})</math> and as <math>q : X' \to (X \to \mathbb{B}),</math> which associate to each point of <math>X\!</math> or <math>X'\!</math> a proposition about states in <math>X'\!</math> or <math>X,\!</math> respectively.  In this way, an intentional proposition embodies a type of value system, in effect, a proposal that places a value on a collection of ends-in-view, or a project that evaluates a set of goals as regarded from each point of view in the state space of a system.

In sum, the intentional proposition q indicates a method for the systematic selection of local goals.  As a general form of description, we may refer to a map of the type ''q''&nbsp;:&nbsp;Q^''i''''X''&nbsp;&rarr;&nbsp;'''B''' as an "''i''^th&nbsp;order intentional proposition".  Naturally, when we speak of intentional propositions without qualification, we usually mean first order intentions.

In sum, the intentional proposition <math>q\!</math> indicates a method for the systematic selection of local goals.  As a general form of description, a map of the type <math>q : \operatorname{Q}^i X \to \mathbb{B}</math> may be referred to as an "<math>i^\operatorname{th}</math> order intentional proposition".  Naturally, when we speak of intentional propositions without qualification, we usually mean first order intentions.

Many different realms of discourse have the same structure as the extensions that have been indicated here.  From a strictly logical point of view, each new layer of terms is composed of independent logical variables that are no different in kind from those that go before, and each further course of logical atoms is treated like so many individual, but otherwise indifferent bricks by the prototype computer program that I use as a propositional interpreter.  Thus, the names that I use to single out the differential and the intentional extensions, and the lexical paradigms that I follow to construct them, are meant to suggest the interpretations that I have in mind, but they can only hint at the extra meanings that human communicators may pack into their terms and inflections.

Many different realms of discourse have the same structure as the extensions that have been indicated here.  From a strictly logical point of view, each new layer of terms is composed of independent logical variables that are no different in kind from those that go before, and each further course of logical atoms is treated like so many individual, but otherwise indifferent bricks by the prototype computer program that I use as a propositional interpreter.  Thus, the names that I use to single out the differential and the intentional extensions, and the lexical paradigms that I follow to construct them, are meant to suggest the interpretations that I have in mind, but they can only hint at the extra meanings that human communicators may pack into their terms and inflections.