Changes

\end{array}</math></p>

\end{array}</math></p>

Viewed in this light, an intentional proposition ''q'' may be rephrased as a map ''q''&nbsp;:&nbsp;''X''&nbsp;&times;&nbsp;''X''&prime;&nbsp;&rarr;&nbsp;'''B''', which judges the juxtaposition of states in ''X'' from one moment to the next.  Alternatively, ''q'' may be parsed in two stages in two different ways, as ''q''&nbsp;:&nbsp;''X''&nbsp;&rarr;&nbsp;(''X''&prime;&nbsp;&rarr;&nbsp;'''B''') and as ''q''&nbsp;:&nbsp;''X''&prime;&nbsp;&rarr;&nbsp;(''X''&nbsp;&rarr;&nbsp;'''B'''), which associate to each point of ''X'' or ''X''&prime; a proposition about states in ''X''&prime; or ''X'', 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 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.