The Waltham Circle

Consider a person P who is performing an action A under certain conditions C. P As in accordance with an intention I to fulfill a goal G. G is an ancillary goal that is only significant because it must be satisfied in order to satisfy a latter goal, G'. Correlated with G' is a broader intention I'. Moreover, let's symbolize the satisfaction of a goal by saying, for any goal X, "X!." Then, P As with I to G. G! is propitious to G'!. So, P As with I to G in order to, with I', G'!. Now, for any sentence S within language L, S(x) is satisisfied when Px Axs with Ix to Gx, where Ix! and Gx!, given Cx, imply I'x! and G'x!.

Now, consider a sentence S'(xy) that contains at least one two-place predicate. Then, S'(xy) entails that Px Axy Ixy Gxy, and therefore Ixy! Gxy! implies I'xy! G'xy!. Similarly, for any sentence S''n(xnyn...nn) with n-place predicates and n terms, Px1...xn Ax1y1r1...xnynrnnn Ix1y1r1...xnynrnnn Gx1y1r1...xnynrnnn, then if Ix1y1r1...xnynrnnn! and Gx1y1r1...xnynrnnn!, then I'x1y1r1...xnynrnnn! and G'x1y1r1...xnynrnnn!.

Good, now I feel rigorous.