  Wolff begins his treatise on the Foundations of Architecture with the claim that “architecture is a science for constructing a building so that it is in complete correspondence with the intentions of the architect” (Wolff, Principles of Architecture, §1, p. 305). This locates the harmony or agreement in which perfection always consists in the relation between the intentions of the architect and the building that results from his plans and supervision. However, as he proceeds Wolff makes it clear that the intention of an architect is always to produce a structure that is both formally beautiful as well as useful and comfortable, so the perfection that subsists in the relation between intention and outcome in fact consists in the perfection of both form and utility in the building itself. On the one hand “A building is space that is enclosed by art in order that certain functions can proceed there securely and unhindered” (Architecture, §4, p. 306), and “A building is comfortable if all necessary functions can proceed within it without hindrance and vexation” (Architecture, §7, p.  307). These definitions form the basis for a requirement of perfection in the utility of a building. On the other hand, however, “Beauty is perfection or the necessary appearance thereof, insofar as the former or the latter is perceived, and causes a pleasure in us” (Architecture, §8, p. 307), and “A building must be constructed beautifully and decoratively” (Architecture, §18, p. 309). This is the basis for the requirement of formal rather than utilitarian perfection in a building. Throughout the remainder of the treatise, both conceptions of perfection are at work. Wolff does not explicitly extend this complex analysis of perfection to other arts, although it is not difficult to imagine how that extension might go: in painting we might respond to formal features of composition as well as to the accuracy of depiction, in sculpture we might respond to the intrinsic beauty of the marble or bronze as well as to the accuracy of depiction, and so on.