Leon Battista Alberti and the Concept of Lineament

A core idea in the architectural theory of Leon Battista Alberti, as expressed in the De re aedificatoria, is the distinction between “lineament,” the line in the mind of the architect, and “matter,” the material presence of the building. This distinction plays a key role in architectural design throughout the history of Western architecture. As Le Corbusier would say in the twentieth century, “architecture is a product of the mind.” The distinction between mind and matter can be found in Vitruvius, in the distinction between “that which signifies and that which is signified”; at the Accademia di San Luca in Rome, between disegno interno and disegno esterno; or in Peter Eisenman’s distinction between deep aspect and surface aspect in architecture, to name just three examples. There are passages in the De amore of Marsilio Ficino where it seems clear that he is referring to his mentor’s concept of lineament. Lines cannot be called bodies, for example, and beauty can only be a property of matter through arrangement, proportion, and aspect (shape and color), which are products of thought, in the Neoplatonic tradition, as in the idea of beauty described by Plotinus, which can be found in Alberti’s concept of beauty or concinnitas. Plotinus distinguished the shape of the matter of a statue from the shape of the statue in the mind of the artist. I would like to suggest that Alberti knew the Enneads of Plotinus, perhaps as a result of a meeting with Gemistos Plethon and Nicholas of Cusa at the Academy of Palestrina, and through the translation of the Enneads by Marius Victorinus. Alberti’s concept of lineament is a Neoplatonic concept, and it plays an important role in architectural theory. Neoplatonism can also be found in Alberti’s proportioning systems in his architecture, as Ficino called Alberti a “Platonic mathematician.” These propositions have never been advanced, that I know of, and they are fundamental to an understanding of architectural theory

Plotinus and the Artistic Imagination

In the thought of Plotinus, the imagination is responsible for the apprehension of the activity of Intellect. If creativity in the arts involves an exercise of the imagination, the image-making power that links sense perception to noetic thought and the nous poietikos, the poetic or creative intellect, then the arts exercise the apprehension of intellectual activity. According to John Dillon in “Plotinus and the Transcendental Imagination,” Plotinus’ conception of the imagination led to the formulation of the imagination as a basis of artistic creativity. In Plotinus, imagination operates on several different levels: it produces images in sense perception, it synthesizes images in dianoetic thought, and it produces images in correspondence with the articulation through logos of noetic thought. The imagination is what connects the intelligible in intellect and the form in sense perception. Plotinus imagines an art which is a product of noetic thought as made possible by the imagination. The primary principle of beauty is Intellect, from which all images should be taken, as facilitated by imagination. Forms of art, like the forms of nature, are the product of Intellect. The production of a work of art is an intellectual or spiritual exercise of the imagination that allows apprehension of Intellect and noesis in nous poietikos. All art is metaphysical, and is an expression of intelligible form in imagination, an expression of an intellectual idea that can be differentiated from sensible form in intellectual apprehension. There are many ways in which the tenets of the thought of Plotinus become currents of art and aesthetic theory as it develops to the present day

Philosophy of Intellect in the Long Commentary on the De anima of Averroes

In the Long Commentary on the De anima, Averroes posits three separate intelligences in the anima rationalis or the rational soul: agent intellect or intellectus agens, material or passible intellect, intellectus possibilis or intellectus passibilis, and speculative intellect, intellectus speculativus, or actualized or acquired intellect, intellectus adeptus. In the De anima 3.1.5, “there are three parts of the intellect in the soul; the first is the receptive intellect, the second, the active intellect, and the third is actual intellection…,” that is, speculative or actualized, agent, and material. While material intellect is “partly generable and corruptible, partly eternal,” corporeal and incorporeal, the speculative and agent intellects are purely eternal and incorporeal. In the De anima 3.1.5, the existence of intelligibles or first principles in intellect, as they are understood in actualized intellect, “does not simply result from the reception of the object,” the sensible form in sense perception in material intellect, “but consists in attention to, or perception of, the represented forms…,” the cognition of the forms in actualized intellect wherein they can be understood as intelligibles, which requires both the participation of active intellect and the motivation of the individual for intellectual development. The goal of intellectual development is to achieve union with active intellect, the final entelechy, and through this union the highest bliss in life can be achieved. Such bliss can only be achieved “in the eve of life.” All individual material intellects are capable of some ability to form concepts and abstract ideas at a basic level, but beyond that intellectual development varies among individuals according to the level of volition. Complete knowledge of the material world results in complete unity between the material intellect and the active intellect

Topological Theory in Bioconstructivism

In the essay “Landscapes of Change: Boccioni’s Stati d’animo as a General Theory of Models,” in Assemblage 19, 1992, Sanford Kwinter proposed a number of theoretical models which could be applied to computer-generated forms in Bioconstructivism. These included topological theory, epigenesis, the epigenetic landscape, morphogenesis, catastrophe and catastrophe theory. Topological theory entails transformational events or deformations in nature which introduce discontinuities into the evolution of a system. Epigenesis entails the generation of smooth landscapes, in waves or the surface of the earth, for example, formed by complex underlying topological interactions. The epigenetic landscape is the smooth forms of relief which are the products of the underlying complex networks of interactions. Morphogenesis describes the structural changes occurring during the development of an organism, wherein forms are seen as discontinuities in a system, as moments of structural instability rather than stability. A catastrophe is a morphogenesis, a jump in a system resulting in a discontinuity. Catastrophe theory is a topological theory describing the discontinuities in the evolution of a system in nature. A project which applies these models, and which helps to establish a theoretical basis for Bioconstructivism by applying topological models, is a design for a theater by Amy Lewis in a Graduate Architecture Design Studio directed by Associate Professor Andrew Thurlow at Roger Williams University, in Spring 2011. In the project, moments of structural stability are juxtaposed with moments of structural instability, to represent the contradiction inherent in self-generation or immanence. The singularity of the surfaces of the forms in the epigenetic landscape contradicts the complex network of interactions of topological forces from which they result. Actions in the environment on unstable, unstructured forms, and undifferentiated structures, result in stable, structured forms, and differentiated structures

Neoplatonism in the Liber Naturalis and Shifā: De anima or Metaphysica of Avicenna (Ibn Sīnā)

Avicenna or Ibn Sīnā was born circa 980 in Afshna, near Bukhara, in Persia. He worked briefly for the Samanid administration, but left Bukhara, and lived in the area of Tehran and Isfahan, where he completed the Shifā (Healing [from error]) under the patronage of the Daylamite ruler, ‘Ala’-al Dawla, and wrote his most important Persian work, the Dānish-nāma, which contains works on logic, metaphysics, physics, and mathematics

Neoplatonism and English Gothic Architecture

A letter written by Robert Grosseteste, the first chancellor of Oxford University and later Bishop of Lincoln from 1235 to 1253, illustrates the role that Neoplatonism played in the creative process of the architect in the Middle Ages. The letter was written from Oxford in around 1200, to Master Adam Rufus, a former student. According to Grosseteste, “It is said that the design is the model to which the craftsman looks to make his handiwork, in imitation of it and in its likeness.” Grosseteste’s letter exhibits a familiarity with the Enneads of Plotinus, which Grosseteste probably was not able to read directly but would have known through texts such as the Theology of Aristotle. In Enneads V.8.1, Plotinus compares two blocks of stone, one of which is carved into a statue by a craftsman, so that in which “the form is not in the material; it is in the designer before ever it enters into the stone…”, the forma artificii of Grosseteste. Grosseteste uses the analogy of architecture: “So imagine in the artist’s mind the design of the work to be made, as in the mind of the architect the design and likeness of the house to be built; to this pattern and model he looks only that he may make the house in imitation of it.” The material of the building is organized in imitation of the idea in the mind of the architect; like the forms of nature in relation to the archetypes of the Platonic demiurge, the building is a shadow or reflection of the architectural idea. In the Enneads I.6.3, Plotinus asked, “On what principle does the architect, when he finds the house standing before him correspondent with his inner ideal of a house, pronounce it beautiful?” In his cosmologies De Luce (or On Light, 1225–1228) and De lineis, angulis et figuris (or On lines, angles and figures, 1228–1233), written at Oxford, Robert Grosseteste would describe natural bodies as being formed by mathematical and geometrical entities created from light, as reflected from the lux spiritualis, the incorporeal, spiritual light; and in the Commentary on the Posterior Analytics (1228–1235) and the Hexaemeron (c. 1237), Grosseteste would describe the ascension of the soul from the material intellect to the agent intellect, in the apprehension of the divine intellect, intelligentia. These concepts show the influence of Plato and Plotinus and explain in part the intentions of the medieval architect