A picture story by Michael Sukale

Leonardo da Vinci (1452 - 1519), not only a painter, sculptor and master builder, but also a naturalist, believed that all reality is already visible or at least can be made visible. Although this philosophical principle cannot be upheld, it did inspire one of the most universal minds of the Renaissance to great achievements - enabling him to relentlessly penetrate reality with his thoughts and capture it in drawings.

Plato tried to recognise the world with clogged senses and feelings. The only instrument he admitted to finding the truth was the intellect and the only method of sorting the results of the intellect into knowledge and opinion was deductive logic. Aristotle tried to recognise the world with an open mind and therefore found in perceptible things what Plato recognised behind or beyond them. He recognised a second instrument of knowledge, perception, and added a new method to it, inductive logic.

Like Aristotle, Leonardo wanted to recognise the world through perception, but he restricted perception primarily to the sense of sight. For him, he invented an instrument, namely the scientific perspective, which allowed him to grasp reality through visualisation; and a method, namely the theory-based experiment, which allowed him to assign laws to reality by comparing theory and sensory experience. Leonardo took the diversions via the senses because he believed that all science begins with the senses and that all science must therefore be empirical science. Accordingly, for him all the arts are the arts of experience, because they are founded on the senses.

Painting and sculpture belong to the sense of sight. Music and poetry belong to the sense of hearing. If one also differentiates according to whether an art has a (mathematically formulable) theoretical core or not, then the following cross-cutting results:

Painting is the science of seeing for Leonardo, but how does science work? Here there are three things that Leonardo takes over from tradition, and a fourth that is completely new:

Science is always an analysis of systematic elements to the end, i.e. science always endeavours to find out the basic concepts that we use in our theories.

The basic concepts are of a purely theoretical nature.

Science always proceeds with mathematical proof in its conclusions.

The truth of science is proven by experiment, not by mathematics.

The third point, that mathematical proof is important in the sciences, is taken from Euclid, but he immediately links it to the fourth point: "No human research can be called true science if it does not take its course through mathematical exposition and proof. If you say that the sciences, which remain in the mind from beginning to end, have truth, this is not conceded, but denied for many reasons, and primarily because experience (or experiment) does not occur in such pure-minded endeavours; without this, however, no thing can be recognised with certainty."

Leonardo's philosophical principle is very simple. Leonardo apparently believed that seeing establishes an excellent relationship to the world and that all reality is either already visible or can be made visible.

Now this principle is obviously wrong. For as we know, reality can only be seen, heard, tasted, smelt and grasped to a limited extent. To a large extent it is not even sensual. But Leonardo believed that the world, insofar as it can be called real, is either visible or can be made visible. In this latter condition lies the reconciliation with the falsity that the world is obviously not fully visible, in large areas even invisible. For it was possible for him to make everything sensual and visible, even the initially invisible and nonsensical. This principle can be used to explain almost all of his research. However, this is an insight that is not entirely self-evident.

For his thesis, Leonardo had to provide constructive proof that everything can be represented graphically, and this poses many difficulties and objections. A first problem is to make all the surfaces of the objects visible. Leonardo's drawings of nature and plants are surface studies: he depicts what he sees in nature with the greatest accuracy, i.e. he transfers it from three-dimensional reality to the two-dimensional surface. However, Leonardo requires the painter to penetrate into the causes and reasons of nature in order to visualise the surface. Sometimes Leonardo draws plants in temporal stages in order to be able to place the moment that is his main interest in the dynamics of growth and decay.

A second problem is to visualise the interior of objects. Leonardo solves this with his anatomy. Leonardo made many independent discoveries in human anatomy, such as the size and shape of the ventricles of the brain, the fact that the eye nerves cross in the so-called chiasm, and the exact position of the maxillary and frontal sinuses. But his greatest merit is the graphic representation of his findings. His notes prove how thoroughly he dealt with the problem of giving the viewer of his drawings a picture of the structures inside the body and making it clear where they are located. The principles he used for this are plausible for us, but completely new in his time. He sometimes rotated the body by just a few degrees to make the arms and legs three-dimensional, for example, as if a camera were slowly swivelling around the body. In order to visualise the internal organs, he imagined a "glass man" through whom one could see without losing sight of his external forms. A comparison with the anatomy of Andreas Vesalius, which appeared in 1543 (incidentally in the same year as "De Revolutionibus" by Copernicus!), is of interest here: Vesalius, who did not draw himself, has the body depicted as a living one that is peeled from the outside inwards like an onion. In this way the form of the surface is not preserved and the sight of the parts lying between the surface and the skeleton appears grotesque, because on the one hand the dissected body gestures towards the viewer in an upright position as if it were alive, but on the other hand it no longer seems to possess anything resembling a human being.

Visualisation also proceeds differently and makes thoughts or theories visible. If it is true that Leonardo believes that speculation must precede experience, and if he believes that everything can be made visible, then there must also be evidence in his work that he gives visible form to a theory even before he has subjected it to an experiment. This would prove that the draughtsman is not only an imitator of nature, but also realises thoughts through drawing. In fact, this can be demonstrated by many examples, one of which I will single out. For artificial flight, Leonardo had to solve the problem of how to pull a body falling downwards against the law of gravity. His difficulties consisted in finding out how a weight could be transported through the air by oscillating a wing, as he observed birds moving their bodies upwards by flapping their wings. He wanted to find out whether he could reproduce the same thing that a bird can do with its natural wings using artificial wings. He therefore made two drawings (see illustration). Firstly, a basic drawing in which he shows two interconnected levers with a weight attached to the second, right-hand lever. If the first, left-hand lever lowers with its left arm to the right, the second lever raises with its left arm, to which the weight is attached, upwards. In another drawing, he has converted the right-hand lever into a wing, which he connects to the left-hand lever by means of a joint. A man is endeavouring to push the left arm of the left lever downwards. If he succeeds, he will be able to lift the weight. The fact that these drawings are a visualisation of a thought experiment is demonstrated by Leonardo's text, which appears below the drawings and is particularly striking in that Leonardo considers a possible result of the experiment to be a falsification of the theory: "If you want to see the real test of the wings, make a wing of paper, reinforced by a net and a tube, 20 cubits wide and 20 cubits long, and fixed to a box weighing 200 pounds; and operate it with all your strength, as shown above. And if the box of 200 pounds rises before the wing lowers, the test will be good; but make sure that the force is strong, and if the said effect does not materialise, lose no more time."

We distinguish between two uses of the word "argument": on the one hand, we mean a purely linguistic entity and say that certain consequences of premises and conclusions are arguments; on the other hand, we also say that a premise is an argument for the conclusion. In this second sense, pictures can also be regarded as arguments for certain conclusions. Yes, pictures can possibly be arguments for other pictures. We are accustomed to admitting only arguments in the first sense of the word, and so we stick entirely to talking or writing when arguing. We therefore miss the fact that a consistent process of visualisation makes pictorial arguments in the second sense possible, because faithful images assert the truth. However, these only became possible in the Italian Renaissance through the theory of perspective. If Leonardo can visualise the world as it is, or as it is or would be visible from a certain point of view, then he can claim to have made a piece of the world directly visible and accessible as an argument.

Leonardo relentlessly penetrated reality with his thoughts, restlessly explored it through experiment and perception and visualised everything: his theories, his experimental arrangements and the results of his observations through his drawing skills and recorded them for posterity:

"Read me, reader, if I give you pleasure, for very seldom do I return to this world. For the patience of this academic appointment is found in few, that they wish to invent similar things anew. And come, ye men, to see the wonders that are discovered in nature by such studies."

The author
Prof Dr Michael Sukale, Head of the Institute of Philosophy, was appointed to the University of Oldenburg in 1992. Born in Berlin, he studied history, psychology and sociology in Freiburg and Mannheim and philosophy at Stanford University. After ten years of teaching and research in Princeton, Chicago, Washington, Jerusalem and Paris, he returned to Germany in 1980 and habilitated in philosophy and science studies in Mannheim. Until his academic appointment in Oldenburg, Sukale taught at the universities of Düsseldorf, Constance, Geneva, Bamberg and Leipzig in addition to Mannheim.