Delivered at the international symposium on Unità e molteplicità nel pensiero filosofico di Leibniz, organised by the Accademia Nazionale dei Lincei and the G.W. Leibniz Gesellschaft, at Rome, 3–5 October 1996.

The theme of the one and the many is central to Leibniz’s philosophy. For Leibniz, it was axiomatic that the created universe is characterised by multiplicity and diversity, whereas God is unique. He criticised both Descartes and Spinoza for failing to establish the individuality of created beings, and hence their distinctness from God. Leibniz’s originality lay in his theory that the created universe consists of an infinity of monads which are distinguished both from each other and from God by their unique perspective on the rest of the universe. As essentially perceiving beings, monads are not atomic components of the world of physical objects — rather, the latter world is a construction out of the perceptions of monads.

Much has been written about whether it is coherent for Leibniz to claim that monads perceive the rest of the universe, given that only monads exist, and that they present no exterior to be perceived. I shall not pursue this topic here, since I have argued elsewhere that a harmony of perceptions does not presuppose that monads are the direct objects of perception, even if Leibniz himself sometimes talks in this way. The objects of perception are constructs, and their connection with other monads is a function of the universal harmony, guaranteed by God. Indeed, some commentators have gone so far as to deny that Leibniz was in fact a phenomenalist in his later years. Again, I shall not address this issue now, since his phenomenalism is clearly attested by his correspondence with De Volder and Des Bosses, and other writings of the period.

My concern is with a topic which has been given less attention, namely the difference between human and divine perception. I shall argue that, while Leibniz’s views on human perception contain valuable philosophical insights, his account of divine perception is highly problematic.

I shall start from a text in which Leibniz contrasts the two forms of perception with exceptional clarity. The passage comes from a preparatory note Leibniz wrote for a letter to Des Bosses of February 1712. However, the text has to be treated with caution, for two reasons:

First, it was not included in the version actually sent to Des Bosses, which might suggest that it was a mere thought experiment, to which Leibniz was not committed.

Second, the majority of commentators (including myself) do not regard Leibniz as wholly sincere in his dealings with Des Bosses. Leibniz’s motive was to bring about a reconciliation between the Lutheran and Catholic churches over the nature of transubstantiation or consubstantiation. Leibniz’s preferred view was that, since physical objects are only phenomena, and their components have only a transitory connection, it makes no sense to argue whether the bread and wine are really changed into the body and blood of Christ. However, this was a crucial issue for Des Bosses, and Leibniz’s compromise was to suggest that Catholics could believe in an optional extra called the vinculum substantiale — a substantial bond linking the parts together into a real substantial entity. Its existence would be guaranteed by God’s perception, since it is a relational entity, and the objectivity of all relations depends on God’s perception of them. Nevertheless, it is simply a diplomatic device. For Leibniz himself, the only unity is organic, and the superimposition of a vinculum substantiale would be a superfluous act of faith on the part of Catholics in order to preserve the doctrine of transubstantiation. It is not required metaphysically, but it would not be in direct conflict with Leibniz’s own metaphysics.

Despite these two caveats, the text is fully in accordance with Leibniz’s position as expressed in numerous other writings of the same period, and it runs as follows:

Leibniz admits that his analogy is only approximate (he includes the crucial qualification quodammodo) — but his intention is clear. Our representations of material objects are limited to a particular point of view, in which most parts are obscured, and shapes and sizes are distorted, like the elevation of a building. God’s representation is complete, undistorted, and without a bias towards any particular point of view, like an architect’s plans. As the Great Architect of the Universe, God has the blueprint for all creation, while we have to make do with partial and limited views after the event.

The main problem with the analogy is that a ground-plan, while certainly more informative in many respects than a simple elevation, does not include all the information about a building. Architects’ drawings include elevations as well as a ground plan. However, it remains true that all an architect’s drawings taken together provide a complete specification for a building, from which its appearance from any particular point of view can be derived; whereas a drawing from a particular point of view does not enable one to deduce what it will look like from different points of view.

Take the simple example of a cube. If you hold it so that you are looking directly at one face, you will see only that face as a perfect square, and nothing else. You have no visual information about what lies behind that face. Similarly, if you hold an edge towards you, you will see two rectangles; and if you hold a vertex towards you, you will see three rhombuses. God, on the other hand, has a non-perspectival way of viewing the cube whereby he perceives it simultaneously as having six square faces, twelve edges each bordering two squares at rightangles, and eight vertices from which radiate three edges and three square faces at rightangles to each other.

What Leibniz seems to be saying is that our perceptions are really only two-dimensional, and as limited as a perspectival drawing of a building on a piece of paper. Even if we build a three-dimensional scale model of a building, we are no better off than with the building itself, since we have to represent it two-dimensionally. Ultimately, our visual knowledge of the world is dependent on the retina of the eye, which is a two-dimensional surface directed towards objects from a particular point of view.

The analogy between ourselves as inferior perceivers and God as a superior perceiver can be illuminated by imagining the perceptual world of two-dimensional creatures (I owe this analogy to Abbot’s Flatland). When we, as three-dimensional beings, watch the sun rise over the horizon, we see a bright disc gradually emerging, and then rising into the sky. If we are knowledgeable enough about astronomy, we might see it as a sphere, and even see the horizon dipping rather then the sphere rising. A two-dimensional creature would see only a bright line gradually increasing in size, and then diminishing again. A clever two-dimensional creature might work out the relationship between the bright line on the horizon, light and day, and circular objects it has to circumnavigate in its two-dimensional world. It would then hypothesise that there is a third dimension in which a bright circular object travels rounds its own flat world. But despite its intellectual understanding, it would not know what it was like to perceive a two-dimensional figure such as a circle, since one has to be removed by a further dimension to perceive it as a whole. Similarly, a being superior to ourselves, such as God, might be able to perceive three-dimensional objects as they really are in their totality, rather than as two-dimensional shapes from a limited point of view.

Christian and other theologies have a long tradition of speculating on the difference between human and divine knowledge. If God is omniscient, he must know at least as much as humans know, but to a superior degree. Although he has no physical sense organs, it would be paradoxical to deny that he has the knowledge that we humans acquire through our sense organs. So the scholastic philosophers (of whom Leibniz was one in his early years) developed the concept of scientia visionis, which I have translated above as ‘perceptual knowledge’. The idea is that God has a special and fully accurate knowledge of how things are in the universe, but without the use of any sense organs, and separate from his intellectual knowledge of abstract objects and eternal truths.

Where Leibniz differs from earlier thinkers is that he holds that the perspectival nature of human perception is more important than its dependence on sense organs. This is because ultimately we are nothing other than non-spatial monads, whose individuality depends on the unique perspective of our perceptions. That we have sense organs at all is a subordinate fact, which applies only to the phenomenal world of physical objects. It would hardly be an exaggeration to say that, for Leibniz, we have sense organs because our perceptions are perspectival, rather than that the perspectival nature of our perceptions is the consequence of our dependence on sense organs. So the defining difference between human and divine perception is not that God has the privilege of perceiving things directly and without the mediation of sense organs, but that God’s representation of the world is devoid of any perspectival limitation or bias.

In the passage quoted above, Leibniz makes it clear that God’s perception is entirely free of perspective, rather than that it consists in the totality of all possible perspectives. God knows how things will appear to every other viewer, because his perception includes all viewpoints eminenter, as he says using the scholastic term. This means that his own perception takes a superior form, in this case a non-perspectival form, but one from which all the others can be derived or deduced. Hence it is analogous to a master plan, which does not itself show what a building will look like from any particular point of view, but from which any particular perspective can be derived.

Furthermore, God perceives things ‘exactly as they are according to geometrical truth’. That is to say, God perceives a cube in all its cubicity — all six faces, all the edges equal, and all the angles rightangles. In the following paragraph, Leibniz extends this to all relations:

So the reality of space, time and other relations consists in their being true of God’s perceptions. Without God, they would be merely partial, variable, and subjective phenomena in the minds of individual perceivers. At this point, Leibniz’s position can be made clearer by considering how he distanced himself from some of his approximate contemporaries.

Leibniz criticised Descartes for making geometrical truths dependent on God, yet in the above passage he seems to be doing much the same. However, as he made clear in his anti-Cartesian writings, what he objected to was Descartes’ making geometry depend on God’s will rather than on his reason. For Descartes, we inhabit a world in which triangles have 180 degrees rather than 190 degrees because God arbitrarily willed it so, whereas for Leibniz God represents triangles as having 180 degrees because it is the only rational possibility. He is very careful to say that God perceives things ‘exactly as they are according to geometrical truth’, and not that what is geometrically true depends on how God perceives it. With the benefit of hindsight, we can see that Leibniz’s belief in the rationality and uniqueness of Euclidean geometry was less well founded than Descartes’ belief on the possibility of alternative geometries.

A second comparison is with Newton. When, in 1715, Princess Caroline of England asked Leibniz to state what he considered to be fundamentally wrong with Newton’s philosophy, the first point he chose was Newton’s assertion that space was God’s sensorium. The question of whether Newton intended this literally or not is a side issue. Leibniz was working from a Latin translation of the Optics from which the word tanquam had been omitted (A. Koyré and I.B. Cohen, ‘The Case of the Missing Tanquam’, Isis 52, 1961, 555–566), and the tanquam is no more significant than the quodammodo in Leibniz’s own description of God’s perceptual space. At first sight, there would appear to be very little difference between Newton’s position that objective space is (as it were) the perceptual space in which God represents to himself the physical universe, and Leibniz’s position outlined above. And it may indeed be the case that Leibniz misunderstood Newton’s position. In his paper which initiated the correspondence with Clarke, he writes:

Whether or not Leibniz was interpreting Newton correctly, this passage makes Leibniz’s own position abundantly clear: God does not perceive things by means of any organs of sense, but things, as phenomena in God’s mind, are produced and sustained by his act of perception.

But how, if it all, does this differ from Malebranche’s view that we see all things in God, or Berkeley’s similar position that real phenomena are ideas sustained by the divine mind? Here the main difference is that both Malebranche and Berkeley treated objective phenomena as if they were shared by human observers and by God, whereas dreams and delusions are private to the individual. Leibniz, on the other hand, maintained that all perceptions are modifications of the perceiver, and are numerically distinct even when qualitatively identical. The perceptions of different perceivers are kept in correspondence through the universal harmony, and not by the sharing of perceptions. Human perceptions are never wholly false, since they all play a part in the universal harmony, however limited or confused. Nor are they ever wholly true, since they all fall short of the complete and non-perspectival phenomena in the mind of God. The closest we can approach to divine perception is to build up as complete a picture as possible of things by sequentially observing them from the maximum variety of points of view.

As long as we confine ourselves to simple examples, such as buildings or geometrical solids, Leibniz’s account of divine perception has a certain plausibility. However, there are a number of serious problems with it, of which I shall mention just three.

First, the examples are of discrete physical objects. But as we know, Leibniz believed that the universe is a plenum. As he says in the Monadology, §§67–68:

The problem here is that we as humans are able to see plants and fishes precisely because we cannot see the microscopic plants and fishes in the intervening spaces. If we could see everything, we would see nothing: there would just be a complete fog before our eyes. If God can see everything all at once — the particles of air and water, and the insides as well as the outsides of solid objects — then his mode of perception is so different from human vision that it cannot be understood by analogy with it.

Secondly, it is central to human perception that we see objects as cohesive entities, separate from the surrounding medium. But for Leibniz, physical objects are not real entities, but only transitory collections like flocks of sheep, or rainbows. In so far as they are illusory, God will not perceive them as entities, since he is not subject to illusion. As he says in his draft letter to Des Bosses, just before introducing the optional concept of a vinculum substantiale to make physical objects real substances:

So again, God perceives a world which is not populated by macroscopic physical objects, and which will be utterly different from the world of human experience.

Thirdly, Leibniz’s account of God’s perception is couched wholly in terms of vision, whereas humans have a variety of senses, of which the sense of touch is arguably the most basic. It is interesting to speculate why he (in common with most other philosophers and theologians) should be happy to attribute to God something analogous to sight, but not to touch, smell, taste, or hearing. Indeed, there are many aspects of reality which we would not be able to perceive with any of our limited array of senses, however acute — for example, gravitational or magnetic forces, to name but a few which were known in Leibniz’s time. Would not an omniscient God have an analogue of all human senses, and many more besides?

A partial explanation is that the possession of certain senses would compromise the transcendence of the Christian God more than others. In Western culture, the main contrast was with the gods of the Greeks and Romans, who had sex, drank wine, listened to music, and enjoyed the smell of a burnt sacrifice. The special feature of the sense of sight (and to a lesser extent, hearing) is that it operates over a great distance, so that a god can observe without himself participating in earthly life.

But even God’s vision becomes impoverished in the hands of philosopher-theologians such as Leibniz. Although Leibniz did not himself adopt the terminology of primary and secondary qualities, the distinction was as fundamental to his thinking as it was to that of Galileo, Descartes, Hobbes, Locke and the other proponents of the mechanical world picture. The only undisputed real qualities possessed by physical objects were the primary qualities of shape, size, and motion, all of which were most readily perceived by the sense of sight. Additions such as mass or energy, while not themselves directly visible, were detectable by their visible effects. All other perceptible properties, including visible properties such as colour, were explained in terms of the interaction between the primary qualities of particles and those of the organs of sense. So, colours, sounds, tastes, smells, and feelings might be useful to humans in conducting their daily life, and sometimes also pleasurable; but they give us a radically misleading picture of what the physical universe is really like. All that God needs in order to have a complete representation of the real universe is something analogous to human vision, only lacking colour. To add anything corresponding to secondary qualities would diminish his perception, since they arise from the limitations of the human sense organs.

In short, the God of the mechanistic philosophers around the turn of the seventeenth century functions primarily as the guarantor of the objectivity of science. The world has just those properties he sees in it, and he ensures that it evolves in accordance with the mechanistic laws which he has ordained.

However, in order to fulfil this function, there does not seem to be any need for God to have anything analogous to perception. Descartes had already shown through his analytic geometry that geometrical truths could be expressed in an entirely abstract form which made geometrical diagrams redundant. His motive may well have been metaphysical and theological, since God, as a non-extended being, could not contain within himself any extended ideas. Indeed, the same was true of the human mind, and he always had difficulty over the question of how the human mind could be conscious of spatially extended images as well as of pure abstractions.

One might have expected Leibniz to pursue the same line as Descartes, especially since he was an avowed Platonist. Like Plato, he regarded the material world as a phenomenon dependent on perception, and hence at best only semi-real. Also like Plato, his archetype of genuine knowledge was abstract, and characterised by necessity rather than contingency; he devoted considerable energy to developing a characteristica universalis, which would enable humans to generate truths a priori rather than empirically; and he sometimes went as far as to express the positively Pythagorean belief that reality consists solely of number (though with the modern twist that the numbers are binary).

It is remarkable how quickly Greek philosophy produced a Plato, with his totally non-anthropomorphic conception of God, despite the continuing anthropomorphism of the official religion. It is equally remarkable how long it took Christianity to rid itself of the traces of anthropomorphism, despite its official espousal of transcendentalism. A God who observes the world, even if only in black and white, and without touching, or hearing, or smelling it, is clearly more anthropomorphic than the God of Plato.

I believe that the reason why Leibniz fell short of the Platonic ideal lies in his theory of substance. He had many interesting reasons for maintaining that the only real constituents of the universe are perceivers. Although, like Descartes, he recognised a difference in kind between humans and inferior beings, the difference lay in the quality of perception (namely the addition of apperception), rather than in their being entirely different kinds of substance. Similarly, when it comes to the distinction between humans and God, Descartes was able to say (with Plato) that God simply lacked the unnecessary encumbrance of perception, whereas Leibniz had to say that God enjoyed a mode of perception which was as superior to human perception as human perception was to that of animals.

The price Leibniz paid for avoiding the crude dualism of Descartes was an unduly anthropomorphic conception of the nature of divine knowledge, which included a scientia visionis derived from human visual perception.

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