Gottfried W. von Leibniz

Thomas Masini

 Every monad, since it can potentially constitute any kind of compound and cannot communicate in any way with the outside, must already contain in itself everything ab origine

     During the years of his cultural education, in 1663 in Leipzig, Gottfried Wilhelm Leibniz argued his baccalaureate thesis entitled Disputatio metaphysica de principio individui. The philosophy taught in German universities then was the alleged ‘second scholasticism’, i.e. medieval scholastic philosophy (particularly of Thomas Aquinas) in the revision and systematisation made by Spanish philosophers, among whom Francisco Suarez. Although this was the ‘institutional’ path, the situation in the cultural environment outside universities was quite different.

     Scholastic philosophy in those years had to deal with other structures of thought that seriously challenged its fundamental demands. These were the so-called Renaissance thoughts and the new science of nature. The positions of thinkers such as Giordano Bruno and Giovanni Pico della Mirandola were flanked by the scientific thought of Galileo Galilei, who instituted a new epistemological method based essentially on two principles: always start from a long experiential investigation of individual cases in order to deduce general principles and laws; and take into account, in the formulation of the latter, only the quantitative aspects of reality, because they are the only ones that can be rigorously calculated and expressed in mathematical terms.

     Leibniz makes both classical philosophy and the new scientific method his own. In fact, he is remembered not only for his metaphysical system but also for his studies on the infinitesimal calculus, without which his ontological system could not be fully understood. After this brief overview, let us now proceed by going through his most significant work The Monadology, to take a closer look at Leibniz’s thought.

     It is worth remembering that in the systems of Descartes and Spinoza the two fundamental ontological dimensions were thought and extension, i.e. the dimension of logical-rational principles and the dimension of materiality. Leibniz starts from the latter and asks himself the following question: what constitutes entia? The answer of scholastic philosophy and Aristotle answers: entia are a unitary compound of formal principle and material principle. Leibniz’s answer, however, is different. Let us look at the first two propositions of the first part of the Monadology:

  1. The Monad, of which we shall here speak, is nothing but a simple substance, which enters into By ‘simple’ is meant ‘without parts.’

  2. And there must be simple substances, since there are compounds; for a compound is nothing but a collection or aggregatum of simple. [1] 

     First of all, he notes that every entia is a compound of simpler elements or, in other words, that every entity can be decomposed into simpler parts. However, decomposition cannot be infinite (regressus in infinitum), thus there must be ultimate simple constituents that cannot be further decomposed. These elements are called by Leibniz ‘monads’ – units. Although at first glance these monads might seem to be Democritus’ atoms, they are quite different: they have no extension, no materiality. As a matter of fact, it seems that this is the only way to guarantee their indivisibility:

  1. Now where there are no parts, there can be neither extension nor form [figure] nor These Monads are the real atoms of nature and, in a word, the elements of things. [2]

Leibniz finds the very concept of a non-divisible body contradictory. Therefore, the only way to avoid falling into this contradiction is to admit that the divisibility of bodies is infinite, in the sense that the monads themselves are infinite in number. By doing so, the result of the division is never zero, nor absolute nothingness, but rather the ‘representative force’ (the monad to be exact) – which is the limit of the infinite division of the extended. The meaning of the term ‘limit’ is exactly what it assumes within the infinitesimal calculus discovered by Leibniz and Isaac Newton.

     Since they are immaterial, they are also consequently unperceivable by our senses because they obviously do not possess a matter that can be perceived or that can act on the passive senses that are in charge of our perception. Another consequence is that they are neither generated nor corruptible. Generation is nothing more than the coalescence of parts that were formerly disintegrated, and corruption is nothing more than the disintegration of parts that were formerly joint:

  1. Thus it may be said that a Monad can only come into being or come to an end all at once; that is to say, it can come into being only by creation and come to an end only by annihilation, while that which is compound comes into being or comes to an end by parts. [3]

The final consequence is their total impermeability in relation to otherness or externalism. In other words, they do not endure alterations of any kind from external causes, nor can they act directly or indirectly on what is outside to modify themselves. Leibniz explains this with a proposition that has become famous: «The Monads have no windows, through which anything could come in or go out». [4]

But if monads are immaterial, imperceptible, ingenerated and incorruptible, what is their nature? They have intrinsic qualities, and these are perception (or consciousness) and the appetition (adpetitus); affections are added to them.

     Leibniz’s reasoning is as follows: every created thing changes and change imposes that there are two complementary dimensions. There has to be a part that undergoes change and a part that remains unchanged, forasmuch as nothing changed, change would not exist. Furthermore, if everything changed, one could not speak of change but of generation. Monads, however, are simple units, and have no parts; what is more, they do not undergo generation nor corruption. Yet each of them must be distinguished from another, or not only differentiation, but also otherness and multiplicity would not be possible. How can all this be sustained without contradiction? There is a permanent dimension in them that determines their self-identity: perception. This principle of permanent identity is not apperception (i.e. the perception of perceiving), but simple perception, and it belongs to every monad, hence to every compound of monads, and thus to every entity. These perceptions, although they are the foundation of self-identity, are also the transitory element, the affections, which thus determine differentiation and multiplicity. This is to say that unity is given by perception – by the principle of perception – and otherness is given by the concrete actualisation of the transitory perception. What moves temporariness, the agent principle of change, is appetite i.e. the drive to movement and action that comes directly from the subject itself. By doing so, the monads are in self-identity with themselves and are, at the same time, multiple and different even though they have none of the qualities that belong to extension, nor to materiality.

     It has been said that every ens is in essence a complex of monads; an example of a monad may be the Ego, or the soul – which has the peculiarity of having in itself, in addition to perception, apperception. Every monad, since it can potentially constitute any kind of compound and cannot communicate in any way with the outside, must already contain in itself everything ab origine. Every monad, therefore, is a mirror of the totality: it potentially contains within itself the perception of the totality, but always realises it imperfectly. The perception of monads, therefore, is always and only the perception of itself, in the sense of perception of something that is ‘inside’ the monad itself.

     One remembers the distinction operated by Descartes about the confused and blurred ideas and those “clear and distinct”; Leibniz adopts this formulation and considers that in the monads there are confused perceptions and clear perceptions. With respect to the former, the monad constitutes itself as passive, while to the latter, it constitutes itself as active. Using an example that is all too simplistic but essentially correct, we can say that a monad that belongs to a compound that we call ‘tree’ has a clear and distinct perception of being a tree, while it has a confused and blurred perception of being a rock, a river, or anything else that is not the tree that it helps to constitute. The double modality of this perception is comparable to the photographic focusing of an object that at the same time implies the blurring of everything that is other than that object itself.

     One last question remains to be answered, in this very brief reconnaissance of Leibnizian thought: if monads are, so to speak, ‘armoured’ and impermeable – that is, they do not act on other monads and do not endure action from them – how is it possible that their aggregations always compose and decompose only according to universal, mathematical and pre-established rules? The answer has already been partially hinted at. The sixth proposition states that monads can only come into being by creation, but if something is created there must certainly be something that creates. Let us diligently follow the reasoning of Leibniz. Entia are in perpetual change, and every change suggests a cause that determines its occurrence. In fact, one could say that every existing thing and every happening implies a causal chain. Now Leibniz defines this causality with the expression ‘sufficient reason’, i.e. that reason (motivation) which is sufficient to explain what is being asked for. If one takes the infinite changes that occur in monads – and therefore in being – and tries to trace the chain of causes, one discovers that it is always possible to find a sufficient reason for the single event, but one cannot find one sufficient to explain the event of the entirety. It is therefore necessary to look for a necessary and sufficient reason to explain the being of the Whole, and it can only be a supreme ens, which is the cause – sufficient reason, in fact – of everything. In Leibniz words:

  1. Thus the final reason of things must be in a necessary substance, in which the variety of particular changes exists only eminently, as in its source; and this substance we call

  2. Now as this substance is a sufficient reason of all this variety of particulars, which are also connected together throughout; there is only one God, and this God is. [5]

God is therefore the supreme ens, or the supreme monad, which has the same characteristics attributed to him in his classical conception: unity, infinity, perfection and creative power. It is precisely in the act of creation that God establishes a fundamental and universal law that Leibniz calls “pre-established harmony”. It is this specific harmony that allows the impermeable monads to constitute themselves in compounds and to operate coalescence and disintegration without being able to communicate with each other in any way. In this way we have that very specific situation whereby God works to guarantee harmony in the universe without acting directly.

[1]  Gottfried W. Leibniz, Monadology, translated by Robert Latta, 1898.

[2] Ibidem.

[3] Ibidem.

[4] Ibidem, proposition 7.

[5] Ibidem.

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