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An Experience of Infinity in Leibniz’s Philosophical Laboratory

 

In 1672, an ambitious young man arrived in Paris on a diplomatic mission. The young German arrived with the idea to divert the French army from invading the Netherlands by convincing Louis XIV to invade Egypt instead.[1] The so-called Egyptian plan was schemed by Gottfried Wilhelm Leibniz and his mentor, Baron Boineburg. Leibniz was sent Paris to promote it. While he was not able to meet the French king, the mission did enable Leibniz to move from the provincial town of Mainz to Paris, and to spend four years at the intellectual center of Europe, where much of the activity forming modern science and philosophy was taking place. Leibniz did not waste his time. By the end of his sojourn in Paris he managed to establish an important intellectual network and to come up with some incredible achievements such as the differential calculus, a calculating machine, important philosophical writings such as the Confession of a philosopher and a great variety of notes on metaphysics of remarkable interest and inventiveness. Some of these notes were collected and edited by the Akademie Ausgabe under the title De summa rerum (DSR), which means both “on the highest of things” and “on all things.”[2]

A very curious note from 1676 evokes a theme that has gone almost unnoticed, however.[3]

The note reads as follows:

The following operation of the mind seems to me most wonderful: namely, when I think that I am thinking, and in the middle of my thinking I note that I am thinking about my thinking, and a little later I wonder at this tripling reflection. Next, I also notice that I am wondering and in some way wonder at this wonder, and fixed in one contemplation I return more and more into myself, […] So, it comes about that we are finally wearied by this effort and feel a headache or, even (if we persist) become insane (DSR 73).

Leibniz is recounting here a strange personal experience, attending to reflections of his own reflections. The experience has a reiterative structure and could go on ad infinitum. Leibniz finds the experience not only possible but also wonderful. He is experimenting, it seems, with our ability to sense infinity. This is not so surprising given that much of his mathematical work during these years is dedicated to dealing with infinity and that much of his philosophical efforts are dedicated to defending the possibility of an infinite Being while rejecting the possibility of an infinite number. [4]

In the sequel to the note mentioned above, Leibniz even provides some instructions as to how one can have such an experience (the perception of perceptions to infinity):

If anyone wants to experience this, all he has to do is this: at some point in the darkness of the night, when it happens that he cannot sleep, let him begin to think of himself and of his thinking and of the perception of perceptions. (DSR 73).

The perception of one’s perceptions could certainly go on for a long time. Hopefully, one would end up falling asleep rather than being wearied by a headache or, if persisting, becoming altogether insane.

The passage ends with the following conclusion: “and so the perception of perception to infinity is perpetually in the mind and in that there consists its existence per se and the necessity of its continuation” (DSR 75). Leibniz is seeking to support his initial point that there is some memory after death, as there is when we fall asleep (DSR 73). This supports the view that an active soul would remain active, unless annihilated by God. It relates to his later notion of “petits perceptions,” perceptions that are always taking place in the background and that we are usually not aware of.

Leibniz’s extraordinary account of his own experience is also important for the other philosophical seeds it sows. While the passage captures a strange nocturnal experience, the ability to have perception of perceptions (later to be called apperception) turns out to mark the difference between the human mind and that of other animals. For Leibniz, the distinctive feature of the human mind is that it can reflect on its own thoughts. This in turn will serve him as one of the necessary requirements for human freedom. This mark of the human mind can be gleaned from other passages in the DSR notes as well. For example, Leibniz writes that, “we do not act as a simple machine but out of reflection, i.e. out of action on ourselves” (DSR 37). He also notes that:

when I think and reflect on myself for a long time, with continuous reflections on a reflection, there is, as it were, a kind of amazement; and a wondering at this reciprocation. […] If this is the nature of the mind, and it consists in the sense of itself, then I do not see how that sense can be impeded or destroyed (DSR 61, my italics).

Reflections on reflections belong to the nature of the human mind. But it is also a defining feature of the divine mind: “it must be demonstrated rigorously that he [God] senses his own actions on himself, for there is nothing more admirable than for the same being to sense and to be affected by itself” (DSR 27). This view echoes Aristotle’s nous (νοῦς) as a mind contemplating itself (hê noêsis noêseôs noesis, 1074b21–35, spec. ll. 34-35).[5] In the Leibnizian context, reflections of reflections acquire additional meaning. Self-reflection is constitutive of God’s mind. It also plays a role in the conceiving of all possibilities, which is central to Leibniz’s metaphysical and modal system. Indeed, as I have argued elsewhere, in the De summa rerum, these possibilities are conceived by God as he reflects on his own attributes.[6] In much later texts, Leibniz explicitly refers to a “Divine Mathematics and Metaphysical Mechanism” figuring at the “radical origin of things” (AG 151). This mechanism is meant to explicate the way all possible worlds are conceived in God’s understanding. What often escapes attention is that such a mechanism presupposes divine self-reflection.

But there is no space for the details here. Instead, in conclusion, I want to draw attention only to the fact that the very ability of reiterative reflection upon reflections turns out to be a feature that the human mind shares with God. It may well be seen as one of the ways in which humans are created in God’s image (imago Dei). Thus, a rather strange and somewhat obscure nocturnal experience the young Leibniz has in the middle of his sleepless nights in Paris turns out to carry some significant consequences for the later development of his philosophy.

OHAD NACHTOMY

[1] See M. R. Antognazza, Leibniz. An Intellectual Biography, Cambridge: Cambridge University Press, 2009.

[2] Most of these texts were translated into English by G.H.R. Parkinson in the Yale Leibniz series in 1992. My citations here refer to this edition, abbreviated as DSR.

[3] Parkinson, for example, notes that, for Leibniz, “to think is to reflect” (Introduction to DSR, p. xlvi) but ignores Leibniz’s point about reflections on reflections. For discussion, see S. di Bella, “Memoria e individualità. L’ontologia della temporalità nelle note parigine di Leibniz (1676): un confronto a distanza con Spinoza?”, in Ontologia e temporalità. Spinoza e i suoi lettori moderni, ed. G. D’Anna-V. Morfino, Milan: Mimesis, 2012, pp. 81–107, esp. pp. 85–88. But, as can be seen from the title, the focus here is the much-debated confrontation between Leibniz and Spinoza.

[4] This is clearly exhibited in the two short pieces Quod Ens Perfectissimum Sit Possible (DSR 91–95), followed by Ens Perfectissimum Existit (DSR 96–100). This is Leibniz’s amendment to Descartes’ proof for the existence of God, which Leibniz also shows Spinoza in their single meeting during Leibniz’s trip from Paris back to Germany. According to Leibniz, only if the notion of the most perfect being is shown to be possible, would it follow that he exists. I have argued for these points at length in Living Mirrors: Infinity, Unity, and Life in Leibniz’s Philosophy, Oxford: Oxford University Press, 2019.

[5] Aristotle’s Metaphysics Book Λ/XII, chapter 9 and De anima III 1.

[6] This is related to Leibniz’s early work on the art of combination (1666) and other texts from Leibniz’s early writings. I have written on this extensively in my Possibility, Agency, and Individuality in Leibniz’s Metaphysics, Dordrecht: Springer, 2007.


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adminnotcom (March 27, 2025). An Experience of Infinity in Leibniz’s Philosophical Laboratory. NOTCOM. Retrieved July 17, 2025 from https://doi.org/10.58079/13l5o


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