At first sight, the philosophical idea that the world is composed of atoms, notably embraced by Greek and Roman authors such as Democritus, Epicurus, and Lucretius, seemed to have disappeared during the middle ages. It has been frequently said that it only reappeared during the Renaissance and then in modern philosophy and chemistry. In fact, atomism never ceased to exist as a theory of matter, space and time, both in western Latin tradition and in the Arabic and Jewish medieval philosophy. Different versions of atomism were developed in these traditions: from theological explanations of creation to pure mathematical theories about the divisibility of the continuum, through physical theories of matter and time. The first detailed accounts of atomism come from the ninth- and tenth-century Arabic theologians of Baghdad and Basra, immediately followed by the Jewish schools, notably in Egypt. A similar revival of atomism appeared in the West from the twelfth-century philosophers of Chartres to the fourteenth-century Christian theologians of Oxford and Paris. Most of these medieval atomist theories have very little in common with ancient atomism, for they are usually linked with more complicated theological concerns, such as the eternity of the world, creation, the existence of prime matter, and more generally the finiteness of created things. On the other hand, they are similar to Platonic and neo-Pythagorean conceptions of reality as constituted from units and numbers, or from atoms and collections of atoms, which are equivalent to units in matter and space.
It has long been thought, until the end of the nineteenth century, that there were no atomist theories in medieval philosophy and that ancient atomists, such as Epicurus or Lucretius, remained unknown until the Renaissance, before Poggio Bracciolini worked on the manuscript of the De natura rerum discovered by him in 1417. This view of the history of atomism has been challenged during the last two centuries. In the nineteenth century, Kurd Lasswitz and Léopold Mabilleau already endeavored to make room for medieval theories in their essays on atomistic philosophy (Lasswitz 1890; Mabilleau 1895). But it is only recently that many efforts have been made to show the existence of very important atomist theories of matter and time in the medieval Arabic philosophy and theology from the ninth to the twelfth century (Pines 1936; Wolfson 1976; Dhanani 1994) and the existence of thorough examinations of them in the Jewish and the Christian traditions (Maier 1949; Murdoch 1974; Pabst 1994; Pyle 1997).
The main dispute in the medieval Arabic natural philosophy opposed hylomorphism (i.e., that the world is composed of matter and form) to atomism (an ontology which accepts only atoms and properties). If the former ontology was accepted by most of the philosophers (falsafa), a majority of the theologians of the kalām (the mutakallimūn), notably in Basra and Baghdad, both on the Muʿtazilite’s (a school of rational theology founded in the ninth century in Basra) and the Ashʿarite’s (another school founded by the theologian Abu al-Hasan al-Ashʿarite against the Muʿtazilites) sides, accepted atomism (Rashed 2005). The first atomists seem to be the Basrian theologians Abū al-Hudhayl and al-Nazzām (ninth century). Abū al-Hudhayl posited the existence of a finite number of discrete atoms without extension, without quality, and without corporeal nature (for they are the constituents of bodies) that can move through the vacuum. The only feature that can really define the nature of atoms is their place or location. Al-Nazzām accepted the main tenets of such a view but argued lengthily against one of its points, namely, that there are a finite number of atoms in a body or in a line. Indeed, al-Nazzām maintained that this is impossible because there are an infinite number of positions in a continuum, for if an atom does not have any extension, this must also hold for its place. Strangely enough, he thus maintained that there are an infinite number of atoms with a typical argument against atomism. Al-Nazzām was conscious that in this case Zeno’s paradoxes of motion and dichotomy may apply, for it is impossible for something to pass through an infinite number of places. In order to explain the possibility of motion, al-Nazzām affirmed that atoms move by means of leaps, which signifies that motion is always discontinuous.
The philosophical discussions in the later mutakallimūn were about the magnitude of the atoms, their number (finite or infinite?), and their qualities but always under the aspect of the possibility of motion. They were also very interested about related topics such as the compatibility of atomism with Euclidian geometry, as it appears in one of the best summaries of these later discussions in Fakhr al-Dīn al-Rāzī. The most vehement critic of atomism in the Arabic tradition was Abū Yūsuf Ya‘qūb ibn Ishāq al-Kindī in the ninth century. Of course, Avicenna (Ibn Sīnā), al-Ġazālī, and Averroes (Ibn Rushd) also detailed long argumentations against the mutakallimūn’s atomism in order to restore the Aristotelian hylomorphism.
If the argumentation seems purely philosophical, the main motives for their acceptance of atomism were theological and were related to their explanation of the creation of the world by God. According to them, the world must have been created because if it were not, the world should have passed an infinite time, which is not possible. Most of their philosophical arguments to support atomism are mainly derived from Zeno’s paradoxes and from John Philoponus’ use of them in his refutation of the eternity of the world. As a consequence, some of them, mainly the Ashʿarites, thought that God can create and destroy the world whenever He wants, for He can destroy or create new aggregates of atoms at each instant of time. As a consequence, they contend that accidents cannot exist longer than one instant. Therefore this radical version of atomism – occasionalist and deterministic – denied the existence of real causality in the created world. It appears that Arabic atomism has very little in common with Democritus’ and Epicurus’ atomist theories, even if they were known to the mutakallimūn.
Important echoes of these discussions can be traced back in the Jewish medieval philosophy, both in the kalām and in the Neoplatonic schools. For example, in the ninth and tenth centuries, Saadhia Gaon (Wolfson 1946) and Isaac Israeli (Zonta 2002) both rejected the Arabic mutakallimūn’s atomism. During the following centuries, Judah Halevi, Ibn Daud, Maimonides, Gersonides, and Crescas also argued against Arabic atomism. Maimonides’ criticism in Chaps. 71–76 of book I of his Guide of the Perplexed is probably the better-known among them and is mostly directed against occasionalism and continuous Creation of the World. As Tamar Rudavsky has shown (Rudavsky 2000), Jewish discussions about continua of space and time are related to the theological problem of creation, as was already the case in the Arabic tradition. Although denying the eternity of the world, they contend that creationism does not necessarily imply atomism about time and matter. This is problematic for them because their argumentation for the non-eternity of the world is reminiscent of Zeno’s paradoxes and is probably derived from Philoponus’ book Against Aristotle on the Eternity of the World, where Zeno’s paradoxes are used against the eternity thesis. If the world were eternal, then an infinite time would have been passed through, which is impossible; therefore the world’s temporality is finite in some sense. But this argument could also be used in favor of atomism and finitism, as will be the case in the Latin world, which we shall see later. Strangely enough they denied on the one hand the eternity of the world with some kind of atomist argument while accepting on the other hand the infinite divisibility of the continuum.
If we now focus on western Latin philosophy, it appears that atomism never really ceased to exist during the Middle Ages. Concerning the myth of Bracciolini, it must be noticed, as Philippe has shown in his pioneering study (Philippe 1895, 1896), that Lucretius’ poem was copied and discussed throughout the Middle Ages with no interruption from the era of the Church Fathers to the twelfth century. The same is also true for Epicurus, whose works were partially known through a still longer chain of intermediate sources (Cicero, Lactantius, St. Jerome, St. Ambrose, St. Augustine). In the twelfth century, John of Salisbury dealt with Epicureanism in his Metalogicon and in his Entheticus, where he tried to refute its principal tenets. On the contrary, we find a defense of Lucretius and the Epicureans in the works of William of Conches, notably in his Dragmaticon philosophiae where he quotes passages from Lucretius’ De natura rerum.
When the Epicureans said that the earth consists of atoms, they were correct. But it must be regarded as a fable when they said that those atoms were without beginning and ‘flew to and fro separately through the great void’, then massed themselves into four great bodies. For nothing can be without beginning and place except God.
This atomist lecture of Creation has never been more detailed until the fourteenth century. What is more, some twelfth-century thinkers, such as William of Champeaux and Peter Abelard, also defended the existence of indivisibles in the continuum in their commentaries on Aristotle’s Categories, in the chapter on quantity (King 2004). Indeed, they suggested reading Aristotle’s view on the continuum with Boethius’ treatise On Arithmetic, which was a Latin translation of the neo-Pythagorean mathematician Nicomachus of Gerasa. Boethius presented a general theory of the derivation of magnitudes from points, which were thought of as units with a particular position in space and called “atoms.” As a result, three-dimensional geometric figures, i.e., solids or bodies, are at the same time continuous and metaphysically constituted of points.
The divisibility of a continuum and the notion of infinite remained of great interest during the thirteenth century (Trifogli 2002), but no atomist theory of matter and time can be found during this period, except in Robert Grosseteste’s metaphysics of light. Indeed, in his De luce and in his Notes on the Physics, the Bishop of Lincoln explains that God created the world from a single point of light multiplied infinitely in all directions. As a result, every part of the material world, and every magnitude, is composed of these points, which were multiplied in the first instant of the world (Lewis 2005). Grosseteste clearly defends the Boethian derivation of magnitudes from points, but with his metaphysics of light, he also gave a new theoretical tool in order to answer the many arguments against atomism coming from Aristotle’s Physics and Arabic sources, such as Al-Ghazali’s Metaphysics, which gives a summary of Avicenna’s arguments against the Mutakallimūn (Robert 2017).
After the thirteenth century, the main sources for this renewal of intense reflections on atoms were not Epicurus or Lucretius, but rather Democritus through the newly translated texts of Aristotle into Latin where the composition and division of a continuous quantity are discussed (Physics, On Heavens, On Generation and Corruption). Can a continuum be divided infinitely? Is it composed of indivisibles? Aristotle argued against Leucippus and Democritus that if the world were made of atoms, it would be impossible to explain how they can form continuous magnitudes. The world would be totally discrete. Atoms either have a magnitude or not. If they have it, they are divisible and then ad infinitum. But if they do not have any magnitude, they cannot form continuous magnitudes because they cannot be in contact (Physics, 231 a26–b6), for if two things are in contact they either touch (1) part to part, (2) part to whole, or (3) whole to whole. The two first possibilities must be rejected for atoms because they do not have any parts by definition. And if they touch whole to whole, it would mean that they are superposed, and therefore they cannot form a new magnitude. Contrarily to thirteenth-century Aristotelians, some fourteenth-century philosophers thought that a continuum can be composed of indivisibles and that it is possible to respond to Aristotle’s arguments.
The first atomist – or indivisibilist – of the fourteenth century is Henry of Harclay, Chancellor of the University of Oxford in 1312, who defended the existence of an infinite number of indivisibles in any continuum when disputing a quaestio about the eternity of the world. His main argument consists in refuting the Aristotelian thesis about contact. Harclay affirmed that two points can touch if they are situated in contiguous places. It is not very clear whether this can explain continuity or only contiguity of atoms, but Harclay clearly asserts that a continuum is composed of points or indivisibles and that they are infinite in number. As in the Arabic tradition, atoms are primarily defined by their position. His successors at Oxford, among them Walter Chatton, William Crathorn, and John Wyclif, also accepted the indivisibilist analysis of the continuum problem but restricted it with the assertion that the number of indivisibles is finite (Zoubov 1959; Murdoch 1974; Kretzmann 1986; Robert 2009). One of their strongest and recurrent arguments is derived from one of Zeno’s paradoxes, called “the metrical paradox of extension.” This paradox – probably known to the medieval philosophers through Simplicius’ commentary on Aristotle’s Physics – runs as follows: an extended thing is either composed of extended or unextended parts; if we accept infinite divisibility of the continuum, then either the extended thing is composed of an infinity of extended parts and is therefore infinite in extension or it is made up of an infinity of unextended parts, but we cannot explain how extension comes from non-extension. Chatton, Crathorn, and Wyclif accepted Harclay’s basic arguments – that is, that indivisibles are firstly defined by their positions in the continuum – but they added the metrical paradox to conclude that the number of indivisibles must be finite. We find the very same kind of argumentation in Gerard of Odo, General Minister of the Franciscan order in 1329 (De Boer 2009). Nicolas Bonetus, another contemporary Franciscan theologian, and Nicholas of Autrecourt also used Zeno’s paradoxes, but they finally accepted the infinity of atoms (Grellard 2004).
According to John Murdoch, fourteenth-century atomism is merely a response to Aristotle’s anti-atomism, and no real traces of ancient physical atomism can be found in this fourteenth-century indivisibilist literature. Therefore atomism would only concern the geometrical continuum and would be only directed against new geometrical arguments (Murdoch 1974, 1982; see also Pabst 1994). At any rate, it is clear that from the divisibilist side – as in Thomas Bradwardine’s, Adam Wodeham’s, or Gregory of Rimini’s works against the atomists and as in the Arabic tradition – the strongest arguments against atomism were geometrical. As an example, the incommensurability of the diagonal and the sides of a square was frequently used against the finite composition of the continuum. For example, assume that the sides of a square are composed of n points. If you draw all the parallels from each point of a side to its counterpart on the opposite side, the diagonal which intersects the parallel lines turns out to be composed of n points too. From a mathematical point of view, however, the diagonal of a square is incommensurable with its sides. According to its opponents, this mathematical argument proved that atomism was an absurd theory (Murdoch 1969). Atomists, however, developed real atomistic physics and even built up some strong criticisms of the mathematical tools used by anti-atomists. Indeed, Chatton, Crathorn, and Wyclif argued against the relevance of geometry to deal with the problem of the continuum. According to them, indivisibles must be considered as elemental components of reality and not as mere unextended points (Robert 2009; Michael 2009). The most representative philosopher of this physicalist way of thought is undoubtedly Nicholas of Autrecourt (Grellard 2009), who explains generation and corruption, condensation and rarefaction, and generally all types of motion by the local motion of atoms. The main motive of Autrecourt’s atomism is the defense of the eternity of the world, one of the reasons why he has been condemned by ecclesiastical authorities. In any case, their positions are never reducible to a mere reaction to Aristotle’s arguments nor to a reconstruction of Democritus through Aristotelian doxography.
It becomes quite clear that all medieval atomists were influenced by the same Platonic and neo-Pythagorean theory of the derivation of magnitudes from points (Robert 2017). For this reason, one finds the same kind of theories in Arabic, Jewish, and Latin writings. Indeed, with the exception of Nicolas Bonetus and Nicolas of Autrécourt, medieval atomists believe that atoms are point-like entities, not corpuscules with a minimal magnitude or shape. As a consequence, medieval atomism is a mathematical conception of reality, in which atoms are like units from numbers. Even though they accept the existence of indivisibles, they do not refuse the existence of continuity in the material world. They do not accept, for instance, the existence of void. There is no gap in matter, time, and space, but all magnitudes must be composed of units, which can be called “atoms.” From the fourteenth century onward, the defenders of this mathematical atomism will try to apply this mathematical analysis to the problems raised by Aristotle’s Physics, giving rise to a more physical form of atomism.
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