The most conspicuous characteristic of early modern in contrast to ancient and medieval science is rightly considered the different kind of recourse to experience in the generation and justification of knowledge.1
Results of observation and experiment were put forward against the authority of the Aristotelian doctrine
From this problematic situation, it is understandable why the insistence on observation and experimentation as the ultimate authorities to judge the truth of scientific propositions was not the only characteristic of the early phase of modern science. There was also the nearly desperate hope and expectation that, through philosophical reflection,2 it would be possible to create an apodictic theoretical framework for the interpretation of empirical experiences, a framework justified solely on the principles of reason. This program was designated by a term going back to Aristotle
The early modern idea that matter has the essential property of being impenetrable has its origins in ancient philosophy, namely in a thought experiment. If one conceives of the perceptible bodies of everyday experience as being divided into ever smaller parts, the following alternative appears to be inevitable: Either the division
The assumed existence of such impenetrable atoms of matter became the point of departure for the ancient philosophical tradition of atomism. In their speculative endeavor to reduce the coming-into-being and passing-away of reality to a permanent, rationally conceivable explanation, Greek philosophers developed the idea that the world of macroscopic phenomena and occurrences could be explained by processes in a microscopic world which is no longer accessible by our senses but only by reason. According to this explanatory model
According to the ancient atomists, our senses merely lead us to believe the colorful world of sensory impressions. In fact there are only atoms, their shapes and their movements, which affect our senses.5
The postulated atoms are different from the objects of our direct experience in yet another respect. Since they are supposed to be indivisible they must have characteristics principally different from these objects, for otherwise there would be no reason why the process of division
thought them [i.e. the atoms] to be uncuttable, indivisible, and unaffectible on account of their being compact and having no share of void
This speculative structure describing the microscopically small contains tacit assumptions about the relationship between space and matter, which were later to constitute the core of the problem to be discussed here. Apparently it is presumed as a matter of course that atoms cannot penetrate each other. Matter is granted the property that, wherever it is located, no other matter can get there without displacing it from its location. Matter, the solid, thus differs from the space in which it is located, the void
Wherein lies the persuasiveness of such assumptions about the structure of the microscopically small? Doubtlessly in the fact that the structures attributed to the microscopically small appear to have such obvious validity in the macroscopic world. Thus Lucretius
But now to resume my task begun of weaving the web of the discourse: the nature of the universe, therefore, as it is in itself, is made up of two things; for there are bodies, and there is void
Atoms thus were assigned properties resembling those of the objects in the macroscopic space that surrounds us. But there is a decisive difference between the world of macroscopic things and the world of atoms. In contrast to the properties of macroscopic things, properties in the world of atoms are absolute properties. The thought experiment’s step of declaring atoms to be absolutely indivisible entails further absolutizations. The matter of the ancient atomists is absolutely impenetrable
Ancient atomism experienced a renaissance in the corpuscular theories of the sixteenth and seventeenth centuries. It was attractive to the representatives of modern science not only as an alternative to Aristotelianism
A typical example of recourse to the ancient theoretical tradition is presented by the corpuscular theory of Robert Boyle, with which he attempted to explain chemical reactions in particular.9 As for the atomists of antiquity, for Boyle, too, the macroscopic properties of matter were secondary qualities, that is, ways of perceiving the primary qualities of size, shape and motion of the microscopically small particles of which matter actually consists. The program he pursued aimed to trace the secondary qualities back to two principles:10
I should likewise, after all this, explain to you how, although matter, motion and rest, seemed to me to be the catholick principles of the universe, I thought the principles of particular bodies might be commodiously enough reduced to two, namely matter, and (what comprehends the two other, and their effects) the result, or aggregate, or complex of those accidents, which are the motion or rest, (for in some bodies both are not to be found) the bigness, figure, texture, and the thence resulting qualities of the small parts, which are necessary to intitle the body whereto they belong to this or that peculiar denomination; and discriminating it from others to appropriate it to a determinate kind of things, (as yellowness, fixtness, such a degree of weight, and of ductility, do make the portion of matter wherein they concur, to be reckoned among perfect metals, and obtain the name of gold) this aggregate or result of accidents you may if you please, call either structure, or texture (though indeed, that do not so properly comprehend the motion of the constituent parts especially in case some of them be fluid) or what other appellation shall appear most expressive.
Yet there are two essential differences between Boyle’s corpuscular theory and ancient atomism. For one, Boyle was convinced that he did not only have to postulate the microscopic corpuscles hypothetically, he believed that they could actually be proven using empirical methods. Second, Boyle believed that the movements of the corpuscles were subject to the laws of mechanics
For this immanent explanation of the world based on mechanical laws, Boyle selected a metaphor common in his day: The world functions like a mechanical clock composed of innumerable small parts, which, once set in motion by its creator, continues moving in accordance with strict laws without any further intervention.
Modern corpuscular theories like that of Boyle were thus, like ancient atomism, associated with constitutive assumptions about the relation between space and matter. Such assumptions drew their persuasiveness from being based on conceptual models
In ancient atomism these conceptual models
The variety of such conceptual models
The ancient atomists absolutized elementary experiences that can be gained in the handling of corporeal objects and had thus arrived at the opposition of impenetrable matter and empty space
We do not call aught Void
Bruno, like the ancient atomists, transferred experiences from the world of macroscopic things to the world of the microscopic, but his assumptions about the relation between matter and space were oriented on the conceptual model
Clearly, the question as to whether there can be a vacuum
Galileo was already aware, however, that the horror vacui has only a limited magnitude. From the observation that water can only be pumped up to a certain height, which Galileo gave fairly accurately as 18 cubits,16
and from the correct theoretical explanation that at this height the horror vacui, i.e. air pressure, is surpassed by the weight of the water column, he drew the conclusion that the horror vacui represented only a limited force, which cannot absolutely prevent the occurrence of an empty space
The assumption that space is not empty, but rather completely filled with matter, represented a profound change in atomism, one which inevitably led to further modifications to its basic assumptions. For instance, ancient atomism had a plausible explanation for the fact that matter can change its volume,18
which could no longer be valid, since it was based on the assumption that material bodies contained empty spaces
Galileo solved the problem as to how “condensation and rarefaction […] can be understood to take place without assuming interpenetration of bodies and [at the same time] without introducing void
The examples outlined above may already be sufficient to show how the structural problem of modern science presented itself to its proponents. Common to these theories was that they were anti-Aristotelian and drew orientation from ancient atomism. The perceptible properties of objects and the changes in these properties were traced back to movements of a matter that obeys absolute mechanical laws on the microscopic level, and these laws were deduced from experiences with macroscopic objects. But owing to the alteration of the experiential basis in early modern times, this approach inevitably resulted in deviations from the traditional, canonical ideas of ancient atomism; and owing to the multiplicity of possible conceptual models
It seemed obvious to blame this unfortunate situation on the fact that the claim to a rational justification was not sufficiently fulfilled, and to aspire to a more methodologically controlled approach as a way out of the situation. This was the goal of rationalism, and in particular of its outstanding representative René Descartes
Descartes’ identification of space and matter had a number of drastic consequences for all of the problems connected with the relation between space and matter. Thus, for instance, the question as to the existence of empty spaces
Descartes meticulously justified his metaphysical
In a similar manner Descartes explained why the possibility of condensing or rarefying matter did not contradict his theory, which eliminated the possibility of empty
Here, too, we thus encounter a plausible conceptual model
The fact that Descartes borrowed from experience in this way did not escape his contemporaries’ attention, such that his rationalistic system had an ambivalent effect. On the one hand, after Descartes it was hardly possible for metaphysics
Newton’s unfinished and unpublished manuscript De Gravitatione …
Newton wanted his own assumptions, which he formulated in a series of definitions and propositions, to be understood as being “either definitions of certain words; or axioms and postulates denied by none.”31 Newton avoided atomistic formulations of his assumptions, although the fact that they at least partly originated in atomistic theories could hardly be denied.
For instance, Newton defined a body as “that which fills place
Further down he formulates:33
In addition to such assumptions, which correspond to those of ancient atomism, Newton formulated further definitions and propositions which clearly reflect the historical distance to ancient atomism. He defined force (vis) as “the causal principle of motion and rest,” tendency (conatus)
Newton’s definition of pressure, according to which pressure is only a tendency of two parts to penetrate each other, “[f]or if they could penetrate, the pressure would cease,”35
especially brings out the contrast with an absolutized concept of impenetrability. In contrast to ancient atomism, the experience of impenetrability, that is, the experience that two bodies cannot be moved to the same place
In his Principia Newton
That all bodies are impenetrable we gather not by reason but by our senses. We find those bodies that we handle to be impenetrable, and hence we conclude that impenetrability is a property of all bodies universally. That all bodies are movable and persevere in motion or in rest by means of certain forces (which we call forces of inertia
For the existence of an absolute space
Newton attempted to avoid basic assumptions of atomism (such as the assumption of the absolute impenetrability
So, for instance, in his Opticks
Tacit assumptions were associated also, and above all, with Newton’s concept of force. Through Newton’s Principia
The concept of the impenetrability of matter could not remain unaffected by such a substantial expansion of the concept of matter. In the atomistic tradition the changes in the motions of two colliding bodies were attributed to the impenetrability of matter. According to Newton’s axioms
There was certainly no shortage of attempts to reconcile Newton’s findings with Descartes’
When two bodies collide, according to Euler, their impenetrability causes the exertion of a force that changes their motions. Euler solved the problem Newton
Connecting Cartesian principles with Newtonian dynamics
Immanuel Kant’s concept of matter represents a break in so far that with it the distinction of matter from space through its impenetrability was for the first time principally challenged. For Kant this distinction was inacceptable:44
What did Kant have to set against this? From the difficulty of reconciling the assumption of the impenetrability of matter with the implications of Newtonian dynamics
We are acquainted with substance in space only through forces that are active in space: either in propelling other substances toward the substance (attraction), or in preventing them from penetrating into the substance (repulsion and impenetrability); we are not acquainted with other properties making up the concept of the substance that appears in space and that we call matter.
According to this theory, solid bodies are constituted by the coaction of the attractive and repulsive forces. The boundary between two bodies is that surface on which the repulsive forces of the respective matters balance each other.50
In the case of a single body in empty space
Through Kant’s redefinition of the concept of matter, not only impenetrability as the characteristic property of matter was traced back to the concept of force, but so was the concept of matter itself. Matter in its conventional form was declared to be a metaphysical
If we allow ourselves an anachronistic comparison, Kant’s concept of matter resembles the later concept of the field
Yet Kant’s goal was not to erect a new theory of physics. Rather, with his Critique of Pure Reason
Kant criticized the metaphysical
In fact, Kant’s
In contrast, the program of a metaphysical
Aristotle (1992). On sophistical refutations. On coming-to-be and passing-away. On the Cosmos. Aristotle in twenty-three volumes. Loeb classical library. Cambridge, MA: Harvard University Press.
Boyle, Robert (1666). The Origine of Formes and Qualities: According to the corpuscular philosophy. Oxford: Davis.
– (1937). The Sceptical Chymist. Ed. by Ernest Rhys. Reprint. London: Dent.
Descartes, René (1998). The philosophical writings of Descartes, Vol. 1. Ed. by John Cottingham, Robert Stoothoff, and Dugald Murdoch. Cambridge: Cambridge University Press.
Diels, Hermann (1951-1952). Die Fragmente der Vorsokratiker. 6th edition. revised by W. Kranz. Berlin: Weidmann.
Einstein, Albert (1992). Autobiographical Notes: A centennial edition. Ed. by Paul Arthur Schilpp. La Salle: Open Court.
Euler, Leonhard (1765). Theoria motus corporum solidorum seu rigidorum: Ex primus nostrae cognitionis principiis stabilita et ad omnes motus, qui in huis modi corpora cadere possunt, accommodata. Rostock: Röse.
– (1823). Letters of Euler on Different Subjects in Natural Philosophy: Addressed to a German Princess, 2 vols. Ed. by David Brewster. Edinburgh: Tait.
– (1848). Leonhard Euler's ‘Mechanik oder analytische Darstellung der Wissenschaft von der Bewegung’: Vol. 1. Ed. by Jakob Philipp Wolfers. Greifswald: Koch.
– (1853). Leonhard Euler's ‘Mechanik oder analytische Darstellung der Wissenschaft von der Bewegung’: Vol. 3. Ed. by Jakob Philipp Wolfers. Greifswald: Koch.
– (1912). Leonhardi Euleri Opera omnia: Vol. 2.1. Leipzig: Teubner.
– (1948). Leonhardi Euleri Opera omnia: Vol. 2.3. Leipzig: Teubner.
Galilei, Galileo (1974). Two New Sciences: Including centers of gravity & force of percussion. Ed. by Stillman Drake. Madison: University of Wisconsin.
Jürß, Fritz, Reimar Müller, and Ernst Günther Schmidt, eds. (1988). Griechische Atomisten: Texte und Kommentare zum materialistischen Denken der Antike. Leipzig: Reclam.
Kant, Immanuel (1907). Immanuel Kants kleinere Schriften zur Naturphilosophie. Ed. by Otto Buek. Leipzig: Dürr.
– (1996). Critique of Pure Reason: Unified edition; with all variants from the 1781 and 1787 editions. Indianapolis: Hackett.
– (2004). Metaphysical Foundations of Natural Science. Cambridge: Cambridge University Press.
Lasswitz, Kurd (1984). Geschichte der Atomistik vom Mittelalter bis Newton, Bd. 1: Die Erneuerung der Korpuskulartheorie. 2nd print of the Hamburg und Leipzig 1890 edition. Hildesheim: Olms.
Lucretius Carus, Titus (1992). De rerum natura. Ed. by William Henry Denham Rouse and Martin Ferguson Smith. Loeb Classical Library 181. Cambridge, MA: Harvard University Press.
Newton, Isaac (1978). Unpublished Scientific Papers of Isaac Newton: A selection from the Portsmouth Collection in the University Library, Cambridge. Ed. by Alfred Rupert Hall and Marie Boas Hall. Cambridge: Cambridge University Press.
– (1979). Opticks or a Treatise of the Reflections, Refractions, Inflections & Colours of Light. Based on the 4th edition London, 1730. New York: Dover.
– (1999). The 'Principia': Mathematical Principles of Natural Philosophy. Berkeley: University of California Press.
Simplicius (2004). On Aristotle On the Heavens 1.5–9. Ed. by R.J. Hankinson. London: Duckworth.
Singer, Dorothea Waley (1968). Giordano Bruno: His Life and Thought. With Annotated Translation of His Work: On the Infinite Universe and Worlds. New York: Greenwood Press.
This chapter is based on a lecture given by Peter Damerow in 1994 at the University of Constance. The supervision of the translation from German into English and the inclusion of additional notes left by Peter Damerow were done by MS. The central concept of the chapter, conceptual models (Modellvorstellungen), is closely related to the mental models introduced in Chapter 1. In particular, the concept is used here to illuminate how metaphysical ideas result from the absolutization of experiences. – [MS]
This reflection was actually not all that different in principle from speculative ancient philosophy.
Thus, Lucretius writes: “[…] you must yield and confess that there are things which no longer consist of any parts and are of the smallest possible nature. And since these exist, you must also confess that the first-beginnings are solid and everlasting” (De rerum natura I, 624–627; translation taken from Lucretius Carus 1992, 51–53).
Aetios 1,15,11, see Diels 1951-1952, Vo. 2, 112; for a German translation, see Jürß, Fritz, Reimar Müller, and Ernst Günther Schmidt 1988, 175 (Fragment 209).
Thus, Aristotle writes: “Democritus […] and Leucippus postulate the ‘figures’ and make ‘alteration’ and coming-to-be result from these, attributing coming-to-be and passing-away to their dissociation and association, and ‘alteration’ to their arrangement and position; […].” Aristotle On Coming-to-be and Passing-Away 315b, 7–9, translation taken from Aristotle 1992, 173.
Simplicius On Aristotle On the Heavens, 242, 17–27; translation taken from Simplicius 2004, 64.
Lucretius De rerum natura, I, 418–428; translation taken from Lucretius Carus 1992, 35–37.
Cf. Boyle 1666.
Boyle 1937, 201.
‘Absolutization’ is here to be understood as elevating cognitive structures such as properties attributed to everyday objects (e.g. the hardness of a billiard ball) to fundamental principles (e.g. the indestructibility of atoms). – [MS]
Owing to the simplicity of its basic assumptions about the relationship between absolutely impenetrable matter and space as an absolute void, ancient atomism constituted little more than a general background for the modern corpuscular theories. After all, these multifarious theories were based on complex, often mutually incompatible assumptions about processes on the microscopically small level.
Cited after Lasswitz 1984, 378.
Singer 1968, 273.
Once it has been introduced, the ether takes on further explanatory functions, which are not rooted in the metaphysical system and cannot be substantiated directly with the original conceptual model. For Bruno this is, above all, the relation between spirit and matter, which is identified with the differentiation between ether and all other matter.
Galilei 1974, 24–25.
Galilei 1974, 27.
Galileo offers as an extreme example “the boundless rarefaction of a small amount of gunpowder, when it is resolved into a vast bulk of fire” (Galilei 1974, 64).
Galilei 1974, 64.
Galilei 1974, 33.
He writes: “In this way there would be no contradiction in expanding, for instance, a little globe of gold into a very great space without introducing quantifiable void spaces – provided, however, that gold is assumed to be composed of infinitely many indivisibles” (Galilei 1974, 33–34).
Descartes Principles of Philosophy, II, 4; Descartes 1998, 224.
“The impossibility of a vacuum, in the philosophical sense of that in which there is no substance whatsoever, is clear from the fact that there is no difference between the extension of a space, or internal place, and the extension of a body” (Descartes Principles of Philosophy, II, 16; Descartes 1998, 229–230).
“We also know that it is impossible that there should exist atoms, that is, pieces of matter that are by their very nature indivisible […]. For if there were any atoms, then no matter how small we imagined them to be, they would necessarily have to be extended; and hence we could in our thought divide each of them into two or more smaller parts, and hence recognize their divisibility. For anything we can divide in our thought must, for that very reason, be known to be divisible; so if we were to judge it to be indivisible, our judgement would conflict with our knowledge” (Descartes Principles of Philosophy, II, 20; Descartes 1998, 231).
“All the variety in matter, all the diversity of its forms, depends on motion” (Descartes Principles of Philosophy, II, 23; Descartes 1998, 232).
Descartes Principles of Philosophy, II, 25; Descartes 1998, 233.
Descartes The World, Chapter 4; Descartes 1998, 86–87. Cf. Descartes Principles of Philosophy, II, 17; Descartes 1998, 230.
Descartes The World, Chapter 4; Descartes 1998, 87.
Descartes Principles of Philosophy, II, 6 and 7; Descartes 1998, 225–226.
Newton 1978, 123.
Newton 1978, 122.
Newton 1978, 122.
Newton 1978, 123.
Newton 1978, 148. In Newton 1978, conatus is translated as ‘endeavour’, not as ‘tendency’.
Newton 1978, 148.
Newton Principia, Book III, “Rules for the study of natural philosophy,” Rule 3; translation taken from Newton 1999, 795–796.
Thus, in his Opticks Newton writes: “[…] to make way for the regular and lasting Motions of the Planets and the Comets, it’s necessary to empty the Heavens of all Matter, except perhaps some very thin Vapours, Steams, or Effluvia, arising from the Atmospheres of the Earth, Planets, and Comets, and from such an exceedingly rare Æthereal Medium as we described above” (Newton 1979, 368).
Thus, Newton writes: “But if the quantity of matter in a given space could be diminished by any rarefaction, why should it not be capable of being diminished indefinitely?” (Newton Principia, Book III, Proposition 6, Corollary 3; Newton 1999, 810)
Newton 1979, 389.
Euler Letters to a German Princess, Letter no. 121 (21 April 1761); Euler 1823, Vol. 2, 17, in this edition it is letter no. 6 of Vol. 2.
Euler Letters to a German Princess, Letter no. 77 (18 November 1760); Euler 1823, Vol. 1, 233.
Euler Letters to a German Princess, Letter no. 78 (22 November 1760); Euler 1823, Vol. 1, 233–236; see also: Euler Theoria motus corporum solidorum sev rigidorum, §134; Euler 1765, 50, Euler 1948, 65; for a German translation, see Euler 1853, 59.
Euler Mechanica, Praefatio; Euler 1912, 10, for a German translation, see Euler 1848, 5.
Kant Metaphysical Foundations of Natural Science, Chapter 2, Explication 4, Remark 2; Kant 2004, 39.
“The mechanical mode of explanation […] has, under the name of atomism or the corpuscular philosophy, always retained its authority and influence on the principles of natural science, with few changes from Democritus of old, up to Descartes, and even to our time. What is essential therein is the presupposition of the absolute impenetrability of the primitive matter, the absolute homogeneity of this material, leaving only differences in the shape, and the absolute insurmountability of the cohesion of matter in these fundamental particles themselves” (Kant Metaphysical Foundations of Natural Science, Chapter 2, “General Note to Dynamics”; Kant 2004, 72).
Kant Critique of Pure Reason, A265, B321; translation taken from Kant 1996, 327. The impenetrability of matter is traced back to the interaction of forces not only in Kant’s writings during his critical period (after 1781), but also in a relatively early tract, the Monadologia physica of 1756, yet with a decisive difference: Here matter exists as an entity independent of forces. It consists of the smallest, indivisible components, which Kant called monads in keeping with Leibniz’s terminology, and which, as for Leibniz, are granted the capability to exert forces. Each monad is surrounded by a sphaera activitatis, a sphere of activity through which it keeps other monads away (Satz VI; Kant 1907, 351), and the repulsive force with which this occurs is perceived empirically as impenetrability (Satz VIII; Kant 1907, 353). Here Kant apparently tried to establish a connection with Newton’s theory by physically reinterpreting Leibniz’s monads.
“Matter is divisible to infinity, and, in fact, into parts such that each is matter in turn” (Kant Metaphysical Foundations of Natural Science, Chapter 2, proposition 4; Kant 2004, 40).
Kant Metaphysical Foundations of Natural Science, Chapter 2, proposition 2; Note 1; Kant 2004, 36–37.
“Matter can be compressed to infinity, but can never be penetrated by a matter, no matter how great the compressing force of the latter may be” (Kant Metaphysical Foundations of Natural Science, Chapter 2, proposition 3; Kant 2004, 37). Kant writes in summary: “The action of the universal attraction immediately exerted by each matter on all matters, and at all distances, is called gravitation; the tendency to move in the direction of greater gravitation is weight. The action of the general repulsive force of the parts of every given matter is called its original elasticity. Hence this property and weight constitute the sole universal characteristics of matter, which are comprehensible a priori, the former internally, and the latter in external relations. For the possibility of matter itself rests on these two properties” (Kant Metaphysical Foundations of Natural Science, Chapter 2, proposition 8, Note 2; Kant 2004, 56–57).
“Physical contact is the interaction of repulsive forces at the common boundary of two matters” (Kant Metaphysical Foundations of Natural Science, Chapter 2, Explication 6, Remark; Kant 2004, 50).
“Thus the original attraction of matter would act in inverse ratio to the squares of the distance at all distances, the original repulsion in inverse ratio to the cubes of the infinitely small distances, and, through such an action and reaction of the two fundamental forces, matter filling its space to a determinate degree would be possible. For since repulsion increases with the approach of the parts to a greater extent than attraction, the limit of approach, beyond which no greater is possible by the given attraction, is thereby determined, and so is that degree of compression which constitutes the measure of the intensive filling of space” (Kant Metaphysical Foundations of Natural Science, Chapter 2, Proposition 8, Remark 1; Kant 2004, 59).
Einstein 1992, 71 ff.; see also Einstein’s letter to Felix Pirani, 2 February 1954 (Einstein Archives 17-447.00).
Kant Metaphysical Foundations of Natural Science, Chapter 3, Proposition 4, Remark 1; Kant 2004, 88.
Table of Contents
1 Towards a Historical Epistemology of Space: An Introduction
2 Spatial Concepts in Non-Literate Societies: Language and Practice in Eipo and Dene Chipewyan
Martin Thiering, Wulf Schiefenhövel
4 Theoretical Reflections on Elementary Actions and Instrumental Practices: The Example of the Mohist Canon
William G. Boltz, Matthias Schemmel
5 Cosmology and Epistemology: A Comparison between Aristotle’s and Ptolemy’s Approaches to Geocentrism
Pietro Daniel Omodeo, Irina Tupikova
6 Space and Matter in Early Modern Science: The Impenetrability of Matter
7 Experience and Representation in Modern Physics: The Reshaping of Space
Alexander Blum, Jürgen Renn, Matthias Schemmel
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