How old is surface science?

Journal of Electron Spectroscopy and Related Phenomena 134 (2004) 9–24

How old is surface science? E. Paparazzo∗ Istituto di Struttura della Materia del CNR, Area della Ricerca di Roma-Tor Vergata, Via Fosso del Cavaliere 100, 00133 Rome, Italy Received 3 April 2003; received in revised form 14 July 2003; accepted 9 September 2003

Abstract Philosophical and literary testimonies from the Classical World (5th century b.c. to 3rd century a.d.) involving solid surfaces are reviewed. Plato thought the surface to be a real entity, whereas Aristotle considered it to possess an unqualified existence, i.e. not to be a substance, but just an accidental entity. The Old Stoics asserted that surfaces do not possess any physical existence, although the Stoic philosopher Posidonius—apparently the only exception in his school—held them to exist both in thought and reality. While both the Atomists and the Epicureans were very little interested in them, the Sceptic philosopher Sextus Empiricus considered surfaces to be the limits of a body, although he maintained that both the view that they are corporeal or the view that they are incorporeal present unsurmountable difficulties. Among Roman authors, the testimony from Pliny the Elder is mostly concerned with metallic surfaces, chemical change occurring there, and surface treatments used in antiquity. Besides the philosophical motivations, the implications of the testimonies are discussed in the light of surface science. The purely geometrical surface of Plato is found to compare favorably to single-crystal surface, Posidonius’ “corporeal” surface is best likened to an air-oxidized, or otherwise ambient-modified surface, and ancient accounts on mixture are compared to XPS results obtained in adhesion studies of enameled steels. I argue that the long-standing dominance of Aristotle’s view from antiquity onwards may have had a part in delaying theoretical speculation into solid surfaces. © 2003 Elsevier B.V. All rights reserved. Keywords: Surface science; XPS spectroscopy; Auger electron spectroscopy; Ancient philosophy; History of science

1. Introduction The electron spectroscopies have played and continue to play a major role in the characterization of solid surfaces. It is thus interesting from the perspective of contemporary scientists using them to study surfaces to look back into the Classical World and consider the notions that the ancients had concerning the nature, properties, and modifications of solid surfaces. ∗

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To begin with more recent history, it is well established that, by the middle of the 19th century, the first successful efforts to exploit surface-specific properties for practical purposes were taking place [1]. These applications grew in number as the Industrial Era matured, but it was not until the mid-1960s that surface science could really evolve into a mature, independent discipline. This development of course benefited from the ability to create ultrahigh vacua, a prerequisite for controlling cleanliness and composition. But as crucial was the simultaneous development of powerful, surface sensitive experimental techniques that

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permitted the quantitative characterizing of surfaces. These include X-ray photoelectron spectroscopy (XPS or ESCA) and Auger electron spectroscopy (AES) that permitted thoroughly analyzing the chemistry of the outermost regions of solids [2–6]. In fact, the early, pioneering developments of the two methods [2,6] mostly involved exploiting the photoelectric effect and the Auger effect as a means of studying the electronic configuration and chemical composition of matter. In order to highlight unique features in spectra (such as, e.g., chemical shifts [7], multiplet splittings [8] and other satellite structure [9]) with the best possible energy resolution, various steps were taken in the design of improved experimental systems. Among others, these included choosing suitable sources (e.g. in XPS and reflection EELS) which would not involve too high-energy, broad “primary” transitions, and designing high-resolution electron analyzers, so as to convolute minimum broadening with the natural energy band-width inherent in the electron transitions of interest [10]. A major consequence of such optimizing compromises is that the electrons analyzed by these techniques typically possess kinetic energies ∼20–1000 eV, and the attendant probing depths, i.e. surface-sensitivities span the range ∼0.5–2 nm [11]. In other words, the extremely high surface-specificity of XPS, AES and other electron spectroscopies was at first in itself incidental—if not accidental, and indeed, none of those techniques bears the word “surface” in its definition. Afterwards, as soon as the enormous and unique potentials of this feature were fully realized, it became one of the main reasons—if not the reason—for the spectacular development and diffusion of electron spectroscopy techniques in the realm of physics, chemistry, materials science, etc. [3,5,12–14]. Turning now to a broader philosophical perspective, one can find recent treatises on the unique attributes of surfaces, as far as their topology, logic and sensual perception are concerned [15,16]. However, from a more historical standpoint, although the ancient views on surfaces are documented at some length and in some detail in primary sources from the Greek and Roman periods, to the best of my knowledge, a general analysis of these sources is still lacking, and they have not been compared with, nor discussed in the light of, modern surface science. Thus, we ask here when surfaces begin to be thought of as distinct objects and

with what characteristics, and how these attitudes have influenced the later course of surface science? The present work shall provide evidence that interest in them dates from as early as the 5th century b.c., and its objective is to answer the following questions. (i) Firstly, if the ancients were interested in surfaces and were aware of their special nature. I shall focus particularly on those aspects that have some analogies with the topics of interest in surface science. Conversely, I shall not address the purely mathematical and geometrical conceptions and definitions of a surface. (ii) Secondly, if in antiquity there were practical examples of surface-related concerns and applications. In this respect, I shall only report those testimonies in which the surface of an object is considered to possess an individual, well-defined nature which differs distinctly from that of the bulk of the same object. (iii) Thirdly, if the relatively young age of surface science may have had some relation to the ancient views about surfaces. To accomplish this, I shall report on ancient Greek and Roman sources which date from the period 5 century b.c. to 1 century a.d. Although I make a claim to offer an exhaustive report of all the testimonies on surfaces available in antiquity, I shall focus the attention to those that I believe would be of some interest to the eye of the modern surface scientist. As the ancient views about surfaces were based on opinions rather than on experimental observations, it seems interesting to discuss their significance and implications in the light both of possible motivations inherent in the relevant philosophical systems, as well as of modern science. Indeed, both surface science practitioners and ancient thinkers seem to have been faced with the common problem of the inherently unique “subtleties” of surfaces. While the former have understood—if not fully solved—(most of) the experimental “subtleties”, major interest of this paper is devoted in analyzing the efforts of the latter in tackling the speculative “subtleties”. The paper is organized as follows. (a) Section 2 reports accounts from the ancient sources from Greece and Rome. (b) In Section 3 some implications of the testimonies are outlined, and analyzed in the light of modern science. This analysis is being presented not to champion the proven knowledge we today possess in thermodynamics and in chemistry against the

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“poor” scientific skills of the ancient thinkers, but rather it appears to be an appropriate means of better highlighting the ancient theories with the aid of notions the modern surface scientist is familiar with. (c) Finally, Appendix A is also provided in order to facilitate the comprehension of the classification used in Classical bibliography, which differs remarkably from the citation style of scientific literature.

2. The ancient testimonies 2.1. Plato (427–347 b.c.) Plato thought surfaces, along with other geometrical and mathematical entities, to be real substances [17], and his view on these topics was heavily influenced by Pythagoreans [18]. In the Timaeus, after the preliminary statement on the geometrical/physical nature of surfaces: “if the body of the universe were required to come to be as a surface, having no depth” [19], Plato says: “In the first place, every one will agree with the fact that fire, earth, water and air [in antiquity, these were thought of as the four main elements of matter] are bodies, and as such, all of them have depth. Whatever has depth, moreover, must include surface, and every surface that is rectilinear is composed of triangles . . . ” [20]. 2.2. Aristotle (384–322 b.c.) Aristotle repeatedly stated that surfaces are not substances and he objected to the Pythagorean position, adopted by Plato in his Timaeus [20], that bodies are composed of planes (and planes of lines) [21]. Aristotle reports a puzzle (or aporia) concerned with the question of whether surfaces (and points, numbers, and solids) are substances or not [22], and in particular he treats two distinct arguments. (i) The first deals with ‘existence’. Aristotle considers a cube (Fig. 1, I) and supposes that it is divided into two semi-cubes along a plane parallel to the base and at half-depth (II), with the production of two “new” surfaces (Fig. 1, III). On the other way round, when the two cubes are re-united, the origi-

Fig. 1. Representation of the geometrical figures and of their transformations referred to by Aristotle in the “aporia” of the metaphysics [22,23].

nal cube is obtained (Fig. 1, IV), and if one divides the latter in the same fashion, one again obtains the two semi-cubes and the relevant surfaces (Fig. 1, V and VI), and so on. Aristotle states that both the pair of semi-cubes and the surfaces of the cube do really exist. Indeed, if the semi-cubes did not, they would never be obtained from the cube (whereas they are indeed obtained from it, see Fig. 1, III and VI). Likewise, no statue of Hermes could be ever carved from a block of marble. Also, if the surface of the (original) cube did not exist, the same should also be said of the surfaces obtained from its sectioning, which in fact are obtained (see again III and VI). As a consequence, the surfaces (and the semi-cubes) possess a real existence [22]. (ii) The kind of existence possessed by the surfaces is then analyzed by Aristotle in the second argument. Specifically, he notes that the surfaces (and the semi-cubes) cannot be classed as “substances”.

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takes time some form (e.g. as in the development of a living being from the fertilized embryo to a mature individual); likewise, he assumes that passing-away involves persisting material which once had a certain form losing it (e.g. the bodily components of an animal losing their organization and functioning in the process of dying). When a surface begins to exist (e.g. through cutting a cube in two), there is no process and no underlying persisting matter which acquires a form—a surface does not have a matter–form composition. (Incidentally, as will also be discussed below in more detail in Section 3, this indicates that Aristotle is thinking about geometrical surfaces, not about the outermost layer of solid bodies.)

Fig. 2. “Democritus’ dilemma”, involving the cutting of a cone, addressed by the Old Stoics: (I) The two segments (A and C) and the intervening layer (B); (II) The two segments left after the cut with the intervening layer removed. The thickness of layer B in (I) is intentionally represented as a thick slab, so as to emphasize the “physical nature” of the cut, and the two segments in (II) are juxtaposed on one another to highlight the “steps and asperities” envisaged in a horn of the dilemma.

Indeed, such a title pertains only to those entities having an absolute existence of their own, and which possess the unmistakable characteristic of undergoing processes of “coming-to-be” and “passing-away” when they pass from non-existence to existence and vice versa, respectively. On the contrary, the fact that the two surfaces at some times exist (Fig. 1, III and VI) and at others do not (Fig. 2, II and IV), cannot be interpreted as involving processes of coming-to-be and passing-away, for two reasons: such changes are instantaneous, and there is nothing from which a surface comes into being [22]. In other words, as I understand it, Aristotle is assuming a model of coming-to-be which involves some persisting material acquiring through a process which

Aristotle then presents his “solution” of the aporia [23]: although they cannot be considered to be substances, surfaces (as well as mathematical and geometrical entities) do indeed exist, although they do so as an accidental attribute of a substance to which they belong, and from which they can be separated only in thought, but not physically [24]. In other words, Aristotle is concerned to deny that planes or surfaces could have a separate existence, prior to the formation of a body, and that a body could be put together out of them. 2.3. The Old Stoics (fourth to fifth century b.c.) (A) According to Apollodorus of Seleucia: “body (soma) has three dimensions: length, breadth and depth, and such a body is also called a solid” [25]. He then goes on to say: “Surface is the limit of body, or that which has length and breadth but not depth.” (It should be noted that both definitions of “surface” go back to the Pythagoreans and Plato, according to the testimony of Aristotle [18].) However, Apollodorus never defines a surface as a body, and thus implies that “surface” does not exist. Indeed, in Stoic doctrine everything that exists is a body (i.e. not only matter, substance, etc., but even to the extent of regarding God as a body) [26]. There are several other testimonies reporting that the Old Stoics regarded surfaces as not bodies, and therefore non-existent. For example, Chrysippus classifies surfaces among things like

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bodies [27], the Old Stoics generally stated that the limit (of a body, i.e. a surface) is not a body [28], and they also stated that a surface only subsists in mere thought [29]. (B) A further, quite representative testimony of the Old Stoics involving surfaces is given by Chrysippus’ response to Democritus’ dilemma, which addresses the question as to whether, in a cone cut by a plane parallel to its base (Fig. 2), the surfaces of the two resulting segments be equal or unequal [30,31]. Indeed, Democritus says, if unequal, the cone should possess asperities, steps, etc., and would be not evenly smooth all over; if equal, this condition should hold at any height at which the cone is cut, and the latter would, in fact, possess the properties of a cylinder. Chrysippus’ answer is: “the surfaces are neither equal nor unequal, but the bodies are unequal in that the surfaces are neither equal nor unequal” and “the asperities in the cone . . . are produced by the inequalities of the bodies, surely and not by that of the surfaces.” [31]. (C) Chrysippus held that some “mixtures occur by juxtaposition of two or more substances put together in the same place, and juxtaposed with one another by ‘joining’, as he says, while they each preserve their substance and quality at their surface contact in such a juxtaposition” [32,33]. By way of contrast, “blendings occur through-and-through, and not by surface contact and juxtaposition” [33,34]. 2.4. The Atomists, Epicurus and Lucretius (5th century b.c. to 1st century b.c.) Although they are spread over an interval of four centuries, these testimonies are gathered together because Epicurus’ doctrine bears a heavy influence from the early Greek Atomists (Leucippus and Democritus, 5th century b.c.), and that of Lucretius (95–ca. 50 b.c.) from Epicurus (341–270 b.c.), as far as the basic concepts of atoms, void, bodies and space are concerned, these latter two being the irreducible contents of the universe [35]. Atomism is the opposite of the position held by the Stoics and Aristotle that bodies are infinitely divisible. (Indeed the Greek word ‘atomos’ literally means ’‘indivisible’, and according to Diogenes Laertius Leucippus was the first “to set up

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atoms as first principles” [36]). It should be remembered that the atomist Democritus raised the puzzle about the surfaces of a cone which Chrysippus felt constrained to address [30,31], and which is dealt with in Section 2.3, item (B). In section 57 of his Letter to Herodotus [37], Epicurus appears to refer to a minimal extremity of a body, which can be distinguished in thought but not by observation. He thus appears to have a conception of a theoretical division to a minimal part of a body, though not of a physical thickness of the surface of a body [38]. Epicurus also postulated “a continuous flow from the surface (epipolˆes) of bodies—not revealed by diminution in their size, thanks to reciprocal replenishment” [39]. The same conception is also reported by Lucretius [40]. The latter poet also reports on the top-most part (extremum cacumen) of atoms, but this region is not its surface but an “extreme point”, which he conceives as having some size but as being indivisible even in thought [41]. 2.5. Scepticism (4th century b.c. to 3rd century a.d.) through Sextus Empiricus (ca. 160–210 a.d.) Sextus’ position is one directed at the notion that surfaces are the limits of bodies; on this assumption, his analysis examines the question of whether the surface either is a body or is incorporeal, two alternatives which both present difficulties. As a consequence, such an analysis leads necessarily to the “suspension” of judgment (epoche), the main tenet of this School which originated with Pyrrho (ca. 360–275 b.c.). (A) After having argued against the Epicurean position that the corporeal atoms are the principles of all things, Sextus discusses the alternative position that the principles of the bodies which can be contemplated by reason, such as, solid figures, surfaces, lines, points and numbers, must be incorporeal [42]. Indeed: “The solid forms also, which are of an incorporeal nature are conceived before bodies; but they, again, are not principles of all things, for the plane forms (i.e. surfaces) precede them in conception, since out of these the solid forms are composed. “Likewise surfaces are preceded by lines.” And since the simple line is not conceived apart from number, but as drawn from a point to a point, involves

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the number two, etc.” In the end, after having analyzed at length and in deep detail the nature and attributes of number, he concludes: “So then, number is nothing.” Thus, the apparent assertion that the principles which can be contemplated by reason (in particular surfaces) must be incorporeal, is just an intermediate step on the way to ultimate puzzlement which is to result in the suspension of judgment. (B) Concerning two bodies in contact with each other, Sextus [43] considers the question of whether “the limits are bodies or incorporeals. But if they are bodies, the Geometers will find that it is false that the surface is without depth . . . for every body must have depth. Then, too, it will not touch anything but will be infinite in magnitude. For if it is body, since body has a limit, that limit too, being a body, will have a limit, and likewise this last one, and so on ad infinitum.” In other words, there would be in this hypothesis an infinite regress of such limits. (A related arguments of the inconsistencies of surface being a body is also given by Sextus elsewhere [44]; if the surface is a body “it is false that the surface is without depth; for every body partakes of depth.”) Conversely, if one should assume that the limits are incorporeal, one would also face as hard problems. Indeed, “ since the incorporeal cannot touch or be touched by anything, the limits will not touch each other, and as they do not touch neither will the things limited (i.e. bodies) touch each other.” Sextus concludes that “the account given of the surface is dubious”; and “doubt is cast on the solid body, seeing it is composed of these” (i.e. surfaces and lines) [43]. (C) An argument similar to those in (B) is also discussed by Sextus in another passage [45], where, considering the case of two bodies touching each other, he discusses the difficulties deriving from the assumption that surfaces have a real existence in bodies. “The surfaces, then, will not be completely unified one with another as a result of touching, since otherwise touch (aphˆe) would be fusion (synchysis) and the separation of things touching a rending apart; and this is not what we find. And if the surface touches the surfaces to the juxtaposed body with some of its parts, and with other parts is united with the body of which it is a

limit, it will not be without depth, since its parts are conceived as different in respect of depth, one part touching the juxtaposed body, the other being that which effects its union with the body whereof it is a limit. Hence, even in connexion with body one cannot imagine length and breadth without depth, nor, consequently, surface.” 2.6. Posidonius (ca. 135–50 b.c.) (A) Although Posidonius accepted the Stoic standard definition of “surface” (in particular the definition reported in Section 2.3, item (A) [25]: “Surface is the limit of body, or that which has length and breadth, but not depth” due to Apollodorus, who is not much earlier than Posidonius), he held among Stoic philosophers a distinctive view about surfaces, which is original with him, as attested by Diogenes Laertius: “This (i.e. surface) was admitted by Posidonius in Meteorological Phenomena, Bk v, to exist both in thought and reality” [46]. Here, the phrase “in reality” (kath’upostasin) is contrasted with “in thought” (kat’epinoian), and it gives the surface the definition of “physical existence” [47]. (B) Plutarch reports that, in interpreting the origin of the soul in Plato’s Timaeus, “Posidonius and his followers” accepted that “the existence (being) of the limits (i.e. surfaces) was the meaning of divisible in the case of bodies” [48]. 2.7. Pliny the Elder (ca. 23–79 a.d.) Apart from Cato (234–149 b.c.) who extols the beneficial effects of amurca (a pasty by-product from the making of olive oil) even as far as metals are concerned [49], Pliny the Elder seems to me the only Roman author worth a mention in relation to the topic dealt with in this paper. (A) In his treatment of copper and copper alloys he says: “When scraped (extersa), bronze (copper) objects draw to themselves a patina faster (celerius) than untouched ones, unless they are spread with oil” [50]. This passage is closely related to a detailed account Pliny gives of corrosion products, resembling millet seeds and of a hairy appearance, unmistakably sitting on the

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outermost regions of copper (summa lanugine), and also mentions a blast of air (flatu) and heat (fornaces) as expedient for the production of copper corrosion [51]. (B) Subsequent passages, describing lead soldering with tin and oil, read: “Neither can lead be joined to itself without tin nor the latter to the former without oil” [52]; and, regarding the (2:1) lead-tin tertiarium alloy: “lead pipes (fistulae) are soldered with this material” [53]. Although the surface is never explicitly mentioned, wherever else—if not through the surfaces—can two parts of lead be fastened to each other thanks to tin and oil, as at, e.g., the joint of a fistula?

3. Discussion and conclusion The first consideration prompted by these testimonies is that as early as the 5th century b.c. the ancient thinkers considered surfaces a topic worth considerable speculation, to an extent which exceeds what one might have suspected. Although a detailed discussion on the philosophical systems addressed here is beyond the aims of the present paper, it seems worthwhile to better clarify the motivations and implications of these testimonies, also in consideration of the fact that some of them occur in such peculiar contexts as, e.g., cosmogony (Plato) and psychogony (Posidonius). The philosophical debate about surfaces seems to essentially involve the geometrical/physical/ontological definitions of ‘body’ and ‘surface’, as well as the distinction between the two. Plato’s interest in surfaces seems to arise mostly from a geometrical standpoint [54]. Indeed, he emphasized their shape and spatial arrangements, rather than the manifestations of the their corporeality and the attendant implications [55]. Conversely, although he admitted their physical existence [22,23], Aristotle thought surfaces not to be “individual substances” [56–58] but only an accidental attribute (having an unqualified existence) of a substance that they enclose [59]. Since Aristotle was always very careful to distinguish geometrical entities from physical objects, the analogy he makes between the statue of Hermes and the semi-cubes (and their surfaces) [22] only means that in both cases the entity spoken about exists potentially, in the sense that it will come into actual ex-

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istence if a certain cut or series of cuts is made. Thus, the main issue of the question seems to involve both a geometrical and ontological distinction between a given object and its surface [24]. It should be remembered that we do not know in what context (i.e. whether in physics or geometry) Democritus proposed the dilemma about the cone [30], and if he himself tried to resolve it. According to Cherniss’ interpretation [31], the two surfaces of the sectioned cone are for Chrysippus a “single geometrical plane”, and his reply to the puzzle relies upon the nature of the cut of the cone which, in Democritus’ formulation is “physical” and not “geometrical” (Fig. 2), so that the asperities and steps envisaged in the first horn of the dilemma are produced by the inequality of the two segments remaining after the removal of an intervening layer, however thin (Fig. 2, I, slab B). However, as noted by Long and Sedley [60], this interpretation does not seem “entirely satisfying.” It should also be noted that neither the “single geometrical plane” nor the “intervening layer” mentioned by Cherniss are explicitly referred to either in Democritus’ formulation or in Chrysippus’ answer. Although a full comprehension of this ancient puzzle has not yet been achieved in the literature [61], surfaces are undoubtedly the main topic on which both formulation and answer are focused. As a consequence, since the Stoics thought the surfaces not to be bodies [27–29], these cannot act on the two segments (which are bodies) obtained from the cut of the cone, nor determine their inequalities and their asperities [62,63]. By way of contrast, Posidonius holds that surface is a physical entity [46], and he also asserts that the “limits” possess existence (ousia) [48]—and thus materiality, since—according to the same philosopher—ousia “that exists in reality differs from matter only in thought” [64]. On the whole, it seems that the Atomist have very little to say about surfaces, either in the geometrical or in the physical sense, except for the claim of Epicurus who thinks of the surface as an “emitter” of simulacra [39]. However, there is no surviving testimony on the Atomists in which surfaces of macroscopic objects are discussed, nor are surfaces ever thought of as being composed of ‘special’ (i.e. different from those of the bulk) combinations of atoms which cause the “chemical” varieties of matter [65]. Sextus has no beliefs about surfaces [42–45]. Using the typical Pyrrhonian strategy, he discusses equally

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powerful arguments on opposite sides of the nature and attributes of surfaces in the form of a destructive dilemma, so as to induce suspension of judgment. In particular, the arguments are often dialectical or ad hominem, in the sense that their premisses are those which proponents of the position under attack (for instance, whether surfaces are corporeal or incorporeal) are assumed to accept, rather than propositions to which Sextus is committing himself. Sextus is probably the ancient philosopher who best highlighted the ‘subtleties’ of surfaces. The literary testimonies from Cato [49] and Pliny [50–53] mainly betray a practical concern with the manufacture, restoration and preservation of surfaces, although, as shown in the following, the Pliny passages perhaps bear some influence from Posidonius. Beside the “philosophical” motivations, it seems worthwhile to try to uncover the science-related bearings of some of the views considered here. In his discussion on the cut and re-union of the cube, Aristotle considered the surface only in the geometrical sense, i.e. that which has length and breadth but not depth. From the present perspectives, a fresh solid surface has a positive area free energy, and this is the thermodynamic driving force for changes of its shape and chemical composition [66]. Thus, the two surfaces produced by a physical cut of the

cube [22] would dismiss the excess free energy by spatial re-arrangements (e.g. strain relaxation of the outermost atoms) and by chemical re-arrangements (e.g. via recombination of non-compensated chemical bonds between surface atoms, and via interaction of these same atoms with ambient agents, e.g. physisorption, chemisorption, oxidation, etc.) On account of these re-arrangements, juxtaposing the two surfaces to one another (as in Fig. 1, sequence III and IV) could obviously never again (or reversibly) produce the same exact interface—or, in Aristotle’s terminology, the two surfaces could never cease to exist actually, and thus make the cube recover its original state. Similarly, neither Chrysippus nor Democritus pay any attention to possible physico-chemical changes occurring at the segment surfaces produced by the cut of the cone [30,31], see, Fig. 2. The equality/inequality issue of the two surfaces of the cone is illustrated in Fig. 3 through a schematic representation of the right triangle generating a cone with a base angle 0◦ < α < 90◦ , and radius r. Also considered are the intermediate radii ri , at heights hi , and the circles of area Si generated by such radii. The difference of the two radii, r = r2 –r1 can be expressed as: r = h cot α

(1)

Fig. 3. Schematic representation of the source triangle of a cone of base radius r and base angle α. Also represented are the radius difference as a function of height, and (linear scale 1:2) the relevant circles of areas S1 and S2 .

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Obviously, if and only if h1 = h2 , does r1 = r2 hold (i.e. the “two” surfaces of the two adjacent segments of the cone are equal), and this is the “non-cut” case both in the physical sense (no cleavage) and in the geometrical one. The same condition, i.e. the two surfaces Si are equal, does not involve the cylinder, because this solid also requires the condition α = 90◦ , which does not fulfill the premiss 0◦ < α < 90◦ . Also in the case h > 0, which gives r > 0, i.e. the two surfaces Si are unequal, no asperities are involved in the cone, as stated in the formulation of the puzzle, because r is a continuous function, as is the relevant circumference difference 2πr for the cone, of h for any value of hi , such that 0 < ∆hi < ∆he , however small he may be, Fig. 4. Although they admitted infinite divisibility of a body [27], the Old Stoics also held that such a process could not produce parts with dimensions “smaller” than those still relevant to bodies. A rough, indicative figure of an “acceptable” limit of physical division can perhaps be estimated from a famous fragment [67], in which Chrysippus states that “nothing prevents a single drop of wine from tempering the ocean . . . and even the whole universe”. Indeed, however small, the drop of wine has three dimensions (i.e. it conforms to the definition of body) [25], and can still be perceived by the senses (sight, touch and taste). The possession of these corporeal attributes is paradoxically highlighted by relating them to, and

by making them coextensive with [68], the largest bodies imaginable (the ocean and the universe itself). Conversely, Posidonius, who thought a surface to possess physical existence [46,47], held that bodies keep their material nature even if they should be divided into magnitudes as thin as limits (i.e. surfaces) [47,48]. On the other hand, Aristotle opposes both the thesis that bodies are composed of indivisible magnitudes [69], be they the atoms postulated by Leucippus and Democritus or the planes of Plato, as well as the thesis that bodies can be divided through and through until one gets to points [70]. While no ancient philosopher explicitly addressed the question of whether “small” bodies and surfaces were somehow mutually related, the dimensions of a physical object and its surface are not independent of each other. Indeed, the smaller the dimension of an object, the higher the contribution of the surface (A) relative to the contribution of the volume (V). We today express this as an increase of the aspect ratio, A/V, and an example is given in Fig. 5 by way of the aspect ratio for a cube as a function of size. Also, surface science studies show that these “geometrical” changes have a heavy bearing on the surface chemistry of ‘physical bodies’, an example being given in Fig. 6 by way of iron-oxide percentages measured by XPS in Fe-alumina and Fe82 B18 -alumina small particle systems as a function of particle size [71]. Indeed, the smaller the dimension of a ‘body’ (as in a so-called small particle system) the higher the manifestation of surface reactivity (in this case, surface oxidation)

Fig. 4. Radius difference (r) as a function of height difference (see Fig. 3) for a cone of base angle α = 30◦ .

Fig. 5. Surface-to-volume ratio for a cube of side “l” as a function of size.

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Fig. 6. Oxidized iron percentages (=100×[Fe2+ ]/{{Fe◦ ]+[Fe2+ ]} measured by XPS at the surface of Fe-Al2 O3 and Fe82 B18 -Al2 O3 small particle systems as a function of particle size.

the extremities (eschata) of bodies—only in connection with the contact stage [73]. On the other hand, Sextus’ arguments in Section 2.5, items (B) and (C) are aimed to demonstrate that surfaces (be they assumed to be either corporal or incorporeal) introduce unsolvable problems into the case of contacting bodies. These ancient surface-related issues on ‘mixture’ have interesting analogies with modern studies of adhesion in enameled steels. Here, the main question is whether successful joining between such diverse materials as a metal (Fe) and porcelain (SiO2 -based) enamel is due to mechanical adhesion (i.e. a mere mutual anchoring of rough microstructures present at their surfaces) or to chemical adhesion (i.e. the two sides are held together by chemical bonds) [74]. XPS analysis [75–77] provided unambiguous evidence (Fig. 7) that high adhesion is achieved only when the interface consists of a fully reacted iron silicate phase produced by the reaction: 2FeO

featured by these materials on account of an enhanced A/V ratio. It seems interesting to discuss how the ancients conceived a ‘body’ would interact, if not with environment agents, with other bodies, i.e. the so-called ‘mixture’, and what role—if any—surfaces played in it. According to Chrysippus (see Section 2.3, item (C)), different substances (ousia) can mix with each other in three ways [32,33]: (i) juxtaposition (parathesei mixeis), i.e. mechanical mixing via surface contact (perigraphˆe); (ii) complete fusion (sunchysis di’olˆon), i.e. a chemical reaction which gives rise to a new compound, the nature and chemical properties (poiotˆeta) of which differ from those of the starting ingredients; and (iii) through-and-through blending (krasis di’olˆon), i.e. the complete dissolution into one another of two or more substances which, however, keep unchanged both their natures and chemical properties. While juxtaposition and blending are reversible, the original substances can never be obtained again after a fusion has occurred. What is more important, surface contact is involved in juxtaposition, ignored for fusion, and explicitly denied to occur in blending [32–34]. In his account on mixture of bodies (which involves: (i) their contact aphˆe, (ii) their mutual interaction poiein/paschein, and (iii) their mixture proper) Aristotle [72] mentions the surfaces of bodies—specifically

(steel surface)

+

SiO2 (enamel surface)

→ Fe2 SiO4 (interface)

(2)

The iron silicate, characterized by a one-component O 1s spectrum peaked at BE ∼ 533.5 eV (Fig. 7, upper panel), bears witness to a “chemical continuity” at the interface, through the sequence of chemical bonds –Fe–O–Si–, which result in both atomic and electronic structure continuity [78]. On the contrary, low adhesion lacks chemical continuity at the interface, since the latter involves only a mixture of unreacted FeO and SiO2 , i.e. the sequence –Fe–O//O–Si– with two “inequivalent” oxygen ions. Indeed, the relevant O 1s spectrum contains two components separated by the ∼3.5 eV, i.e. the chemical shift which is documented to distinguish between iron oxide and silica [75]. On the grounds of these surface science findings [75–77] it is clear that not only the interface (perigraphˆe) is ‘corporeal’, but it is also the place where steel and enamel (somata) adhere to each other firmly or weakly, depending on whether they partake of a complete chemical reaction (synchysis), or of a mere mechanical mixture (parathesei), respectively [79]. Thus, the surfaces of steel and enamel play the leading role in determining the kind of adhesion between the two materials. (And this is so much so, that the long-debated questions of the nature and mechanisms of adhesion in enameled steels [74] were successfully settled thanks to surface-specific XPS studies

E. Paparazzo / Journal of Electron Spectroscopy and Related Phenomena 134 (2004) 9–24

Fig. 7. XPS O 1s spectra of enameled seels. The spectra (not corrected for surface charging) were recorded at the interface generated from a tensile test applied to: upper panel) a sample with high adherence; lower panel) a sample with low adherence. The ‘one-component’ O 1s spectra in the upper panel are indicative of a single oxidized phase, i.e. iron silicate, whereas those in the lower panel result from the coexistence of FeO and silica, see text. Reproduced from Ref. [75] by permission of Elsevier Science B.V. (Line-drawing by Mauro Viola.)

[76,77].) In other words, the adhesion of enameled steels could never be explained within the theory of mixture contemplated by the Old Stoics [32–34], whereas it is consistent with the “heretical” view of the physical surfaces held by Posidonius [46–48]. How can we imagine the old views of surfaces would further compare to the topics experimentally verified by modern surface science? These are some possible examples: the geometrically-ordered surface theorized by Plato could be thought of as bearing some resemblance to a atomically-clean ideal surface (e.g. a single-crystal surface) [80]. Conversely, the char-

19

acteristics of Posidonius’ surface might suitably be thought of as a real world surface, e.g. a metal surface undergoing chemical changes (oxidation, hydration, etc.) as a result of exposure to external fluids [81]. By way of contrast, one expects that according to the Old Stoics oxidation of a solid would occur as a “bulk” or “through-and-through” oxidation with no surface-specific oxidation being involved [32–34]. The passages from Pliny [50–53] seem to involve a practical interest, however unsophisticated, in the physico-chemical properties of surfaces (including their interaction with the environment: air and heat) as something distinctly different from properties of the bulk. Indeed, Pliny makes a direct reference to surfaces (indicated by the term summa, i.e. the standard Latin term for ’surface’) [51]. This interest perhaps bears some influence from Posidonius [82], a philosopher of whom he held a high opinion [83,84]. Also, given that the scraping of bronze objects [50] removes external metallic layers (which are rich in corrosion-resistant SnO2 [85]), the treatment with oil (oleo perunguantur [50]) minimizes any subsequent ambient-induced chemical attack on the copper. The action of oil is all the more effective given that mechanical scraping is quite likely to increase surface roughness, namely a higher number of copper atoms per unit volume are exposed to ambient oxygen [86] and moisture, which therefore would attack them even faster (celerius [50]). Fig. 8 does indeed provide evidence for the presence of sizable amounts of C-bearing species (unmistakably related to intentional addition of hydrocarbon-like organics, and not to adventitious contamination) as given by surface-science studies of a Roman bronze [87]. The [C]/[Cu] ratio measured on the metal side of the bronze is more than five times higher than that on the patina region (Fig. 8). Likewise, the [C]/[Pb] atomic ratio measured in the joint region of the fistula is nearly three times as great as that measured on the pipe region (Fig. 9),—and also noteworthy is the presence of tin species in the joint region (which could be related to the use of the Pb–Sn alloy described by Pliny [53,88], see Fig. 9, curve a). These findings confirm that studies conducted with modern surface science methods can contribute significant insight into the composition of ancient objects [89], and can even succeed in directly unveiling the archaeological significance of what one could call an ante litteram example of

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E. Paparazzo / Journal of Electron Spectroscopy and Related Phenomena 134 (2004) 9–24

Fig. 8. Auger survey spectra for a Roman bronze recorded on: (a) the “bare” metallic surface (freed from the natural patina); (b) the patina region.

surface technology performed in antiquity [85,87,88]. However elementary and empirical, a fairly detailed documentation of such “applied surface science” is provided in the ancient sources [50–53]. Apart from the aforementioned possible influence it might have had on Pliny’s account, Posidonius’ heretical view on surfaces seems not to have had any “subsequent influence on his School” [90], and interest in him lived out his death no longer than two or three centuries. From that time until the 19th–20th centuries, virtually no interest in him is documented in studies on the history of philosophy [91]. In fact, although ancient thinkers could avail themselves of a few elementary notions (rarefaction, condensation, mixture, etc.) as the only key for interpreting the chemical reactivity of solids, it is to be expected that Posidonius’

Fig. 9. XPS survey spectra of a Roman lead pipe fisula recorded in: (a) the joint region; (b) the pipe region. Both regions were analyzed after 2 min Ar+ (3 keV, 1 ␮m cm−2 ) etching.

system might have stimulated further interest in surfaces. Conversely, especially from the 12th century to modern times, Aristotle has been regarded as a most authoritative philosopher (in fact, the philosopher par excellence) [92]. As we have seen, Aristotle held that surfaces are an accident and not a substance, the latter being a primary object of speculation in his system [93]. What is more important, there is no evidence that Aristotle regarded surfaces as something different from a geometrical entity alone, i.e. length and breadth without depth, whereas he never had interest in their physical properties (pathos, [55]). Thus, it is perhaps not irrelevant to wonder whether such influential views as his of the nature and properties

E. Paparazzo / Journal of Electron Spectroscopy and Related Phenomena 134 (2004) 9–24

of surfaces—with Posidonius being meanwhile nearly unknown, and only the somewhat “idealized” views of Plato weakly holding a contrasting position [20]—may have had a part in delaying the birth of a (theoretical) discipline aimed to speculate into the nature and properties of solid surfaces. Fortunately, surface-science experiments can now observe chemical changes that mark sharp departures from bulk chemistry, and in some instances, even highlight the surface itself with a “chemical definition” as good as a single monolayer [94]. It thereby seems that surface science recovered a thread with started to be unravelled by ancient speculation into their unique nature, and explains their physico-chemical and topological features, as well as (most of) their subtleties. In conclusion, ancient philosophers and writers entertained a keen, and perhaps unexpected, interest in surfaces. Thus, it seems that since antiquity the human mind has been puzzled not only by the most “esoteric” mysteries of nature, e.g. as to the boundaries of the universe, but also by the mysteries originated from the boundaries of objects so small that even a hand can hold them. In a true sense, modern surface science is now trying to answer some of the questions which began to be asked nearly 25 centuries ago [95].

Acknowledgements I am most grateful to Prof. David Hitchcock (Department of Philosophy, McMaster University, Canada) for his enlightening guidance to the interpretation of the ancient sources, and for correcting many infelicities contained in the previous versions of this paper. I thank Prof. Massimo Fanfoni (Dipartimento di Fisica, Universita’ di Tor Vergata, Rome) and Dr. Francesco Cilloco (ISM-CNR, Rome) for useful discussions on physical and geometrical topics concerned with surfaces. I should like to express my gratitude to Prof. Ian Kidd (School of Classics, University of St. Andrews, Scotland) for his encouragement, and to Prof. Michael White (Department of Philosophy, Arizona State University, Tempe, USA) for his kindness in sending me very helpful bibliographic documentation, and for his interest in this work. I also wish to thank Mr. Massimo Brolatti (ISM-CNR) for the line drawing of Figs. 8 and 9.

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Appendix A Plato: The passages from the dialogue “Timaeus” will be referred to as: Plato, Tim. XYc, where XY and x indicate, respectively, the page number and the line number in that page as they occur in: J. Burnet, Platonis Opera, vol. iii, Oxford University Press, Oxford, 1899–1906. This citation style is consistently used in the classical literature for Plato’s works. The English translation of the passages is that reported in: F.M. Cornford, Plato’s Timaeus, Macmillan, New York, 1959. Aristotle: The following abbreviations refer to the Latin titles appearing in the collection of Aristotle’s works edited by I. Bekker, Berlin, 1831, whereas the English titles, in parentheses, are those used in the “Loeb Classical Library” edition published by Harvard University Press, Cambridge (MA). Cat.: Categoriae (Categories); GC: De Generatione et Corruptione (On Coming-to-Be and Passing-Away); Phys.: Physica (Physics); De Caelo: De Caelo (On the Heavens); Metaph.: Metaphysica (Metaphysics). A given passage referring to Aristotle will be cited as: Aristotle, AB. XXX y nn, where: AB (italicized characters) is the work title denoted with one of the abbreviations specified above, XXX is the page number where the passage appears in Bekker’s edition, “y” is the column (“a” or “b”) of that page, and “nn” the line number along that column. Since all editions of Aristotle’s work adopt these numberings consistently, the citation style used in the references is defined unambiguously. Old Stoics: Since no work of any of these philosophers has survived, the lines of their doctrine can be learned only from accounts provided by ancient reporters. I shall be referring to these accounts, as they are collected and arranged in: J. von Arnim, Stoicorum Veterum Fragmenta (Fragments of Old Stoics = SVF), Tuebner, Liepzig, 1905. They will be cited as: (Old Stoics), followed by the acronym SVF, and X.nn, where “X” is the Roman numeral of the book (I, II or III) in which the fragment occurs, and “nn” is the arabic numeral of the fragment. Posidonius: As with the Old Stoics, no work of this philosopher has survived and, again, his system can be learned only from accounts provided by ancient reporters; I shall refer to these accounts, as they are listed in: L. Edelstein and I.G. Kidd (Eds.),

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E. Paparazzo / Journal of Electron Spectroscopy and Related Phenomena 134 (2004) 9–24

Posidonius. I. The Fragments, Cambridge University Press, Cambridge (UK), 1972. References to Posidonius will be given as: (Posidonius) XnnEK”, where X: “F” or “T” whether the particular reference is, respectively, a fragment (i.e. it reports a “direct” thought of Posidonius) or a testimony (i.e. it is generic reference to his person and/or work); “nn” is the numeral of the fragment or of the testimony; EK denotes the two editors of the collection (Edelstein and Kidd). The translation of the passages (identified by the exact same notation) is that provided by: I.G. Kidd, Posidonius. III. The Translation of the Fragments, Cambridge University Press, Cambridge (UK) 1999. Pliny the Elder (Gaius Plinius Secundus): All the passages relevant to this author occur in the Naturalis Historia, and they will be referred to as, Plin. Nat. XX.nn, where “XX” denotes the book number (Roman numerals) and “nn” the paragraph (arabic) number, as they appear in: A. Corso, R. Mugellesi, G. Rosati, Plinio, La Storia Naturale, Libri 33–37, Einaudi, Turin, 1988. The references to the remaining ancient sources will cited according to the usual style used in “scientific” literature.

References [1] G.A. Somorjai, Introduction to Surface Chemistry and Catalysis, Wiley, New York, 1994, pp. 1–3. [2] K. Siegbahn, C. Nordling, A. Fahlman, R. Nordberg, K. Hamrin, J. Hedman, G. Johansson, T. Bergmark, S.E. Karlsson, I. Lindgren, B. Lindberg, ESCA: atomic molecular and solid strucure studied by means of electron spectroscopy, Nova Acta Regiae Soc. Sci. Upssala 4 (1967) 20. [3] C.S. Fadley, in: C.R. Brundle, A.D. Baker (Eds.), Electron Spectroscopy: Theory, Techniques and Applications, Vol. 2, Academic Press, London, 1977, p. 2; T.L. Barr, Modern ESCA, CRC, Boca Raton, FA, 1993. [4] E.H.S. Burhop, The Auger Effect and Other Radiationless Transitions, Cambridge University Press, Cambridge, UK, 1952. [5] I.F. Ferguson, Auger Microprobe Analysis, Adam Hilger, Bristol, 1989. [6] L.A. Harris, J. Appl. Phys. 39 (1968) 14; E.H.S. Bishop, J.C. Riviere, J. Appl. Phys. 40 (1969) 1740. [7] C.S. Fadley, S.B.M. Hagstrom, J.M. Hollander, M.P. Klein, D.A. Shirley, Science 157 (1969) 1571. [8] C.S. Fadley, D.A. Shirley, Phys. Rev. A 2 (1970) 1109.

[9] R.L. Martin, D.A. Shirley, in: C.R. Brundle, A.D. Baker (Eds.), Electron Spectroscopy: Theory, Techniques and Applications, vol. 1, Academic Press, London, 1977, p. 76. [10] C.S. Fadley, in: C.R. Brundle, A.D. Baker (Eds.), Electron Spectroscopy: Theory, Techniques and Applications, Vol. 2, Academic Press, London, 1977, pp. 75–6. [11] S. Tanuma, C.J. Powell, D.R. Penn, J. Vac. Sci. Technol. A 8 (1990) 2213. [12] D.A. Shirley (Ed.), Electron Spectroscopy, North-Holland, Amsterdam, 1972. [13] D. Briggs, M.P. Seah (Eds.), Practical surface analysis, in: Auger and X-ray Photoelectron Spectroscopy, vol. 1, Wiley, Chichester, UK, 1990. [14] J.C. Rivière, S. Myhra (Eds.), Handbook of Surface and Interface Analysis, Marcel Dekker, New York, 1998. [15] M.J. White, The Continuum and the Discrete, Clarendon Press, Oxford, 1992, pp. 284–315. [16] A. Stroll, Surfaces, University of Minnesota Press, Minneapolis, MN, 1988. [17] According to Diogenes Laertius [Lives of Eminent Philosophers, vol. 1, III.24, Harvard University Press, Cambridge, MA, 2000, pp. 298–9 (R.D. Hicks, Trans.)] Plato introduced the term “plane surface” (epipedon epiphaneian) into the philosophical debate. Actually, Diogenes Laertius (who retails this information from Favorinus’ Miscellaneous History) misquotes Plato, because the latter always used the term ‘epipedon’ for ‘surface’ and not ‘epiphaneia’. Despite this error, Diogenes’ (i.e. Favorinus’) quotation shows that the ancient historians of philosophy considered ‘surfaces’ as a noteworthy topic of Plato’s system. [18] Aristotle, Metaph. 1028 b16-18. [19] Plato, Tim. 32a. [20] Plato, Tim. 53c. [21] See for example, Aristotle, Phys. 193 b23–35 and 210 b5; De Caelo, 299 a1–10 and 306 a1–28; GC, 316 a2–4 and 329 a25. A general, thorough discussion on the differences between the systems of the two philosophers, is available in: H. Cherniss, Aristotle’s Criticism of Plato and the Academy, The Johns Hopkins Press, Baltimore, 1944. [22] Aristotle, Metaph. 1001 b26-1002 b11. [23] Aristotle, Metaph. 1077 b17-1078 a31. [24] J. Annas, Aristotle’s Metaphysiscs. Books M and N, Oxford University Press, Oxford, 1976, pp. 148–152. [25] (Old Stoics) SVF III.(Apollodorus) 6. [26] A.A. Long, D.N. Sedley, The Hellenistic Philosophers, vol. 1, Cambridge University Press, Cambridge, UK, 1977, pp. 272–274. [27] (Old Stoics) SVF II.482 SVF II.483. [28] (Old Stoics) SVF II.487. [29] (Old Stoics) SVF II.488. [30] (Old Stoics) SVF II.489. [31] Plutarch, Moralia, Vol. XIII, Part II, Against the Stoics on Common Conceptions, Harvard University Press, Cambridge, MA, 1997, pp. 815–22 (H. Cherniss, Trans.). [32] (Old Stoics) SVF II.473. [33] A.A. Long, D.N. Sedley, The Hellenistic Philosophers, vol. 1, Cambridge University Press, Cambridge, UK, 1977, p. 290.

E. Paparazzo / Journal of Electron Spectroscopy and Related Phenomena 134 (2004) 9–24 [34] (Old Stoics) SVF II.479. [35] D.J. Furley, Two Studies in the Greek Atomists, Princeton University Press, Princeton, NJ, 1967, pp. 7– 43. [36] Diogenes Laertius, Lives of Eminent Philosophers, vol. 2, IX.30, Harvard University Press, Cambridge, MA, 2000, pp. 440–441 (R.D. Hicks, Trans.). [37] Epicurus, Epistula ad Herodotum: 56–9, Einaudi, Turin, 1973, pp. 50–55 (G. Arrighetti, Trans.). [38] D.J. Furley, Two Studies in the Greek Atomists, Princeton University Press, Princeton, NJ, 1967, p. 4. [39] A.A. Long, D.N. Sedley, The Hellenistic Philosophers, vol. 1, Cambridge University Press, Cambridge, UK, 1977, p. 72. [40] Titus Lucretius Caro, De Rerum Natura, IV.26–89, Harvard University Press, Cambridge, MA, 1975. [41] Titus Lucretius Caro, De Rerum Natura, I.604, Harvard University Press, Cambridge, MA, 1975. [42] Sextus Empiricus, Against the Physicists, II.259–309, Harvard University Press, Cambridge, MA, 1997, pp. 337–361 (R.G. Bury, Trans.). [43] Sextus Empiricus, Against the Professors, III.81, Harvard University Press, Cambridge, MA, 2000, pp. 284–285 (R.G. Bury, Trans.), Bury’s translation (i.e. plane surface) has been revised because the word “plane” is unreliable in the context (and missing in the Greek text of Sextus) of this passage which is concerned with surfaces of whatever shape. I am indebted to Prof. David Hithchock for drawing my attention to this point. [44] Sextus Empiricus, Against the Physicists, I.434, Harvard University Press, Cambridge, MA, 1997, pp. 206–207 (R.G. Bury, Trans.). [45] Sextus Empiricus, Outlines of Pyrrhonism, III.43, Harvard University Press, Cambridge, MA, 2000, pp. 352–353 (R.G. Bury, Trans.). [46] (Posidonius) F16EK. [47] I.G. Kidd, Posidonius. II. The Commentary: (i) Testimonia and Fragments 1–149, Cambridge University Press, Cambridge, UK, 1999, pp. 125–7; see also Cherniss’ interpretation of this same question in: Plutarch, Moralia, vol. XIII, Part I, Platonic Questions, III.1002, Harvard University Press, Cambridge, MA, 2000, p. 219, n.b. (H. Cherniss, Trans.). [48] (Posidonius) F141EK. [49] Marcus Porcius Cato, On Agriculture, 98.2, Harvard University Press, Cambridge, MA, 1999, pp. 94–5 (W.H. Hooper, Trans.). [50] Plin. Nat. XXXIV.99. [51] Plin. Nat. XXXIV.107–9. [52] Plin. Nat. XXXIV.158. [53] Plin. Nat. XXXIV.160–1. [54] D. Ross, Plato’s Theory of Ideas, Clarendon Press, Oxford, 1951. [55] Aristotle, GC 316 a2–4. [56] Aristotle, Cat. 2 a11 and 14–18 3b 10ff Phys. 185 a 31 ff Metaph. 1028 b16–24 1031 a15–1032 a11 1041 b7–9 1041 b19–33.

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[57] M.V. Wedin, Aristotle’s Theory of Substance. The Categories and Metaphysics Zeta, Oxford University Press, Oxford, 2000, pp. 1–3. [58] G. Reale, Guida alla Lettura della “METAFISICA” di Aristotele, Laterza, Bari, 2001, pp. 141–144. [59] Aristotle, Metaph 1025 a30–34. [60] A.A. Long, D.N. Sedley, The Hellenistic Philosophers, vol. 1, Cambridge University Press, Cambridge, UK, 1977, p. 302. [61] M.J. White, The Continuum and the Discrete, Clarendon Press, Oxford, 1992, pp. 293–314; D.N. Sedley, in: K. Algra, J. Barnes, J. Mansfeld, M. Schofield (Eds.), The Cambridge History of Hellenistic Philosophy, Cambridge University Press, Cambridge, UK, 1999, pp. 393–394. [62] (Old Stocs) SVF II.363: “According to them (the Stoics) the incorporeal is not of a nature either to act or to be acted upon” (Translation by Long and Sedley, Ref. [26], p. 272). It should also be recalled that Plutarch (see Ref. [31]) explicitly reported that for the Stoics “the limit (i.e. the surface) is not body”. [63] S. Sambursky, Physics of the Stoics, Greenwood Press, Westport, CT, 1973, pp. 94–7; J.P. Dumont, in: J. Brunsghwig (Ed.), Les Sto¨ıciens et Leur Logique, Libraire Philosophique J. Vrin, Paris, 1978, pp. 121–34. [64] F92EK; I.G. Kidd, Posidonius II. The Commentary: (i) Testimonia and Fragments 1–149, Cambridge University Press, Cambridge, UK, 1999, p. 532. [65] Aristotle, GC 315 b14. [66] G.A. Somorjai, Chemistry in Two Dimensions: Surfaces, Cornell University Press, Ithaca, NY, 1981, p. 30. [67] (Old Stoics) SVF II. 480. [68] M.J. White, Hist. Philos. Q. 3 (1986) 379. [69] Aristotle, GC 325 b25-33. [70] Aristotle, GC 315 b25-317 a10. [71] E. Paparazzo, J.L. Dormand, D. Fiorani, Phys. Rev. B 28 (1983) 1154; E. Paparazzo, J.L. Dormand, D. Fiorani, Solid State Commun. 50 (1984) 919. [72] Aristotle, GC 322 b1-328 b33. [73] Aristotle, GC 323 a5–7. [74] B.W. King, H.P. Tripp, W.H. Duckworth, J. Am. Ceram. Soc. 42 (1959) 504. [75] E. Paparazzo, J. Electron Spectrosc. Relat. Phenom. 43 (1987) 97. [76] E. Paparazzo, G. Fierro, G.M. Ingo, S. Sturlese, J. Am. Ceram. Soc. 71 (1988) C494. [77] E. Paparazzo, G. Fierro, G.M. Ingo, S. Sturlese, J. Vac. Sci. Technol. A 7 (1989) 2496. [78] M.P. Borom, J.A. Pask, J. Am. Ceram. Soc. 49 (1966) 1. [79] J.A. Pask, Proc. Porcelain Enamel Inst. Tech. Forum 33 (1971) 1. [80] L.E. Klebanoff, S.W. Robey, G. Liu, D.A. Shirley, Phys. Rev. B 30 (1984) 1048. [81] T.L. Barr, J. Phys. Chem. 82 (1978) 1801. [82] (Posidonius) T56EK. [83] (Posidonius) T36EK.

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[84] I.G. Kidd, Posidonius II. The Commentary: (i) Testimonia and Fragments 1-149, Cambridge University Press, Cambridge, UK, 1999, p. 45. [85] E. Paparazzo, in: J.C. Rivière, S. Myhra (Eds.), Handbook of Surface and Interface Analysis, Marcel Dekker, New York, 1998, p. 835; E. Paparazzo, A.S. Lea, D.R. Baer, J.P. Northover, J. Vac. Sci. Technol. A 19 (2001) 1126. [86] A.G. Baca, L.E. Klebanoff, M.A. Schulz, E. Paparazzo, D.A. Shirley, Surf. Sci. 173 (1986) 215. [87] E. Paparazzo, L. Moretto, Vacuum 55 (1999) 59; E. Paparazzo, Archaeometry. 45 (2003) 615. [88] E. Paparazzo, Appl. Surf. Sci. 74 (1994) 61. [89] J.B. Lambert, C.D. McLaughlin, Archaeometry 18 (1976) 169.

[90] I.G. Kidd, Posidonius. II. The Commentary: (i) Testimonia and Fragments 1–149, Cambridge University Press, Cambridge, UK, 1999, pp. 125–7; see also Cherniss’ interpretation of this same question in: Plutarch, Moralia, vol. XIII, Part I, Platonic Questions, III.1002, Harvard University Press, Cambridge, MA, 2000, p. 219, n.b. (H. Cherniss, Trans.). [91] M. Laffranque, Poseidonios d’Apamée, Presses Universitaires de France, Paris, 1964. [92] J. Barnes, Aristotle, Oxford University Press, Oxford, 1982. [93] Aristotle, Cat. 2a11-5b19 Metaph. Book Z 1028 a 10– 32. [94] G.A. Somorjai, U. Starke, Pure Appl. Chem. 64 (1992) 509. [95] E. Paparazzo, Nature Mater. 2 (2003) 351.