Francoise Monnoyeur What is the Value of Geometric Models to Understand Matter? Epekeina, vol. 6, n. 2 (2015), pp. 1-13 History of the Platonic-Aristotelian Tradition ISSN: 2281-3209 DOI: 10.7408/epkn. Published on-line by: CRF – Centro Internazionale per la Ricerca Filosofica Palermo (Italy) www.ricercalosoca.it/epekeina This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. What is the Value of Geometric Models to Understand Matter?∗ Francoise Monnoyeur Introduction The understanding of matter is a philosophical endeavor. Scientists are interested in nding or building adequate models in order to explain phenomena and nd the properties of matter.1 Models are then tested against experience and when validated lead to the formulation of laws. From a philosophical perspective models are not only tools to understand matter and discover laws of nature, but representations that reveal how we acquire knowledge about nature.2 The philosophical perspective takes into account that models are representations of an object under the scrutiny of a viewer, and therefore analyzes the interaction between the mind and the object. We focus on two geometrical models created with more than two millennia apart, and consider how they capture natural phenomena. The rst model appears in one of Plato's dialogues when the young astronomer Timaeus, in a conversation with Socrates, introduces geometric solids to understand the basic structure of matter and interaction of the primary elements: re, air, water, and earth. The second geometric model appeared nowadays with the development of electron microscopy and x-ray diraction and allows physicists to discover the atomic structure of matter. Furthermore, we analyze the value of these geometric models and identify their cognitive function. 1. Function of geometric models in Plato and crystallography 1.1. Platonic models In the Timaeus one of Plato's latest dialogues, Timaeus in the name of Plato gives an account of the creation of the world and origin of ∗ The author acknowledges Mr. Konstantinos Bakoglidis for some of the gures from Plato and inspiring discussions. 1. Hertz 2007 and Hesse 1953, 198. 2. Monnoyeur 2000a. Francoise Monnoyeur matter. This story does not pretend to deliver a scientic theory, but is a possible explanation of the origin of matter when absolute truth falls short. That's why Plato proposes a model of matter and not a theory. At this stage, it seems to me necessary to draw the distinction between theory and model, as Timaeus recalls several times at the beginning of his explanation that he is telling a "story" or a "tale":3 Wherefore, Socrates, if in our treatment of a great host of matters regarding the Gods and the generation of the Universe we prove unable to give accounts that are always in all respects self-consistent and perfectly exact, be not thou surprised; rather we should be content if we can furnish accounts that are inferior to none in likelihood, remembering that both I who speak and you who judge are but human creatures, so that it becomes us to accept the likely account of these matters and forbear to search beyond it. In the introduction of Inventing the Universe, Luc Brisson emphasizes the axiomatic structure of science in the Timaeus and writes:4 In our analysis, we will endeavor to display the axiomatic structure which underlines the Timaeus. In fact, we will exhibit, as completely as possible, the list of axioms, or primordial assumptions, upon which Plato's cosmological system is ultimately founded. In this article, I show how the Platonician mathematical theory of the elements, although founded on certain axioms, relates to our perception. Because we focus on physics, namely the theory of matter and the movement of the elements, a special attention is given to the relationship between mathematics and perception. Further in his introduction,5 Brisson elaborates that Plato develops "scientic knowledge" against "scientic method of choice. . . directly based on the technology of experimentation." Our purpose is to present the Platonician model of the elements as hypothetical in its nature, geometrical in its reasoning, but also relying on perception in some ways. Plato proposes, therefore, a model to explain the movement and nature of matter, and chooses a geometrical model able to express the perception we have of the 3. Plato, Timaeus 29c-29d in Lamb 1925, 29. 4. Brisson and Meyerstein 1995, 6. 5. Brisson and Meyerstein 1995, 7. 2 What is the Value of Geometric Models to Understand Matter? elements. According to my interpretation, Plato's model solves the following problem: how to represent in an intelligible way the matter we sense? There are three actors involved in this problem: the moving matter we sense, the representation supporting this moving matter, and the intelligibility of this representation. Plato's main objective is to nd the best representation or model of the sensible world. Previous philosophers such as Empedocles, Anaxagoras, Thales, and Leucippus used combinations of four basic elements (air, earth, water, re) to identify primordial matter. Plato refers also to these four elements, and conceives his model to understand how the four elements move and transform into each other. This model is not a pure abstraction but relates to the sensible phenomena. For Plato, models tell us something of the essence of matter as they establish the salient and permanent relationships between the elements. According to the analogy of the divided line of the Republic,6 these models belong to the intelligible knowledge namely the mathematical and geometric knowledge. The Platonician solution consists in establishing correspondences between the four elements and four regular polyedres (Figure 1). In the Timaeus, geometry is chosen because it is considered to be the everlasting or reliable representation. More precisely, the explanation of the interaction between the elements follows geometric rules when transposed in geometrical solids. (a) Fire (tetrahedron). (b) Air (octahedron). (c) Water (icosahedra). (d) Earth (cube). Figure 1 – The geometric model of the four elements according to Plato The choice of geometric solids gives a basis to scientic representation and understanding of the changes in physical reality. Plato's main 6. Plato, Republic, Book 6, 509d-513e in Shorey 1969, 509. 3 Francoise Monnoyeur objective is to represent the change of water into air through re, and the stability of earth as it cannot be changed into any other element; on the contrary, earth remains earth when interacting with re, water or air. The geometric explanation is as follows; the solids analyzed by Plato are made of faces, more exactly of triangles. In 54e-55d, Plato explains how we can use equilateral triangles to build three regular polyhedrons representing re, air, and water: the tetrahedron (re) is made of four equilateral triangles, the octahedron (air) is made of eight equilateral triangles, and the icosahedra (water) is made of twenty equilateral triangle.7 The cube representing earth is dierent because it is made of four squares. Each face of the rst three solids (re, air, and water) is built of equilateral triangles. Plato describes how an equilateral triangle consists of six scalene triangles (gure 2); a scalene triangle comprises one right angle with three unequal sides (gure 3). Figure 2 – The equilateral triangle from Plato is built with six scalene triangles (1 to 6) 7. Plato, Timaeus, 54e-55d in Lamb 1925, 54. 4 What is the Value of Geometric Models to Understand Matter? Figure 3 – Isosceles and scalene triangles A square is made of four isosceles triangles (gure 4). Figure 4 – A square formed by four isosceles triangles These two right-angle triangles of gure 3, scalene and isosceles, cover the possible structures of the four primary elements. They are two presuppositions or axioms in this theory: the rst is that elementary right angles triangles cannot be created or destroyed, and the second is that only the solids made of the same triangles can act on each other. Earth is identied with the square, and is the only solid made of four isosceles triangles; consequently, earth cannot act on another element or be acted upon by any other element; thus explaining the stability of the squared face. On the other hand, the faces of re, water and air made of equilateral triangles, and can interact with each other since any change in the fundamental elements can be explained according to the division and re-composition of the fundamental tri5 Francoise Monnoyeur angles. The relationship between the various elements can be written with the following equation: fire air = air water = water earth In the equation above, re and earth are connected through air and water whereas water and air are the «geometrical medians». Plato shows how the four elements are combined in various ratios and how they are made of material substances that interact with each other. For instance, water heated by re dissolves and its fragments recombine and produce two corpuscles of air (vapor) and one corpuscle of re. Plato, taking into account the number of faces, writes8: 〈 water 〉 −−→ heat 2 〈 air 〉 + 〈 fire 〉 20 = 2x8 + 4 Figure 5 – Equation for the transmutation of the elements In this equation, Plato rationally establishes that the transmutation of re, air, and water occurs by redistribution of the faces of these gures and writes a "chemical equation" explaining the transformation of the four elements. For Plato, the type and number of triangles determine the properties of each element. The whole system is supported with a set of relationships expressed with the geometry of the solids. Without these models, we would be unable to scientically determine the way elements interact and move. 1.2. Comparison with the geometric models of matter used in crystallography Crystallography, the science that examines the arrangement of atoms in solids, developed rapidly at the beginning of the twentieth century 8. Plato, Timaeus 56d in Lamb 1925, 56. 6 What is the Value of Geometric Models to Understand Matter? with Sir William Lawrence Bragg's discovery of the x-ray diraction law;9 the subsequent development of x-ray diraction technology and transmission electron microscopy have paved the way towards exploration of the nano-structure of the materials. It is now established that matter made of atoms can only belong to seven dierent crystalline systems: triclinic, monoclinic, orthorhombic, tetragonal, rhombohedral, hexagonal, and cubic. In this paper, we focus solely on three crystalline structures composed of carbon atoms. The rst material, graphite, is soft and composed of carbon atoms that are arranged into a hexagonal shaped structure (gure 6a). The second material, diamond, is the hardest known material and composed of carbon atoms arranged in a tetrahedral (cubic) structure (gure 6b). Finally, the third material, fullerene, is a molecule in the form of a hollow sphere that is composed of sixty atoms interconnected by pentagons and hexagons (gure 6c). Fullerene is elastic and extremely strong.10 The science of crystallography studies the various structures taken by the carbon atoms and identies dierent materials such as graphite, diamond, or fullerene. These geometric models give scientists the ability to identify the location of atoms as well as the distances and angles between atoms. Scientists can then perform further experiments to investigate the properties of materials, for example, hardness/softness, and elasticity. We can see how each material corresponds to a specic structure with specic properties in the same way that Plato relates each of the four elements to a geometric solid with distinct properties. 2. What is the value of these geometric models to understand matter? There are obvious and surprising similarities between the models described by Plato to understand the transmutation of the elements and the models of the various structures of carbon atoms. Both of these models are based on Euclidean geometry, but the Platonician is chosen, and the Crystallographic is observed by electron microscopy and x-ray diraction. Nevertheless, the identity between these two models does not happen by chance, or because Timaeus had good intuition. How 9. Giacovazzo 2002. 10. Broitman and Hultman 2014, 390-392. 7 Francoise Monnoyeur (a) Graphite. (b) Diamond. (c) Fullerene. Figure 6 – Three dierent crystallographic carbon structures 8 What is the Value of Geometric Models to Understand Matter? can we understand how these models, which were developed millennia apart, are so similar? The answer could be that both provide what is required to understand matter and correspond de facto to our cognitive functions. According to Raymond Duval:11 Representation and visualization are at the core of understanding in mathematics. We can apply this conception to the case of the geometrical models because there seems to be two distinct phases in the way we perceive these models; rstly, we conceive the mathematical explanation through visual representation, and secondly, we visualize the solids with their properties. Let's analyze how these two phases work in the Platonic and crystallography models. In the rst phase, we build up a visual representation of the model that allows us to understand the properties of matter. For instance, the Platonic models identify the nature of the triangles composing the faces of the solids while crystallography perceives the atoms and connects them in order to build geometrical solids. The second phase allows us to visualize in three dimensions the solids with the properties they represent. Visual representation (two dimensions) and visualization (three dimensions) are at the core of the understanding of these models. The scientic understanding of the movement of elements and the detection of the structure of carbon atoms is realized thanks to the geometrical models that enable the visualization of the properties of the materials such as mobility, stability, hardness, softness and elasticity. Hans Reichenbach notices in the Philosophy of space and time12 that: It seems to be much easier to make logical inferences with the help of visual representation than by means of abstract concepts. 2.1. What is the value of the Platonic geometric models? 2.1.1 Visual representation in the Platonic solids What can we learn from the geometric decomposition of the elements? Because re has less number of faces, the solid is more acute; it is the 11. Duval 1999, 3. 12. Reichenbach 1958, 117. 9 Francoise Monnoyeur lightest, most mobile and sharpest element, which explains how it can transform water into air. Air has more faces than re but is more mobile and lighter than water. Water has a large number of faces and is less mobile and heavier than air. Earth, the heaviest element, represents stability because its planes are squares and cannot be changed by the other faces.13 Therefore, according to these models, there is a relationship between the number of faces and their mobility. Plato deploys geometrically the properties of the elements, captures the transformation of one element into another and then expresses this phenomenon into an equation. As geometry is a science of relations,14 it gives the opportunity to establish relations between objects, here between the elements. Poincaré explains in the preface of his book Science and Hypothesis the purpose of mathematics:15 Mathematicians do not study objects, but the relations between objects; to them it is a matter of indierence if these objects are replaced by others, provided that the relations do not change. Matter does not engage their attention, they are interested in form alone. The geometric models give a scientic explanation of the properties of the elements. This means that their properties are revealed upon relationships represented geometrically and mathematically. We can see how Plato interpretes the movement and properties of the elements in terms of number and type of triangles in the faces of the solids. The triangles in the geometric solids represent the way the elements move and how they transmute into each other. Having no scientic instruments to analyze matter, we can say that the correspondence discovered between gures and the movement of the elements depends on a combination of observation and intuition. As this model is supported by mathematical equations, we can say that Plato's intuition goes beyond intuition that is delivered by senses alone. Poincaré describes as follows the kind of intuition that comes into play in this case:16 13. Plato, Timaeus, 56a-56b in Lamb 1925, 56. 14. Monnoyeur 2013. 15. Poincare 1952, 20. 16. Poincare 1914, 128. 10 What is the Value of Geometric Models to Understand Matter? The principal aim of mathematical education is to develop certain faculties of the mind, and among these, intuition is not the least precious. It is through it that the mathematical world remains in touch with the real world, and even if pure mathematics could do without it, we should still have to have recourse to it to ll up the gulf that separates the symbol from reality. Geometric spatial representation of movement relates to the properties of the elements, to the «real world». Plato's geometric solids are spatial representations of movement expressed in a proportional equation. Thanks to visual representation of triangles, the rules of division and re-composition of the triangles have been established together with the relationship between the properties and movement of the elements. The visual representation of the Platonic solids paves the way to the understanding of matter. 2.1.2 Visualization of the Platonic solids Geometric models relate nally to the «real world» with the geometric solids that give us a three dimensional representation of the movement and properties of their elements. This visualization completes the visual representation of the relationships between the triangles and gives a picture of how re, air, water and earth interact on each other. Three-dimensional visualization combined with two-dimensional representation allows us to reach an understanding of the movement and properties in the elements. 2.2. What is the value of the geometric models in crystallography? 2.2.1 Visual representation in crystallography In crystallography, the geometric solids are not chosen as in Plato, but observed with scientic instruments. Although technology helps to locate the atoms, the scientist still needs to draw the lines between the atoms in order to construct a gure that accurately represents the spatial arrangement of the atoms. This presupposes the calculation of the atoms quantity, of the respective distance between each other, and the angles they form in the structure. Thanks to the development of 11 Francoise Monnoyeur new technologies (electron microscopes and computers), microscopic data can be calculated. It follows that progress in crystallography is based in the interpretation of the spatial representation detected by the scientist. The human eye and mind together with the image presented by the microscope constitutes the model to be interpreted. 2.2.2 Visualization reveals the various structures of carbon atoms After being able to represent the atomic structure of materials, the scientist can identify the kind of material and consecutively its specic properties embedded in the dierent geometrical structures. The three dimensional visualization of the structure of the carbon atoms indicates their type and properties. We can reach this nal stage after the building up of the visual representation of the structures. The understanding of matter happens via two phases, visual representation and visualization in three dimensions of the whole structure. Conclusions We have discussed how Platonic and crystallographic models are rooted in Euclidean geometry and both explain and reveal the properties of materials. In the Platonic solids, the nature and number of triangles justify their movement or stability; in crystallography the nature of the geometric structure of the carbon atoms (hexagonal, cubic, or fullerene) indicates the type of material and properties: hardness or softness and elasticity. In both cases, scientists are depending upon visual representation and visualization to be able to analyze the nature of matter and measure it. Not only these spatial models give valuable scientic information about the matter studied, but they also are the main cognitive support for scientic activity. Besides the extraordinary fact that these models have important similarities, they nevertheless dier in the way they are obtained. The Platonic models are chosen and the interpretation of matter changes relies in geometry and mathematics. On the contrary, in crystallography the physicists discover atoms and identify their position in dening the structure of these atoms. Besides technology (microscopes, diractometers, and computers) the understanding of matter relies on ne observation, interpretation and design 12 What is the Value of Geometric Models to Understand Matter? by the scientists of the structure itself. In both of these models, the understanding of matter is depending upon active visual representation and visualization that synthetizes the whole process of knowledge. We can conclude that the geometric models are the expression of the mind to understand physical matter. Francoise Monnoyeur Centre Jean Pepin, CNRS, Paris, France monnoyf@gmail.com References Brisson, L. and F. W. Meyerstein 1995, Inventing the Universe, Suny, Albany. Broitman, E. and L. Hultman 2014, "Advanced Carbon-based Coatings", in Cameron 2014, pp. 389-412. Cameron, D. (ed.) 2014, Comprehensive Materials Processing, Elsevier, Amsterdam. Duval, R. 1999, "Representations and visualization: cognitive functions in mathematical thinking", in Santos 1999, pp. 3-26. Giacovazzo, C. 2002, Fundamentals of Crystallography, Oxford University Press, Oxford. Hertz, H. 2007, Principles of Mechanics, Cosimo, New York. Hesse, M. 1953, "Models in Physics", in British Journal for the Philosophy of Science, 4. Lamb, W. (ed.) 1925, Plato, Timaeus, William Heinemann, London. Monnoyeur, F. 2000a, "La matière au kaléidoscope de l'interdisciplinarité", in Monnoyeur 2000b, pp. 13-22. - (ed.) 2000b,Qu'est-ce que lamatière? Regards scientiques et philosophiques, Hachette, Paris. Nicholas of Cusa's methodology of the Innite 2013, History and Philosophy of Innity, University of Cambridge, Cambridge, doi: 10.13140/RG.2.1.1595. 0881. Poincare, H. 1914, Science and Method, ed. by F. Maitland, Routledge, London. - 1952, Science and Hypothesis, ed. by W. J. Greenstreet, Dover, New York. Reichenbach, H. 1958, The Philosophy of Space and Time, Dover Publications, New York. Santos, F. H. M. (ed.) 1999, Proceedings of the Twentieth-First Annual Meeting of the North American Chapter of the International Group for the Psychology of the Mathematics Education, ERIC Clearinghouse, Columbus. Shorey, P. (ed.) 1969, Plato, Republic, William Heinemann, London.


Reply to Yli--‐Vakkuri Timothy Williamson In 'Epistemicism and modality', Juhani Yli--‐Vakkuri rigorously treats the problem of developing a model--‐theoretic semantics for a formal language with the operators 'necessarily' and 'actually', interpreted in terms of metaphysical modality, and an operator 'definitely', interpreted in the spirit of the epistemicist theory of vagueness developed in my book (Williamson 1994). The challenge is especially pertinent because my epistemicist account of definiteness has a modal dimension, whose interaction with other forms of modal variation raises delicate issues for the overall theory. 1. Worldly differences and semantic differences According to epistemicism, vagueness in a language induces no deviation from classical logic or from bivalent semantics. It is a purely epistemic phenomenon: borderline cases are just cases of unavoidable ignorance for a special sort of reason. The actual meaning of a vague 2 expression differs from some of its potential alternative meanings in ways indiscriminable by native speakers of the language. Following John Hawthorne, Yli--‐Vakkuri calls this idea 'Semantic Plasticity'. The upshot is a special obstacle to knowing some truths expressed using the vague expression. Very roughly, the definite truths are those knowledge of which is not blocked by an obstacle of that sort. I developed the underlying epistemology in safety--‐ theoretic terms. Knowledge requires safety from error: one knows in a given case only if it is not relevantly close to an error possibility. Actuality is never close in that sense to metaphysical impossibilities, because they present no real danger. Compare a case where one assents to a true proposition expressed by a vague sentence with a similar case where one assents to a false proposition expressed by the same sentence.1 The difference in truth--‐value may result from either one of two kinds of difference between the cases (perhaps from both). The first kind of difference is worldly. The vague sentence may express the same proposition in the two cases, while the objects under discussion vary in their properties or relations. For instance, in both cases the sentence 'Jack is bald' expresses the proposition that Jack is bald, but Jack has less hair in one case than in the other. Thus the sentence 'Jack is bald' may express a true proposition in the former case and a false proposition in the latter. The second kind of difference between cases is semantic. Even if the objects under discussion have the same properties and relations in the two cases, the sentence 'Jack is bald' may express different propositions, because it is used in very slightly different ways. For instance, in one case the sentence 'Jack is bald' still expresses the proposition that Jack is bald, while in the other it expresses the distinct proposition that Jack is bald*, where the standard for being bald* is slightly more demanding than the standard for being bald. Thus, even though the state of 3 Jack's scalp is exactly the same between the two cases, the sentence 'Jack is bald' may again express a true proposition in the former case and a false proposition in the latter. Of course, two cases may also differ in both worldly and semantic respects simultaneously, and in other respects too. Concerning our ignorance in paradigmatic borderline cases, I proposed that the error possibilities by which vagueness blocks knowledge are the close ones differing from the given case in semantic but not in worldly respects (1994, p. 231). By contrast, most discussions of safety in epistemology concern worldly but not semantic differences; the proposition at issue is held fixed across the cases under discussion. However, if one wants a non--‐trivial safety condition for knowledge of necessary truths, as in mathematics, one must look at semantic rather than worldly differences: if a sentence expresses a necessary truth in a given case, then it expresses a truth in all cases differing from the former only in worldly respects (assuming that all cases, or at least all close cases, are metaphysically possible). Thus there are reasons independent of vagueness for using a safety condition that takes account of cases that differ in semantic respects, as well as of those that differ only in worldly ones (Williamson 2000, pp. 181--‐2). However, the semantic differences relevant to mathematical knowledge will typically be much larger than those relevant to vagueness; the cases will not be semantically indiscriminable to native speakers. For straightforward examples, we can treat the worldly and semantic dimensions as mutually orthogonal: we can vary a case on either dimension while holding it fixed on the other. For more complex examples, however, the independence assumption breaks down: varying a case on one dimension entails varying it on the other too. For instance, a vague word may be both used and mentioned in the same sentence, as in disquotational 4 biconditionals for truth such as '"Jack is bald" is true if and only if Jack is bald', a type of example much discussed in the recent literature on vagueness and featured in Yli--‐Vakkuri's paper. A difference between cases in the use of the word 'bald' is semantic in respect of the right--‐hand side of the biconditional ('Jack is bald') but worldly in respect of the left--‐hand side ('"Jack is bald" is true'), since the latter is about a broadly semantic feature of the former. It is often unclear how to apply the rough dichotomy between the world and our descriptions of it to examples where we cannot ignore the fact that our descriptions are part of the world. Similarly, it is often unclear how to apply the rough dichotomy between the world and our knowledge of it to examples where we cannot ignore the fact that our knowledge is part of the world, as in the so--‐called paradox of knowabilty (we cannot know a conjunction of the form: P and it will never be known that P; see Williamson 2000, pp. 270--‐ 301). Yet any theory of vagueness must be applicable to such complex examples. Problems of vagueness in the law remind us that the distinction between clear cases and borderline cases arises in practice for arbitrarily complex sentences. One benefit of trying to construct an adequate model theory for a formal language with a 'definitely' operator is that it forces us to think systematically and quite generally about how to apply vagueness--‐theoretic distinctions to such sentences. At this point, some philosophers will be inclined to scrap the account of definiteness based on the worldly--‐semantic distinction as insufficiently general, and start again from scratch. But that is just the sort of methodological impatience that so much impedes progress in philosophy. In particular, the fact that the worldly and semantic dimensions are not fully independent of each other does not entail that an initial assumption of their 5 independence makes a bad starting--‐point. After all, if we are trying to understand a phenomenon in natural science, we may initially make the simplifying assumption that two aspects of it are mutually independent, even though we know that the assumption is not strictly correct. For instance, we may treat propositions about the shape of an object as probabilistically independent of propositions about its colour, so that we can calculate the probability of the conjunction of a shape proposition and a colour proposition as simply the product of the probabilities of the conjuncts. We can then use the results obtained under that simplifying assumption as a starting point for a more general account that allows for the interdependence of the two dimensions. The same goes for the treatment of the worldly and semantic dimensions as mutually independent in the initial explanation of ignorance in borderline cases. Rather than scrapping the first pass explanation, we may do better by refining it. A specific reason for optimism is that vagueness in complex expressions derives somehow from vagueness in their atomic constituents and modes of composition. The worldly--‐semantic dichotomy works best for atomic expressions, although doubtless not perfectly even there. A further consideration comes from the nature of the 'definitely' operator. Its treatment as a sentence operator in a formal language with a compositional semantics turns out to involve a significant degree of idealization. Within limits, the theorist has discretion to decide what idealizations of its meaning will conduce to the most illuminating logic of vagueness. 'Definitely' is not just a philosopher's invention. To describe someone as 'neither definitely tall nor definitely not tall' is quite intelligible in ordinary English, even if it sounds a bit pedantic. Although the complement of 'definitely' in English is normally an adjectival 6 phrase rather than a sentence, that goes for modal words such as 'necessarily' and 'possibly' too; it does not prevent them from being most usefully formalized by operators on sentences. Many ordinary uses of 'definitely' are epistemic in a way not specifically related to vagueness. For instance, a detective asking 'Who was definitely in the building last night?' probably means something like 'Who is known to have been in the building last night?'; borderline cases of being in the building last night are probably not at issue. Still, theorists of vagueness can legitimately requisition the word 'definitely' for their more specific purposes. So far, so good. 2. Use and mention A more pressing concern is that the formalization of 'definitely' as a sentence operator Δ tailored to suit the theory of vagueness may not fit the structure of a compositional semantics. To start simple, consider a semantic theory that assigns a set of (metaphysically) possible worlds as the semantic value of a sentence. The compositional semantics makes the semantic value of the sentence operator Δ a function from sets of possible worlds to sets of possible worlds. Let 'small' be a vague predicate of natural numbers whose application to them is nevertheless non--‐contingent. Thus, we may suppose, 17 is a borderline case for 'small'; it is vague whether 17 is small, but not contingent whether 17 is small. If 17 is small, it is necessary that 17 is small; if 17 is not small, it is necessary that 17 is not small. Consequently, the semantic value of '17 is small' is either the set of all worlds or 7 the set of all worlds. In the former case, '17 is small' has the same semantic value as '0 = 0', so by the compositional semantics 'Δ(17 is small)' has the same semantic value as 'Δ(0 = 0)', and so is true (definitely 0 is self--‐identical). In the latter case, the semantic value of '¬(17 is small)' is the set of all worlds and so the same as the semantic value of '0 = 0', so by the compositional semantics 'Δ¬(17 is small)' has the same semantic value as 'Δ(0 =0)', and so is true. Either way, the disjunction 'Δ(17 is small) ∨ Δ¬(17 is small)' is true: it is definite whether 17 is small. But that contradicts the hypothesis that it is vague whether 17 is small. One might simply draw the moral that sets of possible worlds are too coarse--‐grained to serve as the semantic values of sentences in the semantics for a logic of vagueness and modality. That is hardly surprising. The envisaged semantics is one--‐dimensional, whereas Yli--‐ Vakkuri argues powerfully that it needs to be three--‐dimensional rather than two--‐ dimensional, to accommodate both the usual two modal dimensions for the operators 'necessarily' and 'actually' and a further dimension for the operator 'definitely'. But further reflection suggests that the problem goes even deeper. Any compositional semantics for Δ makes the meaning of the sentence Δφ a function of the meaning of the sentence φ, in some appropriate sense of 'meaning'. Thus if φ is synonymous with ψ (they have the same meaning in the relevant sense), then Δφ is synonymous with Δψ, and moreover ¬φ is synonymous with ¬ψ, so Δ¬φ is synonymous with Δ¬ψ; thus φ and ψ have the same borderline cases. But is that principle defensible? To see the difficulty, let us make the standard assumption that the natural kind terms 'furze' and 'gorse' are synonymous. They are also presumably not perfectly precise: for instance, it is slightly vague when furze and gorse first evolved. Nevertheless, for purposes of meaning, the two words are vague in the same way. Let φ be the sentence 'All 8 and only furze is furze' and ψ the sentence 'All and only furze is gorse'. On a standard compositional semantics, φ and ψ have the same semantic structure and synonymous corresponding constituents, and so are synonymous. Thus, by hypothesis, Δφ and Δψ are synonymous too. Since φ is a trivial logical truth, Δφ is true. Hence Δψ is true too. But is it? We may assume that 'furze' and 'gorse' are understood independently of each other; a speaker may understand either word without understanding the other. No special rule co--‐ ordinates them; they just happen to have the same meaning. Although the use of 'furze' happens exactly to match the use of 'gorse', there could very easily have been a slight mismatch, where the use of one word was slightly more liberal than the use of the other, so that the extension of the former included slightly earlier samples than the extension of the latter did. The vagueness of 'furze' and 'gorse' makes it unclear to native speakers whether there is indeed such a slight difference in extension. Thus it seems to be definite that all and only furze is furze, but not definite that all and only furze is gorse. On this view, φ and ψ are synonymous, but Δφ and Δψ differ in truth--‐value and so in meaning. If so, the operator Δ does not have a compositional semantics. Could a theorist respond by individuating meanings in a more fine--‐grained way? We may assume that the only relevant difference between 'furze' and 'gorse' is the syntactic difference between the words themselves. A way of individuating meanings on which 'furze' and 'gorse' differ in meaning makes synonymy between distinct words virtually impossible. A supervaluationist might implement such a fine--‐grained standard by identifying meanings with functions from admissible sharpenings of the language to Kaplanian characters. Suppose that one admissible sharpening assigns the character C to both 'furze' and 'gorse', while another assigns a distinct character C* to both words. Then if a third admissible 9 sharpening assigns C to 'furze' and C* to 'gorse', while a fourth assigns C* to 'furze' and C to 'gorse', the account makes 'furze' and 'gorse' differ in meaning, even if the overall range of admissible sharpenings associates each of them with exactly the same range of characters. The trivialization of synonymy is a high price to pay for such a view, especially since it threatens to trivialize the requirement of compositionality too. An alternative way of interpreting the semantics is to retain a conception of meaning that allows 'furze' and 'gorse' to be synonymous, but to treat the Δ operator as tacitly quotational: Δφ is really about the sentence φ itself, at least partly (a move Yli--‐Vakkuri may accept). In that case, the so--‐called compositional semantics for the language is not what it seems, since it does not determine the meanings of complex expressions just from the meanings of their constituents and the way those constituents are put together. For a genuinely compositional semantics, one might have to make the quotation explicit - and supply a semantics of quotation. These problems are reminiscent of those facing attempts to give a compositional semantics of variable--‐binding, on which Yli--‐Vakkuri has written illuminatingly elsewhere (2013). In the simple case of an extensional, non--‐indexical language, if one identifies the meaning of a singular term with a function that maps each assignment of values to variables to the denotation of the term on that assignment, the variables 'x' and 'y' count as different in meaning, simply because they have distinct values on at least one assignment, even though that is just a corollary of their syntactic difference. In one respect, however, the problems raised by Δ are more acute, since they arise for closed as well as open expressions.2 10 Similar problems arise anyway for epistemic operators, and so pose no threat to the epistemicist view that Δ is an epistemic operator. For instance, even though 'furze' and 'gorse' are synonymous, it may be natural to describe someone as knowing that something is furze without knowing that it is gorse, or as knowing that all and only furze is furze without knowing that all and only furze is gorse. If one is doing the semantics of 'know' in terms of epistemically possible worlds, one may then be driven to assign 'furze' and 'gorse' distinct intensions (here, functions from epistemically possible worlds to extensions), even though they are synonymous. Of course, one may take a more coarse--‐grained view of knowledge and simply tough it out, insisting that to know that all and only furze is furze just is to know that all and only furze is gorse, even if those who recognize that truth under the guise of the sentence 'All and only furze is furze' cannot recognize it under the guise of the sentence 'All and only furze is gorse'. In principle, someone might take the same line with vagueness and simply tough it out, insisting that for it to be definite that all and only furze is furze just is for it to be definite that all and only furze is gorse, even if those who recognize that truth under the guise of the former sentence cannot recognize it under the guise of the latter. However, the tough line is better motivated for 'know' than for 'definite'. When we speak of knowledge and ignorance, we often wish to prescind from the words in which a given piece of knowledge might be expressed. By contrast, when we speak of definiteness and vagueness, the expression in given words is typically central to our interest. To prescind from it would be to miss the very point at issue. These questions also arise for Yli--‐Vakkuri's preferred epistemic interpretation of his three--‐dimensional semantics. To make all the desired distinctions, an intended model will 11 have to assign distinct 3D profiles to sentences that, by a natural compositional standard, are synonymous. That is very far from making the theory useless: it can still serve as a good guide to reasoning about the interaction between vagueness and metaphysical modality. But it will not be a compositional semantics in the sense one might originally have expected. To the two non--‐epistemically modal dimensions needed for a standard semantic treatment of 'necessarily' and 'actually', Yli--‐Vakkuri adds a third modal dimension for the treatment of 'definitely', with promising results.3 He argues that the third dimension is best understood as epistemically modal. Since he is implementing an epistemicist account of vagueness, that is not altogether surprising. He requires the epistemic dimension to include metaphysically impossible epistemic possibilities as well as metaphysically possible ones. On his interpretation, 'when φ is borderline, φ expresses in the actual world, according to some close epistemic possibility, a proposition other than the one it actually expresses in the actual world', but 'any such epistemic possibility will be metaphysically impossible, because it is a noncontingent matter which proposition is actually expressed by a sentence'. Such a use of metaphysically impossible worlds in the semantics for 'definitely' poses an apparent threat to epistemicist theories that explain actual borderline cases in terms of Semantic Plasticity, for surely no metaphysically impossible world is close in the safety--‐relevant sense to the actual world. However, we may be able to reconcile Yli--‐Vakkuri's semantics with the safety--‐ theoretic considerations by elucidating its explanatory ambitions. For just as a theory of the meaning of the word 'light' is not tasked with explaining the underlying nature of light, and a theory of the meaning of the word 'knowledge' is not tasked with explaining the underlying nature of knowledge, so a theory of the meaning of the word 'indefinite' is not 12 tasked with explaining the underlying nature of indefiniteness. The point is easier to miss in the latter case, for while semantics is obviously separate from physics, and only slightly less obviously separate from epistemology, it is not at all obviously separate from the theory of indefiniteness as a linguistic phenomenon. A comprehensive book on semantics should say something about vagueness and indefiniteness. Nevertheless, that task must be distinguished from the task of giving the semantics of the word 'indefinite', just as the task of explaining the underlying nature of meaning must be distinguished from the task of giving the semantics of the word 'meaning'. Thus, even if safety--‐theoretic considerations are central to the underlying nature of indefiniteness, they need not figure in a good semantic account of the word 'indefinite' or the Δ operator, just as, even if safety--‐theoretic considerations are central to the underlying nature of knowledge, they need not figure in a good semantic account of the word 'knowledge'. By itself, the appeal to merely epistemically possible worlds in Yli--‐Vakkuri's semantics for Δ poses no threat to a safety--‐ theoretic account of the underlying nature of indefiniteness, since the semantics is not expected to describe that underlying level. Of course, if for some sentences in some contexts the semantics predicted truth--‐values incompatible with the safety--‐theoretic account, that would be a problem, but just appealing to merely epistemically possible worlds forces no such incompatibility. The point can be restated in terms of the distinction between semantics and metasemantics, where a metasemantic theory is supposed to explain why a given semantic theory holds for the language of a given community at a given time. The possible worlds of the safety--‐theoretic considerations are the concern of the metasemantic theory; Yli--‐Vakkuri's impossible worlds are the concern of his semantic theory. 13 Also to be taken into account is the extent to which the Δ operator and related English words such as 'indefinite', 'borderline', and 'vague' are all being used as theoretical terms, and rightly so. Although their introduction by examples is good enough for initial working purposes, some refinement is needed once they are used in formulating a positive theory of vagueness. For when we encounter more complex cases than the usual sorites series provide, especially cases where the semantic and worldly dimensions fail to be independent, the initial paradigms give no clear guidance as to how those terms should most fruitfully be applied for theoretical purposes. We see many apparent joints, and are unsure where to cut. For any theory that uses an operator like Δ to characterize vagueness--‐ related phenomena, choosing a semantics for Δ is a prescriptive as well as a descriptive task. It is a matter of deciding what it is best to mean by Δ. In this respect, the model--‐theoretic nature of Yli--‐Vakkuri's semantics strikes a helpful balance between informativeness and flexibility. It is primarily designed to generate a good logic for Δ, especially as it interacts with the modal operators. It validates nice structural principles for Δ, in particular those corresponding to the modal system T, thereby imposing constructive discipline on our use of Δ. At the same time, it does not specify in any detail an intended model (or even frame) for the model theory. It thereby leaves considerable scope for fine--‐tuning the specific application of Δ in line with future metasemantic developments. Like most accounts of vagueness, the epistemicist account in my book focusses on simple borderline cases, and does not provide clear guidance on how to apply an operator like Δ to more complex cases, especially those where the semantic and worldly dimensions are not independent. As already noted, that does not make it irrelevant to such cases. Science is full of cases where we know how to apply a theory to simple examples of a 14 phenomenon but not to more complex examples. Typically, progress is then incremental, as models (in the scientific sense, not the semantic one) are developed to permit the theory to be applied to more complex examples, though never all at once, and always under simplifying assumptions. I see no reason why such progress should not also be made in the theory of vagueness, if philosophers are willing to do the hard work of model--‐building. 3. Semantic Plasticity Where do these general methodological considerations leave Semantic Plasticity? In section 5, Yli--‐Vakkuri argues directly against a version of it that appeals to metaphysical possibilities. He formulates the version thus: (*) Whenever φ is true and borderline, there is a close metaphysically possible world in which φ expresses a proposition other than the proposition φ actually expresses, and in which that proposition is false. As a counterexample to (*), he discusses the case where φ is the material conditional # → χ, χ is an actually true borderline sentence, and # is a relevantly precise actually non--‐ borderline specification of the actual use facts that determine which proposition χ actually expresses (so # is actually true). Thus Δ# and ¬Δχ are true, so ¬Δ(# → χ) is also true by the normal logic of Δ. Therefore, since # → χ is true, it is also borderline. Thus, given (*), it follows that there is a close metaphysically possible world w* in which # → χ expresses a proposition other than the proposition # → χ actually expresses, and in which that 15 proposition is false. We may assume that in all close metaphysically possible worlds # and → express what they actually express. Thus if # is true in w*, the actual use facts that determine which proposition χ expresses are the same in w* as in the actual world, so # → χ expresses the same proposition as it actually expresses, contrary to hypothesis. On the other hand, if # is not true in w*, it is false in w* (given epistemicism, bivalence holds), so # → χ is true in w* by the truth--‐table for →, again contrary to hypothesis. Thus # → χ is a counterexample to (*). This argument against (*) does not depend on Yli--‐Vakkuri's formal semantics, although it does use the standard assumption that the logic of Δ is like that of □ in a normal modal logic, which Yli--‐Vakkuri's semantics validates and I happily grant. I will not defend (*). However, the falsity of (*) does not mean that the more general phenomenon of semantic plasticity as described in my book plays no role in explaining the borderline status of # → χ, even when semantic plasticity is understood, as here, to be variation in what is expressed in close, so metaphysically possible, worlds (epistemically possible but metaphysically impossible worlds do not count). For the normal logic of Δ has these theorems, which Yli--‐Vakkuri's semantics also validates: Δ# → (Δ(# → χ) ↔ Δχ) Δ# → (Δ¬(# → χ) ↔ Δ¬χ) Δ# → ((¬Δ(# → χ) & ¬Δ¬(# → χ)) ↔ (¬Δχ & ¬Δ¬χ) In brief, given that # is definite, the question whether # → χ is borderline reduces to the question whether χ is borderline. We can explain the definiteness of # in terms of its truth and lack of semantic plasticity, both of which Yli--‐Vakkuri stipulates. Thus, if we can explain the borderline status of χ in terms of semantic plasticity, then we can also explain the 16 borderline status of # → χ indirectly in terms of semantic plasticity, using our explanations of the definiteness of # and the borderline status of χ in those terms. For instance, if χ is a semantically simple sentence, we may be able to explain its borderline status directly in terms of its semantic plasticity, along the lines I originally proposed, for all that Yli--‐Vakkuri's arguments show. Of course, χ may itself be complex, and present similar difficulties to those # → χ did, but then we can apply the same strategy to χ as we did to # → χ, and so on down in a recursive process terminating at the latest in semantically simple constituents. An encouraging observation is that both the normal logic of Δ and Yli--‐Vakkuri's semantics yield the principle that any truth--‐function of non--‐borderline sentences is itself non--‐borderline. For instance: (Δφ ∨ Δ¬φ) → (Δ¬φ ∨ Δ¬¬φ) ((Δφ ∨ Δ¬φ) & (Δψ ∨ Δ¬ψ) → (Δ(φ & ψ) ∨ Δ¬(φ & ψ)) The negation of a non--‐borderline sentence is itself non--‐borderline, a conjunction of non--‐ borderline conjuncts is itself non--‐borderline, and so on. Contrapositively, if some truth--‐ function θ of the simple sentences φ1, φ2, ..., φn is borderline, then at least one of φ1, φ2, ..., φn is borderline too. Thus if the explanation of borderline status in terms of semantic plasticity works for simple sentences, there is some hope of explaining θ's borderline status indirectly in terms of semantic plasticity through the contributions of its simple constituents. One will not always be able to deduce θ's borderline status from the borderline status of its constituents, for not every truth--‐function of borderline sentences is itself borderline: for instance, φ & ¬φ is a non--‐borderline truth--‐function of φ, even when φ is borderline. Nevertheless, if θ is borderline, a reasonable goal is to explain its borderline status in terms 17 of the interrelated ways in which its constituents are borderline, where those ways essentially involve semantic plasticity. More generally, suppose that only semantically plastic sentences are borderline; Yli--‐ Vakkuri's arguments in no way undermine that principle. Let σ be a complex sentence with a compositionally determined meaning. Thus if all the simple constituents and modes of combination from which σ is composed are semantically non--‐plastic, so is σ itself; by hypothesis, then, σ is non--‐borderline. Contrapositively, if σ is borderline, then some of its simple constituents or modes of combination are semantically plastic. Thus we can hope to explain σ's borderline status in terms of the semantic plasticity of those simple constituents or modes of combination. Although the present considerations do not guarantee success, they suggest that it is a reasonable strategy. How does that strategy square with a safety conception of knowledge? For the truth actually expressed by # → χ is not known, yet in every close metaphysically possible world the sentence # → χ expresses a true proposition (by Yli--‐Vakkuri's argument). Moreover, it is quite compatible with the previous assumptions that the proposition actually expressed by # → χ is both actually believed and true in every close metaphysically possible world. Invoking epistemically but not metaphysically close worlds looks like abandoning the safety conception. If # → χ simply refutes that conception, then the original explanation of our ignorance in terms of semantic plasticity fails even for the simplest borderline cases, because it depends on a false epistemology. At this point, it helps to recall how safety--‐theoretic considerations would explain the failure of irrational but true mathematical beliefs to constitute knowledge. Someone irrationally plumps for believing a proposition p expressed by a precise mathematical 18 sentence π. In fact, p is true, and so necessarily true. Thus in every close world, π expresses p (π is not semantically plastic) and p is true. However, in some close world w, he irrationally plumps in a similar way for believing a different proposition r expressed by a different precise mathematical sentence ρ. But r is false, and so necessarily false. The sentences π and ρ are not semantically indiscriminable to the subject; he understands both and is aware of their semantic difference. It is just that his plumping does not track their difference in truth value. Since his irrational false belief in the close world w is relevantly similar in method to his irrational true belief in the actual world, the latter fails to constitute knowledge. Now consider Yli--‐Vakkuri's case. We may assume that the borderline true sentence χ is semantically plastic along the lines of (*), for otherwise his argument against (*) would assume more than it was entitled to by resting on stipulations hostile to (*). We may also assume that the subject actually believes the proposition expressed by the sentence # → χ, for the challenge is to explain in appropriate terms why such a belief does not constitute knowledge. But then we should expect that in some close metaphysically possible world x, the subject believes in a similar way the proposition expressed in x by the sentence #x → χ, where #x is a relevantly precise non--‐borderline specification of the use facts in x that determine which proposition χ expresses in x (so #x is true in x), while by semantic plasticity the proposition χ expresses in x differs from the one it actually expresses and is false in x, even though x is just like the actual world in the worldly ways relevant to χ, though not in those relevant to # and #x. For we were not supposed to assume that the actual world was uniquely special in the subject's believing the proposition expressed by the material conditional with a true relevantly precise non--‐borderline specification of the use facts that 19 determine which proposition χ expresses as the antecedent and χ as the consequent. But then #x → χ expresses a false proposition in x, for there #x expresses a truth and χ expresses a falsehood. The false belief in the close world x in the proposition there expressed by #x → χ is relevantly similar in method to the true belief in the actual world in the proposition actually expressed by # → χ, so the latter fails to constitute knowledge. Thus we can explain in safety--‐theoretic terms the obstacle to knowing the truth expressed by # → χ, and so the borderline status of # → χ. The explanation crucially invokes semantic plasticity in relation to the vague consequent and a different safety--‐theoretic consideration in relation to the precise antecedent. That is a natural generalization of the original explanation by appeal to semantic plasticity of the obstacle to knowing the truth expressed by a simple vague sentence. The hybrid aspect of the explanans follows the hybrid aspect of the explanandum, where the sentence at issue combines the relevantly vague constituent χ with the relevantly precise constituents # and → . The previous paragraph made various simplifying assumptions. We can construct more complicated scenarios. For instance, we can imagine subjects hard--‐wired to believe propositions expressed by the sentence # → χ but not those expressed by similar sentences #x → χ in any close world. On a suitable development of the story, the true beliefs expressed by # → χ of such bizarre creatures may bizarrely constitute knowledge.4 If so, and they also somehow know the truth expressed by the precise but massively detailed specification #, may they not also know the truth expressed by χ inferentially, by modus ponens? But then χ is presumably not borderline for them. That does not mean that it is not borderline for us: our use of χ is different from theirs, even if we do in fact express the same proposition. If # correctly describes their use, then it does not correctly describe ours. If we enter into 20 communication with them, it may be unclear to us whether χ as they use it expresses the same proposition as χ as we use it. The foregoing line of thought opens up many complex questions that I cannot hope to deal with adequately here. Rich explanatory resources are available to an epistemicist approach to vagueness articulated in terms of safety and semantic plasticity, given a willingness to apply those resources to complex cases in correspondingly complex ways, in the spirit of scientific model--‐building. 21 Notes 1 For the sake of brevity, when I speak of knowing or believing a proposition expressed by a sentence, I will mean that it is known or believed under the guise of that sentence. Thus one may know or believe it expressed by one sentence (say, 'Hesperus is Hesperus') but not expressed by another sentence (say, 'Hesperus is Phosphorus'). 2 The analogy may suggest a treatment along the lines of Fine (2007). This is no place to discuss such a radical departure from the usual form of compositional semantics; Yli--‐ Vakkuri follows the latter. 3 The technical aspects of the logic were developed in collaboration with Jon Litland (Yli--‐Vakkuri and Litland 2016). 4 See Williamson 2016 for an analogous possibility concerning knowledge of mathematical axioms. 22 Fine, Kit 2007: Semantic Relationism. Oxford: Blackwell. Williamson, Timothy 1994: Vagueness. London: Routledge. Williamson, Timothy 2000: Knowledge and its Limits. Oxford: Oxford University Press. Williamson, Timothy 2016: 'Absolute provability and safe knowledge of axioms', in Leon Horsten and Philip Welch (eds.), Gödel's Disjunction, Oxford: Oxford University Press. Yli--‐Vakkuri, Juhani 2013: 'Propositions and compositionality', Philosophical Perspectives 27, pp. 526--‐563. Yli--‐Vakkuri, Juhani 2016: 'Epistemicism and modality', THIS VOLUME. Yli--‐Vakkuri, Juhani, and Litland, Jon 201X: 'Vagueness and modality', MS.


| 257 JEAN CLAUDE LARCHET. (2014). TERAPÉUTICA DE LAS ENFERMEDADES ESPIRITUALES. SALAMANCA: EDICIONES SÍGUEME. (734 PP). Carlos Alberto Rosas Jiménez1 Terapéutica de las enfermedades espirituales es el título del libro escrito por Jean Claude Larchet, publicado en el 2014 por Ediciones Sígueme, traducido del original francés: Thérapeutique des maladies spirituelles, Les Éditions du Cerf; del año 2000. En este texto el autor nos presenta la vida espiritual como una dimensión real del ser humano, que así como en su dimensión física trabaja por su salud, lo debe hacer también en el ámbito de su vida espiritual; no hacerlo, lo conduce a enfermarse, leve o gravemente. El libro plantea la descripción de esas enfermedades espirituales que aquejan al ser humano y cuál es su terapéutica. Jean Claude Larchet nació en Francia en 1949, es doctor en filosofía y teología. Sus estudios, centrados en la Edad Antigua, le han convertido en un experto del pensamiento patrístico. Actualmente es profesor de 1 Magíster en Bioética, 2017. Miembro del Grupo Kheiron Bioética Universidad de la Sabana, Chía, Cundinamarca, Colombia. ORCID: 0000-0003-1529-3785 Correo electrónico: carlosalbertorosasj@gmail.com Atribución – Sin Derivar – No comercial: El material creado por usted puede ser distribuido, copiado y exhibido por terceros si se muestra en los créditos. No se puede obtener ningún beneficio comercial. No se pueden realizar obras derivadas ISSN: 0120-131X • ISSN: 2389-9980 (en línea) | Vol. 45 | No. 103 | Enero-junio • 2018 | pp. 257-261 Cuestiones Teológicas | Medellín-Colombia http://dx.doi.org/10.18566/cueteo.v45n103.a09 Artículo recibido el 29 noviembre de 2017 y aprobado para su publicación el 16 abril de 2018. 258 | Cuestiones Teológicas, Vol. 45, No. 103 (Enero-junio, 2018) Carlos Alberto Rosas Jiménez Filosofía en Forbach, Lorena, Francia. Especialista en Teología Patrística, y en la relación entre la salud, la enfermedad y la curación según la tradición cristiana oriental, pues pertenece a la Iglesia Ortodoxa. Entre sus muchas obras podemos nombrar: Théologie de la maladie, Cerf, Paris, 1991; 1994, II ed.; La divinisation de l'homme selon saint Maxime le Confesseur, Cerf, Paris, 1996. Vie après la mort selon la tradition orthodoxe, Cerf, 2001; Saint Maxime le Confesseur, Cerf, 2003 y Malades des nouveaux médias, Cerf, 2016. La presente obra está organizada en 6 capítulos, con una breve introducción y una, también breve, conclusión. El capítulo 1 trata la salud original y el origen de las enfermedades dando unas premisas antropológicas. El capítulo 2 se titula: "Las pasiones. Nosografía, semiología y patogénesis de las enfermedades espirituales". El capítulo 3 trata las condiciones generales de la terapéutica. El capítulo 4 nos da la aplicación de la terapéutica. El capítulo 5 se dedica a la terapéutica de las pasiones y a la adquisición de las virtudes. Finalmente, el capítulo 6 se titula: "La Salud Recobrada". A continuación queremos resaltar algunos puntos que nos han parecido importantes que pueden motivar la lectura del libro. En primer lugar, podemos decir que el libro es una exhaustiva recopilación de textos de muchos Padres de la Iglesia, principalmente de los primeros siglos después de Cristo. El libro recoge una vasta tradición espiritual consignada en las obras de grandes autores espirituales como: Juan Casiano, San Juan Clímaco, Doroteo de Gaza, San Máximo el Confesor; además de otros grandes teólogos como lo son: San Basilio el Grande, San Gregorio de Nisa, San Gregorio Nacianceno y San Juan Crisóstomo. Estos autores le aportan a la obra una profundidad teológica y espiritual significativa. Las citas textuales son muy pertinentes y han sido tan bien armonizadas en el desarrollo del texto que son fáciles de leer y de entender. La lectura es muy fluida y la organización en pequeños acápites dentro de cada capítulo facilita la lectura, dado que el contenido espiritual y profundo de cada sección hace necesaria una reflexión y meditación para una adecuada comprensión. Por otro lado, para poder hablar de la necesidad de una terapéutica de las enfermedades espirituales, el autor explica clara y brevemente el porqué de estas. En síntesis, el estado enfermizo del ser humano se debe a la separación de Dios, porque permanece apegado al mundo material. Para salir de ese estado es necesaria una terapéutica divino-humana en la que se requiere del Cuestiones Teológicas, Vol. 45, No. 103 (Enero-junio, 2018) | 259 Jean Claude Larchet. (2014). Terapéutica de las enfermedades espirituales. esfuerzo del hombre pero que necesita, principalmente, la acción de Dios. Todo el esfuerzo del hombre para librarse de las enfermedades espirituales consiste en dejar obrar a Dios en su vida; la salud se podría entender como la facilidad para que la voluntad divina encuentre un camino en nosotros (cf. p. 265), una auténtica salud espiritual es un sinónimo de santidad. En este esfuerzo por curarse y obtener la salud Dios le ha dado al hombre la ley, pero ésta no es suficiente para la cura (cf. p. 256). El ser humano tuvo necesidad de un remedio mucho mejor, pues como dice san Gregorio Nacianceno: Reprendido primero de muchas maneras por sus numerosos pecados, que crecieron como retoños de una mala raíz, corregido por diversos motivos en distintas circunstancias por medio de la palabra, la ley, los profetas, los beneficios, las amenazas, los castigos, los signos [...] el hombre tuvo necesidad de un remedio más eficaz para curarse de unos males que no hacían más que empeorar (p. 257). Y es en ese momento que se plantea la necesidad de: "un médico y un cirujano cuya habilidad fuera proporcional a la gravedad de sus enfermedades y sus llagas. Solamente Cristo, por ser Dios, podía, haciéndose hombre sin dejar de ser Dios, ser ese médico eficaz" (p. 257). Cristo es presentado como el médico carnal y espiritual (cfr. p. 259), como dice la Escritura: "El soportó el castigo que nos trae la paz, y con sus cardenales hemos sido curados" (Is 53, 5b). Podemos decir que la base teológica de la sanación de las enfermedades espirituales que menciona el libro es bastante amplia, pero aun así es posible resumirla de la siguiente manera: En su naturaleza, restaurada por la unión con la naturaleza divina en la persona de Cristo muerto y resucitado, el hombre, del que se han eliminado todas las enfermedades, recobra la salud plena. En Cristo, vuelve a ser un hombre normal; recupera sus facultades en su estado primero, conforme a su naturaleza, que, recordémoslo, es estar orientadas hacia Dios (p. 270). El profesor Larchet menciona, por un lado, las pasiones, su semiología y la patogénesis, y, por otro lado, describe la terapéutica de cada una de las enfermedades; las que describe con su terapéutica son: la filautía, la gastrimargía, la lujuria, la filargia, la pleonexia, la tristeza, la acedia, la ira, 260 | Cuestiones Teológicas, Vol. 45, No. 103 (Enero-junio, 2018) Carlos Alberto Rosas Jiménez el temor, la cenodoxia y el orgullo. Si bien es cierto que es necesario que el cristiano se dedique a comprender las enfermedades que padece y a buscar su curación, el autor sostiene que: Conviene ser consciente de que la salud, aunque sea espiritual, no es un fin en sí misma. Es sólo la condición para que el hombre pueda convertirse en "una nueva criatura" (Gal 6,15), llevar una vida nueva, realizar su destino, que es glorificar a Dios dignamente y con la plenitud de los medios que el Creador le ha dado, y vivir plenamente en Dios siendo él mismo deificado por la gracia (p. 712). Otro punto que vale la pena destacar de la aproximación que tiene el profesor Larchet es que da luces para la construcción de un mundo mejor, pues en un mundo tan violento y acelerado como en el que vivimos actualmente, es interesante advertir cómo los autores espirituales plantean la mansedumbre y la paciencia, no sólo como un remedio para tratar la ira, sino para todas las enfermedades del alma (cf. p. 567, 568). Asimismo, nos recuerda que la tristeza es un mal escondido, puede estar muy presente en los ambientes en los que nos movemos, pero pasa siempre desapercibida; para tratarla se insiste en dedicar tiempo a la oración (cf. p. 535), no sólo para la tristeza, sino para las otras enfermedades espirituales. El profesor Larchet también da una renovada aproximación a la ascesis corporal, que puede haber quedado muy desprestigiada por prácticas antiguas muy exageradas, insistiendo que: la finalidad de la ascesis corporal, que es favorecer la vida espiritual [...] no es proponerse agobiar el cuerpo, sino facilitar las funciones del alma [...] Se tratará hacer de modo que la abundancia no posea demasiado y que la indigencia no carezca de nada (p. 492). En conjunto con esto da luces a la acción pastoral de la Iglesia actual, dando elementos muy concretos para quienes se dedican a la cura de almas, a quienes tienen que caracterizar: la paciencia (p. 434), la pureza (p. 424), la humildad; entre otras (424 ss.); pero, sobre todo, el respeto total a la libertad de quien se acompaña (p. 436). Finalmente, tenemos únicamente una muy breve crítica al libro, pues en un momento el autor dice: Cuestiones Teológicas, Vol. 45, No. 103 (Enero-junio, 2018) | 261 Jean Claude Larchet. (2014). Terapéutica de las enfermedades espirituales. Esperamos haber mostrado suficientemente que las nociones de enfermedad, curación y salud son una clave importante ofrecida por la teología, la antropología y la ascética ortodoxas para entender el estado de la humanidad caída y las modalidades de su salvación en Dios (p. 711). No estamos de acuerdo con que toda esta sabiduría recopilada en esta magistral obra se diga que es exclusiva de la Iglesia ortodoxa, pues lo es también de la Iglesia católica. Por lo tanto, es un patrimonio que compartimos ortodoxos y católicos, fruto de la reflexión de muchos autores espirituales que siguieron a los primeros seguidores de Cristo y de la enseñanza de los grandes padres de la Iglesia de los primeros siglos de la era cristiana. En conclusión, recomendamos este libro a todos aquellos que quieran conocer más sobre sus propias enfermedades espirituales y cómo tratarlas, así como a aquellos que se dedican al acompañamiento espiritual y a los que quieran conocer más sobre los padres de la Iglesia de manera muy encarnada en el combate espiritual que vivimos todos los cristianos.