At the third episode of Sophocles’ Electra, the heroine, believing that her brother Orestes is dead, invites her sister Chrisothemis to a plan to kill Aegisthus, in a speech that recalls fifth century Athenian’s public honors to the tyrannicide couple, Harmodius and Aristogiton, and thus presents the two sisters as a kind of democratic champions (v. 947-989). This paper compares the treatment given by contemporary Commentaries to Sophocles’ Electrato this speech with recent gender-oriented studies of Athenian citizenship, in order to (...) argue that the idea of the ancient polisas a “man’s club” depends much more on a modern stereotype about Athenian politics than on the ancient evidence available to us –a stereotype that projects XIX century European conceptions of politics on the ancient context, and perpetuates backwards a supposedly universal masculine domination. In this light, Electra’s attitude, surely exceptional because of her equally exceptional situation, far from strikingly transgressing ancient gender-roles, points to the importance of female citizenship in democratic Athens. (shrink)

Presentation of Dossier Gender and Antiquity: problems and methods.

This paper is a study of Dionysian _lysis_, “liberation”_._ We begin with the suggestion that in the description of the _mania telestike _in Plato’s _Phaedrus_ 244d-245a, the best candidate among Dionysian ritual practices abstracted by Socrates’ rhetoric is maenadic trance. The maenadic references also accompany the testimonies on Dionysos _Lysios_ in Corinth, Sicyon and Thebes, but here the evidence invites us to widen the scope of Dionysian cult practices and look at the god’s Mystery cults, notably at the evidence provided (...) by the golden leaves founded in initiated sepultures. We propose then an exclusively Dionysian reading of the Pelinna leave. This reading leans on: an analysis of the leaf’s text; a critique of the interpretations associating _lysis_ with the expiation of the Titans’ crime; an examination of Persephone’s role; the meaning of _lysis_ in OF 350 Bernabé; and the linking up of the famous passages of Plato’s _Republic_ dealing with initiations with the dynamics of postponed punishment in ancient Greek representations of divine justice. Finally, the article suggests that Dionysian _lysis_ is concerned with liberation not only after death, but also during the life of the initiated. In conclusion, it goes back to Plato’s _Phaedrus_ 245a, in order to contrast Dionysian maenadic and mystic trance. (shrink)

Cet article est une étude sur la lysis, la « libération » dionysiaque. On commence avec la suggestion que dans la description de la mania telestike dans le Phèdre 244d-245a, le meilleur candidat parmi les pratiques cultuelles dionysiaques à l’opération de soustraction résultante de la rhétorique socratique c’est la transe ménadique. Les références ménadiques accompagnent également les témoins sur Dionysos Lysios à Corinthe, Sicyone et Thèbes, mais ici les sources nous invitent à élargir l’horizon des pratiques cultuelles dionysiaques pour regarder (...) les cultes à mystère en l’honneur du dieu, notamment aux renseignements des lamelles d’or trouvées dans des sépultures des initiés. Puis, on entreprend de proposer une lecture exclusivement dionysiaque de la lamelle de Pélinna. Cette lecture prend appui sur: une analyse du texte de la lamelle ; une critique des interprétations qui mettent la lysis en rapport avec l’expiation du crime des Titans ; un examen du rôle de Perséphone ; la signification de lysis dans l’OF 350 Bernabé ; l’articulation des célèbres passages de la République où il est question des initiations avec les dynamiques de la punition différée dans les représentations grecques anciennes de la justice divine. Puis, l’article suggère que la lysis dionysiaque porte sur une délivrance non seulement après la mort, mais aussi pendant la vie des initiés. En conclusion, l’étude revient au Phèdre 245a pour mettre en contraste les transes ménadique et mystique. (shrink)

Over the last eight years, there has been a sharp increase in government censorship and officially sponsored persecution of the Moroccan free press. The Moroccan press still enjoys greater freedoms now than under the late King Hassan II, thanks to the liberalization efforts he facilitated toward the end of his life, which were also continued in the early years of his son’s reign. However, the freedoms media activists worked so hard to obtain at the end of the last century have (...) rapidly begun to erode, particularly after the 2003 terrorist attacks in Casablanca. Morocco remains an important Arab ally to both the United States and Europe, but the monarchy risks that relationship by tightening the reigns on speech and violating international human rights laws. Moreover, the monarchy puts itself at risk domestically every time it imprisons a journalist or imposes a bankrupting fine on a popular periodical, as Moroccan human rights groups grow less enchanted by their king. Over the last two years, criminal charges against the media have increased significantly, causing some publications to close and leaving a number of journalists in jail for their writings. In addition, since 2008, the Moroccan government has begun to censor the Internet, arresting bloggers and satirists and temporarily suspending access to popular websites, such as YouTube. This article explores Morocco's obligations under international and domestic law relating to freedom of expression and examines some recent court cases involving the Moroccan media. (shrink)

With special relativity, we seem to be facing a conundrum. It is a very well-tested theory; in this way, the Minkowski spacetime must be “capturing” essential features of space and time. However, its geometry seems to be incompatible with any sort of global notion of time. We might only have local notions of now (present moment) and time flow, at best. In this note, we will explore the possibility that a pretty much global notion of now (and time flow) might (...) be hiding in plain sight in the geometry of the Minkowski spacetime. (shrink)

In this paper, it is presented a historical account of the formulation of the quantum relativistic wave equation of an electron – the Dirac equation, issues regarding its interpretation that arose from the very beginning, and the later formulation of this equation in relation to a quantized electron-positron field, which implies a new interpretation. The way in which solutions obtained under each interpretation of the equation relate to one another is also considered for the simple case of hydrogen-like problems.

Abstract:AbstractThis article examines how representations of women of color in the 1970s shaped and were shaped by US feminist print cultures. Critiques of the US women's liberation movement importantly focus on its whiteness and US-centrism, deployment of concepts such as sisterhood, and practices such as tokenization. I propose a shift the terms of this conversation through a semiotic and affective analysis of representations of women of color across a range of US feminist periodicals published during the 1970s. Specifically, I identify (...) patterns in the representation of figures of Indochinese and other revolutionary women, attending to what is consistent and what varies in their representation. I argue that the revolutionary, antiracist, antisexist, and anti-imperialist struggles of women of color lent US feminism a weight that countered the ways movement outsiders—particularly mainstream media and the New Left—trivialized and devalued feminist activism. This paper thus seeks to demonstrate that portrayals of women of color countered not only sexism but also the implicit racism in dominant narratives characterizing the women's liberation movement. (shrink)

Este artigo tem como objetivo investigar o papel da música no interior das considerações de Sartre sobre a obra de arte, com base no período de publicação dos primeiros escritos do autor. Sabe-se que Sartre, em suas poucas investidas sobre estética, conferiu maior densidade ao caso pictórico. No entanto, isso não significa que a música não possua notáveis peculiaridades frente às demais manifestações artísticas. Em especial, quando consideramos as análises do autor sobre o contraste entre a irrealidade e o real, (...) o exame sobre a música nos oferece importantes nuances para a compreensão do problema. Em vista disso, buscaremos examinar o papel desempenhado pela música em A náusea, romance de 1938, segundo o pano de fundo teórico exposto em O imaginário, obra de 1940. (shrink)

When addressing the notion of proper time in the theory of relativity, it is usually taken for granted that the time read by an accelerated clock is given by the Minkowski proper time. However, there are authors like Harvey Brown that consider necessary an extra assumption to arrive at this result, the so-called clock hypothesis. In opposition to Brown, Richard TW Arthur takes the clock hypothesis to be already implicit in the theory. In this paper I will present a view (...) different from these authors by taking into account Einstein’s notion of natural clock and showing its relevance to the debate. (shrink)

Este artigo pretende analisar a noção de melancolia tal como apresentada na caracterização de Roquentin, protagonista do romance sartriano _A náusea_, à luz da análise espinosana sobre os afetos, nas partes III e IV da _Ética_. No livro de Sartre, podemos observar sugestões constantes sobre a peculiar tristeza do personagem, baseadas em sua relação com a descoberta da contingência. Por outro lado, de acordo com a necessidade ontológica, as considerações de Espinosa sobre os afetos afirmam a impotência do melancólico e (...) apontam a servidão daquele que crê ser conduzido pela fortuna. Portanto, nesta dinâmica, indicaremos Roquentin como o exemplo do homem que não é senhor de si, nos termos espinosanos. (shrink)

Einstein's gravitational redshift derivation in his famous 1916 paper on general relativity seems to be problematic, being mired in what looks like conceptual difficulties or at least contradictions or gaps in his exposition. Was this derivation a blunder? To answer this question, we will consider Einstein’s redshift derivations from his first one in 1907 to the 1921 derivation made in his Princeton lectures on relativity. This will enable to see the unfolding of an interdependent network of concepts and heuristic derivations (...) in which previous ideas inform and condition later developments. The resulting derivations and views on coordinates and clocks are in fact not without inconsistencies. However, we can see these difficulties as an aspect of an evolving network understood as a “work in progress”. (shrink)

The cognitive basis of geometry is still poorly understood, even the ‘simpler’ issue of what kind of representation of geometric objects we have. In this work, we set forward a tentative model of the neural representation of geometric objects for the case of the pure geometry of Euclid. To arrive at a coherent model, we found it necessary to consider earlier forms of geometry. We start by developing models of the neural representation of the geometric figures of ancient Greek practical (...) geometry. Then, we propose a related model for the earliest form of pure geometry – that of Hippocrates of Chios. Finally, we develop the model of the neural representation of the geometric objects of Euclidean geometry. The models are based on the hub-and-spoke theory. In our view, the existence of specific models opens the possibility of addressing the relationship between geometric figures and geometric objects, in a novel way, in terms of their neural representation. (shrink)

The conventionality of simultaneity thesis as established by Reichenbach and Grünbaum is related to the partial freedom in the definition of simultaneity in an inertial reference frame. An apparently altogether different issue is that of the conventionality of spatial geometry, or more generally the conventionality of chronogeometry when taking also into account the conventionality of the uniformity of time. Here we will consider Einstein’s version of the conventionality of geometry, according to which we might adopt a different spatial geometry and (...) a particular definition of equality of successive time intervals. The choice of a particular chronogeometry would not imply any change in a theory, since its “physical part” can be changed in a way that, regarding experimental results, the theory is the same. Here, we will make the case that the conventionality of simultaneity is closely related to Einstein’s conventionality of chronogeometry, as another conventional element leading to it. (shrink)

We present an approach in which ancient Greek mathematical proofs by Hippocrates of Chios and Euclid are addressed as a form of (guided) intentional reasoning. Schematically, in a proof, we start with a sentence that works as a premise; this sentence is followed by another, the conclusion of what we might take to be an inferential step. That goes on until the last conclusion is reached. Guided by the text, we go through small inferential steps; in each one, we go (...) through an autonomous reasoning process linking the premise to the conclusion. The reasoning process is accompanied by a metareasoning process. Metareasoning gives rise to a feeling-knowing of correctness. In each step/cycle of the proof, we have a feeling-knowing of correctness. Overall, we reach a feeling of correctness for the whole proof. We suggest that this approach allows us to address the issues of how a proof functions, for us, as an enabler to ascertain the correctness of its argument and how we ascertain this correctness. (shrink)

While Einstein considered that sub specie astern the correct philosophical position regarding geometry was that of the conventionality of geometry, he felt that provisionally it was necessary to adopt a non-conventional stance that he called practical geometry. here we will make the case that even when adopting Einstein’s views we must conclude that practical geometry is conventional after all. Einstein missed the fact that the conventionality of simultaneity leads to a conventional element in the chrono-geometry, since it corresponds to the (...) possibility of different space-time metrics. (shrink)

It has been argued in relation to Old Babylonian mathematical procedure texts that their validity or correctness is self-evident. One “sees” that the procedure is correct without it having, or being accompanied by, any explicit arguments for the correctness of the procedure. Even when agreeing with this view, one might still ask about how is the correctness of a procedure articulated? In this work, we present an articulation of the correctness of ancient Egyptian and Old Babylonian mathematical procedure texts – (...) mathematical texts presenting the solution of problems. We endeavor to make explicit and explain how and why the procedures are reliable over and above the fact that their correctness is intuitive. (shrink)

A perverted space-time geodesy results from the idea of variable rods and clocks, whose length and rates are taken to be affected by the gravitational field. By contrast, what we might call a concrete geodesy relies on the idea of invariable unit-measuring rods and clocks. Indeed, this is a basic assumption of general relativity. Variable rods and clocks lead to a perverted geodesy, in the sense that a curved space-time may be seen as a result of a departure from the (...) Minkowskian space-time as an effect of the gravitational field on the rate of clocks and the length of rods. In the case of a concrete geodesy, we have a curved space-time “directly”, the curvature of which can be determined using (invariable) unit-measuring rods and clocks. In this paper, we will make the case for the plausibility of the claim that Einstein’s views on geometry in relation to general relativity are permeated by a perverted geodesy. (shrink)

Archimedes’ statics is considered as an example of ancient Greek applied mathematics; it is even seen as the beginning of mechanics. Wilbur Knorr made the case regarding this work, as other works by him or other mathematicians from ancient Greece, that it lacks references to the physical phenomena it is supposed to address. According to Knorr, this is understandable if we consider the propositions of the treatise in terms of purely mathematical elaborations suggested by quantitative aspects of the phenomena. In (...) this paper, we challenge Knorr’s view, and address propositions of Archimedes’ statics in their relation to physical phenomena. (shrink)

Une géodésie spatio-temporelle pervertie résulte des notions de règles et d’horloges variables, qui sont prises pour avoir leur longueur et leur rythme affectés par le champ gravitationnel. D’autre part ce que nous pourrions appeler une géodésie concrète repose sur les notions de règles et d’horloges invariables de mesure d’unité. En fait, il s’agit d’une hypothèse de base de la relativité générale. Les règles et les horloges variables conduisent à une géodésie pervertie dans le sens où un espace-temps courbe pourrait être (...) vu comme provenant du départ de l’espace-temps Minkowskien comme un effet du champ gravitationnel sur le rythme d’horloges et la longueur des règles. Dans le cas d’une géodésie concrète, nous avons « directement » un espace-temps courbe dont la courbure peut être déterminée en utilisant des règles et des horloges de mesure d’unité (invariables). Dans cet article, nous défendrons la plausibilité que le point de vue d’Einstein sur la géométrie par rapport à la relativité générale est imprégné par une géodésie pervertie. (shrink)

When adopting a sound logical system, reasonings made within this system are correct. The situation with reasonings expressed, at least in part, with natural language is much more ambiguous. One way to be certain of the correctness of these reasonings is to provide a logical model of them. To conclude that a reasoning process is correct we need the logical model to be faithful to the reasoning. In this case, the reasoning inherits, so to speak, the correctness of the logical (...) model. There is a weak link in this procedure, which we call the faithfulness problem: how do we decide that the logical model is faithful to the reasoning that it is supposed to model? That is an issue external to logic, and we do not have rigorous formal methods to make the decision. The purpose of this paper is to expose the faithfulness problem (not to solve it). For that purpose, we will consider two examples, one from the geometrical reasoning in Euclid’s Elements and the other from a study on deductive reasoning in the psychology of reasoning. (shrink)

in this paper we return to Marshall Clagett’s view about the existence of an ancient Greek geometry of motion. It can be read in two ways. As a basic presentation of ancient Greek geometry of motion, followed by some aspects of its further development in landmark works by Galileo and Newton. Conversely, it can be read as a basic presentation of aspects of Galileo’s and Newton’s mathematics that can be considered as developments of a geometry of motion that was first (...) conceived by ancient Greek mathematicians. (shrink)

The purpose of this work is to address the relation existing between ancient Greek practical geometry and ancient Greek pure geometry. In the first part of the work, we will consider practical and pure geometry and how pure geometry can be seen, in some respects, as arising from an idealization of practical geometry. From an analysis of relevant extant texts, we will make explicit the idealizations at play in pure geometry in relation to practical geometry, some of which are basically (...) explicit in definitions, like that of segments in Euclid’s Elements. Then, we will address how in pure geometry we, so to speak, “refer back” to practical geometry. This occurs in two ways. One, in the propositions of pure geometry. The other, when applying pure geometry. In this case, geometrical objects can represent practical figures like, e.g., a practical segment. (shrink)

When modeling informal proofs like that of Euclid’s Elements using a sound logical system, we go from proofs seen as somewhat unrigorous – even having gaps to be filled – to rigorous proofs. However, metalogic grounds the soundness of our logical system, and proofs in metalogic are not like formal proofs and look suspiciously like the informal proofs. This brings about what I am calling here the groundedness problem: how can we decide with certainty that our metalogical proofs are rigorous (...) and sustain our logical system? In this paper, I will expose this problem. I will not try to solve it here. (shrink)

Esse artigo, apresentado previamente em conferência no VIII Colóquio Internacional Schopenhauer, tem por objetivo expor o surgimento e as transformações da psicologia moral na obra de Schopenhauer, desde seu início nos anos de formação até o fim de sua produção intelectual, como requisito prévio para indicar sua função preparatória para o surgimento das psicologias de Paul Rée e Friedrich Nietzsche que com ela confrontam-se paralelamente. Palavras-chave: Psicologia, Caráter, móbeis da vontade.

Die "Consolatio philosophiae" von Boethius war im Mittelalter ausserordentlich verbreitet. Als eines der wichtigsten Werke der mittelalterlichen Ethik und zugleich Schullektüre wurde sie häufig kommentiert und in die Volkssprachen übertragen. Die in MS. Hamilton 46 der Bodleian Library, Oxford, überlieferte, 1465 abgefasste Übersetzung ist eine von insgesamt vier noch erhaltenen deutschsprachigen Versionen der Trostschrift, die in der 2. Hälfte des 15. Jahrhunderts unabhängig voneinander entstanden sind. Nur im Oxforder Codex wird die deutsche Übersetzung mit ihrer lateinischen Vorlage samt lateinischer Glossen (...) überliefert. Dadurch ist eine einzigartige Grundlage gegeben, von der aus die Arbeitsweise und Intention des Übersetzers genau untersucht werden kann. In der vorliegenden Publikation wird der Boethius-Text der Hamiltoner Handschrift, der sich aus Grund-, Paratext und deutscher Übersetzung zusammensetzt und im Original nur sehr schwer zu lesen ist, zum ersten Mal in Form einer wissenschaftlichen Edition und Studie zugänglich gemacht. Der synoptischen Edition des lateinischen Basistextes samt vielschichtiger Glossen und der deutschen Fassung folgen ein vergleichender Kommentar und zwei Glossare, welche jeweils Übersetzungstechniken und Wortschatz eingehend erschliessen. Der Edition vorausgeschickt ist eine Studie, die sich mit der Sprache und Provenienz der Übertragung, ihrem Entstehungs- und Verwendungskontext, ihrer Stellung innerhalb der deutschen "Consolatio"-Tradition, ihrer Abhängigkeit vom lateinischen Text und den Glossen, mit dem lateinischen Grund- und Paratext sowie den unterschiedlichen Textherstellungsphasen detailliert befasst."--Page 4 of cover. (shrink)

ABSTRACT In Einstein’s physical geometry, the geometry of space and the uniformity of time are taken to be non-conventional. However, due to the stipulation of the isotropy of the one-way speed of light in the synchronization of clocks, as it stands, Einstein’s views do not seem to apply to the whole of the Minkowski space-time. In this work we will see how Einstein’s views can be applied to the Minkowski space-time. In this way, when adopting Einstein’s views, chronogeometry is a (...) physical chronogeometry. (shrink)

The received view in philosophical studies of quantum field theory is that Feynman diagrams are simply calculational devices. Alongside this view we have the one that takes virtual quanta to be also simply formal tools. This received view was developed and consolidated in philosophy of physics by Mario Bunge, Paul Teller, Michael Redhead, Robert Weingard, Brigitte Falkenburg, and others. In this article I present an alternative to the received view.

Quantum electrodynamics presents intrinsic limitations in the description of physical processes that make it impossible to recover from it the type of description we have in classical electrodynamics. Hence one cannot consider classical electrodynamics as reducing to quantum electrodynamics and being recovered from it by some sort of limiting procedure. Quantum electrodynamics has to be seen not as a more fundamental theory, but as an upgrade of classical electrodynamics, which permits an extension of classical theory to the description of phenomena (...) that, while being related to the conceptual framework of the classical theory, cannot be addressed from the classical theory. (shrink)

Apresentam-se os resultados clínicos principais de uma primeira investigação efectuada a familiares de doentes sob tratamento paliativo no domicílio da área de Lisboa, com o instrumento de medida da satisfação SERVQUAL Modificado. Dos 58 familiares/doentes que responderam ao questionário apenas uma minona estava insatisfeita (uma classe de 5 indivíduos mostra-se francamente insatisfeita), uma classe de 15 estava moderadamente satisfeita, havendo 38 individuos fortemente satisfeitos com a qualidade e prontidäo dos serviços prestados. Porém urna percentagem elevada de doentes, segundo a opinião (...) retrospectiva dos cuidadores, faleceu com sintomatologia agravada, nomeadamente dores (60%), obstipação (67%) e depressão/ansiedade (43%). Discute-se a consistência e validade do questionáno SERVQUAL Modificado, contextualizam-se os resultados no que é o standard da prática da MCP e integram-se na promoção da dignidade humana no fim da vida. We present the main clinical findings of research on palliative home care, carried out among relatives of patients in the Lisbon area. An adapted version of SERVQUAL was used. Of a total of 58 carers surveyed only a small number (5) was unsatisfied 15 were only moderately satisfied. 38 family carers were strongly satisfied with the services. Yet, a high percentage of patients, as viewed in retrospect by their relatives died with some aggravated symptoms: 60% with more pain, 67% constipation, and 43% anxiety/depression. We discuss the consistency and validity of this adapted SERVQUAL tool and the main results are contextualized beanng in mind the standard practice of palliative medicine and the pursuit of human dignity in death. (shrink)

The purpose of this work is to address what notion of geometrical object and geometrical figure we have in different kinds of geometry: practical, pure, and applied. Also, we address the relation between geometrical objects and figures when this is possible, which is the case of pure and applied geometry. In practical geometry it turns out that there is no conception of geometrical object.

In this work we will consider gauge interpretations of the conventionality of simultaneity as developed initially by Anderson and Stedman, and later by Rynasiewicz. We will make a critical reassessment of these interpretations in relation to the “tradition” as developed in particular by Reichenbach, Grünbaum, and Edwards. This paper will address different issues, including: the relation between these two gauge interpretations; what advantages or defects these gauge approaches might have; how “new” Rynasiewicz’s approach in relation to the previous ones is; (...) how much of the gauge interpretation Rynasiewicz actually applies to deal with objections to the conventionality of simultaneity thesis. The conclusion is that the gauge interpretations, in their current formulation, do not provide a better “rationale” of the conventionality of simultaneity thesis that supersedes the “tradition”. (shrink)

In this work, we consider the views of three exponents of major areas of linguistics – Levelt (psycholinguistics), Jackendoff (theoretical linguistics), and Gil (field linguistics) – regarding the issue of the universality or not of the conceptual structure of languages. In Levelt’s view, during language production, the conceptual structure of the preverbal message is language-specific. In Jackendoff’s theoretical approach to language – his parallel architecture –, there is a universal conceptual structure shared by all languages, in contradiction to Levelt’s view. (...) In Gil’s work on Riau Indonesian, he proposes a conceptual structure that is quite different from that of English, adopted by Jackendoff as universal. We find no reason to disagree with Gil’s view. In this way, we take Gil’s work as vindicating Levelt’s view that during language production preverbal messages are encoded with different conceptual structures for different languages. (shrink)

Philosophy of Physics has emerged recently as a scholarly important subfield of philosophy of science. However outside the small community of experts it is not a well-known field. It is not clear even to experts the exact nature of the field: how much philosophical is it? What is its relation to physics? In this work it is presented an overview of philosophy of physics that tries to answer these and other questions.

A re-evaluation of the notion of vacuum in quantum electrodynamics is presented, focusing on the vacuum of the quantized electromagnetic field. In contrast to the ‘nothingness’ associated to the idea of classical vacuum, subtle aspects are found in relation to the vacuum of the quantized electromagnetic field both at theoretical and experimental levels. These are not the usually called vacuum effects. The view defended here is that the so-called vacuum effects are not due to the ground state of the quantized (...) electromagnetic field. Nevertheless it is possible to maintain an empirically demonstrable notion of vacuum state that is consistent with the interpretation of the formalism of the theory. (shrink)

In this paper, we will make explicit the relationship that exists between geometric objects and geometric figures in planar Euclidean geometry. That will enable us to determine basic features regarding the role of geometric figures and diagrams when used in the context of pure and applied planar Euclidean geometry, arising due to this relationship. By taking into account pure geometry, as developed in Euclid’s Elements, and practical geometry, we will establish a relation between geometric objects and figures. Geometric objects are (...) defined in terms of idealizations of the corresponding figures of practical geometry. We name the relationship between them as a relation of idealization. This relation, existing between objects and figures, is what enables figures to have a role in pure and applied geometry. That is, we can use a figure or diagram as a representation of geometric objects or composite geometric objects because the relation of idealization corresponds to a resemblance-like relationship between objects and figures. Moving beyond pure geometry, we will defend that there are two other ‘layers’ of representation at play in applied geometry. To show that, we will consider Euclid’s Optics. (shrink)