In this work we will deal with ellipses and ovals, comparing them both from the geometric point of view and from the one of applications. There is a notable similarity between these curves so often it’s not possible to recognize which of the two figures is, unless we consider other elements to distinguish them. We will show the presence of both curves in architectural works and in treatises, motivating their use, when it’s possible, with geometric and technological considerations.

The essay argues for a nuanced understanding of the notorious dissonance between Derrida and Agamben despite their shared interest in troubling the metaphysical separation between human and animal. I argue that a close scrutiny of their differing strategies towards the matrix of framing issues (such as sovereignty and violence) is salient for keeping the ontological question of species difference open. I suggest that the dissonance between the two thinkers is best understood in relation to systemic and rhetorical effects—namely, the encompassing (...) figure of the circle that structures sovereignty, and the rhetoric of hyperbole that disfigures the circle into an ellipse and the line. This ironic interplay appears through their mutually dissonant readings of the localization of life (human and animal) and the situation of power and violence in relation to sovereignty. (shrink)

The essay argues for a nuanced understanding of the notorious dissonance between Derrida and Agamben despite their shared interest in troubling the metaphysical separation between human and animal. I argue that a close scrutiny of their differing strategies towards the matrix of framing issues is salient for keeping the ontological question of species difference open. I suggest that the dissonance between the two thinkers is best understood in relation to systemic and rhetorical effects—namely, the encompassing figure of the circle that (...) structures sovereignty, and the rhetoric of hyperbole that disfigures the circle into an ellipse and the line. This ironic interplay appears through their mutually dissonant readings of the localization of life and the situation of power and violence in relation to sovereignty. (shrink)

En 1676, alors qu'il sejourne encore a Paris, Leibniz entreprend de composer un volumineux traite qui restera sans doute l'un de ses ecrits mathematiques les plus fortement charpentes: La quadrature arithmetique du cercle, de l'ellipse et de l'hyperbole et la trigonometrie sans tables qui en est le corollaire. Ce traite se presente comme un abrege exhaustif de la geometrie infinitesimale, dont Leibniz avait pu esperer qu'elle lui ouvrirait les portes de l'Academie des Sciences. Cependant, contraint de quitter la capitale (...) avant sa publication, il abandonnera derriere lui un ouvrage qui n'allait voir le jour qu'en 1993. Le probleme de la quadrature est pretexte a soulever plusieurs enjeux capitaux tant pour les mathematiques que pour la philosophie. Il permet notamment a Leibniz d'examiner avec une grande precision la question de la methode, des fondements, ainsi que des notions cruciales de rigueur et d'infini, tout en mettant en evidence leurs applications pratiques. Si la presente edition de ce texte foisonnant ne reproduit pas l'integralite des variantes, elle en propose une version corrigee et annotee, qui s'accompagne d'une traduction francaise en regard. (shrink)

This article examines the 19th and 20th century European context wherein religion was practiced. In a 'Rip-Van-Winkle' manner it is as if this context had no influence on the Afrikaans speaking church in South Africa. The isolation, that was the result of the apartheid ideology, lead to the Afrikaans speaking church in South Africa not internalising ecumenicity. It is argued that for the church to be able to take an active role in reconciling diversity and therefore contributing to social cohesion (...) in South Africa, the church needs to transcend being a 'nation' church. This is possible by respecting culture and diversity, while recognising the priority of salvation in Christ. This is the ellipse of being church. (shrink)

The little francophone community of Port-au-Port Peninsula in Newfoundland is particularly representative of non-standard French spoken in North America. This paper tries to elaborate a grammatical analysis in order to justify the transcriptions of verb forms in the Dictionnaire des régionalismes de Terre-Neuve. In the sentence “I passait les maisons, [bladʒe] ac le monde”, for instance, [bladʒe] could be interpreted as “blaguait” or “blaguer.” In standard French, the same sentence could be translated as “il allait de porte en porte parler (...) avec les gens” or “il allait de porte en porte, parlait avec les gens.” The omission of the subject pronoun seems to allow the transition toward a unmarked verb form either under a short form, limited to the radical of the verb, without any flexional mark like an imperative form, or a full form, like what Remacle calls “infinitif substitut.” The last stade of this evolution is the nominal phrase, whose use is widely spread in popular French, where it often follows a verb phrase. (shrink)

This article addresses Paul Churchland’s attempt to identify colors with surface reflectance spectra. Of particular concern is Churchland’s novel method of approximating surface reflectance spectra. While those approximations are generated by objective means and yield a striking match with human phenomenological color space, they are not physically meaningful. The reason for this is that the method used to produce the approximations induces equivalence classes on surface reflectances that are not invariant under physically appropriate changes of measurement convention. This result undermines (...) Churchland’s proposed response to the objection from metamers commonly raised against color physicalism, as his surface reflectance approximations are supposed to provide an objective, physical unifying basis for metamers. *Received December 2007; revised July 2009. †To contact the author, please write to: Department of Logic and Philosophy of Science, School of Social Sciences, 3151 Social Science Plaza A, University of California, Irvine, CA 92697; e‐mail: [email protected]. (shrink)

In 1596, in the Mysterium Cosmographicum, a twenty-five-year-old Johannes Kepler rashly banished lines from the universe. They “scarcely admit of order,” he wrote, and God himself could have no use for them in this “well-ordered universe.” Twenty-five years later, though, Kepler had come to repent the temerity of his youth. “O male factum!” he lamented in a 1621 second edition of the Mysterium – “O what a mistake” it was to dismiss lines, for linearity is revealed in those most perfect (...) and divine motions – the revolutions of the heavenly orbs. Why did Kepler come to lament the rashness of his youth? The answer lies deep in the details of Kepler’s discovery of elliptical orbits in 1605. Kepler struggled to find an empirically adequate description and physically plausible explanation of Mars’s path through the heavens. He realized, though, that his originally spherical notion of location and direction were insufficient to reconcile descriptions and explanations of the planet’s motion. Crucially inspired by the “magnetic philosophy” of William Gilbert, Kepler adopted an oriented conception of space, which finally allowed a plausible mechanism to be constructed for elliptical motion – the true path of the planet. Yet, this oriented space required the stipulation of straight lines. Without straight lines, even God could not construct the planets’ elliptical orbits. (shrink)

Comment une connaissance objective est-elle possible pour une subjectivité ? Telle pourrait être la question à l’origine de la tentative husserlienne visant à fournir une fondation objective de la connaissance. Telle semble être également la question qui anime, de façon sous-jacente, toute philosophie de la connaissance. La phénoménologie de Husserl a pris tout d’abord la forme d’une Erkenntnistheorie. Autour du sens et de la portée de ce geste, primitif et fondateur, le livre de Laurent Joum..

Cet article traite de la catégorie des pronoms, de sa définition et de la distinction entre les pronoms et les déterminants. L'article débute par un examen de la définition traditionnelle et étymologique du pronom comme mot mis « à la place d'un nom », une définition bien peu adaptée puisque seuls certains pronoms, par exemple, peuvent avoir un fonctionnement anaphorique. Une redéfinition est ensuite proposée, faisant des pronoms une classe fermée de noms grammaticaux qui ne prennent pas de déterminant et (...) dont les membres centraux s'emploient typiquement de façon anaphorique ou déictique. La dernière partie de l'article porte sur la distinction entre les pronoms et les déterminants et certains problèmes qui y sont liés, tels que l'ellipse nominale. Il y est argué que les déterminants sont eux aussi des noms grammaticaux, mais que le maintien d'une distinction déterminant vs pronom est motivé et descriptivement utile au regard d'au moins certains des mots concernés, à commencer par les articles et les pronoms personnels. (shrink)

Life and the living (on Aristotelian biohorror) -- Supernatural horror as the paradigm for life -- Aristotle's De anima and the problem of life -- The ontology of life -- The entelechy of the weird -- Superlative life -- Life with or without limits -- Life as time in Plotinus -- On the superlative -- Superlative life I: Pseudo-Dionysius -- Negative vs. affirmative theology -- Superlative negation -- Negation and preexistent life -- Excess, evil, and non-being -- Superlative life II: (...) Eriugena -- Negation in the periphyseon -- The quaestio de nihilo: on nothing -- The quaestio de nihilo: superlative nothing -- Dark intelligible abyss -- Apophasis -- The apophatic logic -- Negation in Frege and Ayer -- Negation vs. subtraction in Badiou -- Negation and contradiction in Priest -- The dialetheic vitalism of negative theology -- Ellipses: Suhraward and the luminous void -- Univocal creatures -- On spiritual creatures -- Life as form in Aristotle -- The concept of the creature -- Univocity I: Duns Scotus vs. Aquinas -- Univocity in Aquinas' Summa theologica -- Univocity in Duns Scotus' Opus oxoniense -- The common nature of the creature -- Univocity II: Duns Scotus vs. Henry of Ghent -- Univocity in Henry of Ghent -- Negative vs. privative indetermination -- Absolute indetermination -- Univocity III: Deleuze's scholasticism three variations -- Spinoza et le problème de l'expression -- Différence et répétition -- Cours de Vincennes -- Univocal creatures -- Ellipses: Dgen and uncreated univocity -- Dark pantheism -- Everything and nothing -- Life as spirit in Aquinas -- The concept of the divine nature -- Immanence I: Eriugena's periphyseon -- Natura and the unthought -- Universal life -- Four statements on pantheism -- Immanence II: Duns Scotus' reportatio Ia -- Univocal immanence -- Actual infinity -- The pathology of the triple primacy -- Immanence III: Nicholas of Cusa's De docta ignorantia -- The coincidence of opposites -- The folds of life -- Absolute vs. contracted pantheism -- Speculative pantheism (Deleuze's interlocutors) -- Pantheism and pure immanence -- The insubordination of immanence in Deleuze -- Scholia I: the isomorphism of univocity and immanence -- Scholia II: the vitalist logic of common notions -- Scholia III: the life of substance -- Dark pantheism -- Ellipses: Wang Yangming and idealist naturalism -- Logic and life (on Kantian teratology) -- The wandering line from Aristotle to Kant -- Critique of life -- Spectral life and speculative realism -- Ontotheology in Kant, atheology in Bataille -- The night land. (shrink)

You can perceive things, in many respects, as they really are. For example, you can correctly see a coin as circular from most angles. Nonetheless, your perception of the world is perspectival. The coin looks different when slanted than when head-on, and there is some respect in which the slanted coin looks similar to a head-on ellipse. Many hold that perception is perspectival because you perceive certain properties that correspond to the “looks” of things. I argue that this view (...) is misguided. I consider the two standard versions of this view. What I call the PLURALIST APPROACH fails to give a unified account of the perspectival character of perception, while what I call the PERSPECTIVAL PROPERTIES APPROACH violates central commitments of contemporary psychology. I propose instead that perception is perspectival because of the way perceptual states are structured from their parts. (shrink)

Arguably the most foundational principle in perception research is that our experience of the world goes beyond the retinal image; we perceive the distal environment itself, not the proximal stimulation it causes. Shape may be the paradigm case of such “unconscious inference”: When a coin is rotated in depth, we infer the circular object it truly is, discarding the perspectival ellipse projected on our eyes. But is this really the fate of such perspectival shapes? Or does a tilted coin (...) retain an elliptical appearance even when we know it’s circular? This question has generated heated debate from Locke and Hume to the present; but whereas extant arguments rely primarily on introspection, this problem is also open to empirical test. If tilted coins bear a representational similarity to elliptical objects, then a circular coin should, when rotated, impair search for a distal ellipse. Here, nine experiments demonstrate that this is so, suggesting that perspectival shapes persist in the mind far longer than traditionally assumed. Subjects saw search arrays of three-dimensional “coins,” and simply had to locate a distally elliptical coin. Surprisingly, rotated circular coins slowed search for elliptical targets, even when subjects clearly knew the rotated coins were circular. This pattern arose with static and dynamic cues, couldn’t be explained by strategic responding or unfamiliarity, generalized across shape classes, and occurred even with sustained viewing. Finally, these effects extended beyond artificial displays to real-world objects viewed in naturalistic, full-cue conditions. We conclude that objects have a remarkably persistent dual character: their objective shape “out there,” and their perspectival shape “from here.”. (shrink)

When viewing a circular coin rotated in depth, it fills an elliptical region of the distal scene. For some, this appears to generate a two-fold experience, in which one sees the coin as simultaneously circular (in light of its 3D shape) and elliptical (in light of its 2D ‘perspectival shape’ or ‘p-shape’). An energetic philosophical debate asks whether the latter p-shapes are genuinely presented in perceptual experience (as ‘perspectivalists’ argue) or if, instead, this appearance is somehow derived or inferred from (...) experience (as ‘anti-perspectivalists’ argue). This debate, however, has largely turned on introspection. In a recent study, Morales, Bax, and Firestone (2020) aim to provide the first empirical test of this question. They asked subjects to find an elliptical coin seen face-on from a search array that also included a circular coin seen either face-on or at an angle. They found that subjects reacted more slowly when the distracting circle was seen at an angle, such that it’s p-shape matched that of the target ellipse. From this, they concluded that the similar p-shape between the ellipse and circle constituted a phenomenal similarity between the two, and thus that perspectivalism is true. We show that these results can also be explained by pre-attentive guidance by unconscious representations (in what follows, just “unconscious pre-attentive guidance”) and that this explanation is at least as plausible as one from phenomenal similarity. Thus, we conclude that the experiment does not support perspectivalism over anti-perspectivalism. (shrink)

Shape and slant judgments of rotated or frontoparallel ellipses were elicited from three groups of 10 subjects. A masking stimulus was introduced to control processing time. Backward masking trials were presented with interstimulus intervals of 0, 25, and 50 msec, Reduction of processing time altered shape judgments in the direction of projective shape and slant judgments in the direction of frontoparallelness. This finding is consistent with the shape-slant invariance hypothesis. In order to study the effects of processing load, one group (...) of subjects was given prior knowledge of the kind of judgment to be made on each trial, one group had no prior knowledge, and a third group made both judgments on each trial. The effects of the processing load manipulation were interpreted in terms of the role of attention in perceptual encoding. Consistent with previous findings, allocation of attention did not affect perceptual encoding. (shrink)

Twelve subjects provided shape and orientation judgments for a set of projectively equivalent, variously rotated rectangles under three viewing conditions—monoptic, dichoptic, and binocular—with and without the presence of a pattern mask. In the absence of the mask, partial constancy was exhibited under the first two conditions and near perfect constancy under the binocular condition. Orientation was discriminated. Presence of the mask produced projective shape matching and diminished orientation discrimination. It is argued that the site of masking was postchiasmal, and the (...) results are related to previous work with pattern masking of projectively equivalent ellipses. (shrink)

In contrast with some recent theories of infinitesimals as non-Archimedean entities, Leibniz’s mature interpretation was fully in accord with the Archimedean Axiom: infinitesimals are fictions, whose treatment as entities incomparably smaller than finite quantities is justifiable wholly in terms of variable finite quantities that can be taken as small as desired, i.e. syncategorematically. In this paper I explain this syncategorematic interpretation, and how Leibniz used it to justify the calculus. I then compare it with the approach of Smooth Infinitesimal Analysis, (...) as propounded by John Bell. I find some salient differences, especially with regard to higher-order infinitesimals. I illustrate these differences by a consideration of how each approach might be applied to propositions of Newton’s Principia concerning the derivation of force laws for bodies orbiting in a circle and an ellipse. “If the Leibnizian calculus needs a rehabilitation because of too severe treatment by historians in the past half century, as Robinson suggests (1966, 250), I feel that the legitimate grounds for such a rehabilitation are to be found in the Leibnizian theory itself.”—(Bos 1974–1975, 82–83). (shrink)

When a circular coin is rotated in depth, is there any sense in which it comes to resemble an ellipse? While this question is at the center of a rich and divided philosophical tradition (with some scholars answering affirmatively and some negatively), Morales et al. (2020, 2021) took an empirical approach, reporting 10 experiments whose results favor such perspectival similarity. Recently, Burge and Burge (2022) offered a vigorous critique of this work, objecting to its approach and conclusions on both (...) philosophical and empirical grounds. Here, we answer these objections on both fronts. We show that Burge and Burge’s critique rests on misunderstandings of Morales et al.’s claims; of the relation between the data and conclusions; and of the philosophical context in which the work appears. Specifically, Burge and Burge attribute to us a much stronger (and stranger) view than we hold, involving the introduction of “a new entity” located “in some intermediate position(s) between the distal shape and the retinal image.” We do not hold this view. Indeed, once properly understood, most of Burge and Burge’s objections favor Morales et al.’s claims rather than oppose them. Finally, we discuss several questions that remain unanswered, and reflect on a productive path forward on these issues of foundational scientific and philosophical interest. (shrink)

The first obstacle that confronts the student of induction is that of defining the subject matter. One initial point is to note that much of the relevant subject matter goes under the description ‘the theory of confirmation’. The distinction is primarily that the study of induction concerns inference, i.e. cases where one takes the conclusion to be established by the evidence, whereas confirmation concerns the weight of evidence, which one may take to be something like the credibility of a hypothesis (...) in the light of the evidence. Discussions of confirmation often concern incremental confirmation, i.e. cases where the evidence is taken to increase the credibility of some hypothesis, even if not sufficiently to warrant inferring the truth of that hypothesis. However, some uses of ‘confirmation’ clearly refer to absolute confirmation, cases where the credibility of the hypothesis in the light of the evidence exceeds some (high) threshold. One may ask whether inductive inference corresponds to the case of absolute confirmation for some suitable threshold. I shall discuss inference and confirmation together, though it should be noted that some approaches eschew inference altogether. For example, the Bayesian takes scientific reasoning to be a matter of adjusting credences in propositions in the light of evidence, and says nothing about unqualified belief in a proposition. However, if we are interested in inductive knowledge then we must consider inference, since only then do we have a detached proposition that is the possible content of a mental state of knowing. A more pressing question concerns which inferences (or allegedly confirmatory relations) should be classed as inductive. A natural and straightforward approach is to define induction as encompassing any form of reasoning that extrapolates from one population to another, usually from a sample of a population to the whole population. For example, one might note that all observations of the position of some planet fall on an ellipse that has the Sun at one of its foci; from this one concludes that all the positions that planet takes fall on this ellipse (i.e.. (shrink)

Not the least admirable of the late David Lewis’s attributes was his disdain for technical terminology and jargon. His writings are a model demonstrating that, with skill and care, it is possible to discuss even the most mathematical aspects of logic and semantics in clear English prose, and with only a minimum of symbolism. The main text of Parts of Classes [1, hereafter: PoC], a 120-page essay on the foundations of set theory, follows Aristotle in using letters as variables, and (...) has a few dashes and ellipses where it mentions schemata, but is otherwise free of logical notation. The essential advantages of what Church called “the logistic method” do not depend on its typographical accidents!) It is only natural that writers following him have taken one of his expressive words and turned it into a technical term: he allowed ‘atomless gunk’ as a possible complication in the mereological analysis of things, and ‘gunk’ is now a technical term in mereology. Gunk is stuff every part of which contains further parts, stuff which can be divided endlessly without ever arriving at an indivisible atom. (shrink)

Several studies have demonstrated that individuals’ ability to perceive a speech sound contrast is related to the production of that contrast in their native language. The theoretical account for this relationship is that speech perception and production have a shared multimodal representation in relevant sensory spaces. This gives rise to a prediction that individuals with more narrowly defined targets will produce greater separation between contrasting sounds, as well as lower variability in the production of each sound. However, empirical studies that (...) tested this hypothesis, particularly with regard to variability, have reported mixed outcomes. The current study investigates the relationship between perceptual ability and production ability, focusing on the auditory domain. We examined whether individuals’ categorical labeling consistency for the American English /ε/–/æ/ contrast, measured using a perceptual identification task, is related to distance between the centroids of vowel categories in acoustic space and to two measures of production variability: the overall distribution of repeated tokens for the vowels and the proportional within-trial decrease in variability as defined as the magnitude of self-correction to the initial acoustic variation of each token. No significant associations were found between categorical labeling consistency and vowel contrast distance, between categorical labeling consistency and area of the ellipse, or between categorical labeling consistency and centering ratio. These null results suggest that the perception-production relation may not be as robust as suggested by a widely adopted theoretical framing in terms of the size of auditory target regions. However, the present results may also be attributable to choices in implementation that should be subject to further investigation. (shrink)

This edition of _Leviathan_ is intended to provide the reader with a modestly abridged text that is straightforward and accessible, while preserving Hobbes' main lines of argument and of thought. It is meant for those who wish to focus primarily on the philosophical aspects of the work, apart from its stylish but often daunting early modern prose. The editors have updated language, style, punctuation, and grammar throughout. Very long, complicated sentences have been broken into two or more sentences for enhanced (...) readability. In some instances, terms within a sentence are rearranged for enhanced clarity. Occasionally, an equivalent contemporary word is substituted for an archaic one. Ellipses indicate omissions of more than one sentence. Care has been taken to maintain the strength, nuance, and flavor of the work, especially of Hobbes' most difficult arguments. In addition, the volume offers a general Introduction and concise headnotes to each chapter. Annotation is geared to the student or novice reader. A glossary of key terms is also included, as well as an index. (shrink)

It is frequently alleged that a round plate viewed from an oblique angle looks elliptical, and that when one tree is in front of another that is the same intrinsic size, the front one looks larger than the rear one. And yet there is also a clear sense in which the plate viewed from an angle looks round, and a clear sense in which the two trees look to be the same size. According to the Dual Content Theory (DCT), what (...) explains these and other similar phenomena is that perceptual experiences present us with two different sorts of spatial properties: intrinsic and perspectival spatial properties. I will argue that the Dual Content Theory is false because it rests on flawed phenomenological descriptions of the experience of spatial properties. The only conditions under which a plate tilted away and an ellipse look alike, or two objects which are different in size look the same size, is when at least one of the objects being compared is misperceived. I will consider several responses to the arguments I present, and conclude by suggesting that abandoning DCT would constitute an improvement upon Noë’s enactive theory of perception. (shrink)