Der Begriff Research Articles

Ferdinand Christian Baur on Religion: A Historicist Approach in an Idealist Context

In this article, I consider F.C. Baur’s conception of religion. This has rarely been done because Baur is generally regarded as a historical theologian rather than a theorist of religion. Yet I argue that, if we observe Baur’s own historical work, we discover there a remarkably original conceptual work on the notion of religion. For Baur, I argue, religion was a key concept, in that it aided him in his attempt to bring together theological, historical, and philosophical work. Yet the concept of religion had to be of a particular kind in order to suit his agenda. Therefore, the identification of Baur’s concept of religion will also help ascertain the coherence of his intellectual activity. In the article, I focus on two of Baur’s works, his first monograph, Symbolik und Mythologie (1824/5) and his magisterial Die christliche Gnosis (1835). I show that fundamental ideas across these two books should be seen as Baur’s own (rather than merely borrowed from Schleiermacher and Hegel), and that there is more continuity between them than readers have often found. In a final section, I discuss briefly an essay Baur devoted to the Begriff der Religionsphilosophie (1837).

Excavating Memory: Bilge Karasu's Istanbul and Walter Benjamin's Berlin

Excavating Memory: Bilge Karasu's Istanbul and Walter Benjamin's Berlin

Die Diskussion zwischen Jos\xe9 Gaos und Luis Villoro \xfcber den Begriff der Lebenswelt\u2014\ufeffKritische Auswertung einer entscheidenden Episode der Rezeptionsgeschichte von Husserls Ph\xe4nomenologie in Spanien und Mexiko

Die vorliegende Arbeit thematisiert eine sowohl im deutschen als auch im spanischen und englischen Sprachraum weitgehend unbekannte philosophische Kontroverse zweier herausragender Figuren der Rezeptionsgeschichte von Husserls Phänomenologie in Mexiko zur Zeit des spanischen republikanischen Exils. Es handelt sich um die Diskussion zwischen José Gaos und Luis Villoro über den phänomenologischen Begriff der Lebenswelt. Im ersten Teil meiner Darstellung werde ich den akademischen Kontext dieser Diskussion erörtern. Im zweiten Teil gehe ich auf die Hauptthese eines Vortrags ein, den Gaos 1963 in Mexiko-Stadt vor einem internationalen Publikum hielt und der als die erste dokumentierte Behandlung des Lebensweltbegriffs in der spanischsprachigen Philosophie gilt. Der dritte Teil behandelt Villoros Erwiderung auf Gaos’ Vortrag und die sich daraus ergebende Auseinandersetzung der beiden Philosophen. Im vierten Teil ziehe ich eine kritische Bilanz des Inhalts dieser Diskussion im Licht des aktuellen Stands der Husserlforschung. Dabei, und schließlich auch im fünften Teil, wird sich die unverkennbar radikale Bedeutung dieser Diskussion für die aktuelle phänomenologische Forschung herausstellen, insbesondere im Hinblick auf das Forschungsdesiderat einer Erklärung der systematischen Verhältnisse zwischen transzendentaler Erkenntniskritik und Lebenswelttheorie.

Theology of Carl Schmitt

The paper addresses the theology of Carl Schmitt. Schmitt often stresses his ‘natural born Catholicism.’ At the same time he also claims repeatedly not to be a theologian in the professional sense. On the other hand, his main ideas like the concept of the political (Der Begriff des Politischen), the public character of the church (Römischer Katholizimus und politische Form), and finally, his Politische Theologie II in reaction to Erik Peterson’s refutation of Politische Theologie I show that Schmitt’s ideas imply deep and problematic theological positions. The role of the katechon, or the Grand Inquisitor and his criticism of Peterson’s patristic arguments, especially the rejection of the anti-Arian reasoning of Gregory Nazianzen show a markedly unorthodox theological stance reminiscent of Charles Maurras’ political Catholicism. Schmitt’s transcends patristic orthodoxy in order to apply his historically conditioned 19th-century theology to sacralizing his idea of the political.

Law and psychoanalysis: close intertwining between Hans Kelsen and Sigmund Freud

This paper offers an original analysis of the interconnections between law and psychoanalysis through the personal and academic exchanges between Hans Kelsen (1881-1973) and Sigmund Freud (1856-1939). After a brief analysis of the similar cultural background of both scholars as Jews who grew up in fin-de-siècle Vienna, the text focuses on the personal encounters between them and subsequently analyzes Kelsen's reception of Freud's work in “The State-Concept and Social-Psychology” (Der Begriff des Staates und die Sozialpsychologie). Kelsen’s text was originally published in 1922 in Freud’s review, Imago, resulting from a conference he held at the Viennese Psychoanalytical Society. This paper analyzes the relevance of Freud’s theory to the construction of the Pure Theory of Law, especially regarding his concept of the state. Furthermore, it presents a new hypothesis for the subjective reasons behind Kelsen’s attraction to psychoanalysis, and for his admiration of Freud, which it tries to understand through the personal context of Kelsen’s life. Finally, it deals with the possible influence of Kelsen on Freud's work, especially with regards to the term "Super-Ego."

Nietzsche tegenover Schmitt

Abstract Nietzsche versus Schmitt. Agonal versus political thinking This article concerns the reception of Friedrich Nietzsche by Carl Schmitt with regard to the concept of the agon. In the 1933 edition of Der Begriff des Politischen Schmitt states that there is a ‘great metaphysical opposition’ (große metaphysische Gegensatz) between his political thinking and agonal thinking, the latter of which is associated with Nietzscheans like Alfred Baeumler and Ernst Jünger. It is argued that this metaphysical opposition is best explained in light of Schmitt’s intellectual development from decisionist to concrete order thinker. Moreover, it is argued that the reception of Nietzsche’s concept of the agon by Schmitt took place through Baeumler. Nietzsche’s concept of the agon is best described as a measured productive struggle between opponents who are approximately equal to each other. In the reception of Nietzsche’s concept of the agon a shift of focus occurs from a struggle between individuals to a struggle between collectives. At the same time the social character of the agon is lost, which was expressed in the thought that the individual could only develop his talents in a struggle with others.

Ignaz Semmelweis: avictim of harassment?

SummaryIgnaz Semmelweis’ (1818–1865) discovery of the endemic causes of febris puerperalis is a striking example of the role of pathology in medicine. Transdisciplinarity encounters Semmelweis’ biography, which is neither linear nor totally focused on medicine. He completed the philosophicum (artisterium), studying the septem artes liberales (1835–1837) in Pest, comprising humanities and natural science. After moving to Vienna, he began to study law, but turned to medicine as early as 1838. In 1844, he graduated with a botanical doctoral thesis composed in Neo-Latin, showing linguistic and stylistic talent and a broad knowledge of gynecology and obstetrics. The style and topoi demonstrate the interchangeability of what he learnt during his propaedeuticum. Nowadays, hardly anyone is familiar with this booklet, for two main reasons: the language choice and the life-saving impact of the physician’s opus magnum on the reasons for puerperal fever (Die Aetiologie, der Begriff und die Prophylaxis des Kindbettfiebers). In later life, he became convinced that he had no talent as a (scientific) author—a fatal error that led him to become a victim of what we now call “publish or perish.” Semmelweis had felt rejected for years. This negative feeling was the reason for his decision not to publish his great book for 14 years. When it finally went to the printer in 1861, the scientific community did not accept it. This experience caused psychosomatic symptoms owing to his long-standing and deeply felt disappointment. Bad conscience tortured him. This permanent stress destroyed his health: in 1865, his relatives (including his wife) and friends took him from Budapest to Vienna. He thought he was going to spend some time relaxing, but in fact was led into a newly built asylum for the mentally ill, the Niederösterreichische Landesirrenanstalt. When he realized what was happening, he tried to escape. Badly abused, he died from sepsis caused by open wounds and a dirty straightjacket 2 weeks later. This article will show Semmelweis to be a multilingual author of scientific literature and (open) letters; it will present him as a researcher who became a victim of harassment and what is referred to as the “Semmelweis reflex” (“Semmelweis effect”); and it will focus on his afterlife in (children’s) literature, drama, and film.

Überlegungen zum Gutachten zu Menschenrechten und der Umwelt und zum Begriff der extraterritorialen Gerichtsbarkeit

This article examines the 2017 Inter-American Court of Human Rights advisory opinion on human rights and the environment to discuss the extraterritorial jurisdictional link developed by the Court. The article argues that this is a new jurisdictional link finding origin and justification in the recent practice of other international human rights bodies aimed at progressively enlarging the scope of states’ positive obligations to protect human rights. The article discusses these developments and flags some of the concerns arising from this new extraterritorial jurisdictional model.

Carl Schmitt: Positionen and Begriffe. The Difference Between Politics and the Political

The subject of consideration is the relationship between politics and the political, as it is presented in two dissertations by Carl Schmitt from the 1920s: the famous Der Begriff des Politischen and the most extensive work from this period – Verfassungslehre. The thesis of the article is that, contrary to the fairly widespread interpretation of both these phenomena, that is, politics in the common sense and its special form to which Carl Schmitt referred as the political, should not be treated as explanandum and explanans, but as separate, co-occurring and somewhat complementary phenomena. While politics involves state actions for the public interest, ideologically defined according to classic political categories, the political is a sphere of specific actions in the special space of relations sometimes formed between collective entities, defined by the terms enemy-friend, a space cognitively diagnosed by Carl Schmitt. The political is not a real form of politics, but a form of action in the sphere of collective life other than politics, which is essentially important for building the structure of the state. The disclosure of the political in the activities of individual countries is an important element of analysis in foreign policy, an element of analysis of a situation within international relations. Revealing the political as a kind of arcana imperi of state actions, Carl Schmitt appears not only and not primarily as a neutral theoretician of politics, but as a German national political thinker, analysing primarily the situation of Germany in relation to the Entente countries at a very special moment in the history of twentieth-century Europe.

The Problem of Individuality in Hermann Cohen’s Aesthetics

Franz Rosenzweig devoted particular attention to the problem of individuality in Hermann Cohen’s philosophy. He writes that, in comparison with the individuality of the man of religion, “the human being about which aesthetics knew [...] fades now in all its aesthetic individuality to a ‘mere type’”. This statement is actually based on Cohen’s writings: in Ästhetik des reinen Gefühls (1912), Cohen explicitly maintains that the human being that is the object of artistic representation is not a type, but rather an individual. Just three years later, however, in his first book about philosophy of religion, Der Begriff der Religion im System der Philosophie (1915), Cohen states that the human being that is represented by art is not really an individual; only the man of religion is really individual; the human being represented by art is merely a type. In this paper my aim is to argue for the thesis that these opposite statements belong to different points of view. From an aesthetic point of view the human being represented by art has to be considered as truly individual, but the systematic overview adopted in Der Begriff der Religion can teach us that the individuality of the human being represented by art can’t be maintained from a different point of view than the aesthetic one.

Blasting the past: A rereading of Walter Benjamin’s theses on the philosophy of history

The text offers a reappraisal of Walter Benjamin?s Theses on the Philosophy of History (?ber den Begriff der Geschichte; ?On the Concept of History?) from the perspective of global politics today and its similarities with the socio-economic and political situation in Europe and the Americas during the 1920s and 30s; more specifically, the impact of crises on the erosion of trust in liberal representative democracy and the concomitant rise of mostly rightwing populist movements and their strongmen leaders, aided to a significant degree by the media, ?old? and ?new? alike. The purpose of the text is to draw lessons from Benjamin?s vision of materialist historiography for our current political predicament.

Rethinking Hegel's Conceptual Realism

Readers of Hegel are frequently impressed by his seemingly idiosyncratic use of the term "the concept" (der Begriff) throughout his works. A recent wave of interpreters have held to a "conceptual realist" view, according to which Hegel uses this term to refer either to the monistic structure of reality or to indwelling essences of natural entities. In this essay, the author offers a way to avoid these conceptions of Hegel's conceptual realism by explaining his view of the "isomorphism" between concepts and the world. The isomorphism recommended, however, is metaphysically deflationary, for Hegel's conception of conceptual form creates a conceptually internal standard for the adequacy of concepts; it depends on his view of the negative relations between concepts and the objects they represent. This standard of conceptual adequacy is also "graduated" in that it allows for a lack of fit between concept and world. Nevertheless, the possibility for a "maximally isomorphic" fit between concept and world obtains through the teleological realization of concepts, which marks especially the world of human culture (law, art, religion, and so on). The author contends that some of the most seemingly exaggerated claims Hegel makes about the concept can be understood when we consider the significance Hegel ascribes to human making, which offers the best cases of maximally isomorphic concepts. But the framework here provides an interpretive key for the way Hegel sees concepts imperfectly realized in the natural world as well.

Franz Brentano's theory of judgment (1889): a critique of Aristotle's correspondence theory of truth

Abstract: The purpose of this paper is to discuss the concept of truth formulated by Franz Brentano in 1889. As a textual basis, I take Brentano's communication, presented to the philosophical community of Vienna in March 1889, entitled "On the concept of truth" (Über den Begriff der Wahrheit), and I provide a systematic exposition of Brentano's analysis of the problems surrounding the interpretation of the Aristotelian concept of truth as correspondence. My analysis explains how Brentano reinter-preted the Aristotelian concept of truth as correspondence within the conceptual framework of his descriptive psychology.

Das schwierige Verhältnis von Kulturkritik und Theorie der Kultur. Plädoyer für eine theoretische Auseinandersetzung mit dem Erbe G. Simmels in der Konzeption von ‘Kultur’

The essay argues for taking G. Simmel’s theory of culture (especially Der Begriff und die Tragödie der Kultur, 1911) as a crucial point for guidance regarding conceptional questions and fundamental problems in view of current scientific debates on “culture” – with a theoretical discussion on Simmel’s legacy which hasn’t been sufficiently carried out. Simmel’s work will be shown as a generic explanation of a way of “culture thinking” which also in the current conjuncture of the subject “culture” did not turn obsolete in the course of modern scientific alternatives. Three different scopes are in focus: the term “culture” as a subsequent term of “Geist” (considering the consequences for the relation of empiricism and theory); overcoming harmonistic views of culture (“conflict”); and the capability of the critical thought of “sense” (the objectivity of the cultural “sense”). – At the same time, the “Simmel model” reveals the herein not yet thoroughly resolved (“personalistical”) implications of unity and identity, which are rather concealed and anonymously carried further. In Simmel, they result – again as exemplary – from his tendency of being anthropologically universal in his reasoning and from his strong “philosophy of life” forms of thought.

A Weak Messianic Power: Figures of a Time to Come in Benjamin, Derrida and Celan

A Weak Messianic Power: Figures of a Time to Come in Benjamin, Derrida and Celan

Leben, Selbstbewusstsein, Negativität

AbstractThis paper explores Hegel’s speculative identity thesis as presented in theDifferenzschrift, thePhenomenology of Spirit, and theScience of Logic. I argue that speculative identity refers to the identity and non-identity of life and self-conscious cognition, a relation that establishes the constitutive importance of life for conceptual activity. Speculative identity thus entails that both self-consciousness and the Concept(der Begriff)are doubly constituted. I present this argument in three stages: first, through Hegel’s early critique of Fichte and his defense of the “objective subject-object” in theDifferenzschrift;second, through the concept of experience(Erfahrung)developed in thePhenomenology;and finally, through a brief consideration of the Concept as presented in theLogic. Although there are significant developments that take place between Hegel’s early and mature presentations of speculative identity, I argue that there is a common thread that persists throughout, namely, the constitutive importance of life for the purposive self-determination of thought.

Kritika tzv. moderního člověka u Carla Schmitta a její přesahy

ČlĂĄnek se zabĂ˝vĂĄ Schmittovou kritikou modernity a jejĂ­mi antisemitskĂ˝mi přesahy, a to na pozadĂ­ zpĹŻsobu, jimĹž Schmitt konstruoval centrĂĄlnĂ­ pojem svĂŠ teorie politična  nepřítele. Koncept nepřítele se tak v Schmittově dĂ­le postupně vyvĂ­jĂ­. V předvĂ˝marskĂŠm obdobĂ­, v němĹž vznikajĂ­ předevĹĄĂ­m vĂ˝znamnĂŠ texty Der Wert des Staates und die Bedeutung des Einzelnen a Theodor Däublers "Nordlicht", je nepřítelem předevĹĄĂ­m modernĂ­, individualistickĂ˝ člověk či modernĂ­ duch. V obdobĂ­ vĂ˝marskĂŠm se pak z nepřítele stĂĄvĂĄ jiĹž nepřítel politična, kterĂŠho Schmitt bohuĹžel a velmi odpudivĂ˝m zpĹŻsobem identifikuje v textech nacistickĂŠ diktatury s ĹžidovskĂ˝m myĹĄlenĂ­m příliĹĄ vĂĄzanĂ˝m na abstraktnĂ­ zĂĄkon. ZĂĄvěr člĂĄnku je nĂĄsledujĂ­cĂ­: politickĂĄ teorie Carla Schmitta je zaloĹžena na antiindividualistickĂŠ a tĂŠměř Ăşplně negativnĂ­ antropologii, kterĂĄ je doprovĂĄzenĂĄ teoriĂ­ sekularizace popisujĂ­cĂ­ proces neutralizace a depolitizace lidskĂŠho Ĺživota, kterĂ˝ tak ztrĂĄcĂ­ na vĂĄĹžnosti. Tento zpĹŻsob Ĺživota postrĂĄdajĂ­cĂ­m jakoukoliv transcendenci a utĂĄpějĂ­cĂ­ se pouze v obstarĂĄvĂĄnĂ­ je pak pro Schmitta Ĺživotem velmi bĂ­dnĂ˝m a neautentickĂ˝m. Celou tuto komplexnĂ­ problematiku pak člĂĄnek hodnotĂ­ na pozadĂ­ vĂ˝voje německĂŠho katolicismu v 19. stoletĂ­, do jehoĹž kontextu Schmitt nĂĄleĹžel.

The concept of intelligibility in modern physics (1948)

This is an English translation of Paul Feyerabend's earliest extant essay “Der Begriff der Verständlichkeit in der modernen Physik” (1948). In it, Feyerabend defends positivism as a progressive framework for scientific research in certain stages of scientific development. He argues that in physics visualizability (Anschaulichkeit) and intelligibility (Verständlichkeit) are time-conditioned concepts: what is deemed visualizable in the development of physical theories is relative to a specific historical context and changes over time. He concludes that from time to time the abandonment of visualizability is crucial for progress in physics, as it is conducive to major theory change, illustrating the point on the basis of advances in atomic theory.

"Eternity, from Afar into Intimacy"

work is reflected in the letters-or is it rather the reverse? -Martin Heidegger to Hannah Arendt, September 29,1967And yet it often seems to me as if what has been [das Gewesene] converges on a single moment [einen einzigen Augenblick] that salvages what can last [der das Bleibende birgt].-Martin Heidegger to Hannah Arendt, October 6,1966As known, the criticism of a linear view of history-as a succession of facts that finds its in the end or in view of the end is, in Heidegger, the result of a unique way of experiencing the role and the ontological thickness of temporality. Like temporality, historicity also refers to the way being is being, and it is in this dislocation of the historic that the new thought of ''event unfolds. However, such a turn, as fruitful for all of the philosophical twentieth century as it may be, could not remain immune to ambiguities and contradictions, especially if questioned in the inevitable cross with some events that have marked most intimately and most dramatically the life and times of its protagonist: thus in the difference between the dimension of the and the advent, between destination and destiny there might be room for a messianism of the truth that has something inscrutable and sacral, and today, for us, insane.The following pages aim to some extent to counteract such a suspicion in light of the consideration of the link between time and history that emerges in Heidegger's letters to Hannah Arendt. That link, in fact, does not stretch out its constitutive and insurmountable phenomenological texture: in the configuration of the what it is about is the phenomenon, the phenomenon that phenomenolizes itself, which comes to itself, to its own self-manifestation, in the effectivity of life. What emerges, then, is genesis of the relationship between time, history, destiny and event, whose connection is to be made by the phenomenon of love. In this new assumption of a burden it happens that the event awaits history and originates from it, as an exercise of its memory, and not that history awaits the event-a fatal error which Heidegger, after having taught us to avoid it, perhaps made himself. Revealing the of time, love does not constrain history.1.The well-known lecture on Der Begriff der Zeit held by Heidegger in 1924 in front of the Marburg theologians starts with a concession:If time finds its meaning in eternity, then it must be understood starting from eternity. The point of departure and path of this inquiry are thereby indicated in advance: from eternity to time. This way of posing the question is fine, provided that we have the aforementioned point of departure at our disposal, that is, that we are acquainted with eternity and adequately understand it. If eternity were something other than the empty state of perpetual being, the ael, if God were eternity, then the way of contemplating time initially suggested would necessarily remain in a state of perplexity so long as it knows nothing of God, and fails to understand the inquiry concerning him.1and continues with a refusal:The philosopher does not believe. If the philosopher asks about time, then he has resolved to understand time in terms of time or in terms of the ael, which looks like eternity but proves to be a mere derivative of being temporal.2Nevertheless, from this preliminary theoretical disposition there does not follow a definitive separation between philosophy and theology, in that the treatment of time also continues to be susceptible of being read from a theological point of view, though not being of a theological nature; and since the peculiarity of the theological point of view is to start from eternity, the treatment of time ends up including the latter, though residually, in its horizon. This minimal reception in which the non-indifference of philosophy is expressed in relation to the perspective characterizing theology certainly contains a confutative character (The philosopher does not have faith), but if we look carefully it is a confutation that preserves the aim of posing the problem of eternity in another way, and does not turn destructively towards the object in itself; hence eternity is not rejected, as this passage in the text admits:The following considerations are not theological. …

Kant, Calculus, Consciousness, and the Mathematical Infinite in Us

Kant, Calculus, Consciousness, and the Mathematical Infinite in Us John H. Smith Der Begriff des Unendlichkleinen, darauf die Mathematik so öfters hinauskommt, wird mit einer angemaßten Dreistigkeit so geradezu als erdichtet verworfen, anstatt daß man eher vermuten sollte, daß man noch nicht genug davon verstände, um ein Urteil darüber zu fällen. Die Natur selbst scheint gleichwohl nicht undeutliche Beweistümer an die Hand zu geben, daß dieser Begriff sehr wahr sei. Denn wenn es Kräfte gibt, welche eine Zeit hindurch kontinuierlich wirken, um Bewegungen hervorzubringen, wie allem Ansehen nach die Schwere ist, so muß die Kraft, die sie im Anfangsaugenblicke oder in Ruhe ausübt, gegen die, welche sie in einer Zeit mitteilt, unendlich klein sein. Es ist schwer, ich gestehe es, in die Natur dieser Begriffe hineinzudringen; aber diese Schwierigkeit kann allenfalls nur die Behutsamkeit unsicherer Vermutungen, aber nicht entscheidende Aussprüche der Unmöglichkeit rechtfertigen.1 [The concept of the infinitely small, which comes up so often in mathematics, is rejected straight out with presumptuous audacity as a fiction, instead of assuming that it is not well enough understood to form a judgment about it. Nature itself seems, however, to provide clear proofs that there is truth to this concept. For if there are forces that work continuously through time in order to produce movements, as it would appear is the case with gravity, then the force that effects this movement in an initial instant (or rest) must be infinitely small as opposed to the one that imparts movement in time. It is difficult, I confess, to penetrate into the nature of these concepts; but this difficulty can at most justify cautiously avoiding unfounded suppositions and not claiming decisively that it is impossible.] The question that I address in this essay is simple: what is the mathematical infinite doing at crucial moments in Kant’s philosophy? By doing I mean the way that specific notions of the infinitely small—the infinitesimal, the differential, infinite approximation, continuity—serve as metaphors in a strong Aristotelian sense; that is, they attempt to “bring before the eyes” something abstract and thereby contribute a kind of intuition to the unintuitable.2 And yet, there is something doubly ironic going on in this effort. On the one hand, although mathematics and the mathematization of nature have been criticized by Husserl for abstracting modern thought from the concrete life-world of experience, I will look to places where there is a turn to the mathematical infinite in order to be concrete.3 On the other hand, the clear [End Page 95] intuitions associated with the mathematical infinite can easily get caught up in contradictions that undermine the initial clarity.4 By exploring these moments of metaphoric and paradoxical representation, we can see how major thinkers grappled with a notion of the “immanence of the infinite” that characterizes the epochal turn of modernity.5 First, let me give a general sense of what is at stake in the notion of the mathematical infinite and the issues of representation associated with infinitesimal calculus, which was up through the nineteenth century arguably the most powerful tool for understanding the physical world. Although Kant rarely addresses calculus as such, this tool has particular relevance for him given the fundamental role that both its inventors, Leibniz and Newton, play in the development of his critical project. Consider the problem of a line tangent to a curve—that is, a straight line that touches any curved line at precisely one point. As I hope and expect has just occurred in the mind of any reader at this point, a somewhat-clear image has taken shape. This image can be rendered mathematically precise thanks to the technique of calculus; indeed, calculus was developed in large part to address this problem. The reason is that such a tangent can be considered the rate of change of the curve at any instant, which can be calculated given the curve’s function. Thus, say, a soaring baseball defines a parabolic arc at a changing rate of speed (fast at first, slowing at the peak, then ever faster as it returns to the ground). The tangents at any point indicate...