Příspěvek přináší základní matematické zakotvení pojmů „teorie chaosu". Představuje klíčové vlastnosti modelů chaotického chování dynamického systému s ohledem na explanační a prediktivní sílu modelů. Z pozice filosofie vědy podrobuje analýze především reprezentační aspekty modelů chaotické dynamiky systému. Nejzajímavějším aspektem těchto modelů je přísné omezení jejich reprezentační úlohy s ohledem na splnění podmínky hyperbolicity nutné pro platnost stínového lemma.

The models of internal self-control that have recently been proposed by behavioral economists do not depict motivational interaction that occurs while temptation is present. Those models that include willpower at all either envision a faculty with a motivation (“strength”) different from the motives that are weighed in the marketplace of choice, or rely on incompatible goals among diverse brain centers. Both assumptions are questionable, but these models’ biggest problem is that they do not let resolutions withstand re-examination while being challenged (...) by impulsive alternatives. The economists’ models all attempt to make a single equilibrium preference predictable from a person’s prior incentives. This was the original purpose of these models’ hyperboloid (“β–δ”) delay discount functions, which have been widely justified by the assumption that a person’s intertemporal inconsistency (impulsiveness) can be accounted for by the arousal of appetite for visceral rewards. Although arousal is clearly a factor in some cases of intertemporal inconsistency, it cannot be blamed for others, and furthermore does not necessarily imply hyperboloid discounting. The inadequacy of β–δ functions is particularly evident in models of internal self-control. I have reviewed several of these models, and have argued for a return to pure hyperbolic discount function as originally proposed, the relatively high tails of which can motivate a recursive process of self-prediction and thereby the formation of self-enforcing intertemporal contracts. Such a process does not require a separately motivated faculty of will, or incompatible goals among brain centers; but it also does not permit the prediction of unique preferences from prior incentives. (shrink)

It’s natural for hyperbole to mix with metaphor and irony, and other figures of speech. How do they mix together and what kind of compound, if any, arises out of the mixing? In tackling this question, I shall argue that thinking of hyperbolic figures along the lines familiar from ironic metaphor compounds is a temptation we should resist. Looking in particular at hyperbolic metaphor and hyperbolic irony, I argue, they don’t yield a new encompassing compound figure with one figure building (...) on another. Instead, what we have is one dominant figure colored with hyperbolic tinges. So what does hyperbole bring to the mixing pot? I suggest we should think of hyperbole in hyperbolic figures as being an interpretive effect, modulating the working of the partner figure and thus rendering more emphatic. (shrink)

We use hyperbolic towers to answer some model-theoretic questions around the generic type in the theory of free groups. We show that all the finitely generated models of this theory realize the generic type $p_{0}$ but that there is a finitely generated model which omits $p^{}_{0}$. We exhibit a finitely generated model in which there are two maximal independent sets of realizations of the generic type which have different cardinalities. We also show that a free product of homogeneous groups is (...) not necessarily homogeneous. (shrink)

Hyperbole is an easily misunderstood and misused trope, and it is largely unexplored in current rhetorical studies. Yet, at moments within thought and discourse, the excessiveness of hyperbole elicits a constructive, transformative ambiguity that can reveal alternative epistemological and ontological insights. Indeed, hyperbole is often the most effective way of trying to express seemingly impossible and inexpressible positions. I argue for the reexploration and critical examination of hyperbole, and I offer a theoretical framework from which to view texts and discourse (...) from a hyperbolic perspective. I identify the metafunction of hyperbole, and I offer two specific functions of hyperbole. Hyperbole is more than simply an obvious and intentional exaggeration and thus can benefit from an exploration that considers it beyond its traditional tropological limits. It can be engaged as a mode of inquiry in order to delve into the complexities and paradoxes of theo-philosophical discourse, and it can also be appropriated as a critical position from which one might, for example, propose interpretations of various textual expressions that differ from their more normative interpretations. (shrink)

It is tempting to assume that understatement and overstatement, meiosis and hyperbole, are analogous figures of speech, differing only in whether the speaker represents a quantity as larger, or as smaller, than she means to claim that it is. But these tropes have hugely different roles in conversation. Understatement is akin to irony, perhaps a species of it. Overstatement is an entirely different kettle of fish. Things get interestingly messy when we notice that to overstate how large or expensive or (...) distant something is, is to understate how small or inexpensive or close it is, and vice versa. So it may seem, anyway. I propose an account of the two tropes that counts some utterances, in their conversational contexts, as overstatements of a quantity but not understatements of the opposite quantity, and other utterances as understatements only. This account shows why understatement is closely related to irony and overstatement is not. Although overstatement and understatement (or irony) are very different, they are sometimes combined. An understatement of one quantity may be an overstatement of a different one. (shrink)

In typical critical thinking texts, hyperbole is presented as being largely “argumentationally innocent” - it’s primary role being to express emotion of to bring desired emphases to a particular point. This discounts its prevalent use in argumentation, as it is also used as a device to persuade, and in particular, to persuade an interlocutor that they should take or support a course of action. When it is so used, the exaggerated claims would, if true, provide greater support for the conclusion. (...) But since the claims are not fully accurate, this “greater support” is only illusory. Its use is thus deceptive and counts as fallacious reasoning. (shrink)

Recognition of sarcastic statements has been a challenge in the process of sentiment analysis. A sarcastic sentence contains only positive words conveying a negative sentiment. Therefore, it is tough for any automated machine to identify the exact sentiment of the text in the presence of sarcasm. The existing systems for sarcastic sentiment detection are limited to the text scripted in English. Nowadays, researchers have shown greater interest in low resourced languages such as Hindi, Telugu, Tamil, Arabic, Chinese, Dutch, Indonesian, etc. (...) To analyse these low resource languages, the biggest challenge is the lack of available resources, especially in the context of Indian languages. Indian languages are very rich in morphology which pose a greater challenge for the automated machines. Telugu is one of the most popular languages after Hindi among Indian languages. In this article, we have collected and annotated a corpus of Telugu conversation sentences in the form of a question followed by a reply for sarcasm detection. Further, a set of algorithms are proposed for the analysis of sarcasm in the corpus of Telugu conversation sentences. The proposed algorithms are based on hyperbolic features namely, Interjection, Intensifier, Question mark and Exclamation symbol. The achieved accuracy is 94%. (shrink)

Density matrices for mixed state qubits, parametrized by the Bloch vector in the open unit ball of the Euclidean 3-space, are well known in quantum computation theory. We bring the seemingly structureless set of all these density matrices under the umbrella of gyrovector spaces, where the Bloch vector is treated as a hyperbolic vector, called a gyrovector. As such, this article catalizes and supports interdisciplinary research spreading from mathematical physics to algebra and geometry. Gyrovector spaces are mathematical objects that form (...) the setting for the hyperbolic geometry of Bolyai and Lobachevski just as vector spaces form the setting for Euclidean geometry. It is thus interesting, in geometric quantum computation, to realize that the set of all qubit density matrices has rich structure with strong link to hyperbolic geometry. Concrete examples for the use of the gyro-structure to derive old and new, interesting identities for qubit density matrices are presented. (shrink)

The Perception-Action Model (PAM) is a cogent theory of how organisms get information about others' experiences. However, such a stimulus-driven mechanism does not handle well the complex choices that humans face about how to respond to this information. Hyperbolic reward discounting permits a reward-driven mechanism for both how aversive empathic experiences can compete for attention and how pleasurable empathic experiences are constrained.

This article addresses whether Nietzsche’s naturalism is best understood as exemplifying the principles of scientific method and the spirit of Enlightenment. It does so from a standpoint inspired by Eugen Fink’s contention that Nietzsche’s endorsements of “naturalism” are best read as hyperbole. The discussion engages with Enlightenment-orientated readings (by Walter Kaufmann, Maudemarie Clark, and Brian Leiter), which hold Nietzsche’s naturalism to endorse of the spirit of empirical science, and an alternative view (provided by Richard Schacht and Wolfgang Müller-Lauter), which holds (...) Nietzsche’s “extended naturalism” to be an informing ethos of historically aware thought rather than a mere “method.” The ensuing discussion endorses the latter approach in terms that seek to take more seriously the implications of Fink’s point about the hyperbolic and figural aspects of Nietzsche’s naturalism. I argue that Nietzsche’s naturalism is indeed often hyperbolic and figural but that this exaggerated form of naturalizing thought allows insights that invite explicit theorization. Turning to an approach suggested by Adorno and Horkheimer, I argue that Nietzsche’s exaggeratedly “naturalistic” take on morality is best appreciated as a form of disturbing and disruptive political intervention in the dominant discourse of modernity in which it overtly situates itself, namely, the instrumentalizing, methodologically fixated liberal discourse of scientific Enlightenment. If we approach his thinking in this way, Nietzsche’s naturalism serves as a valuable resource for critical reflection on the hegemony of contemporary scientific culture. The context for such critical reflection is provided by Giorgio Agamben’s work on sovereign power and modernity. Nietzsche’s naturalism, I argue, is foremost biopolitical in its implications. These implications invite critical reflection on aspects of Agamben’s work; they also, following Agamben’s lead, suggest that we must step beyond the fundamental concepts of liberalism. (shrink)

In the first chapter of my book Tradition and Originality in Plautus: Studies of the Amatory Motifs in Plautine Comedy, I have expressed the view that mythological hyperboles in which the Comic character asserts his superiority in one respect or another to a mythological hero, far from being a product of Plautus' own imagination, as suggested by E. Fraenkel, are a specifically Greek element, adapted by Plautus from his originals. Here I should like to draw attention to one particular aspect (...) of the pattern of thought in question, not dealt with in my book, which reinforces my argument and further underlines the traditional framework of which this pattern forms part. (shrink)

Hyperbole is traditionally understood as exaggeration. Instead, in this paper, we shall define it not just in terms of its form, but in terms of its effects and its purpose. Specifically, we characterize its form as a shift of magnitude along a scale of measurement. In terms of its effect, it uses this magnitude shift to make the target property more salient. The purpose of hyperbole is to express with colour and force that the target property is either greater or (...) lesser than expected or desired. This purpose is well suited to hyperbolic expression. This because hyperbole naturally draws a contrast between two points: how things are versus how they were expected to be. We also consider compound figures involving hyperbole. When it combines with other figures hyperbole operates by magnifying the specific effects of the figure it operates on. We shall see that sometimes hyperbole works as an input for irony; and at other times it builds on a metaphor to increase the effects of that metaphor. (shrink)

In this paper, we present a time-varying and non-stationary but non-hyperbolic discount function that explains dynamic preference reversal. The new discount function emerges from an analysis of intertemporal consumption and savings choices with mortality risk and an altruistic factor. Our analysis shows that the process of updating survival information may also account for dynamic preference reversal.

In lieu of an abstract, here is a brief excerpt of the content:When Hyperbole Enters Politics: What Can Be Learned From Antiquity and Our Hyperbolist-In-Chief W. ROBERT CONNOR introduction: an age of hyperbole Everywhere we turn these days we encounter hyperbole—in the colloquialisms of every day speech, advertising, salesmanship, letters of recommendation, sports-casting, and not least in political discourse. This may be a good moment, then, to open a conversation between ancient and modern understandings of verbal “over-shoot,” as the Greek (...) term for exaggeration might be rendered in English. The evidence gathered in H. Lausberg’s Handbook of Literary Rhetoric1 shows that while ancient rhetoricians agreed that hyperbole should be counted among the “figures of speech,” they found much to argue about: was hyperbole a violation of the Aristotelian middle course, hence an extreme to be avoided, or was it a legitimate form of augmentation (auxēsis in Greek, amplificatio in Latin)? Could diminution (meiōsis ) also be regarded as a form of hyperbole? In the interpretation of texts hyperbole poses a further difficulty —unlike simile, alliteration or some other figures of speech, it is “unmarked,” that is, it has no linguistic sign to alert the reader to its presence. Hyperbole likes to disguise itself as if it were going to a masquerade ball, presenting itself as simile or wearing metaphorical dress, or appearing not infrequently as litotes. It can sneak up on you and take you by surprise. The critic Longinus in On the Sublime, ch. 38, and some rhetoricians noted that hyperbole could be most arion 26.3 winter 2019 powerful when least recognized. Many ancient rhetoricians and some modern critics, however, have followed Quintilian, who asserted that “expressions (often hyperbolic), such as “storms of public assemblies, thunderbolts of eloquence, are used merely for ornament” (Institutes 8.6.7). In this view hyperbole is a conspicuous ornament used to embellish speech and make it more elegant and attractive, but today it is more often treated either as an excuse for an outrageous statement (as when the CEO of Cambridge Analytica characterized as “a certain amount of hyperbole” his suggestion of using prostitutes to discredit a political opponent), or as a euphemism for a falsehood (as when a politician promises he will eliminate the national debt—$20 trillion—and his budget director shrugs the claim off as “hyperbole.”) The term seems to extinguish any feeling of embarrassment. None of these understandings of hyperbole is simply wrong, but together they eclipse an alternative view, grounded in one ancient understanding of language, and corroborated by modern experience. In this approach language in general and hyperbole in particular are not simply a set of signs whose meaning is arbitrarily determined by social convention. Instead, they have their own nature (physis, as Isocrates says in Panegyricus 8) and hence their own power to arouse and motivate listeners. Hyperbole, viewed in this light, is a force in its own right, with the ability to give voice to otherwise unarticulated emotions, to intensify them, to push aside doubts and hesitations, and then to turn feelings into action. Language is power, and hyperbole, as an extreme form of language, provides great power to those who use it skillfully. These need not be the docile students of the rhetoricians ; politicians sometimes seem to have an innate understanding of it. The extreme breed among them, the demagogues, are often the ones who know best how to put this extreme of language to use. True, you don’t have to be a politician to put hyperbole to work. It is a favorite mode of speech among lovers, poets, travellers. Holy Men use it, too: Jesus of Nazareth, for exam16 when hyperbole enters politics ple, proclaimed that it was easier for a camel to pass through the eye of a needle than for a rich man to enter into the kingdom of God (Matthew 19.24). Almost everyone uses it at some point, except policy wonks whose soulless prose withers before its onslaughts. When people use hyperbole they may be neither lying nor embroidering the truth to make it more ornamental. They exalt and intensify what they see as truth, make it come alive, and thereby rouse their listeners from apathy and distraction. Ordinary people, too, use... (shrink)

René Descartes' Meditations on First Philosophy is his most celebrated philosophical work. The book remains one of the most significant and influential works in epistemology, metaphysics and philosophy of mind in the history of Western philosophy. In this paper I examine the relationship between the various hyperbolic doubts, the dreaming, imperfect creator, and evil demon hypotheses in Meditation I. The paper shows that the "painting analogy" occupies a central position in the First Meditation not only because it effectively links together (...) the hyperbolic doubts, but also because it lays the groundwork for the claim that although it may be impossible for us to know things outside us as our thoughts represent them to be, we can know at least the feature of our thoughts themselves. By raising the necessary doubt about our sensible experience and the corporeal world, the "painting analogy" makes the case for the primacy of the intellectual world. (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 (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)

There is a growing tendency to hyperbolize the U.S.-Mexican borderlands as a “dystopian zone of terror.” Dystopian borderlands hyperbole is double-edged. It can be used to create virulently racist mischaracterizations of borderlands life, and it can be used critically, as Alicia Gaspar de Alba and Sayak Valencia use it in Desert Blood and Capitalismo gore, to draw attention to structural forms of violence that imperil the borderlands on a daily basis. Desert Blood and Capitalismo gore exemplify a tendency in borderlands (...) literature to hyperbolically magnify borderlands crises of violence, misogyny, exploitation, and racism to all-encompassing dimensions. That magnification serves to highlight historical and structural conditions that have created and perpetuated those crises. The borderlands in Desert Blood and Capitalismo gore are hyperbolically reimagined as dystopias of neoliberal patriarchal violence. Gaspar de Alba and Valencia hyperbolize those dystopias to critique and ultimately abolish them. (shrink)

We show that plane hyperbolic geometry, expressed in terms of points and the ternary relation of collinearity alone, cannot be expressed by means of axioms of complexity at most ∀∃∀, but that there is an axiom system, all of whose axioms are ∀∃∀∃ sentences. This remains true for Klingenberg's generalized hyperbolic planes, with arbitrary ordered fields as coordinate fields.

Ainslie challenges our interpretation of the properties of hyperbolic discount curves in an iterated prisoners’ dilemma model. In this reply, we discuss the emergence of hyperbolic discount functions in the behavioral economics literature and evaluate their properties. Furthermore, we present a summarized version of our IPD model and evaluate Ainslie’s points of contention.

I argue that George Ainslie’s model of Hyperbolic Discounting fails to yield strict akratic action. But it does yield a deflated view. Furthermore, by understanding the nature of a hyperbolically discounting self, we can also offer a deflated view of self-deception, according to which self-deception is motivated error by hyperbolic discounters who desire to view themselves as rational.

The dream argument and its role in Cartesian doubt continue to engage commentators. As recent scholarship shows, a consensus has yet to be attained. In what follows I attempt to resolve the current debate by offering an account of the dream doubt which captures Descartes’s rhetorical strategy in Meditation I. A faithful reading of the text, I propose to show, reveals that the dream doubt is not entertained seriously nor is it proposed merely for the sake of methodological skepticism. It (...) is rather an integral part of a dogmatic intrusion of Cartesian science at a pivotal point in the critique of prescientific experience. After presenting the proposed interpretation, I examine the accounts offered in the current scholarship. (shrink)

What is addiction? Why do some people become addicted while others do not? Is the addict rational? In this book, Craig Hanson attempts to answer these questions and more. Using insights from the beginnings of philosophy to contemporary behavioral economics, Hanson attempts to assess the variety of ways in which we can and cannot, understand addiction. Special consideration is given to a challenging (and controversial) proposal dubbed “hyperbolic discounting.” Hanson proposes some modifications to the hyperbolic discounting view that permit it (...) to explain not only addiction, but also a variety of psychological maladies, such as self-deception. (shrink)

We conduct an experiment to investigate the degree to which deviations from exponential discounting can be accounted for by the hypothesis of hyperbolic discounting. Subjects are asked to choose between an earlier or later payoff in a series of 40 choice questions. Each question consists of a pair of monetary amounts determined by compounding a given base amount at a constant rate per period. Two bases (8 and 20 dollars), three compounding rates (low, medium and high) and three delays (2, (...) 4, and 6 weeks) are each used. There are also 2 initial periods (Today and 2 weeks) and there are two separate questionnaires, one with lower “realistic” compounding rates and the other with higher compounding rates, typical of those used in previous studies. We analyze the detailed patterns of choice in 6 groups of 6 related questions each (in which the base and rate is fixed but the initial period and delay varies), documenting the frequency of patterns consistent with exponential discounting and with hyperbolic discounting. We find that exponential discounting is the clear modal choice pattern in virtually all cases. Hyperbolic discounting is never the modal pattern (except in the sense that constant discounting is a special case of hyperbolic discounting). We also estimate a linear probability model that takes account of individual heterogeneity. The estimates show substantial increases in the probability of choosing the later option when the compounding rate increases, as one would expect. There are small, sometimes significant, increases in this probability when the delay is increased or the initial period is in the future. Such behavior is consistent with hyperbolic discounting, but can account for only a small proportion of choices. Overall, deviations from exponential discounting appear to be due to error, or to other effects not accounted for by hyperbolic discounting. Principal among these is an increase in later choices when the base is larger. (shrink)

In standard Relevance Theory, hyperbole and metaphor are categorized together as loose uses of language, on a continuum with approximations, category extensions and other cases of loosening/broadening of meaning. Specifically, it is claimed that there are no interesting differences between hyperbolic and metaphorical uses. In recent work, we have set out to provide a more fine-grained articulation of the similarities and differences between hyperbolic and metaphorical uses and their relation to literal uses. We have defended the view that hyperbolic use (...) involves a shift of magnitude along a dimension which is intrinsic to the encoded meaning of the hyperbole vehicle, while metaphor involves a multi-dimensional qualitative shift away from the encoded meaning of the metaphor vehicle. In this article, we present three experiments designed to test the predictions of this analysis, using a variety of tasks (paraph. (shrink)

In their brief online presentation "Qu'est-ce que l'Oulipo?", Jacques Roubaud and Marcel Bénabou explain how Oulipians proceed in the exploration of the lipo, littérature potentielle: "Certes, MAIS COMMENT?", they ask, before replying: "En inventant des contraintes. Des contraintes nouvelles et anciennes, difficiles et moins diiffficiles et trop diiffiiciiiles. La Littérature Oulipienne est une LITTÉRATURE SOUS CONTRAINTES." The vigorous tone conveyed by spelling and typography points to the distinct challenge posed by Oulipian writing, which relies on the difficulty of the constraint (...) in its effort to reach as far as possible into the uncharted territory of potential literature.... (shrink)

Hyperbolic theories have the fatal flaw that because of their vertical asymptote they predict irresistible choice of immediate rewards, regardless of future contingencies. They work only for simple situations. Theories incorporating intermediate unconscious choices are more flexible, but are neither exponential nor hyperbolic in their predictions. They don't solve the free will paradox, which may be just a consistent illusion.

We provide a universal axiom system for plane hyperbolic geometry in a firstorder language with two sorts of individual variables, ‘points’ and ‘lines’ , containing three individual constants, A0, A1, A2, standing for three non-collinear points, two binary operation symbols, φ and ι, with φ = l to be interpreted as ‘[MATHEMATICAL SCRIPT SMALL L] is the line joining A and B’ , and ι = P to be interpreted as [MATHEMATICAL SCRIPT SMALL L]P is the point of intersection of (...) g and h , and two binary operation symbols, π1 and —2, with πi = g to be interpreted as ‘g is one of the two limiting paralle lines from P to [MATHEMATICAL SCRIPT SMALL L]. (shrink)

Hyperbolic geometry can be axiomatized using the notions of order andcongruence (as in Euclidean geometry) or using the notion of incidencealone (as in projective geometry). Although the incidence-based axiomatizationmay be considered simpler because it uses the single binary point-linerelation of incidence as a primitive notion, we show that it issyntactically more complex. The incidence-based formulation requires some axioms of the quantifier-type forallexistsforall, while the axiom system based on congruence and order can beformulated using only forallexists-axioms.

This essay connects the mystical concept of “supernothing” with Bergson’s notion of the image of nothingness as a movement in the making. I do this also with respect to the film The Empty Man (David Prior, 2020) – which explicitly cites Gorgias’s four-part embargo on nothing (it exists, it cannot be known, communicated, or understood): nothingness is re-rendered as movement, in particular, the transmission and reception of images in the brain. Indeed, this is precisely Bergson’s theory of the brain too (...) – as the receiver and transmitter of images, a communication of movements. This “nihilistic” approach to the brain (it does not store images, it has no positive content) is not a valorisation of the ego as void à la Metzinger, but the real, processual rethinking of what nothingness and nihilism might mean – with a full, moving “supernothing” at its heart. Though there is a mystical and a film-philosophical account referenced in this renewal of nothingness, it will not lead to any exotic or hyperbolic excess (the brain as supernatural agent), but rather a very “ordinary” account that we will describe in terms of “supernormalisation”: an “unlearning” or mundanising of the supernatural: an extraction of the supernatural by natural means. (shrink)

Errol Morris has claimed that Kuhn threw an ashtray at him during a dispute about some matter in the history of science. Morris also claims that Kuhn threw him out of the graduate program at Princeton for disagreeing with him. I argue that Morris’ attack on Kuhn contains some degree of hyperbole. Further, I present evidence that shows that Morris is mistaken about key events during this period. In fact, Kuhn was supportive of Morris in his pursuit of a career (...) in the history of science. (shrink)

Hyperbolic geometry can be axiomatized using the notions of order andcongruence (as in Euclidean geometry) or using the notion of incidencealone (as in projective geometry). Although the incidence-based axiomatizationmay be considered simpler because it uses the single binary point-linerelation of incidence as a primitive notion, we show that it issyntactically more complex. The incidence-based formulation requires some axioms of the quantifier-type \forall\exists\forall, while the axiom system based on congruence and order can beformulated using only \forall\exists-axioms.

The study of an electric charge in hyperbolic motion is an important aspect of Minkowski’s geometrical formulation of electrodynamics. In “Space and Time”, his last publication before his premature death, Minkowski gives a brief geometrical recipe for calculating the four-force with which an electric charge acts on another electric charge. The subsequent work of Born, Sommerfeld, Laue, and Pauli filled in the missing derivation details. Here, we bring together these early contributions, in an effort to provide a more modern, accessible, (...) and unified exposition of the early history of the electric charge in hyperbolic motion. (shrink)

The use of the axial vector representing a three-dimensional rotation makes the rotation representation much more compact by extending the trigonometric functions to vectorial arguments. Similarly, the pure Lorentz transformations are compactly treated by generalizing a scalar rapidity to a vector quantity in spatial three-dimensional cases and extending hyperbolic functions to vectorial arguments. A calculation of the Wigner rotation simplified by using the extended functions illustrates the fact that the rapidity vector space obeys hyperbolic geometry. New representations bring a Lorentz-invariant (...) fundamental equation of motion corresponding to the Galilei-invariant equation of Newtonian mechanics. (shrink)

Hegel famously argued that Kantian Moralität is an empty formalism. This article offers a defense of Kant’s formalism and suggests that it is crucial to Hegel’s own idealism. My defense, however, depends on reading Kantian morality non-morally, as a theory of normative authority. Through a reading of the Grundlegung and Religion, the article delineates Kant’s hyperbolic formalism—the insistence on giving an account of the form of rational agency by isolating willing from all content. The article accordingly assesses Kant’s understanding of (...) autonomy as a matter of institution-subjection. It also critically engages Henry Allison’s groundbreaking work on Kant. Hegel follows Kant in arguing that determinacy is a matter of institution-subjection, and in the Logic provides a radically formalist justification of the role of normative authority in determinacy. Unlike Kant, who articulates institution-subjection as a matter of an isolated subject, Hegel shows that institution-subjection is a matter of social practices. (shrink)