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)

Abstract: The main aim of this work is to introduce acceleration methods called a hyperbolic acceleration methods which are of series of numerated methods. In general, these methods named as AL-Tememe’s acceleration methods of first kind discovered by (Ali Hassan Mohammed). These are very beneficial to acceleration the numerical results for definite integrations with continuous integrands which are of 2nd order main error, with respect to the accuracy and the number of the used subintervals and the fasting obtaining results. Especially, (...) for acceleration the results which are obviously obtained by trapezoidal and midpoint methods. Moreover, these methods could be enhancing the results of the ordinary differential equations numerically which are of 2nd order main error. (shrink)

Here we introduce a formulation for describing welfare based on a hyperbolic secant function, derived from certain intuitions about the nature of material and experiential conditions, that satisfies a number of normatively critical constraints, making for an elegant and satisfactory welfarist axiology. We first introduce intuitions about experiential conditions, material conditions, and their valences; we second make a mathematical formulation of our hedonic calculus consistent with these intuitions; we third make several manipulations of our formulation in order to make calculations (...) in population ethics; and we fourth show how the calculations are consistent with several critical normative constraints. (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)

As the author has previously argued, a statement of form “Y is X” can often be taken as hyperbolic for a notably high degree of likeness between Y and X, or, instead, as hyperbolically stating how important Y is as a part of X. The present article goes further and argues that these types of hyperbole, as well as various others, are just special cases of reflexive hyperbole, a style that appears not previously to have been explored in (...) its own right. The article therefore serves to introduce this style and to unify under it various more specific, disparate-seeming types of hyperbole, revealing their deep similarity. They all rest in a uniform way on a special property that some relationships have, namely of being reflexive in a broadened sense. The relationship of likeness is reflexive in the standard sense that any entity bears the relationship to itself with maximum possible strength. But some other relationships of interest in this article are only reflexive in a broader way that relaxes these universality and maximality requirements to an extent. The article also explains how reflexive hyperbole about likeness is a novel addition to the theory of metaphor, involving a distinctive interpretative process with special effects, and how reflexive hyperbole about part importance is not reducible to whole-for-part metonymy, because the latter does not systematically access sufficiently important parts. In addition, the article briefly considers the defaultness or otherwise of reflexive hyperbolic interpretations. (shrink)

The electron is found at discrete energy levels within the atom, transition between these levels is considered to involve a `jump' rather than via a continuous motion. If we simulate the transition in the H atom as a series of individual steps, with each step the frequency of the electron, we can map a semi-continuous transition (from n=1 to n=2 requires about 1887860 steps, transition period a function of the photon wavelength). Plotting the electron from n=1 to ionization traces a (...) hyperbolic spiral, the significance being that at specific spiral angles, the angle components cancel returning an integer value for the radius (360°=4r, 360+120°=9r, 360+180°=16r, 360+216°=25r ... 720°). If we set initial radius r = Bohr radius, then we can use the spiral perimeter to calculate the transition frequencies at these angles. As these spiral angles correlate the energy level Bohr radii directly with pi, we may ask if quantization of the atom has a geometrical origin. Furthermore, the closer the vicinity of the electron to the proton, the greater the divergence from the idealized value suggesting the electron maybe causing a distortion within the proton internal structure. (shrink)

In the first part of this article we survey general similarities and differences between biological and social macroevolution. In the second (and main) part, we consider a concrete mathematical model capable of describing important features of both biological and social macroevolution. In mathematical models of historical macrodynamics, a hyperbolic pattern of world population growth arises from non-linear, second-order positive feedback between demographic growth and technological development. Based on diverse paleontological data and an analogy with macrosociological models, we suggest that the (...) hyperbolic character of biodiversity growth can be similarly accounted for by non-linear, second-order positive feedback between diversity growth and the complexity of community structure. We discuss how such positive feedback mechanisms can be modelled mathematically. (shrink)

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.

In the first part of this article we survey general similarities and differences between biological and social macroevolution. In the second (and main) part, we consider a concrete mathematical model capable of describing important features of both biological and social macroevolution. In mathematical models of historical macrodynamics, a hyperbolic pattern of world population growth arises from non-linear, second-order positive feedback between demographic growth and technological development. Based on diverse paleontological data and an analogy with macrosociological models, we suggest that the (...) hyperbolic character of biodiversity growth can be similarly accounted for by non-linear, second-order positive feedback between diversity growth and the complexity of community structure. We discuss how such positive feedback mechanisms can be modelled mathematically. (shrink)

The chapter challenges hyperbolic claims about the centrality of appreciation of beauty to Buddhism. Within the texts, attitudes are more mixed, except for a form of 'inner beauty' - the beauty found in the expression of virtues or wisdom in forms of bodily comportment. Inner beauty is a stable presence throughout Buddhist history, practices, and art.

This paper adds another argument to the rising tide of panic about robots and AI. The argument is intended to have broad civilization-level significance, but to involve less fanciful speculation about the likely future intelligence of machines than is common among many AI-doomsayers. The argument claims that the rise of the robots will create a crisis of moral patiency. That is to say, it will reduce the ability and willingness of humans to act in the world as responsible moral agents, (...) and thereby reduce them to moral patients. Since that ability and willingness is central to the value system in modern liberal democratic states, the crisis of moral patiency has a broad civilization-level significance: it threatens something that is foundational to and presupposed in much contemporary moral and political discourse. I defend this argument in three parts. I start with a brief analysis of an analogous argument made in pop culture. Though those arguments turn out to be hyperbolic and satirical, they do prove instructive as they illustrates a way in which the rise of robots could impact upon civilization, even when the robots themselves are neither malicious nor powerful enough to bring about our doom. I then introduce the argument from the crisis of moral patiency, defend its main premises and address objections. (shrink)

Although he is best known as the founder of pragmatism, the name that Charles Sanders Peirce prefers to use for his comprehensive system of thought is "synechism" because the principle of continuity is its central thesis. This paper arranges and summarizes numerous quotations and citations from his voluminous writings to formalize and explicate his distinctive mathematical conceptions of hyperbolic and topical continuity, both of which are derived from the direct observation of time as their paradigmatic manifestation, and then apply them (...) in normative science and metaphysics, especially logic as semeiotic and cosmology. The resulting conclusion is that the intelligibility of the universe is plausibly explained by conceiving it as one immense sign, a vast inferential process: a semiosic continuum whose connected constituent signs are indefinite until deliberately marked off, with God the Creator as its overall dynamical object in the infinite past and God completely revealed as its overall final interpretant in the infinite future. (shrink)

This paper challenges the conventional wisdom dominating the social sciences and philosophy regarding temporal discounting, the practice of discounting the value of future utility when making decisions. Although there are sharp disagreements about temporal discounting, a kind of standard model has arisen, one that begins with a normative standard about how we should make intertemporal comparisons of utility. This standard demands that in so far as one is rational one discounts utilities at future times with an exponential discount function. Tracing (...) the justification for this standard through economics, philosophy and psychology, I’ll make what I believe is the best case one can for it, showing how a non-arbitrariness assumption and a dominance argument together imply that discounting ought to be exponential. Ultimately, however, I don’t find the case compelling. Non-exponential temporal discounting is often rational. If this is correct, Instead of trying to ‘fix’ non-exponential discounting because it is irrational and associated with negative life outcomes, we might instead focus attention on why the conditions obtain that make such discounting rational. (shrink)

According to a widely held view of assertion and belief, they are each governed by a tacitly acknowledged epistemic norm, and the norm on assertion and norm on belief are so related that believing p is epistemically permissible only if asserting it is. I call it the Same Norm View. A very common type of utterance raises a puzzle for this view, viz. utterances in which we say ‘I believe p' to convey somehow guarded affirmation of the proposition that p. (...) For example, one might respond to a query for directions to the station by saying ‘I believe it is down the first street on your left.' Often, when we reply in this way, it would have been pragmatically preferable simply to assert that p, had we been epistemically warranted in doing so. One's guarded reply thus suggests one is not so warranted. Nevertheless, if one believes what one, at face value, says one believes, one believes p. Contrary to what might seem to be suggested by the Same Norm View, one does not seem to portray oneself as irrational or epistemically beyond the pale in replying in this way. The paper develops this puzzle in detail, and examines a variety of options for a resolving it consistently with the Same Norm view. The most promising of these options, I argue, is to see ‘I believe' guarded affirmations as a form merely approximately correct speech. They would, though, be a form of such speech that interestingly differs from paradigm cases of loose use or conventional hyperbole in that speakers would be comparatively unaware of engaging in approximation. I conclude ‘I believe’—guarded affirmations either show the Same Norm View to be false or must be recognised as such an interestingly distinctive form of merely approximately correct speech. (shrink)

The fructose 6-phosphate (Fru-6P) saturation curve for phosphofructokinase (PFK) from E. coli is sigmoidal in the presence of saturating MgATP levels, while the corresponding curve for B. stearothermophilus PFK is essentially hyperbolic. Sigmoidality can be due to apparent cooperativity arising from the kinetic mechanism of an enzyme. We have determined the kinetic mechanism of B. stearothermophilus PFK (BsPFK). BsPFK was found to obey a non rapid-equilibrium random mechanism similar to the one E. coli PFK (EcPFK) follows. Substrate inhibition by MgATP (...) was observed. We propose that substrates bind to BsPFK through two alternative pathways, one of which is slower. The substrate inhibition arises in part from reaction flux through the slower pathway. Although EcPFK and BsPFK obey similar kinetic mechanisms, they are inhibited differently by MgATP: EcPFK is profoundly inhibited, BsPFK only weakly. The structural basis for this difference could be closure of the active site via a conformational transition that occurs in EcPFK, but not BsPFK. To investigate the importance of this transition for MgATP inhibition of EcPFK, we have constructed a chimeric enzyme (ChiPFK) that contains the "rigid" ATP-binding domain of BsPFK grafted onto the remainder of the EcPFK subunit. Our results indicate that ChiPFK is locked in an "open" structure resembling the activated form of EcPFK. It is insensitive to heterotropic regulation. Nevertheless, ChiPFK exhibits residual cooperativity. Possible explanations for the cooperativity are discussed. The 6F loop is proposed to be important in PFK allosteric behavior. Residues along the loop are largely conserved between BsPFK and EcPFK, except for 161, which is a glutamate in BsPFK, and a glutamine in EcPFK. Using site-directed mutagenesis, Glu 161 of BsPFK has been changed to glutamine and alanine. Similarly, Gin 161 of EcPFK has been changed to glutamate, arginine and alanine. Of the five mutants, one, QA161, was particularly interesting. Though activated normally by GDP, it was completely insensitive to PEP inhibition. This indicates that the hydrogen-bonding ability of residue 161 is critical for PEP inhibition of EcPFK, and that GDP activation and PEP inhibition follow different structural pathways. (shrink)

In the first part of this article we survey general similarities and differences between biological and social macroevolution. In the second (and main) part, we consider a concrete mathematical model capable of describing important features of both biological and social macroevolution. In mathematical models of historical macrodynamics, a hyperbolic pattern of world population growth arises from non-linear, second-order positive feedback between demographic growth and technological development. This is more or less identical with the working of the collective learning mechanism. Based (...) on diverse paleontological data and an analogy with macrosociological models, we suggest that the hyperbolic character of biodiversity growth can be similarly accounted for by non-linear, second-order positive feedback between diversity growth and the complexity of community structure, suggesting the presence within the biosphere of a certain analogue of the collective learning mechanism. We discuss how such positive feedback mechanisms can be modelled mathematically. (shrink)

In this chapter, I first turn to Spinoza’s obscure “ideas of ideas” doctrine and his claim that “as soon as one knows something, one knows that one knows it, and simultaneously knows that one knows that one knows, and so on, to infinity” (E2p21s). On my view, Spinoza, like Descartes, holds that a given idea can be conceived either in terms of what it represents or as an act of thinking: E2p7 (where Spinoza presents his doctrine of the “parallelism” of (...) minds and bodies) primarily concerns the former way of conceiving of an idea while E2p21 primarily concerns the latter. I propose that in E2p21, Spinoza makes a few crucial points about an adequate idea conceived as the “idea of the idea,” or as the activity of thinking: 1) when one has an adequate representation of p, one automatically knows that one is thinking an adequate representation of p, and 2) this reflective knowledge cannot be improved. I then turn to E2p43, “he who has a true idea at the same time knows that he has a true idea, and cannot doubt the truth of the thing." This is a denial of skepticism, but I think we need to be careful. E2p21 and E2p43 rule out the most hyperbolic doubts like those we see in Descartes's Third Meditation (AT VII 36), so it is the case that thinkers need no additional validation for the “adequate ideas of properties of things” and “common notions” employed in "cognition of the second kind," or reason. However, a reasoning thinker might nevertheless be troubled by doubts about the extramental world. As I have argued in other work, we can take Spinoza as following Descartes at least this far: once our reasoning thinker comes to adequate ideas of God and God’s relation to things, their ideas cannot be rendered doubtful. Here I concede that because one can reason to these adequate ideas of God and God's relation to things, scientia intuitiva is not unique in removing doubt. However, scientia intuitiva may still be distinctive in the way it removes doubt. (shrink)

Faith has many aspects. One of them is whether absolute logical proof for God’s existence is a prerequisite for the proper establishment and individual acceptance of a religious system. The treatment of this question, examined here in the Jewish context of Rabbi Prof. Eliezer Berkovits, has been strongly influenced in the modern era by the radical foundationalism and radical skepticism of Descartes, who rooted in the Western mind the notion that religion and religious issues are “all or nothing” questions. Cartesianism, (...) which surprisingly became the basis of modern secularism, was criticized by the classical American pragmatists. Peirce, James and Dewey all rejected the attempt to achieve infallible absolute knowledge, as well as the presumptuousness of establishing such a knowledge by means of casting Cartesian hyperbolic doubt. They advocated an alternative approach which was more holistic and humane. This paper lays out Descartes’s approach and the pragmatists’ critique. Despite the place that pragmatic considerations hold in Jewish tradition, some thinkers reject the relevance of these ideas. Yet Berkovits’s thought suggest a different path. He rejected Descartes’ radical skepticism and his radical foundationalism, in favor of a moderate foundationalism, which allows for a belief in God alongside constructive doubts. Similar to Peirce’s conception of the fixation of belief, Berkovits views local doubts (distinct from the hyperbolic doubt) as necessary for thought. Berkovits’s understanding of the biblical human-divine encounter, following Rosenzweig, Buber, and Heschel, is conceptualized here as “encounter theology”. Berkovits criticizes the propositionalist attempts to prove God’s existence logically, as well as the presumptuousness of basing religious belief on the teleological world-order. However, Berkovits’s conception of the ‘caring God’ is not provable, and thus defined as a pragmatic ‘postulate’. The article concludes by considering Berkovits’s “encounter theology”. In contrast to the approach described by Haym Soloveitchik, of halakhic stringency and lack of subjective experience of God’s face, Berkovits’s approach is dialogic through and through. (shrink)

We investigate the fate of determinism in general relativity, comparing the philosopher’s account with the physicist’s well-posed initial value formulations. The fate of determinism is interwoven with the question of what it is for a spacetime to be ‘physically reasonable’. A central concern is the status of global hyperbolicity, a putatively necessary condition for determinism in GR. While global hyperbolicity may fail to be true of all physically reasonable models, we analyze whether global hyperbolicity should be imposed by fiat; established (...) from weaker assumptions, as in cosmic censorship theorems; or justified by beyond-GR physics. (shrink)

Mobsters and others engaged in risky forms of social coordination and coercion often communicate by saying something that is overtly innocuous but transmits another message ‘off record’. In both ordinary conversation and political discourse, insinuation and other forms of indirection, like joking, offer significant protection from liability. However, they do not confer blanket immunity: speakers can be held to account for an ‘off record’ message, if the only reasonable interpreta- tions of their utterance involve a commitment to it. Legal liability (...) for speech in the service of criminal behavior displays a similar profile of significant protection from indirection along with potential liability for reasonable interpretations. Specifically, in both ordinary and legal contexts, liability depends on how a reasonable speaker would expect a reasonable hearer to interpret their utterance in the context of utter- ance, rather than on the actual speaker’s claimed communicative intentions. (shrink)

Any good ethical theory aspires to provide as comprehensive a guide to moral value and motivation as possible. Within modern moral philosophy, conceptions of moral value have been dominated largely by considerations of justice and concerns for the common good, and moral shortcomings have been accounted for primarily by appeal to ignorance, weakness, indifference or outright hostility to moral values. Yet the ways in which we fall short are far more complicated. By discussing one interesting example here, I hope to (...) provide some support for the claim that our conceptions of moral value and motivation need enrichment. In making my case, I utilize a character who is more like a caricature than a figure from ordinary life. This touch of hyperbole is deliberate. Reflect for a moment on the function of a good cartoon caricature. By exaggerating physical features, it draws our attention to characteristics that go unnoticed in their normal context. Whereas cartoon caricatures aim at amusement, my goal is to distil some of our perceptions of moral excellence. (shrink)

We think and speak in figures. This is key to our creativity. We re-imagine one thing as another, pretend ourself to be another, do one thing in order to achieve another, or say one thing to mean another. This comes easily because of our abilities both to work out meaning in context and re-purpose words. Figures of speech are tools for this re-purposing. Whether we use metaphor, simile, irony, hyperbole, and litotes individually, or as compound figures, the uses are (...) all rooted in literal meanings. These uses invite us to explore the context to find new meanings, new purposes, beyond the literal. -/- This special issue of Philosophical Studies brings together eight papers on various aspects and applications of figurative speech including: David Hills, Mitch Green, Liz Camp, Ofra Magidor, Larry Horn, Ken Walton, Stephen Barker, and Mihaela Popa-Wyatt. (shrink)

The utterance of morals or morality within a communist space is one that may, in the best of cases, raise a few eyebrows or, in the worst of cases, summon calls for condemnation or accusations of being unscientific. The subject of communist morality is one that is often ignored within the broader revolutionary left, while at the same time—especially within our current insurrectionary moment—beckons to be engaged with. As the hydra of neoliberalism begins its inevitable collapse, throwing capitalism once more (...) into a global crisis—and thusly its imperialist head begins to twist fascistically from the periphery back inward toward the United States and Europe—these categories that before seemed abstract and idealistic suddenly become vivid and tangible. Evil is how these injustices are described—in a non-hyperbolic fashion—by those engaged in the frontlines of revolutionary activity. So why is morality eschewed and denounced in left academic discourse? Are morals solely the provenance of the reactionary right or the dreamy idealist? (shrink)

The article aims to critically analyze the conventional tripartite division within Nietzsche’s philosophy that is expressed hyperbolically in the form of personification: the young Nietzsche of the Wagnerian phase, the “positivist” or “enlightened” Nietzsche, and the mature Nietzsche. I aim to contribute to the plea for continuity, paying special attention to a variety of texts in which he acknowledges the continuity of his intellectual development as a coherent unit. This significant retrospection does not indicate rupture or rejection but recognition of (...) a single path. The last section is dedicated to the particular book that is Ecce Homo, understood as a self-presentation strategy. (shrink)

For the classical Geometry, in a geometrical space, all items (concepts, axioms, theorems, etc.) are totally (100%) true. But, in the real world, many items are not totally true. The NeutroGeometry is a geometrical space that has some items that are only partially true (and partially indeterminate, and partially false), and no item that is totally false. The AntiGeometry is a geometrical space that has some item that are totally (100%) false. While the Non-Euclidean Geometries [hyperbolic and elliptic geometries] resulted (...) from the total negation of only one specific axiom (Euclid’s Fifth Postulate), the AntiGeometry results from the total negation of any axiom [and in general: theorem, concept, idea etc.] and even of more axioms [theorem, concept, idea, etc.] and in general from any geometric axiomatic system (Euclid’s five postulates, Hilbert’s 20 axioms, etc.), and the NeutroAxiom results from the partial negation of any axiom (or concept, theorem, idea, etc.). Clearly, the AntiGeometry is a generalization of Non-Euclidean Geometries. (shrink)

Girolamo Saccheri (1667--1733) was an Italian Jesuit priest, scholastic philosopher, and mathematician. He earned a permanent place in the history of mathematics by discovering and rigorously deducing an elaborate chain of consequences of an axiom-set for what is now known as hyperbolic (or Lobachevskian) plane geometry. Reviewer's remarks: (1) On two pages of this book Saccheri refers to his previous and equally original book Logica demonstrativa (Turin, 1697) to which 14 of the 16 pages of the editor's "Introduction" are devoted. (...) At the time of the first edition, 1920, the editor was apparently not acquainted with the secondary literature on Logica demonstrativa which continued to grow in the period preceding the second edition \ref[see D. J. Struik, in Dictionary of scientific biography, Vol. 12, 55--57, Scribner's, New York, 1975]. Of special interest in this connection is a series of three articles by A. F. Emch [Scripta Math. 3 (1935), 51--60; Zbl 10, 386; ibid. 3 (1935), 143--152; Zbl 11, 193; ibid. 3 (1935), 221--333; Zbl 12, 98]. (2) It seems curious that modern writers believe that demonstration of the "nondeducibility" of the parallel postulate vindicates Euclid whereas at first Saccheri seems to have thought that demonstration of its "deducibility" is what would vindicate Euclid. Saccheri is perfectly clear in his commitment to the ancient (and now discredited) view that it is wrong to take as an "axiom" a proposition which is not a "primal verity", which is not "known through itself". So it would seem that Saccheri should think that he was convicting Euclid of error by deducing the parallel postulate. The resolution of this confusion is that Saccheri thought that he had proved, not merely that the parallel postulate was true, but that it was a "primal verity" and, thus, that Euclid was correct in taking it as an "axiom". As implausible as this claim about Saccheri may seem, the passage on p. 237, lines 3--15, seems to admit of no other interpretation. Indeed, Emch takes it this way. (3) As has been noted by many others, Saccheri was fascinated, if not obsessed, by what may be called "reflexive indirect deductions", indirect deductions which show that a conclusion follows from given premises by a chain of reasoning beginning with the given premises augmented by the denial of the desired conclusion and ending with the conclusion itself. It is obvious, of course, that this is simply a species of ordinary indirect deduction; a conclusion follows from given premises if a contradiction is deducible from those given premises augmented by the denial of the conclusion---and it is immaterial whether the contradiction involves one of the premises, the denial of the conclusion, or even, as often happens, intermediate propositions distinct from the given premises and the denial of the conclusion. Saccheri seemed to think that a proposition proved in this way was deduced from its own denial and, thus, that its denial was self-contradictory (p. 207). Inference from this mistake to the idea that propositions proved in this way are "primal verities" would involve yet another confusion. The reviewer gratefully acknowledges extensive communication with his former doctoral students J. Gasser and M. Scanlan. ADDED 14 March 14, 2015: (1) Wikipedia reports that many of Saccheri's ideas have a precedent in the 11th Century Persian polymath Omar Khayyám's Discussion of Difficulties in Euclid, a fact ignored in most Western sources until recently. It is unclear whether Saccheri had access to this work in translation, or developed his ideas independently. (2) This book is another exemplification of the huge difference between indirect deduction and indirect reduction. Indirect deduction requires making an assumption that is inconsistent with the premises previously adopted. This means that the reasoner must perform a certain mental act of assuming a certain proposition. It case the premises are all known truths, indirect deduction—which would then be indirect proof—requires the reasoner to assume a falsehood. This fact has been noted by several prominent mathematicians including Hardy, Hilbert, and Tarski. Indirect reduction requires no new assumption. Indirect reduction is simply a transformation of an argument in one form into another argument in a different form. In an indirect reduction one proposition in the old premise set is replaced by the contradictory opposite of the old conclusion and the new conclusion becomes the contradictory opposite of the replaced premise. Roughly and schematically, P,Q/R becomes P,~R/~Q or ~R, Q/~P. Saccheri’s work involved indirect deduction not indirect reduction. (3) The distinction between indirect deduction and indirect reduction has largely slipped through the cracks, the cracks between medieval-oriented logic and modern-oriented logic. The medievalists have a heavy investment in reduction and, though they have heard of deduction, they think that deduction is a form of reduction, or vice versa, or in some cases they think that the word ‘deduction’ is the modern way of referring to reduction. The modernists have no interest in reduction, i.e. in the process of transforming one argument into another having exactly the same number of premises. Modern logicians, like Aristotle, are concerned with deducing a single proposition from a set of propositions. Some focus on deducing a single proposition from the null set—something difficult to relate to reduction. (shrink)

I find much to like in Craig Callender's [2022] arguments for the rational permissibility of non-exponential time discounting when these arguments are viewed in a conditional form: viz., if one thinks that time discounting is rationally permissible, as the social scientist does, then one should think that non-exponential time discounting is too. However, time neutralists believe that time discounting is rationally impermissible, and thus they take zero time discounting to be the normative standard. The time neutralist rejects time discounting because (...) they think it is rationally impermissible to prefer to live a worse life in expectation because of arbitrariness. Callender’s attack on the time-neutralist position is the following: the time-neutralist’s non-arbitrariness intuition assumes the existence of nonexistent ‘pure’ time preferences. In response, I aim to clarify the time-neutralist position and show that the non-arbitrariness argument does not rely on the existence of pure time preferences. Instead, the debate between time neutralism and permissivism about time discounting boils down to a methodological question: can we ever criticize the content of preferences? If so, we should embrace time neutralism. (shrink)

It is traditionally thought that metaphorical utterances constitute a special— nonliteral—kind of departure from lexical constraints on meaning. Dan Sperber and Deirdre Wilson have been forcefully arguing against this: according to them, relevance theory’s comprehension/interpretation procedure for metaphorical utterances does not require details specifi c to metaphor (or nonliteral discourse); instead, the same type of comprehension procedure as that in place for literal utterances covers metaphors as well. One of Sperber and Wilson’s central reasons for holding this is that metaphorical (...) utterances occupy one end of a continuum that includes literal, loose and hyperbolic utterances with no sharp boundaries in between them. Call this the continuum argument about interpreting metaphors. My aim is to show that this continuum argument doesn’t work. For if it were to work, it would have an unwanted consequence: it could be converted into a continuum argument about interpreting linguistic errors, including slips of the tongue, of which malaprops are a special case. In particular, based on the premise that the literal–loose–metaphorical continuum extends to malaprops also, we could conclude that the relevance-theoretic comprehension procedure for malaprops does not require details specifi c to linguistic errors, that is, details beyond those already in place for interpreting literal utterances. Given that we have good reason to reject this conclusion, we also have good reason to rethink the conclusion of the continuum argument about interpreting metaphors and consider what additional (metaphor-specifi c) details—about the role of constraints due to what is lexically encoded by the words used—might be added to relevance-theoretic comprehension procedures. (shrink)

We present experimental evidence that an interpretation was accurate. Current wisdom notwithstanding, we could interpret from the text alone because its information is redundant: repetition provides internal checks. Knowing neither dreamer nor their associations we made falsifiable predictions that we tested by subsequently gathering information about the dreamer. Predictions were supported. Results were repeated with seven additional dreams. Each dream was tightly crafted, used humor, drama or hyperbole to penetrate the dreamer’s defenses, and furthered the emergence of personality. Our (...) experiment compliments fMRI and statistics because it studies a whole text as a unique narrative: one iteration identified healing steps during therapy; another confirmed the psychological meaning of a myth. Our experiment might generate a body of objective knowledge about interpretation and make interpretation itself more accurate. In the US 20% live with mental illness. Our experiment supports talk therapy against pressure from the drug and insurance industries. (shrink)

What's of our identity in the contemporary age? One of the most original frameworks to rebuild the human condition from the beginning to the present is the Mumford anthropological theory on urbanism. In this work my ambition is not only to present the most important conclusions of Mumford research but to expand them in the actual present time, claiming that the hyperbolic evolution of technology causes a pervasive and pernicious depersonalization.

Research into ancient physical structures, some having been known as the seven wonders of the ancient world, inspired new developments in the early history of mathematics. At the other end of this spectrum of inquiry the research is concerned with the minimum of observations from physical data as exemplified by Eddington's Principle. Current discussions of the interplay between physics and mathematics revive some of this early history of mathematics and offer insight into the fine-structure constant. Arthur Eddington's work leads to (...) a new calculation of the inverse fine-structure constant giving the same approximate value as ancient geometry combined with the golden ratio structure of the hydrogen atom. The hyperbolic function suggested by Alfred Landé leads to another result, involving the Laplace limit of Kepler's equation, with the same approximate value and related to the aforementioned results. The accuracy of these results are consistent with the standard reference. Relationships between the four fundamental coupling constants are also found. (shrink)

Both the slasher movie and its more recent counterpart the "torture porn" film centralize graphic depictions of violence. This article inspects the nature of these portrayals by examining a motif commonly found in the cinema of homicide, dubbed here the "pure moment of murder": that is, the moment in which two characters’ bodies adjoin onscreen in an instance of graphic violence. By exploring a number of these incidents (and their various modes of representation) in American horror films ranging from Psycho (...) (1960) to Saw VI (2009), the article aims to expound how these images of slaughter demonstrate (albeit in an augmented, hyperbolic manner) a number of long-standing problems surrounding selfhood that continue to fuel philosophical discussion. The article argues that the visual adjoining of victim and killer onscreen echoes the conundrum that in order to attain identity, the individual requires and yet simultaneously repudiates the Other that constitutes unique subjectivity. (shrink)

Many natural scientists of the past and the present have imagined that they pursued their activity according to its own inherent rules in a realm distinctly separate from the business world, or at least in a realm where business tended to interfere with science from time to time, but was not ultimately an essential component, ‘because one thought that in science one possessed and loved something unselfish, harmless, self-sufficient, and truly innocent, in which man’s evil impulses had no part whatever’, (...) as Nietzsche once commented (Nietzsche 1974, p.106). With the extreme technological changes that have occurred in the last fifty years and the orchestrated management changes in the culture of science, it is now obvious that science is intimately tied to private businesses, industry, and society. Within this structure, the scientist has generally unknowingly defined him or herself in accordance with obsolete myths that have tended to handicap the scientist’s freedom of action, by obscuring the modern political and economic realities of science, and neglecting the inherent responsibilities of the scientist as a critical actor in the theater of human civilization. The increasing incorporation of academic science and private industry, and the governmentally supervised nature of modem academic science, has corrupted the traditional freedom and character of the scientist. In order to navigate oneself and find meaning within the new structure of science, scientists now desperately need a fresh ethos that at once considers modern realities of the politics and management of science, societal urgencies, and global politics, as well as establishing a moral perspective where modern scientists can be actors with their own intentionality and responsibility. -/- In the culture of science, myths and ideologies are of critical importance for the formation of the scientist, because these ideas determine how scientists conceive of themselves as professionals and free individuals. More importantly, these ideas determine how scientists approach scientific activity, which exists in a social context, and which ultimately has the potential to dramatically change the characteristics of civilization as it is played out on the political and technological battlefield. It is a commonly held notion in the community of the natural sciences that science now is essentially what it was when it was described by the Nobel laureates of the past; those sweet, cushioning, pleasant words consecrating the ‘temple of science’; the picture of a humble, rational, and noble Einstein is imprinted into our memories. By dismantling these obsolete myths of the scientist and surveying contemporary trends in science, this article will explore a more realistic perspective toward the field of science. The goal of this investigation is to determine the modern reality and ultimate meaning of ‘science as a vocation’ (Shorett 2003). Finally, moral philosophy will be demonstrated to be a critical clement in the self-assertion of the scientist and the elucidation of the meaning of science as a vocation in a global technological society. -/- From the Postscript, 2015: This article took final form when I was a postdoctoral researcher in Canada. Reading it now, I recognize the article still has value, despite its many flaws, hyperboles, and idealism. Many issues in the article have become increasingly relevant, such as the need to make constant trade-offs in courses of action and continuously search for more morally significant research paths. Perhaps the greatest goals in writing the article were to increase intellectual control over the path of my scientific research, to escape the increasing conformity and constraints on modern life, to participate in an open society, to formulate my personal goals and goal hierarchies, to dispel any delusions of overconfidence, and to not be corrupted. (shrink)

Nietzsche (1844–1900) struggles with complexity and many-sidedness throughout his life. He is a nuanced thinker who offers fragments instead of a rigid philosophical system, yet he admires the ‘virtuous energy’ with which systematic thinkers, especially the pre-Socratic philosophers, express themselves. His ability to write with comparable energy is hindered by university philosophy, which privileges restraint and consistency. Therefore, he adopts a practice of spontaneous life writing in order to become simple and honest in thought and life. Inspired by figures such (...) as Emerson, Diogenes, and Sterne, he grasps the ‘nearest shoddy words’ and continually produces new insights in disjointed monologues and aphorisms. Nietzsche's vague metaphors, loose language, inconsistency, and hyperbole stem from this practice, and his autobiography, Ecce Homo (1888), is the closest that he ever comes to rekindling the energy of the pre-Socratics. (shrink)

In this work we study dimensional theoretical properties of some a±ne dynamical systems. By dimensional theoretical properties we mean Hausdor® dimension and box- counting dimension of invariant sets and ergodic measures on theses sets. Especially we are interested in two problems. First we ask whether the Hausdor® and box- counting dimension of invariant sets coincide. Second we ask whether there exists an ergodic measure of full Hausdor® dimension on these invariant sets. If this is not the case we ask the (...) question, whether at least the variational principle for Haus- dor® dimension holds, which means that there is a sequence of ergodic measures such that their Hausdor® dimension approximates the Hausdor® dimension of the invariant set. It seems to be well accepted by experts that these questions are of great importance in developing a dimension theory of dynamical systems (see the book of Pesin about dimension theory of dynamical systems [PE2]). Dimensional theoretical properties of conformal dynamical systems are fairly well understood today. For example there are general theorems about conformal repellers and hyperbolic sets for conformal di®eomorphisms (see chapter 7 of [PE2]). On the other hand the existence of two di®erent rates of expansion or contraction forces problems that are not captured by a general theory this days. At this stage of de- velopment of the dimension theory of dynamical systems it seems natural to study non conformal examples. This is the ¯rst step to understand the mechanisms that determine dimensional theoretical properties of non conformal dynamical systems. A±ne dynamical systems represent simple examples of non conformal systems. They are easy to de¯ne, but studying their dimensional theoretical properties does never- theless provide challenging mathematical problems and exemplify interesting phe- nomena. We consider here a special class of self-a±ne repellers in dimension two, depending on four parameters (see 2.1.). Furthermore we study a class of attractors of piecewise a±ne maps in dimension three depending on four parameters as well. The last object of our work are projections of these maps that are known as gener- alized Baker's transformations (see 2.2.). The contents of our work is the following: In chapter two we give an overview about some main results in the area of di- mension theory of a±ne dynamical systems and de¯ne the systems we study in this work. We will explain, what is known about the dimensional theoretical properties of these systems and describe what our new results are. In chapter three we then apply symbolic dynamics to our systems. We will introduce explicit shift codings 4 and ¯nd representations of all ergodic measures for our systems using these codings. From chapter four to chapter eight we study dimensional theoretical properties, which our systems generally or generically have. In chapter four we will prove a formula for the box-counting dimension of the repellers and the attractors (see the- orem 4.1.). Then in chapter ¯ve we apply general dimensional theoretical results for ergodic measures found by Ledrappier and Young [LY] and Barreira, Schmeling and Pesin [BPS] to our systems. These results relate the dimension of ergodic measures to metric entropy and Lyapunov exponents. Using this approach we will be able to reduce questions about the dimension of ergodic measures in our context to ques- tions about certain overlapping and especially overlapping self-similar measures on the line. These overlapping self-similar measures are studied in chapter six. Our main theorem extends a result of Peres and Solomyak [PS2] concerning the absolute continuity resp. singularity of symmetric self-similar measures to asymmetric ones (see theorem 6.1.3.). In chapter seven we bring our results together. We prove that we generically (in the sense of Lebesgue measure on a part of the parameter space) have the iden- tity of box-counting and Hausdor® dimension for the repellers and the attractors. (see theorem 7.1.1. and corollary 7.1.2.). This result suggest that one can expect that the identity of box-counting dimension and Hausdor® dimension holds at least generically in some natural classes of non conformal dynamical systems. Furthermore we will see in chapter seven that there generically exists an ergodic measure of full Hausdor® dimension for the repellers. On the other hand the vari- ational principle for Hausdor® dimension is not generic for the attractors. It holds only if we assume a certain symmetry (see theorem 7.1.1.). For generalized Baker's transformations we will ¯nd a part of the parameter space where there generically is an ergodic measure of full dimension and a part where the variational principle for Hausdor® dimension does not hold (see theorem 7.1.3.). Roughly speaking the reason why the variational principle does not hold here is, that if there exists both a stable and an unstable direction one can not generically maximize the dimension in the stable and in the unstable direction at the same time. In an other setting this phenomenon was observed before by Manning and McCluskey [MM]. In chapter eight we extend some results of the last section to invariant sets that correspond to special Markov chains instead of full shifts (see theorem 8.1.1.). In the last two chapters of our work we are interested in number theoretical excep- tions to our generic results. The starting point of our considerations in section nine are results of ErdÄos [ER1] and Alexander and Yorke [AY] that establish singularity and a decrease of dimension for in¯nite convolved Bernoulli measures under special conditions. Using a generalized notion of the Garsia entropy ([GA1/2]) we are able 5 to understand the consequences of number theoretical peculiarities in broader class of overlapping measures (see theorem 9.1.1.). In chapter ten we then analyze number theoretical peculiarities in the context of our dynamical systems. We restrict our attention to a symmetric situation where we generically have the existence of a Bernoulli measure of full dimension and the identity of Hausdor® and box-counting dimension for all of our systems. In the ¯rst section of chapter ten we ¯nd parameter values such that the variational principle for Hausdor® dimension does not hold for the attractors and for the Fat Baker's transformations (see theorem 10.1.1.). These are the ¯rst known examples of dynamical systems for which the variational principle for Hausdor® dimension does not hold because of number theoretical peculiarities of parameter values. For the repellers we have been able to show that under certain number theoretical conditions there is at least no Bernoulli measure of full Hausdor® dimension; the question if the variational principle for Hausdor® dimension holds remains open in this situation. In the second section of chapter ten we will show that the identity for Hausdor® and box-counting dimension can drops because there are number theoretical pecu- liarities. In the context of Weierstrass-like functions this phenomenon was observed by Przytycki and Urbanski [PU]. Our theorem extends this result to a larger class of sets, invariant under dynamical systems (see theorem 10.2.1). At the end of this work the reader will ¯nd two appendices, a list of notations and the list of references. In appendix A we introduce the notions of dimension we use in this work and collect some general facts in dimension theory. In appendix B we state the facts about Pisot-Vijayarghavan number, we need in our analysis of number theoretical peculiarities. The list of notations contains general notations and a table with a summary of notations we use to describe the dynamical systems that we study. Acknowledgments I wish to thank my supervisor JÄorg Schmeling for a lot of valuable discussion and all his help. Also thanks to Luis Barreira for his great hospitality in Lisboa and many interesting comments. This work was done while I was supported by "Promotionstipendium gem. NaFÄoG der Freien UniversitÄat Berlin". (shrink)

‘Intentionalist’ approaches portray self-deceivers as “akratic believers”, subjects who deliberately choose to believe p despite knowing that p is false. In this paper I argue that the intentionalist model leads to a number of paradoxes that seem to undermine it. I claim that these paradoxes can nevertheless be overcome in light of the rival hypothesis that self-deception is a non-intentional process that stems from the influence of emotions upon cognitive processes. Furthermore, I propose a motivational interpretation of the phenomenon of (...) ‘hyperbolic discounting bias’ which highlights the role of emotional biases in akratic behavior. Finally, I argue that we are not the helpless victims of our irrational attitudes, insofar as we have the ability – and arguably the epistemic obligation – to counteract motivational biases. (shrink)

Jacques Derrida begins the first chapter of his book The Politics of Friendship1 with a statement attributed to Aristotle by both Diogenes Laertes and the 16th Century French philosopher Michel de Montaigne. The statement is this: “O my friends, there is no friend.” Derrida points out the paradox and apparent contradication in such an impossible declaration. Who is Aristotle talking to, given that he is addressing friends to inform them that there are none? How can the statement be taken seriously? (...) We might say that the paradox is a result of a bit of philosophical licence on Aristotle’s part. Aristotle defines the friend as “another self”2 and since it is logically impossible that the friend could actually be another self, then this is simply a bit of philosophical hyperbole that Aristotle engages in, but about which he is not serious. Yet the fact that Derrida has written three hundred pages of text on this subject suggests that this interpretation would be hard to sustain. As the title of his text suggests, Derrida approaches the question of friendship via an analogy with politics, specifically with republican democracy. This paper focuses on three aspects of that analogy. (shrink)

In AI safety research, the median timing of AGI arrival is often taken as a reference point, which various polls predict to happen in the middle of 21 century, but for maximum safety, we should determine the earliest possible time of Dangerous AI arrival. Such Dangerous AI could be either AGI, capable of acting completely independently in the real world and of winning in most real-world conflicts with humans, or an AI helping humans to build weapons of mass destruction, or (...) a national state coupled with AI-based government system. In this article, I demonstrate that the earliest timing of Dangerous AI, corresponding to 10 per cent of its arrival probability, is before 2030. Several partly independent sources of information are in accordance: 1. The growth of the hardware available for AI research makes human-brain-equivalents of compute available for AI research in the 2020s. It is fuelled by specialized AI-chips, the use of many chips in one processing unit, and the larger research budgets, among other things. 2. The neural network performance and other characteristics, like the number of parameters, is quickly increasing every year, and extrapolating this tendency suggests that roughly human-level performance in a few years, around 2025. 3. Expert polls show around 10 per cent of the probability of an early appearance of artificial general intelligence (AGI) in the next decade, that is, before 2030. 4. Hyperbolic growth in different big history models converges around 2025-2030 (the technological singularity). 5. Anthropic arguments (similar to the Doomsday argument) suggest that qualified observers are more likely to appear near the end of the AI research epoch, as the number of such observers grew exponentially. This number doubles every 5-10 years, and thus we are likely to find ourselves around a decade before the end of AI research, which will happen consequently around 2030. (shrink)

In AI safety research, the median timing of AGI creation is often taken as a reference point, which various polls predict will happen in second half of the 21 century, but for maximum safety, we should determine the earliest possible time of dangerous AI arrival and define a minimum acceptable level of AI risk. Such dangerous AI could be either narrow AI facilitating research into potentially dangerous technology like biotech, or AGI, capable of acting completely independently in the real world (...) or an AI capable of starting unlimited self-improvement. In this article, I present arguments that place the earliest timing of dangerous AI in the coming 10–20 years, using several partly independent sources of information: 1. Polls, which show around a 10 percent of the probability of an early creation of artificial general intelligence in the next 10-15 years. 2. The fact that artificial neural network (ANN) performance and other characteristics, like number of “neurons”, are doubling every year, and extrapolating this tendency suggests that roughly human-level performance will be reached in less than a decade. 3. The acceleration of the hardware performance available for AI research, which outperforms Moore’s law thanks to advances in specialized AI hardware, better integration of such hardware in larger computers, cloud computing and larger budgets. 4. Hyperbolic growth extrapolations of big history models. (shrink)

This paper inquires into literariness, a much neglected problem in translation, from a cognitive poetic perspective; it tries to show the nature of proxy as concerns translation through various illustrations, hence what is termed by Bausse-Beier the proxy principle, and in passing answer the philosophical problem of translatability or untranslatability. Literariness, not limited to literature, may exist in all texts. It can be defined as the form of a text that is suggestive of something, different from that of a text (...) that is not. Any text that is literary is a literary text. Literariness may be realized through the use of metaphors, personifications, imagery, hyperbole and so on, and through the employment of pattern such as alliteration, paranomasia, meter, rhyme and so on. In translating a literary text, a translator should capture the literariness, otherwise the translation fails. However, in the process of translation, some of these features that contribute to the form, such as phonological or prosodic ones, will be definitely lost. If literariness is to be maintained, there should be a way for compensation. Analogy comes to the fore, though translation is by nature analogical; it is employed to reveal the iconicity between signifier and signified through some means of representation. In such an endeavor, optimum relevance should be aimed at so that a good proxy can be ensured: what is in the mind of an original reader should be that in the mind of a translation reader. (shrink)

This paper discusses the validity of nudges to tackle time-inconsistent behaviours. I show that libertarian paternalism is grounded on a peculiar model of personal identity, and that the argument according to which nudges may improve one’s self-assessed well-being can be seriously questioned. I show that time inconsistencies do not necessarily reveal that the decision maker is irrational: they can also be the result of discounting over the degree of psychological connectedness between our successive selves rather than over time. Time inconsistency (...) can call for paternalism if and only if we accept that an individual is characterised by stable “true” preferences over time-dependent outcomes, and that she is rationally required to make time-consistent choices. This model is descriptively and normatively questionable. I then argue that behavioural findings may still justify paternalistic interventions, but on a non-welfarist basis. (shrink)

David Skrbina opens this timely and intriguing text with a suitably puzzling line from the Diamond Sutra: ‘‘Mind that abides nowhere must come forth.’’, and he urges us to ‘‘de-emphasise the quest for the specifically human embodiment of mind’’ and follow Empedocles, progressing ‘‘with good will and unclouded attention’’ into the text which he has drawn together as editor. If we do, we are assured that it will ‘‘yield great things’’ (p. xi). This, I am pleased to say, is not (...) an exercise in hyperbole. (shrink)

We propose a theoretical model to explain the usage of time-inconsistent behavior as a strategy to exploit others when reputation and trust have secondary effects on the economic outcome. We consider two agents with time-consistent preferences exploiting common resources. Supposing that an agent is believed to have time-inconsistent preferences with probability p, we analyze whether she uses this misinformation when she has the opportunity to use it. Using the model originally provided by Levhari and Mirman (Bell J Econ 11(1):322–334, 1980), (...) we determine the optimal degree of present bias that the agent would like to have while pretending to have time-inconsistent preferences and we provide the range of present-bias parameter under which deceiving is optimal. Moreover, by allowing the constant relative risk aversion class of utility form, we characterize the distinction between pretending to be naive and sophisticated. (shrink)

1 Th. 5:17 tells us to pray without ceasing. Many have worried that praying without ceasing seems impossible. Most address the problem by giving an account of the true nature of prayer. Unexplored are strategies for dealing with the problem that are neutral on the nature of prayer, strategies consistent, for example, with the view that only petition is prayer. In this article, after clarifying the nature of the problem for praying without ceasing, I identify and explore the prospects of (...) five different strategies that are neutral in this sense. I also raise problems for each strategy. (shrink)