Arithmetical texts involving division are governed by conventions that avoid the risk of problems to do with division by zero (DbZ). A model for elementary arithmetic texts is given, and with the help of many examples and counter examples a partial description of what may be called traditional conventions on DbZ is explored. We introduce the informal notions of legal and illegal texts to analyse these conventions. First, we show that the legality of a text is algorithmically (...) undecidable. As a consequence, we know that there is no simple sound and complete set of guidelines to determine unambiguously how DbZ is to be avoided. We argue that these observations call for further explorations of mathematical conventions. We propose a method using logics to progress the analysis of legality versus illegality: arithmetical texts in a model can be transformed into logical formulae over special total algebras that are able to approximate partiality but in a total world. The algebras we use are called common meadows. Our dive into informal mathematical practice using formal methods opens up questions about DbZ which we address in conclusion. (shrink)

We modify the payment rule of the standard divide the dollar (DD) game by introducing a second stage and thereby resolve the multiplicity problem and implement equal division of the dollar in equilibrium. In the standard DD game, if the sum of players’ demands is less than or equal to a dollar, each player receives what he demanded; if the sum of demands is greater than a dollar, all players receive zero. We modify this second part, which involves (...) a harsh punishment. In the modified game $(D\!D^{\prime })$ , if the demands are incompatible, then players have one more chance. In particular, they play an ultimatum game to avoid the excess. In the two-player version of this game, there is a unique subgame perfect Nash equilibrium in which players demand (and receive) an equal share of the dollar. We also provide an $n$ -player extension of our mechanism. Finally, the mechanism we propose eliminates not only all pure strategy equilibria involving unequal divisions of the dollar, but also all equilibria where players mix over different demands in the first stage. (shrink)

Sir Isaac Newton, writing in Latin, defined his celebrated laws of motion verbally. When the laws of motion are read as relating to his arithmetic and his calculus, division by zero is undefined so his physics fails at mathematical singularities. The situation is unchanged in modern real arithmetic and real calculus: division by zero is undefined so both Newtonian Physics and its modern developments fail at mathematical singularities. However, when Newton’s text is read as relating to (...) transreal arithmetic and transreal calculus, division by zero is defined and we show that the resulting Transreal Newtonian Physics does operate at mathematical singularities. We hold out the hope that the whole of modern physics may be similarly extended. We use the new physics to predict a convection current at the singularity in a black hole and suggest experiments in astronomy and high energy physics that might confirm or rebut our predictions. Thus our exegesis of Newton’s text extends mathematical physics and may, in future, extend experimental physics. (shrink)

A chapter in an edited volume discussing philosophy and Ted Chiang's short stories. In this chapter, I show how philosophical debates about imaginative resistance and what can/can't be fictionally true influence our interpretation of "Division by Zero.".

This book aims to provide a solution to the semantic paradoxes. It argues for a unified solution to the paradoxes generated by our concepts of denotation, predicate extension, and truth. The solution makes two main claims. The first is that our semantic expressions 'denotes', 'extension' and 'true' are context-sensitive. The second, inspired by a brief, tantalizing remark of Godel's, is that these expressions are significant everywhere except for certain singularities, in analogy with division by zero. A formal theory (...) of singularities is presented and applied to a wide variety of versions of the definability paradoxes, Russell's paradox, and the Liar paradox. Keith Simmons argues that the singularity theory satisfies the following desiderata: it recognizes that the proper setting of the semantic paradoxes is natural language, not regimented formal languages; it minimizes any revision to our semantic concepts; it respects as far as possible Tarski's intuition that natural languages are universal; it responds adequately to the threat of revenge paradoxes; and it preserves classical logic and semantics. Simmons draws out the consequences of the singularity theory for deflationary views of our semantic concepts, and concludes that if we accept the singularity theory, we must reject deflationism. (shrink)

Linked with existence of the almighty, the operation of division by zero which is considered as undefined or indeterminate or infinite sometimes, has been a topic of serious altercation among mathematicians and philosophers for so long. History is evident of the various attempts made to clearly define the algebra of zero, including the idea of division by zero. This includes the evolution of the idea of zero division and various insights from mathematicians like (...) Euler, Craig and more. The realm of the paper contains all such significant attempts and it deals with the idea of the history that wishes to explore the evolution of infinity and undefined. The prime aim of this paper is to clearly distinguish the three concepts of Undefined, Indeterminate and Infinity, along with the concept of division by zero. It strives to provide a notation to undefined expressions, along with citing justifications and results with the help of unpretentious examples from key branches. (shrink)

While Bernard Suits's understanding of games has significantly influenced the philosophy of sport, the longest sustained investigation in The Grasshopper is of make-believe and roleplaying games. Suits’s discussion of make-believe and roleplaying is found in chapters 9 through 12, but what he says there is uncharacteristically unclear. To clarify Suits’s account, the present paper distinguishes between two arguments that Suits interweaves. In the first, Suits argues that game playing is not a species of play. In the second, Suits argues that (...) playing a make-believe or role-playing game is the same — at heart — as playing a game of any type. While the paper takes no position on the former, it defends the latter argument against several important objections by Thomas Hurka and C. Thi Nguyen. It contends, furthermore, that Suits is not simply trying to show that his theory of game playing can account for make-believe and roleplaying games. Rather, Suits is also using make-believe and roleplaying games to clarify exactly how his theory of game playing should be understood. (shrink)

Sophists’ apologia. -/- Sophists were the first paid teachers ever. These ancient Greek enlighteners taught wisdom. Protagoras, Antiphon, Prodicus, Hippias, Lykophron are most famous ones. Sophists views and concerns made a unified encyclopedic system aimed at teaching common wisdom, virtue, management and public speaking. Of the contemporary “enlighters”, Deil Carnegy’s educational work seems to be the most similar to sophism. Sophists were the first intellectuals – their trade was to sell knowledge. They introduced a new type of teacher-student relationship – (...) the mutually beneficial communication on equal terms. They taught pupils how to think independently and how to persuade others, which was inseparably connected with the rise of democracy in the most advanced Greek polices. Sophists were the first to proclaim that all people are naturally equal. They put forward the idea of natural rights and social contract, working out the fundamentals of the present-day law. In addition, they developed the basics of philology, psychology, logic, and gave a scientific explanation to the origins of religions. They embodied definite positive ideals of their epoch. Sophistry flourished in the second half of the Vth through he first third of the IVth centuries B. C. The period coincides with the heyday of the entire Greek history – the so called Greek Miracle epoch. Sophists expressed some present-day concepts of Ancient Greek ideology and mentality, characteristic of its Golden Age times. The Ancient Athens of the times of Periclus were similar to the Florence of Renaissance as to the type of social structure. That is why (?) the art of eloquence (public speaking) was highly respected in Florence. The two cities had a lot of features of the present-day capitalist society, which was due to their role as the main centres of industry of their “worlds-economies”. During the subsequent Hellenic period, the Old Order was restored, based on the feudal rent recipients’ rule. The degradation of society resulted in the decline of sophistry. Sophistry represents the highest point in the evolution of Greek philosophy. It is also the most prominent school as to the novelty of its ideas. That was owing to the common propensity for innovation typical of Periclus’ Golden Age, which in its turn resulted from the establishment of the individualistic and rationalistic thinking similar to present-day mentality. Among other aspects, close attention was paid to ethnic issues; some humanistic ideas such as Master and Servant ethics and Enlightment as the primary condition of man’s freedom, received scientific grounding. The genre of philosophical dialogue was developed, as well as the rationalistic scientific gnoceology, aimed at consistently opposing any religion. Dialectics, the most outstanding achievement of the Antiquity, was also worked out by the sophists. Zeno of Helleas was one of the sophists. Democrites’ ideas were, too, quite close to dialectics. Socrates’ contemporaries regarded him ironically, as shown, for example, in the Aristophanes’ comedy “Clouds”. Nevertheless, this scholar can still be referred to as a sophist, although of somewhat weird personality. Socrates’ popularity, which came later, should be attributed to the fact that he was the first philosopher ever to have been sentenced and executed by law, rather than to any valuable scientific contributions. Sophistry as such, rather than Socrates, marks the line between pre-Socratic and post- Socratic schools. Plato, with the exception of his latest works, is considered to belong to the same philosophical school. Specifically, there are valid reasons to believe that he was paid fees by his disciples. In Plato’s Dialogues, all points of view will be proven and then disproved, so that an integral philosophical system is hard to observe. Plato’s “Idealism” is but one of the many possible theories. His ideal philosophy is a high-minded argument of wise men. As late as towards the end of his life, Plato betrayed the ideals of sophistry, turning into the world’s first proponent of totalitarianism. Sophistry is Greek classical literature. Later on, philosophy, as well as the entire Greek civilization, started to fall into decline. Over 500 subsequent years, Hellenistic-Roman scholars never came up with anything novel. The entire process of antique philosophical evolution can be subdivided into the following six stages: Phoenician (IX–VIIth centuries B. C.), archaic (VIth – the first half of IVth century B. C., classic (the epoch of sophistry: the second half of the Vth through the first decades of the IIIrd centuries B. C.), late antique (middle of the IIIrd – first decades of the VI th centuries B.C.) The fact that early in the VIth century B. C. sophistry was rejected in Athens, has a lot to do with the consequences of their defeat in Peloponnesian war, a social catastrophe. Ever since, the prevalent part of the criticism of sophistry is a criticism of sophists’ immoral ways of life and personalities, rather than the essentials of their philosophy. For instance, Aristotle’s criticism primarily concerns their pragmatism and tendency to make a profit out of teaching. However, Aristotle himself taught his disciples along similar lines, showing them how to “be able to prove both opposites”. It was Aristotle who summed up sophists’ century-long elaborations. The traditional modern interpretation of sophists as shown in Plato’s dialogues appears to be groundless. The truth of the matter is that Plato regards sophists as more serious philosophers than Socrates was. It becomes especially clear in the dialogue titled “Protagoras”, which shows the latter as gaining an undoubted victory over Socrates. Generally speaking, Plato’s works never regard sophists as weak or worthless opponents. A common opinion as to the essence of sophists’, in particular, Protagoras’s philosophy, has hitherto not been worked out. Many researchers renounce the very existence of any specific philosophical position in sophistry. The term “relativism” itself now has a bad name. However, it should be borne in mind that Protagoras doctrine emerged as a result of an attempt to get out of the ontological dead-end to which the entire Greek natural philosophy had come. To this purpose, he employed Anaxagoras’s idea about everything comprising everything, whereupon he built his physical-ontological theory, and Zeno of Helleas’s concept that all objects are such and different at the same time in the same respect. According to Protagoras’s philosophy, every object does not only seem, but is different from every other object, including human beings. Therefore, every person is his or her own measure of all other entities. The objective reality is the Ego’s relations with the outer world. Every object’s essence is defined through its interaction with ourselves. Nothing remains stagnant – every existence already contains non-existence, and vice-versa. However, the relativity of being is not to be regarded as absolute. That means, that relatively stable and therefore relatively cognizable entities do exist, among them the words we say. Doubt is not considered absolute by relativists either, which differentiates them from skeptics and agnostics. They dare to believe. Uncertainty is Godly – here, Protagoras becomes very close to the concept of apathetic theology. Gorgius shared Protagoras’s views and tried to prove them applying the same method as Zeno applied when upholding Parmenidis’s philosophy. He argued that if one accepts the opposite point of view and agrees that nothing can exist and not exist at the same time, one is bound to come to an the absurd conclusion that nothing is cognizable and nothing exists. To prove that there is a universal contradiction within the Existence itself, Protagoras and his followers in their turn put forward a number of special logical arguments, called rules of contraries, or sophisms. The most well-known of them is the Euathle’s sophism, which proves that an object can be such and different at the same time in the same respect. Generally speaking, all relationships of any entity are extraneous. The idea that all entities, including concepts, exist and do not exist at the same time, was also accepted by Plato. It should be stressed, that Plato’s philosophy as a whole is relativists’ greatest achievement. In his dispute against relativism, Aristotle put forward the main concepts of his ontology: the existence falls into the existence in possibility and the existence in reality, or substance and accidence – the ever changing “sublunary” world and the stable world of divine heavenly bodies. This division made his system self-contradictory to the point of absurd. Aristotle quite realized, that the direct disproof of relativism is hardly possible, which fact makes his criticism a mere tautology. It is very indicative in this respect that materialists, idealists and even skeptical agnostics applied the same arguments do disprove relativism. That demonstrates that the inner contradiction between any forms of “absolutism” and relativism is the most fundamental philosophical problem. Relativist ideas were repeatedly renewed throughout history, provided the social conditions were favourable. In variations, the concepts were advanced by Tzuan Tsi and ancient Chinese sophists, apostle Paul, Nicolas of Cusa, Galileo, Rene Descartes, G. Berkley, D. Hume, Ch. S. Pierce, E. Mach, A. Bogdanov, F. de Saussure, N. Bore, P. Feuerabend, U. Quain and others. However, no consistent relativist ontological system was developed after Protagoras. Meanwhile, a valid relativist theory could provide a clue to a fuller and more adequate general physical concept of the world, and to a deeper understanding of quantum mechanics. -/- Relativism as an ontological system of beliefs. -/- The relativist principle of relativity of all that exists is fundamental for the entire system of philosophy. Absolutely everything exists, but, at the same time, no existence is absolute. Anything is possible, but those entities only exist for us with which we interact this way or another, i. e., reality is interaction, “I interact – hence, I exist”. However, an overly close relationship between entities leads to non-existence – in other words, there is a certain existential optimum. For all of us, information, or perceptible heterogeneities, is real. Each of us is the center of a definite system of interactions with the world. If God is an endless Possibility, then the World is but the man’s dialogue with God. However, the ties that bind us with the world are of some definite kind, which predetermines our reality. The principle of relativity constrains itself, as any relativity is relative. On the one hand, that calls forth the Evil – caused by our own weakness. On the other hand, it makes our world relatively stable and cognizable. Generally speaking, the world is what we are. Everybody has an own Universe, but since people are fairly similar, our universes can be regarded as one Universe with common laws and regulations. It is possible for us to change the degree of objects’ existence in relation to ourselves and one another. It is equally important, though, to remain ourselves (keep following our “warrior’s path”). Since everything exists and no existence is absolute, the process of cognition should involve a criticism of everything but never a complete rebuttal of anything. The criterion of verity for any theory then is in its capacity to build itself upon a bigger number of diverse statements than in any other theory. Theoretically, all philosophies should ideally be complementary. The question of what in fact happened is meaningless unless we specify the “we”, the “where” and the “when”. The past can only exist as part of the present. When we change, our past undergoes corresponding qualitative objective changes, all of which are irreversible. The contemporary physics regards all objects of the Universe as existing for one another, which results in absurd conclusions. In fact, only what we interact with, exists. The so called “speed of light in vacuum” c is the maximum speed of direct interaction and direct exchange of signals. Specifically, at the oncoming speed c with a significant blue parallax the gamma-quantum is unable to interact with the matter. When this speed is reached, the gravitational mass of objects in relation to one another becomes equal to zero (imaginary), whereas their inertial mass equals infinity. Further acceleration will bring us into an entirely different Universe. That means that the Universe is an open system, which fact destroys all present-day cosmological models. Anything is possible in this world. Our reality is magic. Every bit of space contains a potentially limitless number of bits of other, however virtual, universes, as well as an infinite number of particles, which are still virtual for us (as postulated by quantum mechanics). In other words, there exists an infinity of different realities. With all the above in mind, the different levels of entities’ existence, in particular, of Life and Reason, should be taken into consideration. For example, to which extent a live system exists in relation to the inanimate forms of being is very indefinite, as what life is has to be determined by living creatures. An even greater compass of levels of existence can be brought about through interaction – that is the core idea of Godel’s theorem. As a result, the range of forms of existence tends towards infinity – the evolution of matter through super-intelligence will bring us up to God’s heights. A more generalized mathematical model of the physical world, including a universal operator of the co-existence of objects, can be developed based on the above considerations. The bonds between objects become weaker owing to 1) a high speed, 2) acceleration, 3) rotation, 4) strong gravity, 5) strong fields of other kinds, 6) the difference of levels of existence , 7) phase shifts. Yet, there always is an existential optimum. Such mathematical model is to operate certain non-transitive algebras. Relativist ontology assumes that the notion of “temperature” is relative, thus making it possible to ignore the Second Law of Thermodynamics. In its turn, that will allow for phase shifts. A perpetual motion machine of the second type will become a reality. Rotation could presumably be used to increase inertial and decrease gravitational mass, slowing down the time. An experimental research could shed light on the mentioned effects. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Weight of Rhetoric: Studies in Cultural DeliriumThomas B. FarrellThere is something of this anachronistic doggedness in all importance, and to use it as a criterion of thought is to impose on thought a spellbound fixity, and a loss of self-reflection. The great themes are nothing other than primeval rumblings which cause the animal to pause and try to bring them forth once again. This does not mean that (...) the hierarchy of importance should be ignored. Just as its narrow- mindedness reflects that of the system, so it is saturated with all the latter’s force and stringency. Thought ought not, however, to repeat this hierarchy, but by completing, end it. The division of the world into important and unimportant matters, which has always served to neutralize the key phenomena of social injustice as mere exceptions, should be followed up to the point where it is convicted of its own untruth. The division which makes everything objects must itself become an object of thought, instead of guiding it. The large themes will then make their appearance, though hardly in the traditional “thematic” sense, but refractedly and eccentrically.—Theodor Adorno, Minima MoraliaBoy, you’re going to carry that weight, carry that weight a long time.—The Beatles [End Page 467]Preface: on Attachments—Flowers and the InfinitesimalThe number of adjustments it takes to make a square into a circle, the number of times any real number may be subdivided before reaching zero, the grainy inflections differentiating snowflakes, the differences among petals in a tulip—these are the sort of qualitative distinctions some of us might call minute and other cynical souls might consider trivial. But if the attachment of real human interest to objects of longing is any measure of worth, then they are far from insignificant.Imagine the following sequence of events. A young kid, fourteen or so, is out with some friends one summer evening and decides—on a whimsical adolescent impulse—to pick some tulips from a neighbor’s garden to leave at a girlfriend’s front porch. What follows?The neighbors, one of whom turns out to be a self-professed horticulturist and gardening aficionado, call the police and file a criminal complaint. The girlfriend’s parents give the alleged offender’s name to the same authorities. When the kid comes to the door of the neighbors to apologize, he is verbally threatened. When he writes a letter of contrition and remorse to the neighbors, they turn the letter over to the police as evidence. One day later, the neighbors angrily phone local school officials to complain of his behavior. Two days later, when two of the kid’s accomplices are summarily removed from eighth grade, taken to the police station, fingerprinted, and booked (without being informed of their rights), the parents reluctantly secure the services of an attorney (two attorneys, actually). When an outof- court settlement is finally agreed to, it is discovered that the city police have already passed the case on to the State’s Attorney’s Office. A criminal hearing will now need to be held in juvenile court. When the hearing is held, the charges are summarily dismissed. The cost? Several hundred dollars a tulip (with side effects including migraines, despondency, two trips to the emergency room, not to mention rather hefty attorneys’ fees).As the reader has probably surmised by now, this thinly disguised episode did not occur to Gregor Samsa but to someone near and dear to your author. It did not occur in Singapore but in Evanston, Illinois. All of us can probably recall occasions when things seemed to careen wildly out of control and apparently minor matters took on disproportionately inflated significance. We struggle to “make sense” of these episodes, for ourselves and others. In the above example, two allegories about magnitude surfaced. One, relayed to me by our grizzled Chicago attorney, addressed the question [End Page 468] of how to explain these events to our son. “Tell him,” he said, “that there are a lot of jerks in the world” (except he didn’t use the word “jerks”). A second allegory emerged rather belatedly. There was more than one nonrational attachment in... (shrink)

Outside (though not completely so) the circuit of the international division of labor, there are people whose consciousness we cannot grasp if we close off our benevolence by constructing a homogeneous Other referring only to our own place in the seat of the Same or the Self. Here are subsistence farmers, unorganized peasant labor, the tribals, and the communities of zero workers on the street or in the countryside. To confront them is not to represent (vertreten) them but (...) to learn to represent (darstellen) ourselves. Spivak (1988, 288-9). (shrink)

Most properties have comparatives, which are relations. For instance, the property of width has the comparative relation denoted by `_ is wider than _'. Let us say a property is reducible to its comparative if any statement that refers to the property has the same meaning as another statement that refers to the comparative instead. Width is not reducible to its comparative. To be sure, many statements that refer to width are reducible: for instance, `The Mississippi is wide' means the (...) same as `The Mississippi is wider than most rivers'. But some statements that refer to width are not reducible: for instance, `Electrons have zero width' is not. A property is not reducible to its comparative if it has absolute degrees, and specifically an absolute zero. A property's comparative relation places things in an order from those that have the property least to those that have it most. If there is an absolute zero point somewhere in this ordering, the property is not reducible to its comparative. For width, there is an absolute zero at one end of the ordering, so width is not reducible. The property of goodness is reducible to its comparative, betterness. In particular, there is no absolute zero of goodness. Things are ordered by betterness – some things are better than others – but nothing is absolutely good or absolutely bad. This is an exaggeration. In certain applications, goodness does have absolute degrees of a sort, and an absolute zero. For instance, it makes sense to say an event is good, and another event bad. These are absolute degrees of a sort, but they are themselves reducible to betterness. To say an event is good simply means the event is better than what would otherwise have happened. The goodness of lives has a different sort of absolute zero. Lives are ordered by betterness; some lives are better than others. We can make sense of the question `Where in this ordering is the division between lives that are good and those that are bad?' The division between good and bad lives is again reducible to betterness. To say a person's life is good means it is better that the person should continue living, rather than that she should die. Or it may mean it is better that her life should be lived rather than that it should never have been lived at all. As it is often put: a good life is a life worth living. Derek Parfit appears to attach a different sense to the idea of a good life. He appears to mean a life that contains a preponderance of good things (such as pleasure) over bad things (such as pain). If a life contains no good things and no bad things, it has zero goodness in this sense. In this sense, absolute goodness and the absolute zero of goodness are not reducible to betterness. However, this is a naturalistic sense of goodness, and it is subject to the open-question objection. If a life contains no good things and no bad things, it is an open question whether it has zero goodness. It might, for instance, be a bad thing that this life should be lived. In discussing the evil of death, some philosophers seem to have been searching for an absolute goodness that is not reducible to betterness. Thomas Nagel speaks of an asymmetry between what is good about life and what is bad about death. But if a person's life is good, that only means it would be better that she should continue living than that she should die. And if a person's death would be bad, that only means it would be worse that she should die than that she should continue living. So there can be no asymmetry. (shrink)

Exemption claims remain a tangled and divisive moral and legal issue both in academia and in the public sphere. In his book Exemptions: Necessary, Justified, or Misguided?, the constitutional scholar Kent Greenawalt zeros in on the vexed question of whether exemptions from rules of general applicability based on the conscientious convictions of individuals or groups are sometimes justified or prudent by discussing a wide range of cases drawn from the American jurisprudence. Although he does not engage in a significant way (...) with political and legal philosophy and comparative law, his contextualist and pragmatic approach is a powerful antidote against oversimplification and dogmatism with regard to exemption claims. Unsurprisingly, Greenawalt’s approach comes at times dangerously close to casuistry, and some of his analyses and normative recommendations would benefit from a firmer footing in moral principles and rational argumentation. In this review, I flesh out some of the strengths and limits of Greenawalt’s valuable book. (shrink)

In _The Immaterial_,_ _French social philosopher André Gorz argues, in his finely-tuned and polemical style, that the economic boom that accelerated in the 1990s and crashed so spectacularly in 2008 was based largely on an immaterial consumption of symbols and ideas, as capitalism tried to overcome the crisis of the formally industrial regime by throwing itself into a new, so-called knowledge economy. In this, the last full-length theoretical work Gorz completed before his death, he argues instead for the creation of (...) a true knowledge economy. This economy would be based on zero-cost exchange and pooled resources, and knowledge would be treated as humanity’s common property. Currently, in order to exploit knowledge and turn it into capital, the capitalist enterprise privatizes specialized knowledge and claims ownership through private licenses and copyright. But as Gorz shows, the traditional foundations of such capitalist economics have begun to crumble because of the immaterial nature of this new form of product, which makes it almost impossible to measure in monetary terms. The knowledge economy, Gorz declares, _is_ the crisis of capitalism. Thought-provoking and divisive, _The Immaterial _is the perfect book for our time, as we begin to reimagine the structures of our economic system in order to rebuild and move forward. “It is to Gorz... that readers should turn for a compelling combination of sharp analysis, well-wrought polemic, and suggestions for the future.”—_Red Pepper_ “A great figure of the intellectual Left.”—Nicolas Sarkozy “Gorz’s intelligence strikes you at the very first glance: it is one of the nimblest, acutest intelligences I know.”—Jean-Paul Sartre. (shrink)

Newtonian physics is based on Newtonian calculus applied to Newtonian dynamics. New paradigms such as ‘modified Newtonian dynamics’ change the dynamics, but do not alter the calculus. However, calculus is dependent on arithmetic, that is the ways we add and multiply numbers. For example, in special relativity we add and subtract velocities by means of addition β1⊕β2=tanh+tanh-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta _1\oplus \beta _2=\tanh \big +\tanh ^{-1}\big )$$\end{document}, although multiplication β1⊙β2=tanh·tanh-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} (...) \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta _1\odot \beta _2=\tanh \big \cdot \tanh ^{-1}\big )$$\end{document}, and division β1⊘β2=tanh/tanh-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\beta _1\oslash \beta _2=\tanh \big /\tanh ^{-1}\big )$$\end{document} do not seem to appear in the literature. The map fX=tanh-1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_{\mathbb{X}}=\tanh ^{-1}$$\end{document} defines an isomorphism of the arithmetic in X=\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{X}}=$$\end{document} with the standard one in R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}}$$\end{document}. The new arithmetic is projective and non-Diophantine in the sense of Burgin, 1977), while ultrarelativistic velocities are super-large in the sense of Kolmogorov, 1961). Velocity of light plays a role of non-Diophantine infinity. The new arithmetic allows us to define the corresponding derivative and integral, and thus a new calculus which is non-Newtonian in the sense of Grossman and Katz. Treating the above example as a paradigm, we ask what can be said about the set X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{X}}$$\end{document} of ‘real numbers’, and the isomorphism fX:X→R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_{{\mathbb{X}}}:{\mathbb{X}}\rightarrow {\mathbb{R}}$$\end{document}, if we assume the standard form of Newtonian mechanics and general relativity but demand agreement with astrophysical observations. It turns out that the observable accelerated expansion of the Universe can be reconstructed with zero cosmological constant if fX≈0.8sinh/\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f_{\mathbb{X}}\approx 0.8\sinh /$$\end{document}. The resulting non-Newtonian model is exactly equivalent to the standard Newtonian one with ΩΛ=0.7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega _\Lambda =0.7$$\end{document}, ΩM=0.3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega _M=0.3$$\end{document}. Asymptotically flat rotation curves are obtained if ‘zero’, the neutral element 0X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0_{{\mathbb{X}}}$$\end{document} of addition, is nonzero from the point of view of the standard arithmetic of R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}}$$\end{document}. This implies fX-1=0X>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f^{-1}_{{\mathbb{X}}}=0_{{\mathbb{X}}}>0$$\end{document}. The opposition Diophantine versus non-Diophantine, or Newtonian versus non-Newtonian, is an arithmetic analogue of Euclidean versus non-Euclidean in geometry. We do not yet know if the proposed generalization ultimately removes any need of dark matter, but it will certainly change estimates of its parameters. Physics of the dark universe seems to be both geometry and arithmetic. (shrink)

I offer a novel solution to Zeno’s paradox of The Arrow by introducing nilpotent infinitesimal lengths of time. Nilpotents are nonzero numbers that yield zero when multiplied by themselves a certain number of times. Zeno’s Arrow goes like this: during the present, a flying arrow is moving in virtue of its being in flight. However, if the present is a single point in time, then the arrow is frozen in place during that time. Therefore, the arrow is both moving (...) and at rest. In “Zeno’s Arrow, Divisible Infinitesimals, and Chrysippus,” White suggests using an infinitesimal value as the length of the present. Contra Zeno, this allows the arrow to be moving in the present, rather than frozen in place. In this paper, I follow the basic outline of White’s solution but argue that his solution suffers from arbitrariness and a related theoretical artificiality in relation to the system of infinitesimals he invokes, viz. in relation to the hyperreal infinitesimals of nonstandard analysis. After arguing that any solution to the paradox must satisfy certain theoretical requirements, I examine White’s solution alongside two nilpotent solutions. One of these solutions is inspired by F.W. Lawvere’s Smooth Infinitesimal Analysis and the other is inspired by Paolo Giordano’s ring of Fermat Reals. I argue that Giordano’s nilpotents supply the best answer to Zeno’s paradox. (shrink)

Take any putative ordinary object which is divisible into a finite number of small units and tolerant to the loss of one of them. We can remove these units one at a time, and since our object definitely doesn’t exist when there are zero units, and since we cannot pinpoint which removal brings about this destruction, the Sorites Puzzle threatens common sense. We can rescue ordinary objects from its grip, but since independently motivated linguistic explanations of vagueness depend on (...) there being multiple candidate contents of vague terms, these efforts succeed only if there are multiple candidates that can be meant by ordinary object terms. Thus, many more objects than common sense accepts have to exist. The 'arguments from vagueness' also offer soritical reasons for object proliferation. Problematising the categories composite object and persisting thing (rather than specific object concepts), these show that either there are none of these (except simples) or every candidate for making up one, does. The latter, less revisionary alternative is plenitudinism. I defend Modally Full Plenitude, because it is three-dimensionalist and non-reductivist about de re modality – a distinct persisting object in any region, and for every modal profile satisfied by the matter in that region. (shrink)

continent. 1.3 (2011): 201-207. “Poetry is experience, linked to a vital approach, to a movement which is accomplished in the serious, purposeful course of life. In order to write a single line, one must have exhausted life.” —Maurice Blanchot (1982, 89) Nikos Karouzos had a communist teacher for a father and an orthodox priest for a grandfather. From his four years up to his high school graduation he was incessantly educated, reading the entire private library of his granddad, comprising mainly (...) the Orthodox Church Fathers and the ancient classics. Later on in his life he sold the library for money, only to buy a little more time before he went broke again: “I carry sorrow like a cage/ I got no birds/ as I come back from her hair/ I see the profit emptied/ cool from terror.” (1993, Ι, 101) Nowadays—and ridiculously recently—we are more than apt to speak of a certain insouciance pertaining to the Greek form of expenditure: expenditure without any type of investment, sometimes not (even) symbolic. In the vaults of the European unconscious, this imprudent stance still conjures a “capital punishment” in the form of de-capitation, reflecting back the fear of excess and the terror of its consequences.1 Thus the Greek way of living is very close to what a stranger could have termed as “the Greek way of dying.” Yet, what is not often understood is that the Greek esprit , the same one that invented the maxim μηδ?ν ?γαν (“nothing in excess”), does not experience death solely as an imminent fear of bankruptcy. For it miraculously combines its unconditional acceptance with the promise of a resurrection that is always there in the scents of Spring, from Dionysus to the orthodox Christ: “Everyone resurrects himself through dying [….] Resurrection is the switching of mortalities.” (2002, 94) Hence, if an entire library was imprudently traded for a plate with seven olives, a sliced tomato and some fresh goat cheese, let us not be fooled: this is not the meal of the pauper, but that of “an aristocrat from God” (1993, II, 491) feeding his eloquent loudmouth, ridiculously cut open in an otherwise rock-solid caput . *** To speak of the Greek experience is to speak about a half-dead language that still utters in life what is seemingly excluded from it and thus forbidden to be talked about: death. Death as anything that is out of this world, as something that will never return . Still, along with an experience of death that recently waned as a worn-out academic fashion, the Greek experience is dead too. Nearly 2300 years of written words separating Homer from the fall of Byzantium equal 500 books on a library traded for money: “I am with the killed. Hence my deepest solitude. I do not feel this tremendous macho society, beyond from the fact that it is a ruthlessly consuming one. It is me who pays all the time .” (2002, 57) Let us do the math and see how much this dealing with the Greek experience is costing the poet and how much dealing with the Greek experience might cost us today. *** “I do not guarantee a single word.” (Karouzos, 1993, II, 454) Through its various dialects and forms, the Greek language speaks through an incessant historical dissemination. Anyone who is aware of this terrifying polymorphy and still calls himself a poet, must stand against a white sheet of paper, pen-in-hand, with a very particular duty: to be as fully inconsistent as possible. In the formally ironic uniqueness of the poem, the poet functions as “a band-aid for lesser and greater antinomies.” (1993, I, 251) Of course these antinomies are not exhausted in language—they are historical, political and, alas, existential. Yet, beyond appearances , it is language that ruthlessly encodes them through history, submitting the poet to the temptation of placing them one next to the other on a single white sheet. The closer their neighboring, the greater the scattering of the writer in the ironic uniqueness of the paper. In a work where poetic license is described as a “freedom-impasse” (2002, 51), this task is undertaken in full conscience of its personal consequences: “what I am interested in is to escape my individuality (envisioning the non-ego) […] Nevertheless, my dissociations never achieve duration.” (2002, 74-75) Hence, though poetry is the “deserted direction of will,” (1998, 62) the stance of the poet is not that of a Nietzschean “great man.”2 Whereas drunkenness provides a thread between the poem and the excess it both presupposes and infuses (“Poetry always enlarges. ‘Drunkenness’ is nothing more than that,” (2002, 85)), whereas language flashes in loudmouth spurts of déraison (“When I am alone I do something else. I utter words. For example, while having my ouzo and listening to music I am most likely capable of randomly shouting ‘Electricity!’” (2002, 138)), the poet never gives in to the double affirmation that would eventually risk the “element of pleasure in discourse.” (2002, 80)” It is exactly because the gap of the antinomies is so vast that poetry is not meant to be written with a hammer. Neither does writing consist in a reevaluation of those elements. In short, poetry is not an affirmation of difference, but the surprising beauty of chiming antinomies. We might never transcend them, but it is up to us to put them together. Yet again, this voisinage is not to be identified with the necessity of chance as an eternal return.4 On the contrary it is a return from that very return : Let us treat Yes as a No to No and No as a Yes […] And let us not forget that this pissed affirmation crumbled down Nietzsche’s intellect in the dark paths of this world. (2002, 88) This return from the “vicious circle” should in no way be taken as a form of artistic prudence. Rather it can be seen as a dribble of demonic inconsistency as Dionysus transforms himself into a Christ that is in turn de-theologized: “Who can forbid that? Every man is capable of his own theology, nothing can stop him.” (2002, 73-74) This is a turn towards an existential vision of the world, historically coinciding with a particular political defeat of the Left, to which the poet devoted all his life: after the defeat of the popular front I raised the question “why do we exist?” while others were asking “why we failed.” (2002, 57)5 But most of all it is a return to poetry that exceeds the existential question itself, going beyond the issue of faith. Poetry comes in as a question of return after a defeat that is confessed in full profanity. Though it accepts the necessity of the defeat, it does not affirm it. Though it negates it, the negation is not in the name of a promise to be delivered in the kingdom of heavens. Following a historical and existential defeat, poetry is born post mortem . It signals a return to Christ as “groundless religiousness in the surprise of the real as such” (2002, 72) which is at once a return to the refuge of childhood. It is not a question of endurance towards an eternal return. Rather it is a question on the possibility of an existential return. Returning in a world as someone who cannot enjoy any returns exactly because he is averse to guarantees. A return without returns. *** PHOTOCOPY OF HAPPINESS When I was young I used to pin down cicadas and step on ant nests. I used to stand there silent for hours. With threads I decapitated bees. Now I am a dead man breathing. (Karouzos, 1993, II, 336.) The return to the “paradise of childhood” (2002, 68) constitutes the devouring refuge of its own memory when defeat becomes the synonym of adulthood. The political struggles of a young communist in a country torn up by a civil war right after World War II fraught with incarcerations and exiles. Historically they resulted in the defeat of the communist movement in Greece and opened up a long turbulent road that would peak in the dictatorship of 1967. Existentially they led to a series of disillusionments: mental breakdown, divorce, abandonment of studies in law school. To the question “why do we exist” the answer was poetry. Still this exposé should not be read as a sweeping chronography of a man. For it actually happens to coincide with the historical fate of a nation that after its modern constitution never stopped dreaming of the glories of its past youth, in a present that was (and is) sweepingly disappointing. But isn’t this return to youth finally a way of compensating for a loss of youth that necessarily results in a losing adulthood? Will Greeks, the eternal children of Plato and Nietzsche, ever learn? How to return without dying, how to remember without wasting time? WE ARE IN THE OPEN MEANING Living the coldest mauve night right across Parthenon I went to take a piss on some foliage and I was enjoying the foliage as it was steaming. (Karouzos, 1993, II, 340) Beyond the historical tragedies of modern Greece and away from any personal disappointments, the relation that this land holds with language and history is mediated through the Greek light—whose omnipresence is the very condition of its transcendence. All historical contradictions from Dionysus to Christ took place under this light; all those disseminated dialects were spoken beneath its warmth. To paraphrase Lévinas,6 light is both the condition of the world and of our withdrawal from it—a withdrawal towards the invisibility of God, of the dead, of meta-physics, resulting from the temptation that all is still here, behind this light the visibility of which they once evaded: “birds, the allurement of God.” (1993, I, 17) Under that luminous sky, if Greeks can do anything at all, it is to envision a return that will never come. All they can do is write poetry—which is doing nothing; other than lending an ear to a disseminated language whispering a unity that cannot be promised, as an adulthood in defeat is ready to recognize. Trying “to trap the invisible in visibility” (1993, II, 483) they forget that they have grown up and one day they die—with the promise of return. Hence an additional meaning must be given to this return to childhood. It does not signal salvation but rather its promise. To the ears of an aged continent it means that the return to/of poetry is a losing game, a return without returns. “Europe, Europe… you are nothing more than the continuation of Barabbas.” (1993, I, 295) *** “Life is not there to verify theories.”7 The records show that Karouzos was finally given a second-class pension from the Greek government, at the time when he was being recognized by the literary press as one of Greece’s major contemporary poets. Being neither a bourgeois nor a nobelist, he proclaimed himself to be an anarcho-communist, unconditionally faithful to the utopia of a classless society. He also drank, heavily. “Capitalism made an animal out of man/ Marxism made an animal out of truth/ Shut up.” (1993, II, 369) Perhaps one of the most scandalous divides of our times has been the one between the living and the dead, the latent prohibition that the living should not be concerned with the dead based on the mere impossibility of the dead to be concerned with the living in the first place. What adds to this scandal is that this divide abuses anything that cannot return to us by subsuming it under the same futility. Hence death is no longer “loss” in the usual sense. It no more refers to the things we lost but to our “loss” (of time, money and well-being) as we insist to dwell on them. Death is a waste —of time. It is this waste that we find in the insouciance of Greek expenditure; the waste in dealing with a language that most of its historical part is no longer spoken (a dead language); the waste in translating a poet who is ex definitio untranslatable; the waste of his vision, his money, his life. The waste of dealing with anything that cannot return and that cannot bring in any returns . But it is also the waste of life that poetry itself presupposes, the waste of dealing with invisibility, with anything that is out of this world and thus invokes the fear of death that is in turn—and surprisingly— nowhere to be found. Instead of death, what is there, beyond the light, is the being without us (to recall the Lévinasian il y a ), the mumble of our own nothingness which constitutes the price to be paid for writing poetry under an evergreek light. To understand this to-and-fro, is to realize that poetry is something out of this world that nevertheless takes place in this world, by virtue of this world. But to ridiculously equate this to-and-fro with death as non-existence, is to exile poetry along with its own possibility from this same old world: I do not believe that poetry will ever disappear from this world. […] But I am also sure that it does not have many chances of playing, as you say, a redemptive role in our vertiginous technological future. Without being endangered as a creative need, it will be placed on the side of history. (2002, 32) It is mainly there that we would like to locate the meaning of Nikos Karouzos’s poetry today. If we are willing to include the Greek original it is because we consider that it will be both a waste of time for us to do so (since most of you cannot read Greek) and because it might induce you to the even larger waste of learning it. We would additionally be glad if this small introduction served as an equally wasteful, academically useless piece of reading, gesturing towards a taboo of investing in anything Greek—that is in anything dead among the living, in anything that will never come back and maybe was never here in the first place. This is the only way to reserve for ourselves the possibility of poetry and preserve the light of its promise. “To return: that is the miracle.” (1993, I, 17) Athens, Greece July 10, 2011 NOTES 1 “ Capitale (a Late Latin word based on caput “head”) emerged in the twelfth to thirteenth centuries in the sense of funds, stock of merchandise, sum of money or money carrying interest.[…] The word and the reality it stood for appear in the sermons of St. Bernardino of Siena (1380-1444) ‘… quamdam seminalem rationem lucrosi quam communiter capitale vocamus ’, ‘that prolific cause of wealth that we commonly call capital’” (Braudel, 1992, 232-233). 2 “A great man – a man whom nature has constructed and invented in the grand style – what is he? First : there is a long logic in all of his activity, hard to survey because of its length, and consequently misleading; he has the ability to extend his will across great stretches of his life and to despise and reject everything petty about him, including even the fairest, ‘divinest’ things in the world.” (Nietzsche, 1968, 505, §962) 3 Cf. Deleuze, 1986, 186-9. 4 “Return is the being of becoming, the unity of multiplicity, the necessity of chance: the being of difference as such or the eternal return.” (Deleuze, 189)5 In this 1982 interview Karouzos refers to the defeat of the communist movement in Greece after the civil war of 1946-1949 between the Governmental Army and the Democratic Army of Greece, the military division of the Greek communist party. Karouzos’s father was a member of the communist National Liberation front (EAM) members of which formed the mainl resistance movement (ELAS) in Greece during WWII. The poet was a member of the United Panhellenic Organization of Youth (EPON), which was a youth division of EAM. After the end of the war, ELAS was called to disarmament in view of the formation of a National Army. The members of EAM resigned from the government of national unity and a series of protests led to a 3 year civil war between ELAS and the Government Army. After the defeat of ELAS the Communist party was outlawed and many communists were exiled in deserted Greek islands. Karouzos, who took action in the Greek resistance and was active during the Greek civil war, was exiled in Icaria on 1947 and in Makronisos on 1953 where he was called two years earlier to do his military service. 6 “Existence in the world qua light, which makes desire possible, is then, in the midst of being, the possibility of detaching oneself from being. To enter into being is to link up with objects; it is in effect a bond that is already tainted with nullity. It is already to escape anonymity. In this world where everything seems to affirm our solidarity with the totality of existence, where we are caught up in the gears of a universal mechanism, our first feeling, our ineradicable illusion, is a feeling or illusion of freedom. To be in the world is this hesitation, this interval in existing, which we have seen in the analyses of fatigue and the present.” (Lévinas, 1988,43-4) 7from a TV interview. THE POETRY OF NIKOS KAROUZOS From Redwriter [ Ερυθρογρ?φος ], in Collected Works, Vol . II, Athens: Ikaros. 1993, 463-4. [Athens: Apopeira, 1990, 9-10.] JESUS ANTI-OEDIPUS* Why were we once saving till the fifth day the Paschal lamb? The scriptures say: with this victim’s meat we ought to cleanse all of our senses. To give life to the whitest wave miraculous odors in the extension of the chest. Ideals to death. For us to witness the illustrious dawns of Absinthe and for the soul to be a deeply carved ornament on the fore we named will. Then many deer running amidst the evergreen growth with watery hymns, then, the unintended angels descending with heights spiraling in their momentum offer themselves to the luminous Adventure. Whence the need for speech and our sufferings covered with flags like the glorified dead. An incorporeal finger pointing at the flamboyant and fragrant holocausts within the tired horizons and the exhausted breadths with joys of the mistletoe on fire and shivering all of the green-leaved love. Something would have chirped again had we not driven it away— maybe the ewe’s grass. Something would have called us to the eternal resurrection— maybe the grace of spring. But now our heart is fiercely blinded, withdrawn to the appearances of Hades. Silence and ice incessantly cover the Infant Spirit in thatched times. While the cherry trees are dreaming faintly glowing in absolute darkness there’s nothing the Babylonians can contemplate in labs with automatic colored lights. How to rejoice now in the fifth day of the lamb? We have forked the stars. We’ve gradually become supposedly sublime with plucked chimeras in our hands. Avenged relentlessly by science. *Though the poem appears in a 1990 collection, it was actually written in 1968. Hence the reader must be aware in not associating Karouzos’ Anti-Oedipus with the famous 1972 work of Deleuze and Guattari, given that the former precedes the latter. ΙΗΣΟΥΣ ΑΝΤΙ-ΟΙΔΙΠΟΥΣ Γιατ? κρατο?σαμε κ?ποτε ?ς την π?μπτη μ?ρα το πασχαλιν? πρ?βατο; Τα κε?μενα λ?νε: μ’ αυτο? του θ?ματος το κρ?ας ?πρεπε να καθαρ?σουμε ?λες τις αισθ?σεις. Για να δ?σουμε κ?μα στη ζω? λευκ?τατο θαυμ?σιες ευωδι?ς στην ?κταση του στ?θους. Ιδανικ? στο χ?ρο. Για να βλ?πουμε τα λαμπρ? χαρ?ματα του ?ψινθου και να ’ναι η ψυχ? στ?λισμα βαθυχ?ρακτο της πλ?ρης που την ε?παμε θ?ληση. Τ?τε πολλ?ς δορκ?δες τρ?χοντας αν?μεσα στην καταπρ?σινη φ?ση με τους υδ?τινους ?μνους, τ?τε, κατεβα?νοντας οι αθ?λητοι ?γγελοι με κυλινδο?μενο το ?ψος στην ορμ? τους χαρ?ζονται της αστραφτερ?ς Περιπ?τειας. ?θεν η μιλι? γι’ αυτ? χρει?ζεται και τα δειν? σκεπ?ζονται ωσ?ν τους τιμημ?νους νεκρο?ς με σημα?ες. Ασ?ματο δ?χτυλο δε?χνει τα φλογ?δη και μοσχοβ?λα ολοκαυτ?ματα στους κουρασμ?νους ορ?ζοντες στα εξουθενωμ?να πλ?τη καθ?ς αν?βουν οι χαρ?ς του νερα?δ?ξυλου και τρ?μει ολ?κληρη η πρασιν?φυλλη αγ?πη. Κ?τι θα κελαηδο?σε π?λι αν δεν το δι?χναμε— μπορε? της προβατ?νας το χορτ?ρι. Κ?τι θα μας καλο?σε στην απ?ραντη αν?σταση— μπορε? του ?αρος η χ?ρη. Μα η καρδι? μας ?γρια τυφλ?θηκε π?ρασε στα φαιν?μενα του ?δη. Σιγ? και π?γος αδι?κοπα σκεπ?ζει στους αχυρ?νιους καιρο?ς το Ν?πιο Πνε?μα. Την ?ρα που ονειρε?ονται οι βυσσινι?ς και λ?μπουν αμυδρ? μεσ’ στο απλ?τατο σκοτ?δι τ?ποτα δε στοχ?ζονται οι βαβυλ?νιοι στα εργαστ?ρια με τ’ αυτ?ματα χρωματιστ? φ?τα. Π?ς να χαρο?με πια την π?μπτη μ?ρα του προβ?του; Φουρκ?σαμε τ’ αστ?ρια. Γ?ναμε σιγ?-σιγ? δ?θεν υπ?ροχοι με μαδημ?νες χ?μαιρες στα χ?ρια. Μας ν?μεται σκληρ? η επιστ?μη. From: Redwriter [Ερυθρογρ?φος], in Collected Works, Vol. II, Athens: Ikaros. 1993, 472. [Athens: Apopeira, 1990, 18.] DIALECTΙCS OF SPRING Christ the straight angle; Christ the Pythagorean theorem. Christ the infinitesimal calculus from above the blessed Sets Christ. Christ the tessellation of massive particles Christ the zero mass. Hence we spray numbers and fields of lust. We are carabineers of diseased logic plus something— Observed means observer and Hekate The darkness luminous and light in the dark Astarte banqueters demons from today. ΔΙΑΛΕΚΤΙΚΗ ΤΟΥ ΕΑΡΟΣ Χριστ?ς η ορθ? γων?α· Χριστ?ς το πυθαγ?ριο θε?ρημα. Χριστ?ς ο απειροστικ?ς λογισμ?ς ?νωθεν ?λβια Χριστ?ς τα Σ?νολα. Χριστ?ς η ψηφιδογραφ?α στα μαζικ? σωμ?τια Χριστ?ς η μ?ζα μηδ?ν. ?ρα ψεκ?ζουμε αριθμο?ς και πεδ?α λαγνε?ας. Ε?μαστε τυφεκιοφ?ροι νοσο?σης λογικ?ς και κ?τι-- παρατηρο?μενο σημα?νει παρατηρητ?ς και Εκ?τη σκ?τος το π?μφωτο και φως εν τ? σκοτ?? η Αστ?ρτη συνδαιτημ?νες δα?μονες απ’ ?ρτι. From: Redwriter [Ερυθρογρ?φος], Athens: Apopeira, 1990, 18. [1993, II, 472]. CREDO (as we are used to say in Latin) Α I believe in one Poet expelled from heavens / fugitive from the god and vagabond, Empedocles / and here on earth / exile on the earth etc. of Baudelaire /. Β I believe in one Computer inside thunder and through matter. Γ Suffering undefiled / substantive / the Poet uplifts himself slow-burning suicidal implying lengthy sleeps. Δ Cutting down on prospective mistakes. Ε Of all things visible and invisible officiating the onion-peelings. Ζ The Poet has nothing / see the departed /. Η I believe in one Poet that says: madness I enjoy; he ridicules existence; let me light up from my mana. Θ Syntax he doesn’t care about when musicality commands him. Along with still more licenses, and Ts are played according to the concept sound anywhere. E.g. the winters here, he winters there; it will not come—I will not rest, etc. etc. Ι The Poet exercises thought until it’s stripped down. Κ And if he’s Greek he must always study the fineness of Attica, in light, mountains, fields and sea. For this fineness teaches language. Λ And if he’s deeply destined the Poet expresses the unexplainable of the explained; he happens to be a rightful heir to the scientist and his predecessor. Μ On the froth he does not last; the Poet blusters at the bottom of the pot. Ν Flamebred and never redeemed. Ξ The Poet must sometimes say: what a consumption of presence — be a bit lonely for a change! Ο The Poet is twilit. Π He is susceptible of deaths and resurrections. Ρ He looks from the corner of his eye and exists in a glance. Σ He follows behind the mother. Τ Eveningless when it comes to age. Υ I believe in one Poet who says: let the purities coincide. Until the Corinth of the Universe or even further. Φ In a higher despair. Χ In a brighter quintessence. Ψ In one sensation that lifts off. Ω Forgiving everyone. CREDO (ως ε?θισται να λ?με λατινιστ?) Α Πιστε?ω εις ?να Ποιητ?ν εκτ?ς ουρανο? / φυγ?ς θε?θεν και αλ?της, Εμπεδοκλ?ς / και επ? της γης / εξ?ριστος π?νω στη γη κ.λπ. του Βωδελα?ρου /. Β Πιστε?ω εις ?να Υπολογιστ?ν εντ?ς κεραυνο? και δια της ?λης. Γ Υποφ?ροντας ?χραντα / ουσιαστικ?ν / ο Ποιητ?ς ανατε?νεται βραδυφλεγ?ς αυτ?χειρας εξυπακο?οντας πολ?ωρους ?πνους. Δ Τα υποψ?φια λ?θη λιγοστε?οντας. Ε Ορατ?ν τε π?ντων και αορ?των ιερουργ?ντας την αποκρομμ?ωση. Ζ Ο Ποιτ?ς ?χει τ?ποτα / βλ?πε τους αναχωρ?σαντες /. Η Πιστε?ω εις ?να Ποιητ?ν που λ?ει: η τρ?λα μ’ αρ?σει· γελοιοποιε? την ?παρξη· ας αν?ψω απ’ τη μ?να μου. Θ Συνταχτικ? δεν το γνοι?ζεται στην προσταγ? της μουσικ?τητας. Μαζ? και μ’ ?λλες ακ?μη λευτερι?ς, και τα νυ πα?ζονται κατ? την ?ννοια ?χος οπουδ?ποτε. Π.χ. τον χειμ?να εδ?, το χειμ?να εκε?· δε θ? ’ρθει – δεν θα καταλαγι?σουμε, κ. λπ. κ.λπ. Ι Ο Ποιητ?ς γυμν?ζει τη σκ?ψη σε απογ?μνωση. Κ Κι αν ε?ναι ?λληνας οφε?λει να σπουδ?ζει π?ντοτε της Αττικ?ς τη λεπτ?τητα, σε φως, βουν?, χωρ?φια και θ?λασσα. Διδ?σκει γλ?σσα η λεπτ?τητα το?τη. Λ Κι αν ε?ναι βαθι? πεπρωμ?νος ο Ποιητ?ς εκφρ?ζει το ανεξ?γητο του εξηγητο?· τυγχ?νει ν?μιμος δι?δοχος του επιστ?μονα και προκ?τοχ?ς του. Μ Στον αφρ? δεν ?χει δι?ρκεια· στο πατοκ?ζανο μα?νεται ο Ποιητ?ς. Ν Φλογοδ?αιτος και ποτ? ξελυτρωμ?νος. Ξ Ο Ποιητ?ς κ?ποτε πρ?πει να λ?ει: μεγ?λη καταν?λωση παρουσ?ας – γενε?τε και λ?γο μοναξι?ρηδες! Ο Ο Ποιητ?ς ε?ναι αμφ?φλοξ. Π Επιδ?χεται θαν?τους και αναστ?σεις. Ρ Ακροθωρ?ζει και υπ?ρχει σε ξαφνοκο?ταγμα. Σ Ε?ναι ουραγ?ς της μητ?ρας. Τ Αν?σπερος απ? ηλικ?α. Υ Πιστε?ω εις ?να Ποιητ?ν που λ?ει: να συμπ?σουν οι αγν?τητες. Μ?χρι την Κ?ρινθο του Σ?μπαντος ? μακρ?τερα. Φ Σε αν?τερη απελπισ?α. Χ Σε φαειν?τερη πεμπτουσ?α. Ψ Σε μια α?σθηση που πτηνο?ται. Ω Συγχωρ?ντας τους π?ντες. From Large Sized Logic [ Λογικ? μεγ?λου σχ?ματος ], Athens: Erato, 1989, n.p. [1993, II, 521-3]. (shrink)

In this article, I examine how Syrian refugee men and women shifted their household divisions of labor in their initial years of resettlement in the United States. I combine and extend relational approaches from gender theory and economic sociology to examine how men’s and women’s behaviors shifted, the resources engendered by behavioral shifts, and how they interpreted and compensated for new behaviors and resources. I show that shifts in Syrian household divisions of labor occurred at the intersection of inequalities in (...) social policies, labor markets, and households. As a result of limited social assistance, the refugee families needed to earn an income within months of their arrival. The Syrian men entered the labor market, in keeping with a breadwinning expectation for their labor, but could only access menial jobs that limited their time and opportunity to learn English. Women, meanwhile, did not enter the labor market full-time and could attend English classes. By observing this divergence in men’s and women’s language learning, I theorize human capital as a gendered outcome of household divisions of labor. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Books ReceivedAt the Eleventh Hour: The Biography of Swami Rama. By Pandit Rajmani Tigunait, Ph.D. Honesdale, Pennsylvania: Himalayan Institute Press, 2002. Pp. 427. Hardcover $18.95.Awakening and Insight: Zen Buddhism and Psychotherapy. Edited by Polly Young Eisendrath and Shoji Muramoto. Hove, England: Brunner-Routledge, 2002. Pp. xii + 275. Paper $24.95.Beyond Metaphysics Revisited: Krishnamurti and Western Philosophy. By J. Richard Wingerter. Lanham, Maryland: University Press of America, 2002. Pp. vii + (...) 391. Hardcover $71.00.Bhāmatī and Vivaraṇa Schools of Advaita Vedānta: A Critical Approach. By Pulasth Soobah Roodurmun, foreword by V. N. Jha, and edited by Kanshi Ram. New Delhi: Motilal Banarsidass Publishers, 2002. Pp. xv + 297. Price not given.A Bibliography of Ananda Kentish Coomaraswamy. By James S. Crouch. New Delhi: Indira Gandhi National Centre for the Arts and Manohar Publishers and Distributors, 2002. Pp. 430. Price not given.Crisis Theory and World Order: Heideggerian Reflections. By Norman K. Swazo. Albany: State University of New York Press, 2002. Pp. x + 289. Hardcover $78.50. Paper $26.95.Devotional Literature in South Asia: Current Research 1997-2000: Proceedings of the Eighth International Conference on Early Literature in New Indo-Aryan Languages, Leuven, 23-26 August 2000. Edited by Winand M. Callewaert and Dieter Taillieu. New Delhi: Manohar Publishers and Distributors, 2002. Pp. xxii + 324. Price not given.Dharma Bell and Dhāraṇī Pillar: Li Po's Buddhist Inscriptions. By Paul W. Kroll. Kyoto: Italian School of East Asian Studies, 2001. Pp. viii + 95. Price not given.Essays on the Moral Philosophy of Mengzi. Edited, with introduction, by Xiusheng Liu and Philip J. Ivanhoe. Indianapolis and Cambridge: Hackett Publishing Company, 2002. Pp. xiv + 249. Hardcover $39.95. Paper $16.95. Professional price $12.95.Ethical Questions: East and West. Edited by Bina Gupta. Lanham, Maryland: Rowman and Littlefield Publishers, 2002. Pp. vi + 279. Hardcover $70.00. Paper $26.95.Ethical Relativism and Universalism. By Saral Jhingran. New Delhi: Motilal Banarsidass Publishers, 2001. Pp. xiv + 385. Price not given.Genius-In Their Own Words: The Intellectual Journeys of Seven Great 20th Century [End Page 431] Thinkers. Edited and with introduction by David Ramsay Steele, foreword by Arthur C. Danto. Chicago and La Salle: Open Court, 2002. Pp. xxii + 366. Paper $24.95.The Hatha Yoga Pradipika. The original Sanskrit by Svatmarama, an English translation by Brian Dana Akers. Woodstock, New York: YogaVidya.com, 2002. Pp. xii + 115. Hardcover $19.95. Paper $11.95.Human Rights and Chinese Thought: A Cross-Cultural Inquiry. By Stephen C. Angle. New York: Cambridge University Press, 2002. Pp. xviii + 285. Hardcover $65.00. Paper $23.00.Indestructible Truth: The Living Spirituality of Tibetan Buddhism. By Reginald A. Ray. Boston and London: Shambhala Publications, 2002. Pp. x + 495. Paper $17.95.Introduction to Eastern Thought. By Marietta Stepaniants. Edited by James Behuniak and translated by Rommela Kohanovskaya. Lanham, Maryland: AltaMira Press, a division of Rowman and Littlefield Publishers, 2002. Pp. xiv + 293. Hardcover $69.00. Paper $24.95.Jainism and Ecology: Nonviolence in the Web of Life. Edited by Christopher Key Chapple. Cambridge: Harvard University Press for the Center for the Study of World Religions, 2002. Pp. xliv + 252. Hardcover $32.95. Paper $22.95.Mediating the Power of Buddhas: Ritual in the Mañjuśrīmūlakalpa. By Glenn Wallis. Albany: State University of New York Press, 2002. Pp. xiii + 263. Hardcover $86.50. Paper $29.95.Methodology in Religious Studies: The Interface with Women's Studies. Edited by Arvind Sharma. Albany: State University of New York Press, 2002. Pp. xi + 253. Hardcover $78.50. Paper $26.95.Persons and Valuable Worlds: A Global Philosophy. By Eliot Deutsch. Lanham, Maryland: Rowman and Littlefield Publishers, 2002. Pp. x + 309. Hardcover $80.00. Paper $34.95.Philosophy and Art in Gurdjieff's Beelzebub: A Modern Sufi Odyssey. By Anna T. Challenger. Amsterdam and New York: Editions Rodopi B.V., 2002. Pp. xi + 145. Paper EUR 27,00, U.S. $25.00.The Pratyabhijñā Philosophy. By G. V. Tagare. New Delhi: Motilal Banarsidass Publishers, 2002. Pp. xii + 165. Price not given.Reflections on Reality: The Three Natures and Non-Natures in the Mind-Only School: Dynamic Responses to ong-ka-a's The... (shrink)

Using data on submitted and published manuscripts in Feminist Economics from 1995 to 2019, we examine differences in method and scope used by authors residing in the Global North and Global South. We specifically focus on research methods, intersectional analyses, region of analysis, and co-authorship status. Further, using logistic regression models, we examine the relationship between authors’ location and use of research methods. We find authors in the Global South are more likely to engage in empirical and mixed-methods papers compared (...) to Global North authors in our sample. Moreover, a greater share of Global South authors engage in intersectional analysis and exhibit geographical focus on developing countries. Drawing insights from the Feminist Economics manuscripts data, we argue that encouraging Global South research can contribute to the goals of the field of feminist economics – aimed at inclusivity, diversity of standpoints, and plurality in research methods, thereby improving overall economic research. (shrink)

A modus tollens against zero-dimensional material objects is presented from the premises (i) that if there are zero-dimensional material objects then there are bare particulars, and (ii) that there are no bare particulars. The argument for the first premise proceeds by elimination. First, bare particular theory and bundle theory are motivated as the most appealing theories of property exemplification. It is then argued that the bundle theorist’s Ockhamism ought to lead her to reject spatiotemporally located zero-dimensional property (...) instances. Finally, it is argued that since she must accept such instances if she accepts zero-dimensional material object bundles, she ought to avoid the latter. This leaves bare particular theory as the default view of zero-dimensional material objects. The argument for the second premise invokes the thesis that the exemplification of at least one sparse property is a prerequisite for the existence of any particular. It is argued from Humean considerations that bare particulars fail this prerequisite. (shrink)

COVID-19 has stolen millions of lives and devastated livelihoods around the world and led to the exacerbation of existing inequities within and between countries. This part of a tragic pattern in catastrophes, where the most vulnerable populations are typically the ones to bear the greatest burdens. Jecker and Au1 offer a keen observation of how one particular COVID-19 response—Zero COVID—appears particularly problematic from a health equity perspective. Under Zero COVID, countries enact stringent lockdowns and movement restrictions in order (...) to keep cases as low as possible. Yet such restrictive policies hurt disadvantaged populations the most, by severely curtailing their ability to earn a living and forcing them to remain in cramped living spaces for potentially extended periods of time. However, the link between Zero COVID and health inequity is more complex than it might at first appear. This is because Zero COVID is itself compatible with meaningful efforts to mitigate inequities, including those caused by Zero COVID policies themselves. Conversely, certain inequities seemingly characterised by Zero COVID may persist even when Zero COVID is abandoned, indicating their ultimate root and …. (shrink)

We further investigate a divisibility relation on the set of BN ultrafilters on the set of natural numbers. We single out prime ultrafilters (divisible only by 1 and themselves) and establish a hierarchy in which a position of every ultrafilter depends on the set of prime ultrafilters it is divisible by. We also construct ultrafilters with many immediate successors in this hierarchy and find positions of products of ultrafilters.

This article examines the structures of the epico-Purāṇic divisions of time (yugas/sandhyās/kalpas) and asks what is joined by the Purāṇic ages known as yugas or joinings. It concludes that these structures reflect a combining of three systems of number—Greek acrophonic, Babylonian sexagesimal and Hindu decimal— represented as divisions of time. Since most interpretations of these structures, particularly yugas, focus on questions of dharma and its decline over the various ages rather than on number, it asks in conclusion if there is (...) any necessary relationship between number and dharma. (shrink)

A Dedekind-finite set is said to be divisible by a natural number n if it can be partitioned into pieces of size n. We study several aspects of this notion, as well as the stronger notion of being partitionable into n pieces of equal size. Among our results are that the divisors of a Dedekind-finite set can consistently be any set of natural numbers, that a Dedekind-finite power of 2 cannot be divisible by 3, and that a Dedekind-finite set can (...) be congruent modulo 3, to all of 0, 1, and 2 simultaneously. (shrink)

This paper deals with an (otherwise classical) two-(non-interacting) particle system immersed in a common stochastic zero-point radiation field. The treatment is an extension of the one-particle case for which it has been shown that the quantum properties of the particle emerge from its interaction with the background field under stationary and ergodic conditions. In the present case we show that non-classical correlations—describable only in terms of entanglement—arise between the (nearby) particles whenever both of them resonate to a common frequency (...) of the field. For identical particles the entanglement becomes maximum and must be described by totally (anti)symmetric states. (shrink)

The notion of the ‘division of physiological labour’ is today an outdated relic in the history of science. This contrasts with the fate of another notion, which was so frequently paired with the division of physiological labour, which is the concept of ‘morphological differentiation.’ This is one of the elementary modal concepts of ontogenesis. In this paper, we intend to target the problems and causes that gradually led biologists to combine these two notions during the 19th century, and (...) to progressively dissociate them, retaining only the concept of differentiation by the early 20th century. We shall adhere to the following: 1. The primitive economic concept of the division of labour is not a descriptive notion denoting a type of organisation of labour, but an etiological one: the idea of a causal relationship between this type of organization and the improvement of the whole. 2. This concept rapidly interested naturalists such as Henri Milne-Edwards, who were keen to find a rational ground for hierarchizing living forms based on anatomical complexity. 3. The validation of this notion in the realms of biology was subject to at least two conditions which were far from being fully satisfied. This did not prevent, however, the initial success of the concept of the division of physiological labour during the second half of the 19th century. 4. Finally, the gradual disqualification, within the Darwinian theoretical context, of the conception of an intrinsic hierarchical rank of organisms, led to a lack of interest in the concept of the physiological division of labour, at least in its non-Darwinian and non-ecological variant. (shrink)

Zero pronominals challenge Type Logical Grammar in two ways. One, TLG displays a linear resource management regime for semantic composition, meaning that pronominals call for special treatment if they want to do resource multiplication. Two, as a grammar of lexicalism, TLG applies to phonologically realized lexical entries only, illegitimating the phonetically null items during syntactic derivation. Jägor extends the inventory of category-forming connectives of TLG by a third kind of implication that creates categories of anaphoric items and solves the (...) first problem above. This article goes a step further to tackle the second one. In order to formalize the constructions with zero pronominals, we design a ternary category A B C and include the latter into Jägor’s system. The proposed system is proof-theoretically well-behaved. It is complete, sound, and decidable. More importantly, zero pronominals of various forms can be derived in the system. (shrink)

In the first half of the 15ᵗʰ century there was a coherent philosophical system of teaching at the Jagiellonian university, so-called ars vetus, concerning the interpretation of three treatises: Aristotle’s Categories and Hermeneutics and Porphyry’s Isagoge. The question-commentaries on the Categories that have been preserved in several manuscripts show astonishing similarity in solving individual problems – there are three copies of Benedict Hesse’s commentary and one copy of Paul of Pyskowice’s work, moreover, in BJ 1941 there is an anonymous commentary (...) on the Categories that is also very close to the ones mentioned before, to prove that fact. This paper, discussing the four-fold division of opposition in those Polish commentaries on Aristotle’s Categories, is part of the studies on the manuscript material that has not been critically edited yet. The main goal is to show the philosophical views on contraries, contradictories, relatives and possession and privation in a wider perspective, comparing the Polish commentaries’ doctrine with the authoritative text itself. (shrink)

Tarski 1968 makes a move in the course of providing an account of ?definitionally equivalent? classes of algebras with a businesslike lack of fanfare and commentary, the significance of which may accordingly be lost on the casual reader. In ?1 we present this move as a response to a certain difficulty in the received account of what it is to define a function symbol (or ?operation symbol?). This difficulty, which presents itself as a minor technicality needing to be got around (...) especially for the case of symbols for zero-place functions (for ?distinguished elements?), has repercussions?not widely recognised?for the account of functional completeness in sentential logic. A similarly stark comment in Church 1956 reveals an appreciation of this difficulty, though not every subsequent author on the topic has taken the point. We fill out this side of the picture in ?2. The discussion of functional completeness in ?2 is supplemented by some remarks on what is involved in defining a connective, which have been included in an Appendix. The emphasis throughout is on conceptual clarification rather than on proving theorems, and the main body of the paper may be regarded as an elaboration on the remarks just mentioned by Tarski and Church. The Appendix (?3) is intended to be similarly clarificatory, though this time with some corrective intent, of remarks made in and about Makinson 1973. (shrink)

If the Aristotelian division has above all an epistemic and heuristic purpose, this article aims to examine the ontological appropriation of division by Aristotle in the Metaphysics, too often neglected by secondary literature. Division is also an ontological operation, insofar it governs the relationship between the eidos (which is identified, in the context of the central books of the Metaphysics, with the primary substance, i.e. what is properly speaking), its genus and the final differentia of this genus. (...) More precisely, we will show that division is a case of the hylemorphic relation: the genus is an (intelligible) matter to which the final differentia obtained by division is predicated, and which then acts as the formal cause of this genus being such a determined eidos. However, this ontological and hylemorphic dimension of Aristotelian division is largely compatible with its methodological use. (shrink)

Considerable attention has focused on studying reviewer agreement via inter-rater reliability (IRR) as a way to assess the quality of the peer review process. Inspired by a recent study that reported an IRR of zero in the mock peer review of top-quality grant proposals, we use real data from a complete range of submissions to the National Institutes of Health and to the American Institute of Biological Sciences to bring awareness to two important issues with using IRR for assessing (...) peer review quality. First, we demonstrate that estimating local IRR from subsets of restricted-quality proposals will likely result in zero estimates under many scenarios. In both data sets, we find that zero local IRR estimates are more likely when subsets of top-quality proposals rather than bottom-quality proposals are considered. However, zero estimates from range-restricted data should not be interpreted as indicating arbitrariness in peer review. On the contrary, despite different scoring scales used by the two agencies, when complete ranges of proposals are considered, IRR estimates are above 0.6 which indicates good reviewer agreement. Furthermore, we demonstrate that, with a small number of reviewers per proposal, zero estimates of IRR are possible even when the true value is not zero. (shrink)

The proposition expressed by a sentence is relative to a context. But what determines the content of the context? Many theorists would include among these determinants aspects of the speaker’s intention in speaking. My thesis is that, on the contrary, the determinants of the context never include the speaker’s intention. My argument for this thesis turns on a consideration of the role that the concept of proposition expressed in context is supposed to play in a theory of linguistic communication. To (...) illustrate an alternative approach, I present an original theory of the reference of demonstratives according to which the referent of a demonstrative is the object that adequately and best satisfies certain accessibility criteria. Although I call my thesis zero tolerance for pragmatics, it is not an expression of intolerance for everything that might be called “pragmatics.”. (shrink)

This essay links Barthes’ late development on the Neutral in his 1978 Collège de France lecture course to his early reflections on the ‘white’ or ‘neutral’ writing by looking at lesser-known materials: articles published in the sanatorial student journal Existences (1942–4), and in the newspaper Combat (1947–51), as well as how these pieces were integrated into his first book, Writing Degree Zero (1953). I show that Barthes’ first approaches to the ‘neutral’, under the spell of Sartre’s theory of committed (...) literature, both ‘consents’ to the idea of the political responsibility of literature and rejects it, creating a third, crosswise notion of writing that prefigures the recalcitrant force of the Neutral. By exploring the complexities of these early pieces, I argue that some of the unsolved issues will reappear in the Collège de France lecture course, notably the figure of ‘aporia’, and I discuss the ethical implications of this ‘impossibility’. (shrink)

We construct a G δ set G ⊆ ω ω ×2 ω with null vertical sections such that each perfect set P ⊆2 ω meets almost all vertical sections of G in the following sense: we can define from P subsets S of ω of density zero such that whenever the section determined by x ∈ ω ω does not meet P , then x ∈ S for all but finitely many i . This generalizes theorems of Mokobodzki and (...) Brendle et al. 185–199). (shrink)

Quotatives have been studied extensively in the language of teenagers in recent years as they present distinctive features of their own that make them different in part from those used by adults in mainstream English and Spanish. However, zero quoting has not received all the attention it certainly deserves as it has not been fully probed in terms of its discourse and pragmatic functions. This corpus-based study is focused on the strategies used by British and Spanish teenagers to introduce (...) constructed dialogue without the use of a particular marked and an explicit quotative form. The results indicate that the absence of quotatives is not casual; there are some linguistic contexts that favor the existence of this type of quotatives, namely non-lexicalized and sound words, and the dramatic recreation of situations where the speaker perform new voices. The lack of quotatives also serves to involve the interlocutor more directly and in a higher degree in what is being told, and gives more self-assurance to the narrator. These tendencies apply equally to English and Spanish. The study of null/zero quotatives should go then beyond the simple reporting of an absence of a verbal mark, and should address pragmatic and interpersonal factors closely associated with the context where they occur and with the speaker’s attitude and communicative intention and purpose. (shrink)

Recent debates over adults' theory of mind use have been fueled by surprising failures of perspective-taking in communication, suggesting that perspective-taking may be relatively effortful. Yet adults routinely engage in effortful processes when needed. How, then, should speakers and listeners allocate their resources to achieve successful communication? We begin with the observation that the shared goal of communication induces a natural division of labor: The resources one agent chooses to allocate toward perspective-taking should depend on their expectations about the (...) other's allocation. We formalize this idea in a resource-rational model augmenting recent probabilistic weighting accounts with a mechanism for (costly) control over the degree of perspective-taking. In a series of simulations, we first derive an intermediate degree of perspective weighting as an optimal trade-off between expected costs and benefits of perspective-taking. We then present two behavioral experiments testing novel predictions of our model. In Experiment 1, we manipulated the presence or absence of occlusions in a director–matcher task. We found that speakers spontaneously modulated the informativeness of their descriptions to account for “known unknowns” in their partner's private view, reflecting a higher degree of speaker perspective-taking than previously acknowledged. In Experiment 2, we then compared the scripted utterances used by confederates in prior work with those produced in interactions with unscripted directors. We found that confederates were systematically less informative than listeners would initially expect given the presence of occlusions, but listeners used violations to adaptively make fewer errors over time. Taken together, our work suggests that people are not simply “mindblind”; they use contextually appropriate expectations to navigate the division of labor with their partner. We discuss how a resource-rational framework may provide a more deeply explanatory foundation for understanding flexible perspective-taking under processing constraints. (shrink)

The physicists of the early twentieth century were unaware of two aspects which are vital to understanding some aspects of modern physics within classical theory. The two aspects are: the presence of classical electromagnetic zero-point radiation, and the importance of special relativity. In classes in modern physics today, the problem of atomic collapse is still mentioned in the historical context of the early twentieth century. However, the classical problem of atomic collapse is currently being treated in the presence of (...) classical zero-point radiation where the problem has been transformed. The presence of classical zero-point radiation indeed keeps the electron from falling into the Coulomb potential center. However, the old collapse problem has been replaced by a new problem where the zero-point radiation may give too much energy to the electron so as to cause “self-ionization.” Special relativity may play a role in understanding this modern variation on the atomic collapse problem, just as relativity has proved crucial for a classical understanding of blackbody radiation. (shrink)

We introduceself-divisibleultrafilters, which we prove to be precisely those$w$such that the weak congruence relation$\equiv _w$introduced by Šobot is an equivalence relation on$\beta {\mathbb Z}$. We provide several examples and additional characterisations; notably we show that$w$is self-divisible if and only if$\equiv _w$coincides with the strong congruence relation$\mathrel {\equiv ^{\mathrm {s}}_{w}}$, if and only if the quotient$(\beta {\mathbb Z},\oplus )/\mathord {\mathrel {\equiv ^{\mathrm {s}}_{w}}}$is a profinite group. We also construct an ultrafilter$w$such that$\equiv _w$fails to be symmetric, and describe the interaction between the (...) aforementioned quotient and the profinite completion$\hat {{\mathbb Z}}$of the integers. (shrink)

This chapter focuses on one of the common fallacies in Western philosophy called 'division'. The fallacy of division occurs when one incorrectly infers that the characteristics, attributes, or features of the group as a whole will also be found in the individuals comprising the group. The easiest way to avoid this fallacy is never to assume that the characteristics, attributes, or features of the group as a whole will also be found in the individuals comprising the group. One (...) must inspect and evaluate the characteristics, attributes, or features of the whole separately from the parts of which the whole is comprised. Inferences from a whole to a part can be made, however, if additional assumptions are added to the argument that link together the property had by the whole with the property had by the part. (shrink)

We propose a reformulation of the ideal $\mathcal {N}$ of Lebesgue measure zero sets of reals modulo an ideal J on $\omega $, which we denote by $\mathcal {N}_J$. In the same way, we reformulate the ideal $\mathcal {E}$ generated by $F_\sigma $ measure zero sets of reals modulo J, which we denote by $\mathcal {N}^*_J$. We show that these are $\sigma $ -ideals and that $\mathcal {N}_J=\mathcal {N}$ iff J has the Baire property, which in turn is (...) equivalent to $\mathcal {N}^*_J=\mathcal {E}$. Moreover, we prove that $\mathcal {N}_J$ does not contain co-meager sets and $\mathcal {N}^*_J$ contains non-meager sets when J does not have the Baire property. We also prove a deep connection between these ideals modulo J and the notion of nearly coherence of filters (or ideals). We also study the cardinal characteristics associated with $\mathcal {N}_J$ and $\mathcal {N}^*_J$. We show their position with respect to Cichoń’s diagram and prove consistency results in connection with other very classical cardinal characteristics of the continuum, leaving just very few open questions. To achieve this, we discovered a new characterization of $\mathrm {add}(\mathcal {N})$ and $\mathrm {cof}(\mathcal {N})$. We also show that, in Cohen model, we can obtain many different values to the cardinal characteristics associated with our new ideals. (shrink)

The procurement decision-making process for complex military product systems (CoPS) has significant implications for military end-users, suppliers, and exchequers. This study examines the usefulness of adopting a fast and frugal decision-making approach for the acquisition of military CoPS. Defence procurement environment is complex. On the one hand, there are uncertainties and severe resource constraints due to regularly changing threat perceptions, limited flow of information about new technologies, and the growing demand to reduce defence related expenses. On the other hand, several (...) stakeholders remain pre-occupied with the demand for ‘zero-error’ technologies. In such a setting, recurrent cost overruns and delays in supply are common in defence procurement programmes, across countries. Taking the illustrative examples of the missile system, fighter jet, and radar system acquisitions in India, we elucidate on ‘optimising’ versus ‘satisficing’ dynamics in the procurement decisions. The paper argues that a fast and frugal decision-making process by relying on judgement, experiential knowledge, and intuitive learning might make procurement processes, adaptively, more efficient. Such an approach would enable a ‘good enough’ technology to be inducted, and improved upon, through regular feedback from the actual environment. The study has implications for policy scholarships on innovation policy instruments under uncertainty. (shrink)