Mental disorders in university students are very frequent, therefore higher education institutions have established in-campus mental healthcare centres. These clinics have particular characteristics that differ from other mental health centres, as they report to and represent an educational institution, while at the same time looking after the interests and well-being of patients requesting assistance, thus generating unique bioethical conflicts. Ethics Committees are useful tools to offer support to mental health professionals in making ethical decisions. In order to respond to these (...) issues, it was decided that an Ethics Committee would be created in the mental health clinic of a private university in Mexico City. This article describes the implementation process for this Committee, its duties and scope, as well as the case work and review methodology. A list of the most frequent ethical conflicts is attached, jointly with the ethical analysis of the cases treated throughout the year and a half or work by the Committee. (shrink)

A review of U. Mäki (ed.). Fact and Fiction in Economics, Cambridge: Cambridge University Press, 2003. pp. xvi 384. ISBN 0521 00957. As people interested mainly in theory, methodologists and philos...

We discuss a `negative' way of defining frame classes in (multi)modal logic, and address the question of whether these classes can be axiomatized by derivation rules, the `non-ξ rules', styled after Gabbay's Irreflexivity Rule. The main result of this paper is a metatheorem on completeness, of the following kind: If Λ is a derivation system having a set of axioms that are special Sahlqvist formulas and Λ+ is the extension of Λ with a set of non-ξ rules, then Λ+ is (...) strongly sound and complete with respect to the class of frames determined by the axioms and the rules. (shrink)

Moral philosophers draw an important distinction between two kinds of moral responsibility. An agent can be directly morally responsible, or they can be derivatively morally responsible. Direct moral responsibility, so many believe, presupposes that the agent could have behaved differently. However, in some situations, we hold agents responsible even though they could not have behaved differently, such as when they recklessly cause an accident or do not take adequate precautions to avoid harmful consequences. Moral philosophers typically argue that what we (...) ascribe in these cases is derivative moral responsibility. In this paper, I apply this conceptual distinction to the experimental debate about so-called folk-compatibilism. I argue that experimental philosophers have failed to consider this distinction when designing experiments and interpreting their results. I demonstrate that while compatibilism requires judgments of direct moral responsibility, participants in some of the most influential studies ascribed derivative moral responsibility. For this reason, these studies do not speak in favour of compatibilism at all. (shrink)

As is well known the derivative of a computable and C1 function may not be computable. For a computable and C∞ function f, the sequence {f} of its derivatives may fail to be computable as a sequence, even though its derivative of any order is computable. In this paper we present a necessary and sufficient condition for the sequence {f} of derivatives of a computable and C∞ function f to be computable. We also give a sharp regularity condition on an (...) initial computable function f which insures the computability of its derivative f′. (shrink)

Derivatives and the real economy The paper describes the development of the derivatives market and compares it with the development of the real economy. Based on official data the paper describes how the derivatives market has significantly increased its volume of trading, mainly after the abolishment of the Glass-Steagal Act. The growing volume of the derivatives market also significantly contributed to the global financial crisis. This paper also compares the growth of the global nominal and real gross domestic product with (...) the pace of growth of the overall derivatives market, but mainly the over-the-counter market. Based on preliminary findings, the paper came to the conclusion that it is critical to implement all the requisite measures in order to eliminate non-transparent transactions with certain derivatives products in order to put the global economy on a sustainable, solid and balanced economic growth path. (shrink)

Financial derivatives have been singled out as the major villain in the latest crisis, particularly through speculative trading by banks. Yet little attention has been paid to the fundamental rôle that derivatives play in modern capitalism. Even less has there been a focus on how the boom in derivatives-trading was prompted by the crisis of profitability and capital-accumulation. This article shows that while derivatives were one means by which speculation took off, the momentum behind this was driven by low profitability. (...) That was why banks turned their mortgage-loans into derivative-driven securities, why pension-funds placed bets on commodity-futures and why countries such as Greece used derivatives to hide the real state of their finances. Derivatives helped determine the form and magnitude of the crisis, but were not its underlying cause. Proposed reforms of the derivatives-market ignore the fundamental determinants of the financial crisis, assuming it to be a failure of regulation. (shrink)

Globalization of financial markets led to the enormous growth of volume and diversification of financial transactions. Financial derivatives were the basic elements of this growth. Derivatives play a useful and important role in hedging and risk management, but they also pose several dangers to the stability of financial markets and thereby the overall economy. Derivatives are used to hedge and speculate the risk associated with commerce and finance. When used to hedge risks, derivative instruments transfer the risks from the hedgers, (...) who are unwilling to bear the risks, to parties better able or more willing to bear them. In this regard, derivatives help allocate risks efficiently between different individuals and groups in the economy. Investors can also use derivatives to speculate and to engage in arbitrage activity. Speculators are traders who want to take a position in the market; they are betting that the price of the underlying asset or commodity will move in a particular direction over the life of the contract. In addition to risk management, derivatives play a very useful economic role in price discovery and arbitrage. Financial derivatives trading are based on leverage techniques, earning enormous profits with small amount of money. (shrink)

Interactional expertise is said to be a form of knowledge achieved in a linguistic community and, therefore, obtained entirely outside practice. Supposedly, it is not or only minimally sustained by the so-called embodied knowledge. Here, drawing upon studies in contemporary neuroscience and cognitive psychology, I propose that ‘derived’ embodiment is deeply involved in competent language use and, therefore, also in interactional expertise. My argument consists of two parts. First, I argue for a strong relationship among language acquisition, language use and (...) the real world (i.e. the world accessible to the senses). Biological constraints in very early childhood anchor language to the body. These constraints are by-products of our evolutionary peculiarity that we gain because of our physical and psychological immaturity at birth. Thus, infancy is predominantly concerned with the bodily needs and experiences of the concrete while language acquisition takes place. Particular interest in the concrete furnishes our linguistic world and installs ‘concrete’ language as the principal constituent of competent language use. Second, I argue that well-established concrete language implicitly and explicitly elicits mental representations, namely partial reactivations of sensorimotor states that occur during experience. These are stepping stones by which we subsequently make sense of expressions in new linguistic areas. Like any competent language user, the interactional expert, therefore, prompts multimodal imagination and re-enacts concrete experiences when acquiring linguistic knowledge pertaining to a specialist field. Finally, I outline the characteristics of those imaginative powers to identify mechanisms that improve interactional expertise and discuss the obvious relation between interactional expertise and ordinary knowledge acquisition after the concrete language stage. (shrink)

Derivational robustness may increase the degree to which various pieces of evidence indirectly confirm a robust result. There are two ways in which this increase may come about. First, if one can show that a result is robust, and that the various individual models used to derive it also have other confirmed results, these other results may indirectly confirm the robust result. Confirmation derives from the fact that data not known to bear on a result are shown to be relevant (...) when it is shown to be robust. Second, robustness may increase the degree to which the robust result is indirectly confirmed if it increases the weight with which existing evidence indirectly confirms it. This may happen when it strengthens the connection between the core and the robust result by showing that auxiliaries are not responsible for the result. (shrink)

In Bolzano's view, a proposition is necessarily true iff it is derivable from true propositions that include no intuition (Anschauung). This analysis is historically important because it displays close similarities to Quine's and Kripke's ideas. Its systematic significance, however, is reduced by the fact that derivability is defined with recourse to the method of variation, which we are allowed to apply even to propositions containing none of the respective variables. This liberality leads to the result that, according to Bolzano's (...) analysis, every truth is necessarily true. Even by introducing his condition of relevance (shared variables), Bolzano cannot avoid that some propositions come out as necessarily true which are merely contingently true. (shrink)

Orthodoxy has it that only metaphysically elite properties can be invoked in scientifically elite laws. We argue that this claim does not fit scientific practice. An examination of candidate scientifically elite laws like Newton’s F = ma reveals properties invoked that are irreversibly defined and thus metaphysically non-elite by the lights of the surrounding theory: Newtonian acceleration is irreversibly defined as the second derivative of position, and Newtonian resultant force is irreversibly defined as the sum of the component forces. We (...) think that scientists are happy to invoke metaphysically non-elite properties in scientifically elite laws for reasons of convenience, such as to simplify the equations and to make them more modular. On this basis, we draw a deflationary moral about laws themselves, as being merely convenient summaries. 1 Introduction2 Orthodoxy2.1 Orthodoxy stated2.2 Orthodoxy explained2.3 A worrisome commitment: Term objectivism3 The Loose View3.1 The argument from practice3.2 Finding the scientifically elite equations3.3 Diagnosing the metaphysically non-elite properties3.4 Situating our challenge4 Newtonian Mechanics4.1 Newtonian acceleration4.2 Newtonian resultant force4.3 A metaphysical discovery?5 Objections5.1 Metaphysically elite after all?5.2 Scientifically non-elite after all?5.3 But our world is not Newtonian!6 Consequences6.1 Consequences for the motivations for link6.2 Consequences for metaphysically elite properties6.3 Consequences for lawhood. (shrink)

According to the objection from positive duties, Kant's Formula of Universal Law is flawed because it cannot be used to derive any affirmative moral requirements. This paper offers a response to that objection and proposes a novel way to derive positive duties from Kant's formula. The Formula of Universal Law yields positive duties to adopt our own perfection and others’ happiness as ends because we could not rationally fail to will those ends as universal ends.

A normalization procedure is given for classical natural deduction with the standard rule of indirect proof applied to arbitrary formulas. For normal derivability and the subformula property, it is sufficient to permute down instances of indirect proof whenever they have been used for concluding a major premiss of an elimination rule. The result applies even to natural deduction for classical modal logic.

The aim of this article is to study the notion of derivability and its semantic counterpart in the context of non-transitive and non-reflexive substructural logics. For this purpose we focus on the study cases of the logics _S__T_ and _T__S_. In this respect, we show that this notion doesn’t coincide, in general, with a nowadays broadly used semantic approach towards metainferential validity: the notion of local validity. Following this, and building on some previous work by Humberstone, we prove that (...) in these systems derivability can be characterized in terms of a notion we call absolute global validity. However, arriving at these results doesn’t lead us to disregard local validity. First, because we discuss the conditions under which local, and also global validity, can be expected to coincide with derivability. Secondly, because we show how taking into account certain families of valuations can be useful to describe derivability for different calculi used to present _S__T_ and _T__S_. (shrink)

Indeterminacy is metaphysical (or worldly) if it has its source in the way the world is (rather than how it is represented or known). There are two questions we could ask about indeterminacy. First: does it exist? Second: is indeterminacy derivative? I focus on the second question. Specifically, I argue that (at least some) metaphysical indeterminacy can be derivative, where this roughly means that facts about indeterminacy are metaphysically grounded in facts about what is determinate.

In ‘‘The Myth of Original Intentionality,’’ Daniel Dennett appears to want to argue for four claims involving the familiar distinction between original (or underived) and derived intentionality.

At the heart of Rik Peels’s Responsible Belief: A Theory in Ethics and Epistemology is the idea that responsibility for belief ought to be understood on the model of responsibility for states of affairs that are subject to our influence but not under our intentional control, or what he calls derivative responsibility. In this article, I argue that reflection on the nature and scope of derivative responsibility reveals important lacunae in Peels’s account of responsible belief and his account of responsibility (...) for belief. (shrink)

This paper has two goals. First, I offer an interpretation of Nietzsche’s puzzling claims about will to power. I argue that the will to power thesis is a version of constitutivism. Constitutivism is the view that we can derive substantive normative conclusions from an account of the nature of agency; in particular, constitutivism rests on the idea that all actions are motivated by a common, higher-order aim, whose presence generates a standard of assessment for actions. Nietzsche’s version of constitutivism is (...) based on a series of subtle claims about the psychology of willing and the nature of satisfaction, which imply that all actions aim at encountering and overcoming resistance (this is what Nietzsche means by “will to power”). Second, I argue that Nietzsche’s theory, thus interpreted, generates a new, a posteriori version of constitutivism that is not vulnerable to certain familiar objections. If this is right, then we can deploy Nietzschean ideas in order to make a substantive contribution to issues that are currently at the forefront of ethics and action theory. (shrink)

The purpose of the paper, part of a project by Boston University Law School, is to examine derivatives law and practice in selected Middle Eastern countries including the UAE.

Standard accounts of derivational morphology assume that it is incremental: some words are formed on the basis of others, and each derivational family has a base from which all of the other words are derived. The importance of the base has been questioned by paradigmatic approaches to morphology, which posit that word systems are about multidirectional relationships between words and paradigm cells, in which no word has a privileged status. This paper seeks to test which of these two views makes (...) more accurate predictions about speakers’ cognitive representations of derivational families. We perform an acceptability judgement experiment in which speakers are asked to evaluate the acceptability of a pseudoword conditional on another pseudoword in the same derivational family. We find that speakers are aware of implicative relationships between words in the same family, and that they opportunistically exploit probabilistic relationships between surface words, regardless of whether the base form is the predictor, the target of prediction, or not at all involved in the task. (shrink)

In a quiet London office, a software designer muses on the algorithms that will make possible the risk flags to be visualized on the screens of border guards from Heathrow to St Pancras International. There is, he says, ‘real time decision making’ – to detain, to deport, to secondarily question or search – but there is also the ‘offline team who run the analytics and work out the best set of rules’. Writing the code that will decide the association rules (...) between items of data, prosaic and mundane – flight route, payment type, passport – the analysts derive a novel preemptive security measure. This paper proposes the analytic of the data derivative – a visualized risk flag or score drawn from an amalgam of disaggregated fragments of data, inferred from across the gaps between data and projected onto an array of uncertain futures. In contrast to disciplinary and enclosed techniques of collecting data to govern population, the data derivative functions via ‘differential curves of normality’, imagining a range of potential futures through the association rule, thus ‘opening up to let things happen’. In some senses akin to the risk orientation of the financial derivative, itself indifferent to actual underlying people, places or events by virtue of modulated norms, the contemporary security derivative is not centred on who we are, nor even on what our data say about us, but on what can be imagined and inferred about who we might be – on our very proclivities and potentialities. (shrink)

This paper contributes to the debate on the role of financial derivatives for capitalism. It responds to Bryan and Rafferty’s defence of their analysis and their critique of my own. The paper argues that their analysis confuses what a financial derivative does, and mixes together different kinds of derivative – and non-derivative – that play very different roles. After detailing these points, the paper discusses the relationship between gold, money and derivatives, rejecting their notion that derivatives are some kind of (...) new ‘commodity money’. An important theme absent from Bryan and Rafferty’s analysis is the relationship of financial trading and derivatives markets to parasitism in the imperialist world economy. To illustrate this, the paper notes advantages enjoyed by the major financial powers – the US and the UK – that are the main centres for the origination of derivatives and for derivatives trading. (shrink)

The central objection to the constitution view is the too many thinkers problem - if the animal that constitutes you thinks and you are not it, then there are two thinkers within the region you occupy. Lynne Rudder Baker claims that the animal thinks only derivatively, in virtue of constituting the person that thinks nonderivatively, and this leads to a solution to the too many thinkers problem. This paper offers two objections to Baker’s solution. First, the idea of derivative/ nonderivative (...) properties faces a dilemma unacceptable to constitutionalists: either the too many thinkers problem is reinstated or the constitution view is undermined by the idea itself. Further, Baker should concede that the person thinks in virtue of brain functions. This implies, contra Baker’s claim, that the person thinks derivatively and the animal thinks nonderivatively. The paper also considers a way in which Baker might respond to the two objections. (shrink)

This chapter derives and refines a novel normative moral theory and descriptive theory of moral psychology--Rightness as Fairness--from the theory of prudence defended in Chapter 2. It briefly summarizes Chapter 2’s finding that prudent agents typically internalize ‘moral risk-aversion’. It then outlines how this prudential psychology leads prudent agents to want to know how to act in ways they will not regret in morally salient cases, as well as to regard moral actions as the only types of actions that satisfy (...) this prudential interest. It then uses these findings to defend a new derivation of my (2016) theory of morality, Rightness as Fairness, showing how the derivation successfully defends Rightness as Fairness against a variety of objections. The chapter also details how this book’s theory helps to substantiate the claim that Rightness as Fairness unifies a variety of competing moral frameworks: deontology, consequentialism, contractualism, and virtue ethics. Finally, the chapter shows how Chapter 2’s theory of prudence entails some revisions to Rightness as Fairness, including the adoption of a series of Rawlsian original positions to settle moral and social-political issues under ideal and nonideal circumstances—thus entailing a unified normative and descriptive psychological framework for prudence, morality, and justice. (shrink)

This paper supports the literature which argues that derivational robustness can have epistemic import in highly idealized economic models. The defense is based on a particular example from mathematical economic theory, the dynamic Walrasian general equilibrium model. It is argued that derivational robustness first increased and later decreased the credibility of the Walrasian model. The example demonstrates that derivational robustness correctly describes the practices of a particular group of influential economic theorists and provides support for the arguments of philosophers who (...) have offered a general epistemic justification of such practices. (shrink)

Frank Hindriks has attempted to derive a variant of Timothy Williamson’s knowledge rule for assertion on the basis of a more fundamental belief expression analysis of that speech act. I show that his attempted derivation involves a crucial equivocation between two senses of ‘must,’ and therefore fails. I suggest two possible repairs; but I argue that even if they are successful, we should prefer Williamson’s fully general knowledge rule to Hindriks’s restricted moral norm.

In a rather old paper, Mario Liu described a hydrodynamic Maxwell equations. While he also discussed potential implications of these new approaches to superconductors, such a discussion of electrodynamics of superconductors is made only after Tajmar’s paper. Therefore, in this paper we present for the first time a derivation of fluidic Maxwell-Proca equations. The name of fluidic Maxwell-Proca is proposed because the equations were based on modifying Maxwell-Proca and Hirsch’s theory of electrodynamics of superconductor. It is hoped that this paper (...) may stimulate further investigations and experiments in superconductor. It may be expected to have some impact to cosmology modeling too, for instance we consider a hypothetical argument that photon mass can be origin of gravitation. Then, after combining with the so-called chiral modification of Maxwell equations (after Spröessig), then we consider chiral Maxwell-Proca equations as possible alternative of gravitation theory. Such a hypothesis has never considered in literature to the best of our knowledge. (shrink)

The main result of this paper is Theorem, which shows that it is possible for derived models to satisfy “ω1 is ‐supercompact”. Other constructions of models of this theory are also discussed; in particular, Theorem constructs a normal fine measure on and hence a model of “Θ is regular”+“ω1 is ‐supercompact” from a model of “Θ is measurable”.

This chapter argues that quantum indeterminacy can be construed as a merely derivative phenomenon. The possibility of merely derivative quantum indeterminacy undermines both a recent argument against quantum indeterminacy due to David Glick, and an argument against the possibility of merely derivative indeterminacy due to Elizabeth Barnes.

The article presents so-called “derivational” theory of legal interpretation and analyzes its basic assumptions. The derivational theory of legal interpretation is still little known outside of Poland. The article is divided into two parts. The first part is presenting the normative model of legal interpretation according to the derivational theory. In the second part, the basic assumptions and features of the theory are analysed in context of some other approaches to legal interpretation. The author argues that there are two levels (...) of the derivational theory: local and universal. The local level of theory is related to the fact that it was designed for Polish legal system and legal culture. However, beyond its local features, the derivational theory is presenting strong theoretical framework and some significant universal ideas about legal interpretation. This creates universal level that can be called the “hard core” of the theory. The author characterizes the elements of this hard core, and in particular the most important element: the idea that the legal interpretation consists in the reconstruction of legal norms from legal provisions. (shrink)

In this note the well-ordering principle for the derivative \ of normal functions \ on ordinals is shown to be equivalent to the existence of arbitrarily large countable coded \-models of the well-ordering principle for the function \.

In previous articles we presented a simple set of axioms named “Contexts, Systems and Modalities”, where the structure of quantum mechanics appears as a result of the interplay between the quantized number of modalities accessible to a quantum system, and the continuum of contexts that are required to define these modalities. In the present article we discuss further how to obtain Born’s rule within this framework. Our approach is compared with other former and recent derivations, and its strong links with (...) Gleason’s theorem are particularly emphasized. (shrink)

Implants and drugs with animal and human derived content are widely used in medicine and surgery, but information regarding ingredients is rarely obtainable by health practitioners. A religious perspective concerning the use of animal and human derived drug ingredients has not thoroughly been investigated. The purpose of this study was to clarify which parts of the medical and surgical treatments offered in western world-hospitals that conflicts with believers of major religions.

Let $R$ be a (finite) rewrite system over a (finite) signature. Let $\succ$ be a strict well-founded termination ordering on the set of terms in question so that the rules of $R$ are reducing under $\succ$ . Then $R$ is terminating. In this article it is proved for a certain class of far reaching termination orderings (of order type reaching up to the first subrecursively inaccessible ordinal, i.e. the proof-theoretic ordinal of $ID_{<\omega}$ ) that – under some reasonable assumptions which (...) are met in current applications – the derivation lengths function for $R$ is bounded by a function from the slow growing hierarchy of level determined by the order type of the underlying termination ordering. This result is a (correction of the proof of and a) strong generalization of theorem 8.1 in Cichon's article Termination orderings and complexity characterisations. Leeds, Proof Theory 1990, (Aczel, Simmons, and Wainer, editors), Cambridge University Press 1992, 171-193. (shrink)

The Born rule is derived from operational assumptions, together with assumptions of quantum mechanics that concern only the deterministic development of the state. Unlike Gleason’s theorem, the argument applies even if probabilities are de…ned for only a single resolution of the identity, so it applies to a variety of foundational approaches to quantum mechanics. It also provides a probability rule for state spaces that are not Hilbert spaces.

A rigorous ab initio derivation of the (square of) Dirac’s equation for a particle with spin is presented. The Lagrangian of the classical relativistic spherical top is modified so to render it invariant with respect conformal changes of the metric of the top configuration space. The conformal invariance is achieved by replacing the particle mass in the Lagrangian with the conformal Weyl scalar curvature. The Hamilton-Jacobi equation for the particle is found to be linearized, exactly and in closed form, by (...) an ansatz solution that can be straightforwardly interpreted as the “quantum wave function” of the 4-spinor solution of Dirac’s equation. All quantum features arise from the subtle interplay between the conformal curvature acting on the particle as a potential and the particle motion which affects the geometric “pre-potential” associated to the conformal curvature itself. The theory, carried out here by assuming a Minkowski metric, can be easily extended to arbitrary space-time Riemann metric, e.g. the one adopted in the context of General Relativity. This novel theoretical scenario appears to be of general application and is expected to open a promising perspective in the modern endeavor aimed at the unification of the natural forces with gravitation. (shrink)

Derivative moral responsibility is not moral responsibility at all. Much of the confusion found in the literature concerning moral responsibility and the free will problem can be traced back to a penchant to reconcile our philosophical theories of moral responsibility with our folk commonsense linguistic accounts of moral responsibility, a tradition that is notable for its utter lack of making two important distinctions - the distinction between derivative moral responsibility and non-derivative moral responsibility and the distinction between the scope and (...) degree of one’s moral responsibility.1 The failure to make such distinctions, ultimately, leads to confusion in interpreting the content of folk intuitions about moral responsibility, and as a result leads many philosophers to adopt watered down, or overly complex theories of moral responsibility. In “The Epistemic Requirements for Moral Responsibility,” Carl Ginet fails to make such distinctions, and as a result the requirement he arrives at is unwieldy at best. By making such distinctions, I will provide a much more straightforward account of what moral responsibility requires. (shrink)

I explore the question of when an agent is derivatively, rather than directly, culpable for an undesirable outcome. The undesirable outcome might be a harmful incompetent or unwitting act, or it might be a harmful event. By examining various cases, I develop a sophisticated account of indirect culpability that is neutral about controversies regarding normative ethical issues and the condition on direct culpability.

We introduce reflection properties of cardinals in which the attributes that reflect are expressible by infinitary formulas whose lengths can be strictly larger than the cardinal under consideration. This kind of generalized reflection principle leads to the definitions of [Formula: see text]-indescribability and [Formula: see text]-indescribability of a cardinal [Formula: see text] for all [Formula: see text]. In this context, universal [Formula: see text] formulas exist, there is a normal ideal associated to [Formula: see text]-indescribability and the notions of [Formula: (...) see text]-indescribability yield a strict hierarchy below a subtle cardinal. Additionally, given a regular cardinal [Formula: see text], we introduce a diagonal version of Cantor’s derivative operator and use it to extend Bagaria’s [Derived topologies on ordinals and stationary reflection, Trans. Amer. Math. Soc. 371(3) (2019) 1981–2002] sequence [Formula: see text] of derived topologies on [Formula: see text] to [Formula: see text]. Finally, we prove that for all [Formula: see text], if there is a stationary set of [Formula: see text] that have a high enough degree of indescribability, then there are stationarily many [Formula: see text] that are nonisolated points in the space [Formula: see text]. (shrink)

This article examines the financial technology of derivatives. Derivatives are financial products whose values are based on possible fluctuations in the values of underlying assets. Hence derivatives markets are markets that trade in the risks of other markets. In order for derivatives markets to function, forms of prognostication that can assess the possible future fluctuations of the underlying markets are necessary. What such prognostications do, the article argues, is to create information out of future possibilities. Building upon a notion of (...) virtuality derived from Gilles Deleuze, Ulrich Beck and Niklas Luhmann, the article shows how market risks and uncertainties, by means of prognostications, cease to be mere possibilities and instead come to have virtual existence. Through the technology of derivatives, uncertainty and risk can be rendered virtual and be traded. The article suggests that this technology is an example of a new way in which capitalism is now expanding self-referentially as it creates markets out of markets; and of how it is colonizing the future by developing new technologies for ‘hyper-speculation’, that is, speculation not in the possible developments of a given asset but simply in the risk of such speculation. (shrink)

One of the earliest applications of transfinite numbers is in the construction of derived sequences by Cantor [2]. In [6], the existence of derived sequences for countable closed sets is proved in ATR0. This existence theorem is an intermediate step in a proof that a statement concerning topological comparability is equivalent to ATR0. In actuality, the full strength of ATR0 is used in proving the existence theorem. To show this, we will derive a statement known to be equivalent to ATR0, (...) using only RCA0 and the assertion that every countable closed set has a derived sequence. We will use three of the subsystems of second order arithmetic defined by H. Friedman , which can be roughly characterized by the strength of their set comprehension axioms. RCA0 includes comprehension for Δmath image definable sets, ACA0 includes comprehension for arithmetical sets, and ATR0 appends to ACA0 a comprehension scheme for sets defined by transfinite recursion on arithmetical formulas. MSC: 03F35, 54B99. (shrink)

The traditional view of evidence in mathematics is that evidence is just proof and proof is just derivation. There are good reasons for thinking that this view should be rejected: it misrepresents both historical and current mathematical practice. Nonetheless, evidence, proof, and derivation are closely intertwined. This paper seeks to tease these concepts apart. It emphasizes the role of argumentation as a context shared by evidence, proofs, and derivations. The utility of argumentation theory, in general, and argumentation schemes, in particular, (...) as a methodology for the study of mathematical practice is thereby demonstrated. Argumentation schemes represent an almost untapped resource for mathematics education. Notably, they provide a consistent treatment of rigorous and non-rigorous argumentation, thereby working to exhibit the continuity of reasoning in mathematics with reasoning in other areas. Moreover, since argumentation schemes are a comparatively mature methodology, there is a substantial body of existing work to draw upon, including some increasingly sophisticated software tools. Such tools have significant potential for the analysis and evaluation of mathematical argumentation. The first four sections of the paper address the relationships of evidence to proof, proof to derivation, argument to proof, and argument to evidence, respectively. The final section directly addresses some of the educational implications of an argumentation scheme account of mathematical reasoning. (shrink)