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...

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.

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)

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)

Bi-intuitionistic logic is the union of intuitionistic and dual intuitionistic logic, and was introduced by Rauszer as a Hilbert calculus with algebraic and Kripke semantics. But her subsequent ‘cut-free’ sequent calculus has recently been shown to fail cut-elimination. We present a new cut-free sequent calculus for bi-intuitionistic logic, and prove it sound and complete with respect to its Kripke semantics. Ensuring completeness is complicated by the interaction between intuitionistic implication and dual intuitionistic exclusion, similarly to future and past modalities in (...) tense logic. Our calculus handles this interaction using derivations and refutations as first class citizens. We employ extended sequents which pass information from premises to conclusions using variables instantiated at the leaves of refutations, and rules which compose certain refutations and derivations to form derivations. Automated deduction using terminating backward search is also possible, although this is not our main purpose. (shrink)

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)

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)

Let${\mathbb K}$be an algebraically bounded structure, and letTbe its theory. IfTis model complete, then the theory of${\mathbb K}$endowed with a derivation, denoted by$T^{\delta }$, has a model completion. Additionally, we prove that if the theoryTis stable/NIP then the model completion of$T^{\delta }$is also stable/NIP. Similar results hold for the theory with several derivations, either commuting or non-commuting.

ARGUMENT ABOUT whether in any significant sense we can derive an ought from an is has been persistent and intractable. Fifteen to twenty years ago it was orthodoxy in analytical philosophical circles to claim that for all their other differences Hume and Moore were right in agreeing that in no significant sense can we derive an ought from an is. At present there is no orthodoxy or even anything like a dominant view and, given our current understanding of how language (...) works and our understanding of moral and ideological discourse, we could not possibly reasonably remain content with old orthodoxies or take the question to be as straightforward as it was often thought to be. (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’ ( Foucault 2007 ). 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)

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)

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)

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 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)

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.

Many arguments offered by the free culture movement emphasize the ways in which new works rely on works, which have gone before, the discoveries and data of other scientists, and a general stock of common knowledge. An exammation of the ways in which old works mform new works will show that drawmg on previous works is a necessary and inevitable part of the act of creation. Despite the negative connotations surrounding the label "derivative," all works are, in an important sense, (...) derivative, and must be so in order to be recognized as novel and creative. As such, there should be greater freedom in the creation and circulation of derivative works. Under the current intellectual property regime, the creation of derivative works can be controlled at the discretion of the author. Therefore, any system of intellectual property rights must preserve the ability of creators to draw on previous works, including the ability to employ significant elements of protected works in their own creations. (shrink)

Information transmission from tumor cells to non‐tumor cells in the surrounding microenvironment via microvesicles is a more recently studied form of intercellular signaling that can have a marked impact on the tumor microenvironment. Tumor‐derived microvesicles (TMVs) are packed with information including signaling proteins and nucleic acids, and can be taken up by target cells, enabling paracrine signaling. While previous research has focused on how vesicles released from pathologic cells differ from normal cells, the heterogeneity that exists within the TMV population (...) itself is not fully characterized, and only beginning to be appreciated. In this review, we summarize current understanding of the biogenesis and roles of shed TMVs in the tumor microenvironment, and speculate on the consequences for tumor cell signaling in light of the hypothesis that there exists variance within the TMV population. The analysis of differential signaling upon cell‐TMV interactions provides insights into potential mechanisms of intercellular communication. (shrink)

Conventional quantum mechanics with a complex Hilbert space and the Born Rule is derived from five axioms describing experimentally observable properties of probability distributions for the outcome of measurements. Axioms I, II, III are common to quantum mechanics and hidden variable theories. Axiom IV recognizes a phenomenon, first noted by von Neumann (in Mathematical Foundations of Quantum Mechanics, Princeton University Press, Princeton, 1955) and independently by Turing (Teuscher and Hofstadter, Alan Turing: Life and Legacy of a Great Thinker, Springer, Berlin, (...) 2004), in which the increase in entropy resulting from a measurement is reduced by a suitable intermediate measurement. This is shown to be impossible for local hidden variable theories. Axiom IV, together with the first three, almost suffice to deduce the conventional rules but allow some exotic, alternatives such as real or quaternionic quantum mechanics. Axiom V recognizes a property of the distribution of outcomes of random measurements on qubits which holds only in the complex Hilbert space model. It is then shown that the five axioms also imply the conventional rules for any finite dimension. (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)

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.

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.

For the first time in over thirty years a revolution is happening in phonology, with the advent of constraint-based approaches which directly oppose the rule-and-derivation tradition of mainstream Generative Phonology. The success of Optimality Theory and the rapidity of its spread since its official launch in 1993 is remarkable even by the general standards of post-1950s linguistics. Many phonologists appear to have been caught up in the whirlwind, as witnessed by the substance of many current working papers and conferences the (...) world over, and the recent contents of well-established journals. Two questions naturally arise: What is Optimality Theory about? In what way is Optimality Theory superior to traditional theory, if indeed it is? In this book, leading specialists and active researchers address these issues directly, and focus deliberately on the evaluation of the two competing approaches rather than on simple displays of their applicability to limited bodies of data. (shrink)

The analysis of dispositions is used to consider cases where the effect of one disposition operating is the existence of another disposition. This may arise from rearrangements within aggregated structures of dispositional parts, or, it is argued, also as stages of derivative dispositions within a set of multiple generative levels. Inspection of examples in both classical and quantum physics suggests a general principle of `Conditional Forward Causation': that dispositions act 'forwards' in a way conditional on certain circumstances or occasions already (...) existing at the `later' levels. (shrink)

In this article, I derive a weak version of Kant's categorical imperative within an informal game-theoretic framework. More specifically, I argue that Hobbesian agents would choose what I call the weak principle of universalization, if they had to decide on a rule of conflict resolution in an idealized but empirically defensible hypothetical decision situation. The discussion clarifies (i) the rationality requirements imposed on agents, (ii) the empirical conditions assumed to warrant the conclusion, and (iii) the political institutions that are necessary (...) to implement the derived principle. The analysis demonstrates the moral significance of the weak principle of universalization and its epistemic advantage over the categorical imperative. (shrink)

Building upon previous research on the therapeutic object, specifically the objet re-petit-ive abc, which draws from Lacan, Winnicott, and Guattari, I explore the generation, contribution, and erosion of knowledge in the so-called smart city. I will investigate how digital pedagogical objects, functioning as transitional objects, can serve as therapeutic purposes both within and outside institutional settings. I examine the notions of the dérive and psychogeography and compare them with Bernard Stiegler’s concept of the “journey of knowledge” and then delve into (...) the curation of “negentropic forms of knowledge” and the mnemonic technique of the dérive. Taking ecological and ecosophical perspectives into account, I consider mnemonic techniques as a means to critically reflect upon the urban landscape and its transformation into a technical milieu. My overall goal is to contemplate the possibility of a Stieglerian and/or Guattarian détournement (philosophical hijacking) of the smart city. (shrink)

This paper shows how to derive nested calculi from labelled calculi for propositional intuitionistic logic and first-order intuitionistic logic with constant domains, thus connecting the general results for labelled calculi with the more refined formalism of nested sequents. The extraction of nested calculi from labelled calculi obtains via considerations pertaining to the elimination of structural rules in labelled derivations. Each aspect of the extraction process is motivated and detailed, showing that each nested calculus inherits favorable proof-theoretic properties from its associated (...) labelled calculus. (shrink)

General relativity is the exact theory of gravity which has been experimentally found to be correct with extremely high accuracy. One of the most surprising predictions of the general theory is that time runs slow in a gravitational field. Its proof formally comes from Schwarzschild metric which is a solution of Einstein field equation for a spherically symmetric mass. However, as Einstein field equation is too complex, attempts have been made earlier to derive gravitational time dilation by direct use of (...) principle of equivalence and special theory of relativity. But, this objective has been accomplished partially till date as the resulting expression agrees with the exact expression only upto first order. In this paper, by using principle of equivalence and special relativity, we present a thought experiment which helps us to derive an expression that exactly matches with the expression for gravitational time delay. (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)

The Korean particle -nun combined with an accent indicates contrast :269–320, 1972; Heycock, in: Merce Proceedings of NELS, vol 24, pp 159–187, 1993; in: Miyagawa, Saito Handbook of Japanese linguistics, Oxford University Press, Cambridge, 2007; Hara, in: Dekker, Franke Fifteenth Amsterdam colloquium, Universiteit van Amsterdam, pp 101–106, 2006; Lee, in: Lee, Gordon, Büring Topic and focus: meaning and intonation from a crosslinguistic perspective. Springer, Berlin, 2003; Tomioka, in: Zimmermann, Fery Information structure, Oxford University Press, Cambridge, pp 115–138, 2009, among many (...) others). While this is not controversial, what it means to be contrastive remains unclear. In this paper, instead of analyzing contrastive -nun as a discourse device in the sense of information structure, as has been done in previous studies, I explore how the contrastive meaning is derived compositionally. I treat contrastive -nun as a focus sensitive particle that associates with prosodic accents in two places, generating a non-at-issue meaning. The non-at-issue meaning contains a polyadic quantifier that establishes a contrastive relationship between two elements in a given set. This analysis explains how focus following contrastive -nun is associated with -nun. It also provides an explanation for the uncertainty implicature that contrastive -nun gives rise to. Finally, it clarifies the logical relationship among different focus particles in Korean. (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)

The standard rule of necessitation in systems of natural deduction for the modal logic S4 concludes □A from A whenever all assumptions A depends on are modal formulas. This condition prevents the composability and normalization of derivations, and therefore modifications of the rule have been suggested. It is shown that both properties hold if, instead of changing the rule of necessitation, all elimination rules are formulated in the manner of disjunction elimination, i.e. with an arbitrary consequence.

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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)

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 derived embodiment, intangible phenomena become as-if tangible as a result of their almost promiscuous borrowing of corporeality from experiences of real objects.

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.

Melchizedek is one of the most mysterious characters of the book of Genesis. As priest of God Almighty he blessed Abraham, the patriarch returning from war, and received tithes from him. The Epistle to the Hebrews presents Jesus Christ as high priest according to Melchizedek’s priestly order, based on God’s oath found in Psalm 110:4. While Christ’s priestly order according to Melchizedek is higher than Aaron’s priestly order, it is important to remember that Christ is greater than Melchizedek. In other (...) words, Melchizedek derives his pattern from the preexistent Christ, and not the other way around. It is the purpose of this paper to bring to attention that the superiority of the characteristics of and blessings derived from Christ’s priesthood according to Melchizedek’s order is best understood only within this frame. (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.

A theory of the joint measurement of quantum mechanical observables is generalized in order to make it applicable to the measurement of the local observables of field theory. Subsequently, the property of local commutativity, which is usually introduced as a postulate, is derived by means of the theory of measurement from a requirement of mutual nondisturbance, which, for local observables performed at a spacelike distance from each other, is interpreted as a requirement of macrocausality. Alternative attempts at establishing a deductive (...) relationship between relativistic causality and local commutativity are reviewed, but found wanting, either because of the assumption of an unwarranted objectivity of the object system (algebraic approach) or because of the use of a projection postulate (operational approach). Finally, the quantum mechanical nonobjectivity is related to certain features of nonlocality which are present in the formalism of quantum mechanics. (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)

This document collects natural derivation systems for logics described in Priest, An Introduction to Non-Classical Logic [4]. It provides an alternative or supplement to the semantic tableaux of his text. Except that some chapters are collapsed, there are sections for each chapter in Priest, with an additional, final section on quantified modal logic. In each case, (i) the language is briefly described and key semantic definitions stated, (ii) the derivation system is presented with a few examples given, and (iii) soundness (...) and completeness are proved. There should be enough detail to make the parts accessible to students would work through parallel sections of Priest. (shrink)

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)