An argument of A. Borel [Bor—61, Proposition 3.1] shows that every compact connected Lie group is homeomorphic to the Cartesian product of its derived subgroup and a torus. We prove a parallel result for definably compact definably connected groups definable in an o-minimal expansion of a real closed field. As opposed to the Lie case, however, we provide an example showing that the derived subgroup may not have a definable semidirect complement.

This paper presents a representational theory of derived physical measurements. The theory proceeds from a formal definition of a class of similar systems. It is shown that such a class of systems possesses a natural proportionality structure. A derived measure of a class of systems is defined to be a proportionality-preserving representation whose values are n-tuples of positive real numbers. Therefore, the derived measures are measures of entire physical systems. The theory provides an interpretation of the dimensional parameters in a (...) large class of physical laws, and it accounts for the monomial dimensions of these parameters. It is also shown that a class of similar systems obeys a dimensionally invariant law, which one may safely subject to a dimensional analysis. (shrink)

The concept of moral distress comes from nursing ethics, and was initially defined as ‘…when one knows the right thing to do, but institutional constraints make it nearly impossible to pursue the right course of action’. There is a large body of literature associated with moral distress, yet multiple definitions now exist, significantly limiting its usefulness. We undertook a systematic review of the argument-based bioethics literature on this topic as the basis for a critical appraisal, identifying 55 papers for analysis. (...) We found that moral distress is most frequently framed around individual experiences of distress in relation to local practices and constraints, and understood in terms of power relations and workplace hierarchies. This understanding is directly derived from, and often still seen as specific to, nursing. Frequently the perspective of the morally distressed individual is privileged. Understandings of moral distress have evolved towards an ‘occupational health approach’, with the assumption that moral distress should be measured and prevented. Counter-perspectives were identified, highlighting conceptual problems. Based on our review, we propose a redefinition of moral distress: ‘Ethical unease or disquiet resulting from a situation where a clinician believes they have contributed to avoidable patient or community harm through their involvement in an action, inaction or decision that conflicts with their own values’. This definition is specific enough for research use, anchored in clinicians’ professional responsibilities and concerns about harms to patients, framed relationally rather than hierarchically, and amenable to multiple perspectives on any given morally distressing situation. (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)

Many biological systems experience a periodic environment. Floquet theory is a mathematical tool to deal with such time periodic systems. It is not often applied in biology, because linkage between the mathematics and the biology is not available. To create this linkage, we derive the Floquet theory for natural systems. We construct a framework, where the rotation of the Earth is causing the periodicity. Within this framework the angular momentum operator is introduced to describe the Earth’s rotation. The Fourier operators (...) and the Fourier states are defined to link the rotation to the biological system. Using these operators, the biological system can be transformed into a rotating frame in which the environment becomes static. In this rotating frame the Floquet solution can be derived. Two examples demonstrate how to apply this natural framework. (shrink)

We study punctual categoricity on a cone and intrinsically punctual functions and obtain complete structural characterizations in terms of model-theoretic notions. As a corollary, we answer a question of Bazhenov, Downey, Kalimullin, and Melnikov by showing that relational structures are not punctually universal. We will also apply this characterisation to derive an algebraic characterisation of relatively punctually categorical mono-unary structures.

A broad class of inductive logics that includes the probability calculus is defined by the conditions that the inductive strengths [A|B] are defined fully in terms of deductive relations in preferred partitions and that they are asymptotically stable. Inductive independence is shown to be generic for propositions in such logics; a notion of a scale-free inductive logic is identified; and a limit theorem is derived. If the presence of preferred partitions is not presumed, no inductive logic is definable. This (...) no-go result precludes many possible inductive logics, including versions of hypothetico-deductivism. (shrink)

Thomists do not have an account of how modern mathematics relates to classical mathematics or more generally fits into the Aristotelian hierarchy of sciences. Rather than treat primarily of Aquinas’s theses on mathematical abstraction, I turn to considering what modern mathematics is in itself, seen from a broadly classical perspective. I argue that many modern quantities can be considered to be, not quantities as such or in themselves, but derived quantities, i.e., quantities that can be defined wholly in terms of (...) the principles of number or magnitude. I also interpret the parts of modern mathematics that study quantitative change as being properly-speaking parts of natural philosophy, for example, probability theory, statistics, calculus, etc. In conclusion, I consider the place that quantity as such has in the order of the world and why we should expect the world to be highly mathematical, as we have found it to be. (shrink)

In this paper, we define the notions of (l,r)-symmetric bi-derivations and (r,l)-symmetric bi-derivations on UP-algebras and investigate some properties of them. For these derivations, we introduce the sets Kerd(U), Fixd(U) and FixD(U). Moreover, we examine with examples whether these sets are UP-subalgebra or UP-ideal.

The word _meṇḍaka_, a derivative of _meṇḍa_ (“ram”), is generally translated as “made of the ram” or “about the ram” or “horned.” However, in the Pāli _Milindapañha_ (_Questions of Milinda_), the word _meṇḍakapañha_, literally, a question about the ram, is also rendered as a logical conclusion that refutes an imaginary dilemma. Hence, in this treatise, the word _meṇḍaka_ is a special logical term which means an imaginary dilemma that can be logically refuted. This raises the question as to why the (...) word _meṇḍaka_ has come to be associated with this logical technique. To answer this question, this paper examines various aspects of the word and its possible connections to a dilemma and its refutation. The discussion ranges from the meaning of this word in a tale in the _Jātaka_ (Birth Stories), within the contextual usage in a _meṇḍaka_ question, to a relatively recent commentarial text (_aṭṭhakathā_) which gives a different perspective on the etymology of the word. The _Milindapañha_ is explicit in defining a _meṇḍaka_ question as knotty, hard to penetrate, and difficult to resolve, some of which an opponent puts forth to undermine certain aspects of the Buddhist system. However, the way certain _meṇḍaka_ questions are framed, though not directly stated, seem to utilize the principles of logic in a dilemmatic form of argument. With that, a _meṇḍaka_ question, at least in the _Milindapañha_, could also mean “a dilemmatic expression put forth by a challenger to undermine an opponent, but which can be logically refuted.”. (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)

We present an approach to database update as a form of non monotonic temporal reasoning, the main idea of which is the (circumscriptive) minimization of changes with respect to a set of facts declared persistent by default. The focus of the paper is on the relation between this approach and the update semantics recently proposed by Katsuno and Mendelzon. Our contribution in this regard is twofold: • We prove a representation theorem for KM semantics in terms of a restricted subfamily (...) of the operators defined by our construction. • We show how the KM semantics can be generalized by relaxing our construction in a number of ways, each justified in certain intuitive circumstances and each corresponding to one specific postulate. It follows that there are reasonable update operators outside the KM family. • Our approach is not dependent for its plausibility on this connection with KM semantics. Rather, it provides a relatively rich and flexible framework in which the frame and ramification problems can be solved in a systematic way by reasoning about default persistence of facts. (shrink)

The following strong form of density of definable types is introduced for theoriesTadmitting a fibered dimension functiond: given a modelMofTand a definable setX⊆Mn, there is a definable typepinX, definable over a code forXand of the samed-dimension asX. Both o-minimal theories and the theory of closed ordered differential fields are shown to have this property. As an application, we derive a new proof of elimination of imaginaries for CODF.

The bounded arithmetic theories R2i, S2i, and T2i are closely connected with complexity theory. This paper is motivated by the questions: what are the Σi+1b-definable multifunctions of R2i? and when is one theory conservative over another? To answer these questions we consider theories , and where induction is restricted to prenex formulas. We also define which has induction up to the 0 or 1-ary L2-terms in the set τ. We show and and for . We show that the -multifunctions (...) of are FPΣip and that those of are FPΣip. For -definability we get FPΣi+k+1p for all these theories. Write for the set of terms 2min,t) where ℓ is a finite product of terms in τ and tL2. We prove and we show - INDτ provided τO2. This gives a proof theoretic proof that S2iΔi+1b-LIND and -LLIND solving an open problem. For τO2, we define using weak replacement axioms and show . We show if or if or if where τ′ has an unbounded term then PH=B. We separate PΣip from PΣip for behaved ℓ and deduce theory separations. We lastly introduce a notion of a model separating two theories and derive some consequences. (shrink)

The aim of this paper is to provide a definition of the the notion of complete and immediate formal grounding through the concepts of derivability and complexity. It will be shown that this definition yields a subtle and precise analysis of the concept of grounding in several paradigmatic cases.

Phylogenetic systematics is one of the most important analytical frameworks of modern Biology. It seems to be common knowledge that within phylogenetics, ‘groups’ must be defined based solely on the synapomorphies or on the “derived” characters that unite two or more taxa in a clade or monophyletic group. Thus, the idea of synapomorphy seems to be of fundamental influence and importance. Here I will show that the most common and straightforward understanding of synapomorphy as a shared derived character is not (...) sufficient and eventually must be rejected in favor of Nelson’s relational interpretation of such term. Arguing for this point and using three examples from previously published Apes’ genomic matrices, I explicitly demonstrate that the relationship )) with Hylobatidae as a sister taxon, may be successfully recovered by three-taxon statement analysis and three-taxon statement average consensus analysis even if all of the evident standard shared derived molecular characters of the relationship )) with Hylobatidae as a sister taxon, have been excluded from the molecular alignments. Neither conventional Maximum Parsimony nor Maximum Likelihood or Bayesian Inference can do this in such situation. Thus, our results show that the relationship )) with Hylobatidae as a sister taxon has appeared, in some way, behind standard shared derived characters: the last ones could be excluded, but the relationship remains the same. (shrink)

In this paper, we are concerned with the arithmetical definability of certain notions of integers and rationals in terms of other notions. The results derived will be applied to obtain a negative solution of corresponding decision problems.In Section 1, we show that addition of positive integers can be defined arithmetically in terms of multiplication and the unary operation of successorS(whereSa=a+ 1). Also, it is shown that both addition and multiplication can be defined arithmetically in terms of successor and the relation (...) of divisibility | (wherex|ymeansxdividesy). (shrink)

This book deals with the way in which certain "forms of knowledge" evolved in modern Chinese history and how they interacted with the mainstream intellectual and social environment. But the book is not merely about the serialization methodologies that have been used to produce history from the thought of historical personalities. First, the question of "epistemology" is set out: Does the development of "knowledge" coincide completely with the chronological serialization of historical facts? Alternatively, is it possible that the development of (...) "knowledge" itself merely derives its own meaning from within a comparatively self-sufficient and closed discourse, alienated from genuine serialization of historical facts? (shrink)

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)

We prove a Gleason-type theorem for the quantum probability rule using frame functions defined on positive-operator-valued measures, as opposed to the restricted class of orthogonal projection-valued measures used in the original theorem. The advantage of this method is that it works for two-dimensional quantum systems and even for vector spaces over rational fields—settings where the standard theorem fails. Furthermore, unlike the method necessary for proving the original result, the present one is rather elementary. In the case of a qubit, we (...) investigate similar results for frame functions defined upon various restricted classes of POVMs. For the so-called trine measurements, the standard quantum probability rule is again recovered. (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)

We define a complete theory SHF e of separably closed fields of finite invariant e (= degree of imperfection) which carry an infinite stack of Hasse-derivations. We show that SHF e has quantifier elimination and eliminates imaginaries.

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)

In the present paper, we show the first-order definability of the jump operator in the upper semi-lattice of the \-enumeration degrees. As a consequence, we derive the isomorphicity of the automorphism groups of the enumeration and the \-enumeration degrees.

Let M = 〈M, +, <, 0, {λ}λ∈D〉 be an ordered vector space over an ordered division ring D, and G = 〈G, ⊕, eG〉 an n-dimensional group definable in M. We show that if G is definably compact and definably connected with respect to the t-topology, then it is definably isomorphic to a 'definable quotient group' U/L, for some convex V-definable subgroup U of 〈Mⁿ, +〉 and a lattice L of rank n. As two consequences, we (...) derive Pillay's conjecture for a saturated M as above and we show that the o-minimal fundamental group of G is isomorphic to L. (shrink)

Research on work values shows that respectful leadership is highly desired by employees. On the applied side, however, the extant research does not offer many insights as to which concrete leadership behaviors are perceived by employees as indications of respectful leadership. Thus, to offer such insights, we collected and content analyzed employees’ narrations of encounters with respectful leadership (N1 = 426). The coding process resulted in 19 categories of respectful leadership spanning 149 leadership behaviors. Furthermore, to also harness this comprehensive (...) repertoire for quantitative organizational research, we undertook two more studies (N2a = 228; N2b = 412) to empirically derive a feasible item-based measurement of respectful leadership and assess its psychometric qualities. In these studies, we additionally investigated the relationships between respectful leadership as assessed with this new measurement and employees’ vertical and contextual followership as assessed via subordinates’ identification with their leaders, their appraisal respect for their leaders, their feeling of self-determination, and their job satisfaction. (shrink)

In derivations of a sequent system, $\mathcal{L}\mathcal{J}$, and a natural deduction system, $\mathcal{N}\mathcal{J}$, the trails of formulae and the subformula property based on these trails will be defined. The derivations of $\mathcal{N}\mathcal{J}$ and $\mathcal{L}\mathcal{J}$ will be connected by the map $g$, and it will be proved the following: an $\mathcal{N}\mathcal{J}$-derivation is normal $\Longleftrightarrow $ it has the subformula property based on trails $\Longleftrightarrow $ its $g$-image in $\mathcal{L}\mathcal{J}$ is without maximum cuts $\Longrightarrow $ that $g$-image has the subformula property (...) based on trails. In $\mathcal{L}\mathcal{J}$-derivations, another type of cuts, sub-cuts, will be introduced, and it will be proved the following: all cuts of an $\mathcal{L}\mathcal{J}$-derivation are sub-cuts $\Longleftrightarrow $ it has the subformula property based on trails. (shrink)

Mathematics is about proofs, that is the derivation of correct statements; and calculations, that is the production of results according to well-defined sets of rules. The two notions are intimately related. Proofs can involve calculations, and the algorithm underlying a calculation should be proved correct. The aim of the author is to explore this relationship. The book itself forms an introduction to simple type theory. Starting from the familiar propositional calculus the author develops the central idea of an applied (...) lambda-calculus. This is illustrated by an account of Gödel's T, a system which codifies number-theoretic function hierarchies. Each of the book's 52 sections ends with a set of exercises, some 200 in total. These are designed to help the reader get to grips with the subject, and develop a further understanding. An appendix contains complete solutions of these exercises. (shrink)

The fine structure constant appears in several fields of physics and its value is experimentally obtained with a high accuracy. Its physical origin however is unsolved long-standing problem. Richard Feynman expressed the idea that it could be similar to the natural irrational numbers, pi, and e. Amongst the proposed theoretical expressions with values closer to the experimental one is the formula of I. Gorelik which is based on rotating dipole with two empirically suggested coefficients, while the physical origin is unknown. (...) BSM-Supergravitation Unified Theory suggests a physical mechanism defining the fine structure constant. The mathematical expression is based on a spatial precession mode of vibrations in a tetrahedron of spheres with specific properties. The value from the derived expression differs from the CODATA 98 value by 0.000008% only. The conclusion is that the fine structure constant is a natural irrational number. While the irrational number pi, is defined in a 2D space, the fine structure constant is related to a vibration property of a specific formation in 3D space. (shrink)

The notion of the human embryo is not immutable. Various scientific and technological breakthroughs in reproductive biology have compelled us to revisit the definition of the human embryo during the past 2 decades. Somatic cell nuclear transfer, oocyte haploidisation and, more recently, human stem cell-derived embryo models have challenged this scientific term, which has both ethical and legal repercussions. Here, we offer a legal perspective to identify a universally accepted definition of ‘embryo’ which could help to ease and unify the (...) regulation of such entities in different countries. (shrink)

T cells, which are derived from hematopoietic stem cells (HSCs), are the most important components of adaptive immune system. Based on the expression of αβ and γδ receptors, T cells are mainly divided into αβ and γδ T cells. In the thymus, they share common progenitor cells, while undergoing a series of well‐characterized and different developmental processes. N6‐Methyladenosine (m6A), one of the most abundant modifications in mRNAs, plays critical roles in cell development and maintenance of function. Recently, we have demonstrated (...) that the depletion of m6A demethylase ALKBH5 in lymphocytes specifically induces an expansion of γδ T cells through the regulation of Jag1/Notch2 signaling, but not αβ T cells, indicating a checkpoint role of ALKBH5 and m6A modification in the early development of γδ T cells. Based on previous studies, many key pathway molecules, which exert dominant roles in γδ T cell fate determination, have been identified as the targets regulated by m6A modification. In this review, we mainly summarize the potential regulation between m6A modification and these key signaling molecules in the γδ T cell lineage commitment, to provide new perspectives in the checkpoint of γδ T cell development. (shrink)

The reason for physics’ failure to find a final theory of the universe is examined. Problems identified are: the lack of unequivocal definitions for its fundamental elements (time, length, mass, electric charge, energy, work, matter-waves); the danger of relying too much on mathematics for solutions; especially as philosophical arguments conclude the universe cannot have a mathematical basis. It does not even need the concept of number to exist. Numbers and mathematics are human inventions arising from the human predilection for measurement. (...) Following Aristotle, a single fundamental cause is proposed to explore the efficacy of using pure non-mathematical philosophy to explain the universe, contrary to current quantum physical views. The cause is taken as Time, which is then defined, surprisingly leading automatically to a definition of a three-dimensional space answering the question into what can a universe be placed (space before space seems non-sensical). This enables the philosophical arguments to derive a universal rule giving clear-cut descriptions (definitions) of force (both gravitational and electromagnetic), motion, energy, and particles. The formation of atomic nuclei and atomic properties together with an unexpected role for neutrinos follow. In particular, a Popper-test can be prepared by introducing the concept of measurement to allow the philosophy arguments to be tested in another discipline - mathematics. The solution agrees with human physical observations to a remarkable degree of accuracy, automatically explaining and predicting values for Planck’s and the fine-structure constants. Although mathematical, it is included as confirming the efficacy of philosophy in attaining a final theory. (shrink)

Source: Author: Liliya Ponomaryova Studying structural, phono-morphological, semantic, stylistic, word-forming and lexical conformities regulating syntagmatic connections in word-formation, requires studying system restrictions of the word-forming morphemes combinability, predetermined by the meaning of a word sign as well. The aim of the article is to identify semantic restrictions and those close to them in forming deverbative nouns from the process verbs. It was defined that such kinds of restrictions as semantic, semantic-pragmatic, semantic-stylistic, lexical and structural-morphological can counteract the possibility of the (...) process verbs to take part in derivation processes. Semantic restrictions are located at the level of syntagmatic, differentiating semes and the abstract subcategoric seme “becoming”. Aspect semes don’t influence the possibility of the process verbs to take part in the word formation processes. Semantic restrictions can be predetermined both by the presence and by the absence of definite semes in a semantic structure of a word. ]]>. (shrink)

Research on work values shows that respectful leadership is highly desired by employees. On the applied side, however, the extant research does not offer many insights as to which concrete leadership behaviors are perceived by employees as indications of respectful leadership. Thus, to offer such insights, we collected and content analyzed employees’ narrations of encounters with respectful leadership ( N 1 = 426). The coding process resulted in 19 categories of respectful leadership spanning 149 leadership behaviors. Furthermore, to also harness (...) this comprehensive repertoire for quantitative organizational research, we undertook two more studies ( N 2a = 228; N 2b = 412) to empirically derive a feasible item-based measurement of respectful leadership and assess its psychometric qualities. In these studies, we additionally investigated the relationships between respectful leadership as assessed with this new measurement and employees’ vertical and contextual followership as assessed via subordinates’ identification with their leaders, their appraisal respect for their leaders, their feeling of self-determination, and their job satisfaction. (shrink)

Where ethical or regulatory questions arise about an individual’s interests in accessing bioinformation about herself, the value of this information has traditionally been construed in terms of its clinical utility. It is increasingly argued, however, that the “personal utility” of findings should also be taken into account. This article characterizes one particular aspect of personal utility: that derived from the role of personal bioinformation in identity construction. The suggestion that some kinds of information are relevant to identity is not in (...) itself new. However, the account outlined here seeks to advance the debate by proposing a conception of the relationship between bioinformation and identity that does not depend on essentialist assumptions and applies beyond the narrow genetic contexts in which identity is customarily invoked. The proposal is that the identity-value of personal bioinformation may be understood in terms of its instrumental role in the construction of our narrative identities, specifically that its value lies in helping us to develop self-narratives that support us in navigating our embodied existences. I argue that this narrative conception provides useful insights that are pertinent to the ethical governance of personal bioinformation. It illuminates a wider range of ethical considerations in relation to information access; it accounts for variations in the utility of different kinds of information; and it highlights that the context in which information is conveyed can be as important as whether it is disclosed at all. These arguments are illustrated using an example drawn from psychiatric neuroimaging research. (shrink)

Presents a philosophical model of partially defined predicates, illustrates how a language could come to contain them, and provides a natural way of understanding the truth predicate in which it conforms to this model. On this view, there are sentences, including Liar sentences like this sentence is not true and “Truth Tellers” like This sentence is true, about which the rules determining whether or not a sentence is true provide no result – thereby blocking the usual derivation of the (...) paradox. However, despite these promising results, it is shown that a general solution to the Liar paradox is not forthcoming, since the very activity of solving the paradox in a particular limited case provides material for recreating it in a new and strengthened form. In the second half of the chapter, it is argued that this philosophical model provides the best way of understanding Saul Kripke's formal theory of truth. In addition to laying out the philosophical basis for Kripke's theory of truth, explanations are given of his basic technical apparatus and formal results – including fixed points, minimal fixed points, monotonicity, intrinsic fixed points, ungrounded sentences, and paradoxical sentences. (shrink)

The Denjoy integral is an integral that extends the Lebesgue integral and can integrate any derivative. In this paper, it is shown that the graph of the indefinite Denjoy integral f↦∫xaf is a coanalytic non-Borel relation on the product space M[a,b]×C[a,b], where M[a,b] is the Polish space of real-valued measurable functions on [a,b] and where C[a,b] is the Polish space of real-valued continuous functions on [a,b]. Using the same methods, it is also shown that the class of indefinite Denjoy integrals, (...) called ACG∗[a,b], is a coanalytic but not Borel subclass of the space C[a,b], thus answering a question posed by Dougherty and Kechris. Some basic model theory of the associated spaces of integrable functions is also studied. Here the main result is that, when viewed as an ℝ[X]-module with the indeterminate X being interpreted as the indefinite integral, the space of continuous functions on the interval [a,b] is elementarily equivalent to the Lebesgue-integrable and Denjoy-integrable functions on this interval, and each is stable but not superstable, and that they all have a common decidable theory when viewed as ℚ[X]-modules. (shrink)

We study the coherence, that is the equality of canonical natural transformations in non-free symmetric monoidal closed categories . To this aim, we use proof theory for intuitionistic multiplicative linear logic with unit. The study of coherence in non-free smccs is reduced to the study of equivalences on terms in the free category, which include the equivalences induced by the smcc structure. The free category is reformulated as the sequent calculus for imll with unit so that only equivalences on derivations (...) in this system are to be considered. We establish that any equivalence induced by the equality of canonical natural transformations over a model can be axiomatized by some set of “critical” pairs of derivations. From this, we derive certain sufficient conditions for full coherence, and establish that the system of identities defining smccs is not Post-complete: extending this system with an identity that does not hold in the free smcc does not in general cause the free smcc to collapse into a preorder. In order to give a larger context to these results, we study the equality of canonical morphisms in non-free symmetric monoidal categories, and establish that w.r.t. a broad subclass of smccs, the equivalences induced by the equality of canonical natural transformations over a model coincide with the equivalences induced by the equality of canonical morphisms for all interpretations in that model. (shrink)

This article proposes a conceptual mapping to outline salient properties and relations that allow for a knowledge transfer from the well-established greenwashing phenomenon to the more recent machinewashing. We account for relevant dissimilarities, indicating where conceptual boundaries may be drawn. Guided by a “reasoning by analogy” approach, the article addresses the structural analogy and machinewashing idiosyncrasies leading to a novel and theoretically informed model of machinewashing. Consequently, machinewashing is defined as a strategy that organizations adopt to engage in misleading behavior (...) about ethical Artificial Intelligence /algorithmic systems. Machinewashing involves misleading information about ethical AI communicated or omitted via words, visuals, or the underlying algorithm of AI itself. Furthermore, and going beyond greenwashing, machinewashing may be used for symbolic actions such as lobbying and prevention of stricter regulation. By outlining diverse theoretical foundations of the established greenwashing domain and their relation to specific research questions, the article proposes a machinewashing model and a set of theory-related research questions on the macro, meso, and micro-level for future machinewashing research. We conclude by stressing limitations and by outlining practical implications for organizations and policymakers. (shrink)

To determine when the life of a human organism begins, Mark T. Brown has developed the somatic integration definition of life. Derived from diagnostic criteria for human death, Brown’s account requires the presence of a life‐regulation internal control system for an entity to be considered a living organism. According to Brown, the earliest point at which a developing human could satisfy this requirement is at the beginning of the fetal stage, and so the embryo is not regarded as a living (...) human organism. This, Brown claims, has significant bioethical implications for both abortion and embryo experimentation. Here, we dispute the cogency of Brown’s derivation. Diagnostic criteria for death are used to determine when an organism irreversibly ceases functioning as an integrated whole, and may vary significantly depending on how developed the organism is. Brown’s definition is derived from a specific definition of death applicable to postnatal human beings, which is insufficient for generating a general definition for human organismal life. We have also examined the bioethical implications of Brown’s view, and have concluded that they are not as significant as he believes. Whether the embryo is classified as a human organism is of peripheral interest—a far more morally relevant question is whether the embryo is a biological individual with an identity that is capable of persisting during development. (shrink)

Two reports have shown that mammalian artificial chromosomes (MAC) can be constructed from cloned human centromere DNA and telomere repeats, proving the principle that chromosomes can form from naked DNA molecules transfected into human cells. The MACs were mitotically stable, low copy number and bound antibodies associated with active centromeres. As a step toward second-generation MACs, yeast and bacterial cloning systems will have to be adapted to achieve large MAC constructs having a centromere, two telomeres, and genomic copies of mammalian (...) genes. Available construction techniques are discussed along with a new P1 artificial chromosome (PAC)-derived telomere vector (pTAT) that can be joined to other PACs in vitro, avoiding a cloning step during which large repetitive arrays often rearrange. The PAC system can be used as a route to further define the optimal DNA elements required for efficient MAC formation, to investigate the expression of genes on MACs, and possibly to develop efficient MAC-delivery protocols. BioEssays 1999;21:76–83. © 1999 John Wiley & Sons, Inc. (shrink)

In this paper, DSEK model with fractional derivatives of the Atangana-Baleanu Caputo is proposed. This paper gives a brief overview of the ABC fractional derivative and its attributes. Fixed point theory has been used to establish the uniqueness and existence of solutions for the fractional DSEK model. According to this theory, we will define two operators based on Lipschitzian and prove that they are contraction mapping and relatively compact. Ulam-Hyers stability theorem is implemented to prove the fractional DSEK model’s stability (...) in Banach space. Also, fractional Euler’s numerical method is derived for initial value problems with ABC fractional derivative and implemented on fractional DSEK model. The symmetric properties contribute to determining the appropriate method for finding the correct solution to fractional differential equations. The numerical solutions generated using fractional Euler’s method have been plotted for different values of α where α ∈ 0,1 and different step sizes h. Result discussion will be given, describing the changes that occur due to the step size h. (shrink)

Guided by the example of gauge transformations associated with classical Yang-Mills fields, a very general class of transformations is considered. The explicit representation of these transformations involves not only the independent and the dependent field variables, but also a set of position-dependent parameters together with their first derivatives. The stipulation that an action integral associated with the field variables be invariant under such transformations gives rise to a set of three conditions involving the Lagrangian and its derivatives, together with derivatives (...) of the functions that define the transformations. These invariance identities constitute an extension of the classical theorem of Noether to general transformations of this kind. An application to the case of gauge fields demonstrates the existence of two distinct types of conservation laws for such fields. (shrink)

Michael Nair-Collins and Franklin Miller are right to emphasise that, in order to deliberate responsibly about ethical and legal questions related to brain death and organ donation, it is crucial to answer the question of whether or not ‘brain death’i does indeed mark the biological death of the organism. Nonetheless, I disagree with the authors’ conclusion that brain death does not indicate the death of the human organism. Death can never be defined in merely biological terms, because any biological conception (...) of death relies on metaphysical presuppositions regarding what it means to be an ‘organism as a whole’, rather than an aggregate of cells and tissues. Death is a change in substance —that is, a change from one type of entity to another — not the cessation of all biological life. Organismal death occurs well before all of the organism’s parts irreversibly cease vital activity and decompose into inorganic matter. Biological life in some form can and usually does continue after organismal death at least for a time, with recent evidence indicating that animal cell networks continue to perform complex functions like stress response, immune response and inflammation response up to several days postmortem.1 With external support, many cells and tissues can continue to perform their functions ex vivo for long periods of time or even indefinitely.2 Henrietta Lax died in 1951, but cells derived from her cancerous cervical cells …. (shrink)

Six planetary boundaries have already been exceeded, including climate change, loss of biodiversity, chemical pollution, and land-system change. The health research sector contributes to the environmental crisis we are facing, though to a lesser extent than healthcare or agriculture sectors. It could take steps to reduce its environmental impact but generally has not done so, even as the planetary emergency worsens. So far, the normative case for why the health research sector should rectify that failure has not been made. This (...) paper argues strong philosophical grounds, derived from theories of health and social justice, exist to support the claim that the sector has a duty to avoid or minimise causing or contributing to ecological harms that threaten human health or worsen health inequity. The paper next develops ideas about the duty’s content, explaining why it should entail more than reducing carbon emissions, and considers what limits might be placed on the duty. (shrink)

A relative tensor calculus is formulated for expressing equations of mathematical physics. A tensor time derivative operator ▽ b a is defined which operates on tensors λia...ib. Equations are written in a rigid, flat, inertial or other coordinate system a, altered to relative tensor notation, and are thereby expressed in general flowing coordinate systems or materials b, c, d, .... Mirror tensor expressions for ▽ b a λic...id and ▽ b a λic...id exist in a relative geometry G if and (...) only if a rigid coordinate system a exists in G, where ▽ b a λic = λ ,0c ic + λkev ckc aic + λ kc ic v b ckc , ▽jcλic = λ ,jc ic + λkcΓ jc kc ie , and v b aic is the velocity of b relative to a with components in c. These operators are convenient in theoretical analyses and can be incorporated into machine programs for the numerical solution of physical problems. (shrink)

We explore the relationship between analytic behavior of a computable real valued function and the computability-theoretic complexity of the individual values of its derivative almost-everywhere. Given a computable function f, the values of its derivative \\), where they are defined, are uniformly computable from \, the Turing jump of the input. It is known that when f is \, the values of \\) are actually computable from x. We construct a \ function f so that, almost everywhere, \\ge _T x'\). (...) Although the values \\) at each point x cannot uniformly compute the corresponding jumps \ of the inputs x almost everywhere for any \ function f, we produce an example of a \ function f such that \\ge _T \emptyset '\) uniformly on subsets of arbitrarily large measure, effectively. We also explore analogous questions for weaker smoothness conditions, such as for f differentiable everywhere, and f differentiable almost everywhere. (shrink)

Dedekind’s structuralism is a crucial source for the structuralism of mathematical practice—with its focus on abstract concepts like groups and fields. It plays an equally central role for the structuralism of philosophical analysis—with its focus on particular mathematical objects like natural and real numbers. Tensions between these structuralisms are palpable in Dedekind’s work, but are resolved in his essay Was sind und was sollen die Zahlen? In a radical shift, Dedekind extends his mathematical approach to “the” natural numbers. He creates (...) the abstract concept of a simply infinite system, proves the existence of a “model”, insists on the stepwise derivation of theorems, and defines structure-preserving mappings between different systems that fall under the abstract concept. Crucial parts of these considerations were added, however, only to the penultimate manuscript, for example, the very concept of a simply infinite system. The methodological consequences of this radical shift are elucidated by an analysis of Dedekind’s metamathematics. Our analysis provides a deeper understanding of the essay and, in addition, illuminates its impact on the evolution of the axiomatic method and of “semantics” before Tarski. This understanding allows us to make connections to contemporary issues in the philosophy of mathematics and science. (shrink)