This section discusses mostly some unsolved problems. . . .I hope that some mathematicians who are interested in a classification of sets of real numbers, in particular sets with Lebesgue measure zero, will read it and try to find solutions for the problems here outlined.

We propose an alternative approach to probability theory closely related to the framework of numerosity theory: non-Archimedean probability (NAP). In our approach, unlike in classical probability theory, all subsets of an infinite sample space are measurable and only the empty set gets assigned probability zero (in other words: the probability functions are regular). We use a non-Archimedean field as the range of the probability function. As a result, the property of countable additivity in Kolmogorov’s axiomatization of probability (...) is replaced by a different type of infinite additivity. (shrink)

We relate Popper functions to regular and perfectly additive such non-Archimedean probability functions by means of a representation theorem: every such non-Archimedean probability function is infinitesimally close to some Popper function, and vice versa. We also show that regular and perfectly additive non-Archimedean probability functions can be given a lexicographic representation. Thus Popper functions, a specific kind of non-Archimedean probability functions, and lexicographic probability functions triangulate to the same place: they (...) are in a good sense interchangeable. (shrink)

Fibring has been shown to be useful for combining logics endowed withtruth-functional semantics. However, the techniques used so far are unableto cope with fibring of logics endowed with non-truth-functional semanticsas, for example, paraconsistent logics. The first main contribution of thepaper is the development of a suitable abstract notion of logic, that mayalso encompass systems with non-truth-functional connectives, and wherefibring can still be dealt with. Furthermore, it is shown that thisextended notion of fibring preserves completeness under certain reasonableconditions. This completeness transfer (...) result, the second main contributionof the paper, generalizes the one established in Zanardo et al. (2001) butis obtained using new techniques that explore the properties of a suitablemeta-logic (conditional equational logic) where the (possibly)non-truth-functional valuations are specified. The modal paraconsistentlogic of da Costa and Carnielli (1988) is studied in the context of this novel notionof fibring and its completeness is so established. (shrink)

This paper reinforces the current consensus against the applicability of the selected effect theory of function in ecology. It does so by presenting an argument which, in contrast with the usual argument invoked in support of this consensus, is not based on claims about whether ecosystems are customary units of natural selection. Instead, the argument developed here is based on observations about the use of the function concept in functional ecology, and more specifically, research into the relationship between biodiversity and (...) ecosystem functioning. It is argued that a selected effect account of ecological functions is made implausible by the fact that it would conflict with important aspects of the understanding of function and ecosystem functional organization which underpins functional ecology’s research program. Specifically, it would conflict with (1) Functional ecology’s adoption of a context-based understanding of function and its aim to study the functional equivalence between phylogenetically-divergent organisms; (2) Functional ecology’s attribution to ecosystems of a lower degree of part-whole integration than the one found in paradigm individual organisms; and (3) Functional ecology’s adoption of a physiological or metabolic perspective on ecosystems rather than an evolutionary one. (shrink)

Dyadic semantics is a sort of non-truth-functional bivalued semantics introduced in Caleiro et al. Logica Universalis, Birkhäuser, Basel, pp 169–189, 2005). Here we introduce an algorithmic procedure for constructing conservative translations of logics characterised by dyadic semantics into classical propositional logic. The procedure uses fresh propositional variables, which we call hidden variables, to represent the indeterminism of dyadic semantics. An alternative algorithmic procedure for constructing conservative translations of any finite-valued logic into classical logic is also introduced. In this alternative procedure (...) hidden variables are also used, but in this case to represent the degree of true or falsehood of propositions. (shrink)

We study o-minimal expansions of Archimedean totally ordered groups. We first prove that any such expansion must be elementarily embeddable via a unique (provided some nonzero element is 0-definable) elementary embedding into a unique o-minimal expansion of the additive ordered group of real numbers R. We then show that a definable function in an o-minimal expansion of R enjoys good differentiability properties and use this to prove that an Archimedean real closed field is definable in any nonsemilinear expansion (...) of R. Combining these results, we obtain several restrictions on possible o-minimal expansions of arbitrary Archimedean ordered groups and in particular of the rational ordered group. (shrink)

A categorical, higher dimensional algebra and generalized topos framework for Łukasiewicz–Moisil Algebraic–Logic models of non-linear dynamics in complex functional genomes and cell interactomes is proposed. Łukasiewicz–Moisil Algebraic–Logic models of neural, genetic and neoplastic cell networks, as well as signaling pathways in cells are formulated in terms of non-linear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable ‘next-state functions’ is extended to a (...) Łukasiewicz–Moisil Topos with an n-valued Łukasiewicz–Moisil Algebraic Logic subobject classifier description that represents non-random and non-linear network activities as well as their transformations in developmental processes and carcinogenesis. The unification of the theories of organismic sets, molecular sets and Robert Rosen’s (M,R)-systems is also considered here in terms of natural transformations of organismal structures which generate higher dimensional algebras based on consistent axioms, thus avoiding well known logical paradoxes occurring with sets. Quantum bionetworks, such as quantum neural nets and quantum genetic networks, are also discussed and their underlying, non-commutative quantum logics are considered in the context of an emerging Quantum Relational Biology. (shrink)

A categorical, higher dimensional algebra and generalized topos framework for Łukasiewicz–Moisil Algebraic–Logic models of non-linear dynamics in complex functional genomes and cell interactomes is proposed. Łukasiewicz–Moisil Algebraic–Logic models of neural, genetic and neoplastic cell networks, as well as signaling pathways in cells are formulated in terms of non-linear dynamic systems with n-state components that allow for the generalization of previous logical models of both genetic activities and neural networks. An algebraic formulation of variable ‘next-state functions’ is extended to a (...) Łukasiewicz–Moisil Topos with an n-valued Łukasiewicz–Moisil Algebraic Logic subobject classifier description that represents non-random and non-linear network activities as well as their transformations in developmental processes and carcinogenesis. The unification of the theories of organismic sets, molecular sets and Robert Rosen’s (M,R)-systems is also considered here in terms of natural transformations of organismal structures which generate higher dimensional algebras based on consistent axioms, thus avoiding well known logical paradoxes occurring with sets. Quantum bionetworks, such as quantum neural nets and quantum genetic networks, are also discussed and their underlying, non-commutative quantum logics are considered in the context of an emerging Quantum Relational Biology. (shrink)

Most philosophical accounts of emergence are incompatible with reduction. Most scientists regard a system property as emergent relative to properties of its parts if it depends upon their mode of organization-a view consistent with reduction. Emergence is a failure of aggregativity, in which ``the whole is nothing more than the sum of its parts''. Aggregativity requires four conditions, giving powerful tools for analyzing modes of organization. Differently met for different decompositions of the system, and in different degrees, the structural conditions (...) can provide evaluation criteria for choosing decompositions, ``natural kinds'', and detecting functional localization fallacies, approximations, and various biases of vulgar reductionisms. This analysis of emergence and use of these conditions as heuristics is consistent with a broader reductionistic methodology. (shrink)

Experiments are described, using electroencephalography (EEG) and simple tests of performance, which support the hypothesis that collapse of a quantum field is of importance to the functioning of the brain. The theoretical basis of our experiments is derived from Penrose (1989) who suggested that conscious decision-making is a manifestation of the outcome of quantum computation in the brain involving collapse of some relevant wave function. He also proposed that collapse of any wave function depends on a gravitational criterion. As different (...) brain areas are known to subserve different functions, we argue that `Penrose collapse' must occur in a particular brain area when performing a task that uses it. Further, taking an EEG from the area should amplify the gravitational prerequisite for collapse, so affecting task performance. There are no non-quantum theories which could lead one to expect that taking an EEG could directly affect task performance by subjects. The results of both pilot and main experiments indicated that task performance was indeed influenced by taking an EEG from relevant brain areas. Control experiments suggested that the influence was quantum mechanical in origin, and was not due to any experimental artefact. The results are statistically significant and merit attempts at replication in an independent laboratory, preferably with more sophisticated equipment than was available to us. (shrink)

Interpreting a seemingly simple function word like “or,” “behind,” or “more” can require logical, numerical, and relational reasoning. How are such words learned by children? Prior acquisition theories have often relied on positing a foundation of innate knowledge. Yet recent neural‐network‐based visual question answering models apparently can learn to use function words as part of answering questions about complex visual scenes. In this paper, we study what these models learn about function words, in the hope of better understanding how the (...) meanings of these words can be learned by both models and children. We show that recurrent models trained on visually grounded language learn gradient semantics for function words requiring spatial and numerical reasoning. Furthermore, we find that these models can learn the meanings of logical connectives and and or without any prior knowledge of logical reasoning as well as early evidence that they are sensitive to alternative expressions when interpreting language. Finally, we show that word learning difficulty is dependent on the frequency of models' input. Our findings offer proof‐of‐concept evidence that it is possible to learn the nuanced interpretations of function words in a visually grounded context by using non‐symbolic general statistical learning algorithms, without any prior knowledge of linguistic meaning. (shrink)

It is often thought that non-junk or coding DNA is more significant than other cellular elements, including so-called junk DNA. This is for two main reasons: because coding DNA is often targeted by historical or current selection, it is considered functionally special and because its mode of action is uniquely specific amongst the other actual difference makers in the cell, it is considered causally special. Here, we challenge both these presumptions. With respect to function, we argue that there is previously (...) unappreciated reason to think that junk DNA is significant, since it can alter the cellular environment, and those alterations can influence how organism-level selection operates. With respect to causality, we argue that there is again reason to think that junk DNA is significant, since it too is remarkably causally specific. As a result, something is missing from the received view of significance in molecular biology—a view which emphasizes specificity and neglects something we term ‘reach’. With the special case of junk DNA in mind, we explore how to model and understand the causal specificity, reach, and corresponding efficacy of difference makers in biology. The account contains implications for how evolution shapes the genome, as well as advances our understanding of multi-level selection. (shrink)

The present study examined whether strategy moderated the relationship between visuospatial perspective-taking and empathy. Participants undertook both a perspective-taking task requiring speeded spatial judgements made from the perspective of an observed figure and the Empathy Quotient questionnaire, a measure of trait empathy. Perspective-taking performance was found to be related to empathy in that more empathic individuals showed facilitated performance particularly for figures sharing their own spatial orientation. This relationship was restricted to participants that reported perspective-taking by mentally transforming their spatial (...) orientation to align with that of the figure; it was absent in those adopting an alternative strategy of transposing left and right whenever confronted with a front-view figure. Our finding that strategy moderates the relationship between empathy and visuospatial perspective-taking enables a reconciliation of the apparently inconclusive findings of previous studies and provides evidence for functionally dissociable empathic and non-empathic routes to visuospatial perspective-taking. (shrink)

Scientists’ language use in communication to or with the public has often been criticised as merely strategic. This article explores three terms employed in stem cell and genomic research, to support the hypothesis that biomedical terminology is heavily influenced by different legal, cultural, and ethical backgrounds in different societies. The word ‘pre-embryo’ has never been part of any acceptable official rhetoric in Germany but was important in Britain. The ‘toti-’, ‘pluri-’, or ‘multipotency’ of specific stem cells became a topical issue (...) of scientific expertise in countries with strict regulations on embryo research. The distinction between ‘reproductive’ and ‘therapeutic’ cloning has become very common but problematic due to its obvious strategic purpose, and is intensely debated in the scientific community. The examination of these examples and the cultural framework in which they gain importance will demonstrate the mutual interconnectedness of biomedical science and social and cultural conditions. Separation of a purely descriptive terminology that belongs to science itself, adequately describing its discoveries, and a rhetoric that addresses external, non-scientific attitudes is impossible. Regulations, social discourses, and cultural traditions influence biomedical sciences, their scientific research projects and the terminology employed therein. Biomedical practices are considered ethically problematic not only by those external to the scientific realms, but also by some professionals participating in the research. Biomedical science is not a discrete field with clear boundaries and has to be re-conceptualized as an integral and important part of modern culture. (shrink)

The probability ‘measure’ for measurements at two consecutive mo- ments of time is non-additive. These probabilities, on the other hand, may be determined by the limit of relative frequency of measured events, which are by nature additive. We demonstrate that there are only two ways to resolve this problem. The first solution places emphasis on the precise use of the concept of conditional probability for successive mea- surements. The physically correct conditional probabilities define additive probabilities for two-time measurements. These probabilities (...) depend ex- plicitly on the resolution of the physical device and do not, therefore, correspond to a function of the associated projection operators. It follows that quantum theory distinguishes between physical events and proposi- tions about events, the latter are not represented by projection operators and that the outcomes of two-time experiments cannot be described by quantum logic. The alternative explanation is rather radical: it is conceivable that the relative frequencies for two-time measurements do not converge, unless a particular consistency condition is satisfied. If this is true, a strong revision of the quantum mechanical formalism may prove necessary. We stress that it is possible to perform experiments that will distinguish the two alternatives. (shrink)

All animals have evolved solutions to manage their genomes, enabling the efficient organization of meters of DNA strands in the nucleus and allowing for nuanced regulation of gene expression while keeping transposable elements suppressed. Epigenetic modifications are central to accomplishing all these. Recent advances in sequencing technologies and the development of techniques that profile epigenetic marks and chromatin accessibility using reagents that can be used in any species has catapulted epigenomic studies in diverse animal species, shedding light on the multitude (...) of epigenomic mechanisms utilized across the evolutionary tree. Now, comparative epigenomics is a rapidly growing field that is uncovering mechanistic aspects of epigenetic modifications and chromatin organization in non‐model invertebrates, ranging from octopus to sponges. This review puts recent discoveries in the epigenetics of non‐model invertebrates in historical context, and describes new insight into the patterning and functions of DNA methylation and other highly conserved epigenetic modifications. (shrink)

Stereotypes of social construction suggest that the existence of social constructs is accidental and that such constructs have arbitrary and subjective features. In this paper, I explore a conception of social construction according to which it consists in the collective imposition of function onto reality and show that, according to this conception, these stereotypes are incorrect. In particular, I argue that the collective imposition of function onto reality is typically non-accidental and that the products of such imposition frequently have non-arbitrary (...) and objective features. These conclusions are interesting in and of themselves since they debunk important aspects of our socially constructed conception of social construction. Yet, additionally, they have important implications for the viability of mathematical social constructivism since resistance to such constructivism is frequently grounded in the observation that mathematics is non-accidental, non-arbitrary, and objective. As a secondary focus, I explore these implications in this paper. (shrink)

Wnt glycoproteins are signaling molecules that control a wide range of developmental processes in organisms ranging from the simple metazoan Hydra to vertebrates. Wnt signaling also plays a key role in the development of the nematode C. elegans, and is involved in cell fate specification and determination of cell polarity and cell migration. Surprisingly, the first genetic studies of Wnt signaling in C. elegans revealed major differences with the established (canonical) Wnt signaling pathways of Drosophila and vertebrates. Thus, the Wnt-dependent (...) induction of endoderm in the early embryo and the specification of several asymmetric cell divisions during larval development are mediated by as yet novel Wnt signaling pathways that repress, rather than activate the TCF/LEF-1 transcription factor POP-1. Recently, however, it has been shown that, in addition to these divergent Wnt pathways, C. elegans also has a canonical Wnt pathway that converts POP-1 into an activator and controls the expression of several homeobox genes. Interestingly, these different Wnt pathways use distinct beta-catenins to control POP-1 function: the endoderm induction pathway requires the beta-catenin WRM-1 and parallel input from a mitogen-activated kinase (MAPK) pathway to downregulate POP-1, whereas the canonical Wnt pathway employs the beta-catenin BAR-1 to activate Wnt target gene expression. (shrink)

Actual-sequence views of responsibility are views according to which moral responsibility is a function of actual sequences, histories, or ancestries. In recent years these views have acquired much popularity as an attractive kind of compatibilist answer to the problem of determinism and the freedom of the will. But what does it mean to say that responsibility is ‘a function of the actual sequence’? In this paper I examine different possible ways to cash out this idea. I show that one of (...) them is immune to important objections to which the others are prey. This motivates a type of actual-sequence view that is unorthodox in two main respects. First, it understands the expression ‘the actual sequence’ in a way that is different from the way in which it seems typically to have been understood. Second, on this view, non-actualized possibilities of a certain kind are always relevant to the moral responsibility of agents. (shrink)

Joshua Greene and Peter Singer argue, on the basis of empirical evidence, that deontological moral judgments result from emotional reactions while dispassionate reasoning leads to consequentialist judgments. Given that there are good reasons to doubt these emotionally driven intuitions, they argue that we should reject Kantian ethics. I argue that the evidence does not support the claim that consequentialism is inherently more reason-based or less emotion-based than Kantian ethics. This is partly because the experiments employ a functional definition of ‘deontological’ (...) that is so broad as to include any non-consequentialist theory, including virtue ethics, divine command theory, and even rule-utilitarianism. Thus the experiments failed to capture the reasons behind the judgments. Also, the results of the experiments are partly due to the extensive use of moral dilemmas like the footbridge version of the trolley scenario. The options in these dilemmas involve different levels of moral thinking. The consequ.. (shrink)

In the past years motor imagery turned out to be also an innovative and effective tool for motor learning and improvement of sports performance. Whereas many studies investigating sports MI focusing on upper or lower limbs involvement, knowledge about involved neural structures during whole-body movements is still limited. In the present study we investigated brain activity of climbers during a kinesthetic motor imagery climbing task with different difficulties by means of functional near infrared spectroscopy. Twenty healthy participants were split into (...) two groups according to their climbing skill level. The aim of the current study is investigating neural correlates of a whole-body sports MI task with an additional focus on skill level dependency. Climbing experts and non-experts imagined bouldering an “easy” and “difficult” route from a first-person perspective while hemodynamic responses were recorded simultaneously. We found significant differences between the two climbing routes, easy and difficult within participants as well as between the two groups of different climbing skill levels. Overall beginners showed increased hemodynamic responses compared to experts in all defined regions of interest supporting the claim of the neural efficiency hypothesis. Even though climbing is a complex, coordinated movement of upper and lower limbs we found a stronger activation focus of the upper limbs, especially of the dominant hand-area, while the foot area seems to be deactivated or inhibited simultaneously. Summarizing, these findings provide novel insights into brain activation during the imagery of a whole-body movement and its relation to climbing expertise. (shrink)

Behaviorally, children’s explicit theory of mind (ToM) proceeds in a progression of mental-state understandings: developmentally, children demonstrate accurate explicit desire-reasoning before accurate explicit belief-reasoning. Given its robust and cross-cultural nature, we hypothesize this progression may be paced in part by maturation/specialization of the brain. Neuroimaging research demonstrates that the right temporoparietal junction (TPJ) becomes increasingly selective for ToM reasoning as children age, and as their ToM improves. But this research has narrowly focused on beliefs or on undifferentiated mental-states. A recent (...) ERP study in children included a critical contrast to desire-reasoning, and demonstrated that right posterior potentials differentiated belief-reasoning from desire-reasoning. Taken together, the literature suggests that children’s desire-belief progression may be paced by specialization of the right TPJ for belief-reasoning specifically, beyond desire-reasoning. In the present study, we tested this hypothesis directly by examining children’s belief- and desire-reasoning using functional near-infrared spectroscopy in conjunction with structural magnetic resonance imaging to pinpoint brain activation in the right TPJ. Results showed greatest activation in the right TPJ for belief-reasoning, beyond desire-reasoning, and beyond non-mental reasoning (control). Findings replicate and critically extend prior ERP results, and provide clear evidence for a specific neural mechanism underlying children’s progression from understanding desires to understanding beliefs. (shrink)

This paper aims to explain how the Tractatus attempts to unify logic by deriving the truth-functionality of logical necessity from the thesis that a proposition shows its sense. I first interpret the Tractarian notion of showing as the displaying of what is intrinsic to an expression (or a symbol). Then I argue that, according to the Tractatus, the thesis that a proposition shows its sense implies the determinacy of sense, the possibility of the complete elimination of non-primitive symbols, the analyticity (...) thesis and the strong analyticity thesis. The picture theory emerges as what provides the only acceptable account of an elementary proposition, subject to the constraint that a proposition must show its sense. The picture theory and the analyticity thesis then entail the contingency thesis (that an elementary proposition is contingent) and the independence thesis (that elementary propositions are mutually logically independent) which, together with the strong analyticity thesis, imply that all logical propositions are tautologies. (shrink)

This paper makes the case for using the independent non-executive directors of a company listed in the United Kingdom exclusively as monitors and regulators of management, particularly as regulators of executive directors’ conflicts of interest, rather than as participants in management who also have a control function. It is suggested that these proposals can be accommodated within current corporate law in the United Kingdom, that they are practicable, and that they are desirable. The proposals are made against the background of (...) a continued strong emphasis in the United Kingdom on non-executive directors’ dual role both as managers of a company’s business and as monitors of its executive directors. It is suggested that this dual role for non-executive directors tends significantly to undermine the effectiveness of their control function, and that consequently the dual role should be abandoned in favor of the more focused role proposed in the paper. Improving the effectiveness of non-executive directors as regulators of executive directors’ conflicts of interest is vitally important to corporate governance in the United Kingdom: as the paper explains, other legal methods of controlling those conflicts in the United Kingdom suffer from serious deficiencies. (shrink)

Quantum theory does not only predict probabilities, but also relative phases for any experiment, that involves measurements of an ensemble of systems at different moments of time. We argue, that any operational formulation of quantum theory needs an algebra of observables and an object that incorporates the information about relative phases and probabilities. The latter is the (de)coherence functional, introduced by the consistent histories approach to quantum theory. The acceptance of relative phases as a primitive ingredient of any quantum theory, (...) liberates us from the need to use a Hilbert space and non-commutative observables. It is shown, that quantum phenomena are adequately described by a theory of relative phases and non-additive probabilities on the classical phase space. The only difference lies on the type of observables that correspond to sharp measurements. This class of theories does not suffer from the consequences of Bell's theorem (it is not a theory of Kolmogorov probabilities) and Kochen–Specker's theorem (it has distributive “logic”). We discuss its predictability properties, the meaning of the classical limit and attempt to see if it can be experimentally distinguished from standard quantum theory. Our construction is operational and statistical, in the spirit of Copenhagen, but makes plausible the existence of a realist, geometric theory for individual quantum systems. (shrink)

According to history texts, philosophers searched for a unifying natural law whereby natural phenomena and numbers are related. More than 2300 years ago, Aristotle postulated that nature requires minimum energy. More than 220 years ago, Euler applied the minimum energy postulate. More than 200 years ago, Lagrange provided a mathematical “proof” of the postulate for conservative systems. The resulting Principle of Least Action served only to derive the differential equations of motion of a conservative system. Then, 170 years ago, Hamilton (...) presented what he claimed to be a “general method in dynamics.” Hamilton's resulting “Law of Varying Action” was supposed to apply to both conservative and non-conservative systems and was supposed to yield either the differential equations of motion or the integrals of those differential equations. However, no direct evaluation of the integrals of motion ever resulted from Hamilton's law of varying action. In 1975, a scant 29 years ago, following five years of controversy with engineer mechanicians, Dr. Wolfgang Yourgrau, Editor, Foundations of Physics, published my first paper based on Aristotle's postulate, without mathematical proof. That and subsequent papers present, through applications, a true “general method in dynamics.” In this essay, I present the mathematical proof that is missing from my 1975 and subsequent papers. Six fundamental integrals of analytical mechanics are derived from Aristotle's postulate. First, however, Hamilton must be revisited to show why his H function and his “force function” prevents the law of varying action from being the general method in dynamics that he claimed it to be. I have found that Hamilton’s Law of Varying Action (HLVA), as Hamilton presented it, cannot be applied to systems for which the force function is non-integrable. In 1972, Dr. B.E. Gatewood and Dr. D.P. Beres (then a graduate student) discovered that the end-point term associated with the principle of least action does not vanish. I named the new equation, “the general energy equation.” In 1973, because I was doing with it what Hamilton claimed could be done with HLVA, I simply assumed that this new equation was HLVA. I gave the new equation the misnomer HLVA. In 2001, I learned that I had made a grave mistake. I found that HLVA is at most a special case of the general energy equation. My interpretation of Aristotle's postulate permits one to by-pass the differential equations of motion completely for both conservative and non-conservative systems (no calculus of variations). (shrink)

The concept of time emerges as an ordering structure in a classical statistical ensemble. Probability distributions p τ (t) at a given time t obtain by integrating out the past and future. We discuss all-time probability distributions that realize a unitary time evolution as described by rotations of the real wave function $q_{\tau}(t)=\pm \sqrt{p_{\tau}(t)}$ . We establish a map to quantum physics and the Schrödinger equation. Suitable classical observables are mapped to quantum operators. The non-commutativity of the operator product is (...) traced back to the incomplete statistics of the local-time subsystem. Our investigation of classical statistics is based on two-level observables that take the values one or zero. Then the wave functions can be mapped to elements of a Grassmann algebra. Quantum field theories for fermions arise naturally from our formulation of probabilistic time. (shrink)

This dissertation is an investigation into the degree to which the mathematics used in physical theories can be constructivized. The techniques of recursive function theory and classical logic are used to separate out the algorithmic content of mathematical theories rather than attempting to reformulate them in terms of "intuitionistic" logic. The guiding question is: are there experimentally testable predictions in physics which are not computable from the data? ;The nature of Church's thesis, that the class of effectively calculable functions (...) on the natural numbers is identical to the class of general recursive functions, is discussed. It is argued that this thesis is an example of an explication of the very notion of an effectively calculable function. This is contrary to a view of the thesis as a hypothesis about the limitations of the human mind. ;The extension to functions of a real variable of the notion of effective calculability is discussed, and it is argued that a function of a real variable must be continuous in order to be considered effectively calculable . The relation between continuity and computability is significant for the problem at hand. The results of a well-designed experiment do not depend critically upon the precise values of the relevant parameters. Accordingly, if the solution to a problem in mathematical physics depends discontinuously upon the data, it cannot be regarded as an experimentally testable prediction of the theory. The principle that the testable predictions of a physical theory cannot be singular is known as the principle of regularity. This principle is significant, because discontinuities generate non-computability, but they also disqualify a prediction from being experimentally testable. ;A mathematical framework is set up for discussing computability in physical theories. This framework is then applied to the case of quantum mechanics. It is found that, due to the use of unbounded operators in the theory, noncomputable objects appear, but predictions which satisfy the principle of regularity are nevertheless computable functions of the data. (shrink)

Provability, Computability and Reflection.

A theme that emerged at the Sheffield Conference with particular force, to my way of thinking, was a new way of recognizing, and then avoiding, a seductive bad idea. One of its many guises is what I have called the Cartesian Theater, but it also appears in the roles of Central Processing, or Central Executive, or Norman and Shallice's SAS, or Fodor's non-modular central arena of belief fixation. What is wrong with this idea is not (just) that it (apparently) postulates (...) an _anatomically_ discernible central region of the brain--maximally non-peripheral, one might say--but that it supposes that there is a functionally identifiable _subsystem_ (however located or even distributed in the brain) that has some all too remarkable competences achieved by some all too remarkable means. There are many routes to it. Here is one that starts off in an excellent direction but then veers off. The mistaken fork is not explicitly endorsed by anybody that I can think of, but I daresay it has covertly influenced a lot of thinking on the topic. (shrink)

'This book is an excellent, theoretically sound and politically relevant reader', Professor Wolfschaefer, Universitat des Bundeswehr, Hamburg 'Up to date complete overview of European monetary and fiscal policy issues. Highly readable, good mix of theory and data' 'I think the book contains a wealth of useful, precise information, presented in a straightforward, readable way in a quintessentially comparative perspective', Dr M Mclean, Royal Holloway University 'Excellent treatment - quite comprehensive, full references, accessible for non-economists', Charlotte Bretherton, Liverpool John Moores Univesity (...) 'A useful addition to student literature', MJ Macmillan, Exeter University 'This is a top class book and does not limit itself to assessing the adequacy of the European political economy to the precepts of advanced monetary economics...This book is an excellent tool for teaching EMU economics, and raising the level of EMU economics in the reaserch-field of international political economy. Students and scholars will appreciate the explicit assessment the authors make of complex economic issues, and their unbiased stance in the study of EMU economic and political interplay.' Miriam L.Campamella, Jean Monnet Professor, Faculty of Political Science, University of Turin. ECSA Review, Winter 2001This textbook offers a fresh and comprehensive examination of European monetary and fiscal policy in the third stage of Economic and Monetary Union. Professors Eijffinger and de Haan give a brief history of European economic integration before the transition to EMU, and continue with a comprehensive analysis of institutions, legislation, and policies. Their analysis includes the functions and goals of the European Central Bank, the Treaty on European Union, the Stability and Growth Pact, and the harmonization of taxes. Other topics discussed include the targets and instruments of European monetary policy, the integration of European financial markets, and the competition between financial institutions in Europe. (shrink)

Aristotle argues for and relies on the view that a constitutive norm prescribing true belief binds all rational subjects. This normativity is peculiar to belief, and derives but is distinct from the epistemic value of true belief, which is grounded in a teleological function that governs even non-rational cognition. Only rational creatures can have beliefs, and Aristotle uses the normative constraint on belief to distinguish it from imagining, its closest non-rational counterpart. This subjection to norms is therefore part of what (...) separates rational from non-rational cognition. (shrink)

At the heart of China's remarkable economic growth is a new economic system, which has emerged out of radical reforms in virtually all areas of economic activity. Understanding this system is the key to understanding the Chinese economy. This book, the culmination of many years of research in Hong Kong and China, is a comprehensive account of these systemic reforms, as well as of their transferability to other economies in transition. The starting-point of Dr Chai's analysis is a careful examination (...) of the structural elements of China's new economic system, focusing particularly on the decentralization of property rights in both the agricultural and industrial sectors. There follows a detailed analysis of changes in the functional elements of the system: its price and financial mechanisms. An assessment of the open-door policy also considers the twin impact of the liberalization of China's foreign trade and foreign investment regimes. Finally, China: Transition to a Market Economy highlights the increasingly important role of the non-state sector in facilitating economic growth and structural transformation. It will be essential reading for any student or researcher concerned with the Chinese economy, or with transition economies in general. (shrink)

We investigate introduction and elimination rules for truth-functional connectives, focusing on the general questions of the existence, for a given connective, of at least one such rule that it satisfies, and the uniqueness of a connective with respect to the set of all of them. The answers are straightforward in the context of rules using general set/set sequents of formulae, but rather complex and asymmetric in the restricted (but more often used) context of set/formula sequents, as also in the intermediate (...) set/formula-or-empty context. (shrink)

We investigate introduction and elimination rules for truth-functional connectives, focusing on the general questions of the existence, for a given connective, of at least one such rule that it satisfies, and the uniqueness of a connective with respect to the set of all of them. The answers are straightforward in the context of rules using general set/set sequents of formulae, but rather complex and asymmetric in the restricted (but more often used) context of set/formula sequents, as also in the intermediate (...) set/formula-or-empty context. (shrink)

The historical association between functionalism and physicalism is not an unbreakable one. There are reasons for finding some version of a functional account of the mental attractive that are independent of the plausibility of physicalism. I develop a non-physicalist version of func- tionalism and explain how this model is able to secure genuine emergence of the mental, despite Kim’s arguments that such emergence theories are incoherent. The kind of teleological emergence of the mental required by this model is in fact (...) fully compatible with the best available interpre- tations of physics and does not simply repeat the mistakes of vitalism. In addition, this model of teleological, emergent causation provides an attractive account of free/libertarian agency. (shrink)

The ipsilesional arm of stroke patients often has functionally limiting deficits in motor control and dexterity that depend on the side of the brain that is lesioned and that increase with the severity of paretic arm impairment. However, remediation of the ipsilesional arm has yet to be integrated into the usual standard of care for upper limb rehabilitation in stroke, largely due to a lack of translational research examining the effects of ipsilesional-arm intervention. We now ask whether ipsilesional-arm training, tailored (...) to the hemisphere-specific nature of ipsilesional-arm motor deficits in participants with moderate to severe contralesional paresis, improves ipsilesional arm performance and generalizes to improve functional independence. We assessed the effects of this intervention on ipsilesional arm unilateral performance [Jebsen–Taylor Hand Function Test ], ipsilesional grip strength, contralesional arm impairment level [Fugl–Meyer Assessment ], and functional independence [Functional independence measure ]. Intervention occurred over a 3 week period for 1.5 h/session, three times each week. All sessions included virtual reality tasks that targeted the specific motor control deficits associated with either left or right hemisphere damage, followed by graded dexterity training in real-world tasks. We also exposed participants to 3 weeks of sham training to control for the non-specific effects of therapy visits and interactions. We conducted five test-sessions: two pre-tests and three post-tests. Our results indicate substantial improvements in the less-impaired arm performance, without detriment to the paretic arm that transferred to improved functional independence in all three posttests, indicating durability of training effects for at least 3 weeks. We provide evidence for establishing the basis of a rehabilitation approach that includes evaluation and remediation of the ipsilesional arm in moderately to severely impaired stroke survivors. This study was originally a crossover design; however, we were unable to complete the second arm of the study due to the COVID-19 pandemic. We report the results from the first arm of the planned design as a longitudinal study. (shrink)

At the intersection of meta-ethics and philosophy of science, Nicholas Sturgeon’s “Moral Explanation” ([1985] 1988), Richard Boyd’s “How to be a Moral Realist” (1988), and David Brink’s Moral Realism and the Foundations of Ethics (1989) inaugurated a sustained argument for the claim that moral kinds like right action and virtuous agent are scientifically investigable natural kinds. The corresponding position is called “non-reductive ethical naturalism,” or “NEN.” Ethical nonnaturalists, by contrast, argue that moral kinds are genuine and objective, but not natural. (...) This dissertation is largely a challenge to non-reductive ethical naturalism from the viewpoint of ethical nonnaturalism. An introduction, four fairly independent chapters, and a conclusion comprise this dissertation. The introduction (chapter one) situates and summarizes the arguments in the four chapters that immediately follow, and the concluding chapter (chapter six) describes future work related to the arguments in this dissertation. I now turn to chapters two through five. In chapter two, I shore up what I believe are weakness in Derek Parfit’s Triviality Objection to reductive ethical naturalism and then present a challenge to the NEN theorist, which, I argue, the NEN theorist must but ultimately cannot meet. The challenge is to sketch an empirical experiment whereby we can adjudicate between competing moral hypotheses. I explain in terms of experimental design and evaluation why the challenge cannot be met. Chapters three and four focus on the semantics and reference relations of kind terms. In chapter three, I defend the Causal Externalist (CE) theory of semantics and reference against an objection distilled from two articles by Åsa Marie Wikforss. The objection is that CE implies a paradox, escape from which forces the CE theorist upon the horns of a dilemma. I show how the CE theorist can avoid the dilemma by allowing that the intensions of some artificial-kind terms (e.g., ‘jade’) are not given by descriptions associated with the terms. One consequence of this move, however, is that it casts doubt upon the coherence of the claim that moral-kind terms (e.g., ‘morally required action’) are natural-kind terms. In chapter four, I defend Terence Horgan and Mark Timmons’s Moral-Twin Earth argument from three critical responses put forward in recent paper by David Merli. NEN theorists claim that CE can account for the semantics and reference of moral-kind terms. As per Horgan and Timmons (H&T), however, our responses to the Moral-Twin Earth thought experiment give us reason to doubt the NEN theorists’ claim. Against H&T’s argument, however, Merli presents three independent, critical responses, and in this chapter I defend H&T’s argument in a way that is friendly to the ethical nonnaturalist. One upshot is, I contend, that the ethical nonnaturalist can and indeed should co-opt H&T’s argument for his own use. In chapter five, I return to kinds themselves, specifically those in biology. I first point out that ethical nonnaturalism appeals to a metaphysical thesis about nonnatural value, which need not be limited to the moral domain. Then, I argue that biological naturalism alone cannot give a satisfying realist account of biological kinds like HEART and NEURON. Finally, I show that by conjoining the concept of Cummins functions as recently defended by Paul Davies, a thesis about nonnatural value, and Ned Block’s Disney Principle regarding structural properties, the nonnaturalist, unlike the naturalist, can offer a satisfying realist account of biological kinds. (shrink)

An original and independent treatment of epistemology's central question--that concerning the relation between the mind and its objects. The author's answer is that of naive realism: the mind is a spectator of its objects, and the objects themselves are real and independent of it and its activity. The classical objections to such a view are examined forthrightly and yet with care; error, e.g., appears as a function of the unclarity with which some objects are apprehended rather than as evidence that (...) all objects are fictions. Professor Earle is quite willing to spell out the somewhat startling ontological consequences of his view; since whatever is an object of consciousness is real and independent, illusions differ from, say, material objects, not as non-being differs from being, but as one kind of being differs from another. The result is a contribution to metaphysics as well as to epistemology, and its conclusions in both areas are fresh and important. Part of Chapter I first appeared in this Review, VIII, 211-24.--V. C. C. (shrink)

Non-governmental organizations increasingly hold firms responsible for harm caused in their supply chains. In this paper, we explore how firms and NGOs talk about cosmopolitan claims regarding supply chain responsibility. We investigate the language used by Apple and a group of Chinese NGOs as well as Adidas and the international NGO Greenpeace about the firms’ environmental responsibilities in their supply chains. We apply electronic text analytic methods to firm and NGO reports totaling over 155,000 words. We identify different conceptualizations of (...) cosmopolitanism in this discourse: a legalistic approach to cosmopolitanism for Apple and a group of Chinese NGOs and a moralistic approach for Adidas and Greenpeace. We argue that these differences connect to the roles that the firms are expected and perhaps willing to take in SCR: legalistic discourse connects to a governmental function of rule development and enforcement; in contrast, moralistic discourse connects to a citizenship function that focuses on doing good to the global community. We discuss implications for companies’ non-market strategies and future research. (shrink)

Every living entity requires the capacity to defend against viruses in some form. From bacteria to plants to arthropods, cells retain the capacity to capture genetic material, process it in a variety of ways, and subsequently use it to generate pathogen-specific small RNAs. These small RNAs can then be used to provide specificity to an otherwise non-specific nuclease, generating a potent antiviral system. While small RNA-based defenses in chordates are less utilized, the protein-based antiviral invention in this phylum appears to (...) have derived from components of the same ancestral small RNA machinery. Based on recent evidence, it would seem that RNase III nucleases have been reiteratively repurposed over billions of years to provide cells with the capacity to recognize and destroy unwanted genetic material. Here we describe an overview of what is known on this subject and provide a model for how these defenses may have evolved. RNase III nuclease domains are widely used in an array of RNA metabolic functions as well as antiviral defenses. Here, we review their current usage as well as provide insight into how these domains may have shaped all major antiviral pathways over the course of evolution. (shrink)

Evolutionary developmental biology (Evo-devo) is a vibrant area of contemporary life science that should be (and is) increasingly incorporated into teaching curricula. Although the inclusion of this content is important for biological pedagogy at multiple levels of instruction, there are also philosophical lessons that can be drawn from the scientific practices found in Evo-devo. One feature of particular significance is the interdisciplinary nature of Evo-devo investigations and their resulting explanations. Instead of a single disciplinary approach being the most explanatory or (...) fundamental, different methodologies from biological disciplines must be synthesized to generate empirically adequate explanations. Thus, Evo-devo points toward a non-reductionist epistemology in biology. I review three areas where these synthetic efforts become manifest as a result of Evo-devo’s practices (form versus function reasoning styles; problem-structured investigations; idealizations related to studying model organisms), and then sketch some possible applications to teaching biology. These philosophical considerations provide resources for life science educators to address (and challenge) key aspects of the National Science Education Standards and Benchmarks for Scientific Literacy. (shrink)

In ‘Rethinking Disease’, Powell and Scarffe1 propose what in effect is a modification of Jerome Wakefield’s2 3 harmful dysfunction analysis of medical disorder. The HDA maintains that ‘disorder’ is a hybrid factual and value concept requiring that a biological dysfunction, understood as a failure of some feature to perform a naturally selected function, causes harm to the individual as evaluated by social values. Powell and Scarffe accept both the HDA’s evolutionary biological function component and its incorporation of a value component. (...) Their proposed ‘new twist’ is to revise the value component: ‘Our proposed definition of disease is as follows: a biomedical state is a disease only if it implicates a biological dysfunction that is, or would be, properly disvalued’. So, they propose that a disorder is a ‘properly disvalued dysfunction’ rather than a ‘harmful dysfunction’, an approach they term ‘thickly normative’ in contrast to the thin normative approach of the HDA. There has been a surge of interest recently in better understanding the ‘harm’ component of the HDA. Powell and Scarffe’s analysis is a helpful contribution to this discussion. We focus here exclusively on their proposal regarding the analysis of the concept of disorder and ignore many important related issues that the authors address, ranging from prioritising resource allocation between disorders and non-disorders to whether the concept of disorder should be replaced by a generic welfarist concept. The resolution of these additional issues depends on first understanding ‘disorder’. The authors’ proposed changes to the HDA also deserve evaluation because the HDA, which has been endorsed by leading nosologists,4 plays an influential role in nosological debate across categories of disorder ranging, for example, from sexual paraphilias5 to psychopathy.6 A basic problem is that Powell and Scarffe misinterpret …. (shrink)