Intentional action involves both a series of neural events in the motor areas of the brain, and also a distinctive conscious experience that ''I'' am the author of the action. This paper investigates some possible ways in which these neural and phenomenal events may be related. Recent models of motor prediction are relevant to the conscious experience of action as well as to its neural control. Such models depend critically on matching the actual consequences of a movement against its internally (...) predicted effects. However, it remains unclear whether our conscious experience of action depends on a precise matching process, or a retrospective inference that ''I'' must have been responsible for a particular event. We report an experiment in which normal subjects judged the perceived time of either intentional actions, involuntary movements, or subsequent effects (auditory tones) of these. We found that the subject's intention to produce the auditory tone produced an intentional binding between the perceived times of the subject's action and the tone. However, if the intention was interrupted by an imposed involuntary movement, followed by the identical tone, no such binding occurred. The phenomenology of intentional action requires an appropriate predictive link between intentions and effects, rather than a retrospective inference that ''I'' caused the effect. (shrink)

We study the logical and computational properties of basic theorems of uncountable mathematics, including the Cousin and Lindelöf lemma published in 1895 and 1903. Historically, these lemmas were among the first formulations of open-cover compactness and the Lindelöf property, respectively. These notions are of great conceptual importance: the former is commonly viewed as a way of treating uncountable sets like e.g. [Formula: see text] as “almost finite”, while the latter allows one to treat uncountable sets like e.g. [Formula: see text] (...) as “almost countable”. This reduction of the uncountable to the finite/countable turns out to have a considerable logical and computational cost: we show that the aforementioned lemmas, and many related theorems, are extremely hard to prove, while the associated sub-covers are extremely hard to compute. Indeed, in terms of the standard scale (based on comprehension axioms), a proof of these lemmas requires at least the full extent of second-order arithmetic, a system originating from Hilbert–Bernays’ Grundlagen der Mathematik. This observation has far-reaching implications for the Grundlagen’s spiritual successor, the program of Reverse Mathematics, and the associated Gödel hierarchy. We also show that the Cousin lemma is essential for the development of the gauge integral, a generalization of the Lebesgue and improper Riemann integrals that also uniquely provides a direct formalization of Feynman’s path integral. (shrink)

We study the logical and computational properties of basic theorems of uncountable mathematics, in particular Pincherle's theorem, published in 1882. This theorem states that a locally bounded function is bounded on certain domains, i.e. one of the first ‘local-to-global’ principles. It is well-known that such principles in analysis are intimately connected to (open-cover) compactness, but we nonetheless exhibit fundamental differences between compactness and Pincherle's theorem. For instance, the main question of Reverse Mathematics, namely which set existence axioms are necessary to (...) prove Pincherle's theorem, does not have an unique or unambiguous answer, in contrast to compactness. We establish similar differences for the computational properties of compactness and Pincherle's theorem. We establish the same differences for other local-to-global principles, even going back to Weierstrass. We also greatly sharpen the known computational power of compactness, for the most shared with Pincherle's theorem however. Finally, countable choice plays an important role in the previous, we therefore study this axiom together with the intimately related Lindelöf lemma. (shrink)

The aim of Reverse Mathematics (RM for short) is to find the minimal axioms needed to prove a given theorem of ordinary mathematics. These minimal axioms are almost always equivalent to the theorem, working over the base theory of RM, a weak system of computable mathematics. The Big Five phenomenon of RM is the observation that a large number of theorems from ordinary mathematics are either provable in the base theory or equivalent to one of only four systems; these five (...) systems together are called the ‘Big Five’. The aim of this paper is to greatly extend the Big Five phenomenon as follows: there are two supposedly fundamentally different approaches to RM where the main difference is whether the language is restricted to second-order objects or if one allows third-order objects. In this paper, we unite these two strands of RM by establishing numerous equivalences involving the second-order Big Five systems on one hand, and well-known third-order theorems from analysis about (possibly) discontinuous functions on the other hand. We both study relatively tame notions, like cadlag or Baire 1, and potentially wild ones, like quasi-continuity. We also show that slight generalizations and variations of the aforementioned third-order theorems fall far outside of the Big Five. (shrink)

We investigate the connections between computability theory and Nonstandard Analysis. In particular, we investigate the two following topics and show that they are intimately related. A basic property of Cantor space$2^ $ is Heine–Borel compactness: for any open covering of $2^ $, there is a finite subcovering. A natural question is: How hard is it to compute such a finite subcovering? We make this precise by analysing the complexity of so-called fan functionals that given any $G:2^ \to $, output a (...) finite sequence $\langle f_0, \ldots,f_n \rangle $ in $2^ $ such that the neighbourhoods defined from $\overline {f_i } G\left$ for $i \le n$ form a covering of $2^ $. A basic property of Cantor space in Nonstandard Analysis is Abraham Robinson’s nonstandard compactness, i.e., that every binary sequence is “infinitely close” to a standard binary sequence. We analyse the strength of this nonstandard compactness property of Cantor space, compared to the other axioms of Nonstandard Analysis and usual mathematics.Our study of yields exotic objects in computability theory, while leads to surprising results in Reverse Mathematics. We stress that and are highly intertwined, i.e., our study is holistic in nature in that results in computability theory yield results in Nonstandard Analysis and vice versa. (shrink)

Cantor’s first set theory paper (1874) establishes the uncountability of ${\mathbb R}$. We study this most basic mathematical fact formulated in the language of higher-order arithmetic. In particular, we investigate the logical and computational properties of ${\mathsf {NIN}}$ (resp. ${\mathsf {NBI}}$ ), i.e., the third-order statement there is no injection resp. bijection from $[0,1]$ to ${\mathbb N}$. Working in Kohlenbach’s higher-order Reverse Mathematics, we show that ${\mathsf {NIN}}$ and ${\mathsf {NBI}}$ are hard to prove in terms of (conventional) comprehension axioms, (...) while many basic theorems, like Arzelà’s convergence theorem for the Riemann integral (1885), are shown to imply ${\mathsf {NIN}}$ and/or ${\mathsf {NBI}}$. Working in Kleene’s higher-order computability theory based on S1–S9, we show that the following fourth-order process based on ${\mathsf {NIN}}$ is similarly hard to compute: for a given $[0,1]\rightarrow {\mathbb N}$ -function, find reals in the unit interval that map to the same natural number. (shrink)

Reverse Mathematics (RM hereafter) is a program in the foundations of mathematics where the aim is to identify the minimal axioms needed to prove a given theorem from ordinary, i.e., non-set theoretic, mathematics. This program has unveiled surprising regularities: the minimal axioms are very often equivalent to the theorem over the base theory, a weak system of ‘computable mathematics’, while most theorems are either provable in this base theory, or equivalent to one of only four logical systems. The latter plus (...) the base theory are called the ‘Big Five’ and the associated equivalences are robust following Montalbán, i.e., stable under small variations of the theorems at hand. Working in Kohlenbach’s higher-order RM, we obtain two new and long series of equivalences based on theorems due to Bolzano, Weierstrass, Jordan, and Cantor; these equivalences are extremely robust and have no counterpart among the Big Five systems. Thus, higher-order RM is much richer than its second-order cousin, boasting at least two extra ‘Big’ systems. (shrink)

This article reveals the outcome of a study on the perceptions of elders, family members, and healthcare professionals and administration providing care in a range of different long-term care facilities in Hong Kong with primary focus on the concepts of autonomy and dignity of elders, quality and location of care, decision making, and financing of long term care. It was found that aging in place and family care were considered the best approaches to long term care insofar as procuring and (...) balancing the values of dignity, autonomy, family integrity and social sustainability were concerned. An elder having the final say was generally accepted. The results also initiated the importance of sharing of financial responsibility among elders, children and government albeit the emphasis was placed on individuals. Furthermore, dignity of elders was not considered purely a synonym of autonomy, but it had also to do with respect, family and social connections. (shrink)

We prove that the problem of determining the minimum propositional proof length is NP- hard to approximate within a factor of 2 log 1 - o(1) n . These results are very robust in that they hold for almost all natural proof systems, including: Frege systems, extended Frege systems, resolution, Horn resolution, the polynomial calculus, the sequent calculus, the cut-free sequent calculus, as well as the polynomial calculus. Our hardness of approximation results usually apply to proof length measured either by (...) number of symbols or by number of inferences, for tree-like or dag-like proofs. We introduce the Monotone Minimum (Circuit) Satisfying Assignment problem and reduce it to the problems of approximation of the length of proofs. (shrink)

This paper explores definitions of death from the perspectives of several world and indigenous religions, with practical application for health care providers in relation to end of life decisions and organ and tissue donation after death. It provides background material on several traditions and explains how different religions derive their conclusions for end of life decisions from the ethical guidelines they proffer.

Nature Network Groups hosted an invited workshop on 'Theories of Consciousness' during the second semester of 2009. There were presentations by each of 15 authors active in the field, followed by debate with other presenters and invitees. A week was allocated to each of the theories proposed; general discussion threads were also opened from time to time, as seemed appropriate. We offer here an account of the principal outcomes. It can be regarded as a contemporary, 'state of the art' snapshot (...) of thinking in this field. (shrink)

This paper examines the relationship between North American beef consumption and deforestation in South and Central America. Some writers have argued that consumption of hamburgers in North America, particularly hamburgers consumed in fast food restaurants, contributes to the depletion of the rainforest in South and Central America. We survey the published policy literature on the causes of rainforest depletion in the region. We also review the published estimates of the rate and extent of clearing of rainforest that has occurred in (...) South and Central America since 1970. Finally, we review the data on beef imports and consumption in Canada and the United States in a effort to assess the importance of South and Central America as suppliers of beef to the North American market. We conclude that the relationship between beef consumption in North America should not be considered an important cause of forest depletion in South and Central America. Domestic policies and market forces in the countries where rainforests are located are the leading causes of rainforest depletion in this region. This lesson seems to have been lost on some popular and even some textbook writers on this subject. (shrink)

Shared group identifications can significantly subdivide populations. However, groups with mutual recognition may not be territorial. In the deep ocean, territoriality is absent but some species have important groups based upon shared identification. Control over access to physical space should be dropped from the definition of “society,” although “territorial society” could be retained as an important subcategory.

Background: Randomized controlled trials have been criticized for their inability to identify and differentiate the causal mechanisms that generate the outcomes they measure. One solution is the development of realist trials that combine the empirical precision of trials' outcome data with realism's theoretical capacity to identify the powers that generate outcomes. Main Body: We review arguments for and against this position and conclude that critical realist trials are viable. Using the example of an evaluation of the educational effectiveness of virtual (...) reality simulation, we explore whether Partial Least Squares Structural Equation Modelling can move statistical analysis beyond correlational analysis to support realist identification of the mechanisms that generate correlations. Conclusion: We tentatively conclude that PLS-SEM, with its ability to identify ‘points of action’, has the potential to provide direction for researchers and practitioners in terms of how, for whom, when, where and in what circumstances an intervention has worked. (shrink)

We present a study comparing, in English, perceived distributions of men and women in 422 named occupations with actual real world distributions. The first set of data was obtained from previous a large-scale norming study, whereas the second set was mostly drawn from UK governmental sources. In total, real world ratios for 290 occupations were obtained for our perceive vs. real world comparison, of which 205 were deemed to be unproblematic. The means for the two sources were similar and the (...) correlation between them was high, suggesting that people are generally accurate at judging real gender ratios, though there were some notable exceptions. Beside this correlation, some interesting patterns emerged from the two sources, suggesting some response strategies when people complete norming studies. We discuss these patterns in terms of the way real world data might complement norming studies in determining gender stereotypicality. (shrink)

The first three sections of this lecture address the need for better historical-materialist theorisations of capitalist competition, capitalist classes and capitalist states, and in particular the institutional dimensions of these – which is fundamental for understanding why and how capitalism has survived into the twenty-first century. The fourth section addresses historical materialism’s under-theorisation of the institutional dimensions of working-class formation, and how this figures in explaining why, despite the expectations of the founders of historical materialism, the working classes have not, (...) at least yet, become capitalism’s gravediggers. While recognising that a better historical materialism along these lines will not necessarily provide us with a gps route to a socialist world beyond capitalism, it does suggest a number of guidelines for socialist strategy, with which the lecture concludes. This includes the need for building new institutions capable of defining, mobilising and representing the working class broadly, as well as recognising that the types of parties that can transform working classes into leading agents of social transformation have yet to be invented. A strategic priority must be to start anew at creating the kinds of working-class political institutions which can rekindle the socialist imagination, and develop the socialist capacities to get there. (shrink)

Bibliographic records published by the British Education Index (BEI) between 1957 and 2000 are analysed in the context of a history of the BEI's changing presentation of information about the field. The value of frequency counts for BEI subject terms is discussed, in relation to their potential for revealing trends in the fields of educational studies and information management.

In a recent article (Inquiry, Vol. 19 [1976]), J. W. Meiland addresses the issue of psychologism in logic, which holds that logic is a branch of psychology and that logical laws (such as the Principle of Non?Contradiction) are contingent upon the nature of the mind. Meiland examines Husserl's critique of psychologism, argues that Husserl is not convincing, and offers two new objections to the psychologistic thesis. In this paper I attempt to rebut those objections. In question are the acceptable criteria (...) for determining the possibility or impossibility of systems of logic significantly different from our own. I argue that a criteriological application of our accepted laws of logic to this question commits a circular fallacy. I then argue that, even if we accept logical consistency as a criterion for possibility, a plausible argument for the possibility of valid alternative logics can be constructed by using the functionalist analogy between minds and automata. Finally, I attempt to rebut the claim that in logic the only changes possible are conceptual changes that would not permit a proposition to be both true and false. (shrink)

This book is about how we make choices. It is a compelling analysis of the nature of free will, drawing together evidence from chemistry, literature, politics, history and beyond. Psychiatrist Chris Nunn elegantly explores the revolutions in medicine, genetics, bioethics and neuroscience spurred by Julien de la Mettrie's 300-year-old tract Man the Machine . Nunn concludes that a mechanistic view of the human brain, though once fruitful, is now moribund. He proposes a powerful alternative: that stories, recorded in (...) our memories throughout life, are the mediators of free choice. Nunn demonstrates how this original approach could reconcile the latest brain-imaging results and our seemingly contradictory intuition about decision making and responsibility. (shrink)

In this enlightening book, Sam Harris argues that free will is an illusion but that this truth should not undermine morality or diminish the importance of social and political freedom; indeed, this truth can and should change the way we think about some of the most important questions in life.

Before any attempt is made to solve the problem with which this paper deals, it is necessary to convince the reader that the problem exists. Much is written and said to-day about class distinctions, both by those who announce with satisfaction their growing disappearance, and by those who half guiltily admit their existence, but it never seems to occur to such writers that the nature of these distinctions is itself something of a mystery. We take it for granted as one (...) of the most obvious and commonplace facts of daily life. It seems hardly likely that the examination of a thing so ubiquitous and immemorial will yield anything new. My object will be to maintain that this attitude is mistaken, and that the idea of “class” is not really self-explanatory, but deserves a closer analysis than it usually gets. And if this proves to be the case, it must be admitted that the subject is of importance. Many political and social problems are deeply involved in the fact of class distinctions. Many who believe in a possible regeneration of human society would gladly surrender much to secure a world where poverty should be no more, yet hesitate before the prospect of a loss, through diffusion, of cultural values which they feel to be infinitely precious, and which give to the existing order a greater claim to permanence than it would otherwise possess. We most of us hardly know our own minds in this matter. We yield social distinctions their place, but we do so shamefacedly, as though confessing to a mere unjustified conservatism. (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)

Analogy with the monisms of fundamental physics suggests that a concept of symmetry breaking is likely to help towards developing an understanding of mind/matter monism. I explore some possible consequences of this concept, arguing that a broken symmetry, involving energy and 'what-it-is-like-to-be-ness'along with time, may occur and may manifest in the course of energy measurements. The resultant proto-panpsychist picture has the advantage of indicating how our complex, human consciousness could emerge from proto-conscious elements. It's an account that has empirical, refutable (...) implications which are briefly discussed. (shrink)