Despite its significance in neuroscience and computation, McCulloch and Pitts's celebrated 1943 paper has received little historical and philosophical attention. In 1943 there already existed a lively community of biophysicists doing mathematical work on neural networks. What was novel in McCulloch and Pitts's paper was their use of logic and computation to understand neural, and thus mental, activity. McCulloch and Pitts's contributions included (i) a formalism whose refinement and generalization led to the notion of (...) finite automata (an important formalism in computability theory), (ii) a technique that inspired the notion of logic design (a fundamental part of modern computer design), (iii) the first use of computation to address the mind–body problem, and (iv) the first modern computational theory of mind and brain. (shrink)

Writings by a thinker—a psychiatrist, a philosopher, a cybernetician, and a poet—whose ideas about mind and brain were far ahead of his time. Warren S. McCulloch was an original thinker, in many respects far ahead of his time. McCulloch, who was a psychiatrist, a philosopher, a teacher, a mathematician, and a poet, termed his work “experimental epistemology.” He said, “There is one answer, only one, toward which I've groped for thirty years: to find out how brains work.” Embodiments (...) of Mind, first published more than fifty years ago, teems with intriguing concepts about the mind/brain that are highly relevant to recent developments in neuroscience and neural networks. It includes two classic papers coauthored with Walter Pitts, one of which applies Boolean algebra to neurons considered as gates, and the other of which shows the kind of nervous circuitry that could be used in perceiving universals. These first models are part of the basis of artificial intelligence. Chapters range from “What Is a Number, that a Man May Know It, and a Man, that He May Know a Number,” and “Why the Mind Is in the Head,” to “What the Frog's Eye Tells the Frog's Brain” (with Jerome Lettvin, Humberto Maturana, and Walter Pitts), “Machines that Think and Want,” and “A Logical Calculus of the Ideas Immanent in Nervous Activity” (with Walter Pitts). Embodiments of Mind concludes with a selection of McCulloch's poems and sonnets. This reissued edition offers a new foreword and a biographical essay by McCulloch's one-time research assistant, the neuroscientist and computer scientist Michael Arbib. (shrink)

Many years after the publication of “A Logical Calculus of the Ideas Immanent in Nervous Activity,” Warren McCulloch gave Walter Pitts credit for contributing his knowledge of modular mathematics to their joint project. In 1941 I presented my notions on the flow of information through ranks of neurons to Rashevsky’s seminar in the Committee on Mathematical Biology of the University of Chicago and met Walter Pitts, who then was about seventeen years old. He was working on a (...) mathematical theory of learning and I was much impressed. He was interested in problems of circularity, how to handle regenerative nervous activity in closed loops....For two years Walter and I worked on these problems whose solution depended upon modular mathematics of which I knew nothing, but Walter did.. In this paper, we will fill in some of the details regarding Pitts’s interest in problems of circularity, regenerative activity in closed loops of neurons, and modular mathematics, and the way in which they relate to “A Logical Calculus.”. (shrink)

In the last decade, we have observed a continuous increase of interest in eye movement research. According to a recent investigation, eye movements are discussed in over one million publications. The number of publications with eye movement in the title or abstract has been steadily increasing over the years, with over 1,200 papers published alone in 2013. The last decade has also witnessed the emergence of many new sub-disciplines in the field of neuroscience and cognition - one of them is (...) neuroaesthetics, which refers to the [neuro-]science of aesthetic perception of art.The title and contents of our book have been inspired by a very influential research article. It is one of the most cited scientific papers of all time, published in 1959 by a team of neurophysiologists and engineers, Lettvin, McCulloch and Pitts who are considered to be the founders of modern cybernetics. Their article, "What the Frog's Eye Tells the Frog's Brain," refers to the role of internal cortical models in the communication or interfacing of the information in the outside world with the practical contextual task of the viewer. It shows how eye movements are the modality of this communication. The same duality between eye movements and internal models plays a fundamental role in humans. When we look, for example, at art, it explains those neurological processes involved in neuroaesthetics. Our book undertakes this innovative approach to neuroaesthetics. It explains this duality and discusses the communication between the artist and the viewer's aesthetic perception. It is structured into five chapters.Chapter One discusses the neurology of aesthetics, the idea of art as a form of communication, and explains perception as an active matching between a "top" (the viewer's mind) and a "down" (the viewer's sensorial machinery). It goes deep into the philosophical quandary of what beauty is in terms of art. Chapter Two is about eye movements and the scanpath theory of vision perception. It discusses the role of visual attention for controlling active vision, the meaning of mental binding and the analysis of eye movements as the key to understanding aesthetic processes. Chapter Three introduces Claude Shannon's information theory using it as a matrix into which to embed the top down active vision scanpath theory. The authors explain the main concept of neuroaesthetics as a form of communication mediated by the sequence of eye fixations. Chapter Four discusses art critique: The role of the viewer's training and expectation, the dilemma of the aesthetics of art versus non-art and how all of this affects the viewing mode. Finally, Chapter Five treats the intimacy of the artistic process, showing the unique implementation of the communicative experience between the artist and the viewer - the relation between a pictorial representation defined by the artist and modes of AWE generated in the viewer during active looking. (shrink)

In their work McCulloch and Pitts describe an idea of representing all of nervous activity in terms of propositional logic. This idea was quickly challenged. One of reasons for this challenge was rising believe that logic is unable to describe most of human cognitive processes. In this paper we will analyse premises of original McCulloch and Pitts proposition. Following that, we will ask about ability of symbolic systems to represent human cognition. We will finish by analysing (...) relation between symbolic and subsymbolic computing, in hope of bridging the gap between the two. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Philosophic Foundations of Mimetic Theory and Cognitive Science(Including Artificial Intelligence)Jean-Pierre Dupuy (bio)In the mid 1970s I discovered at the same time cognitive science and mimetic theory. Being a philosopher with a scientific background, I immediately brought them together and tried to reconceptualize the latter in terms of the former. In a sense, I haven't stopped doing that in the last 45 years. That is why I feel fully (...) at home with the goals pursued by the organizers of this conference.I do not believe it is feasible or even desirable to operate the rapprochement between the two disciplines at a global level. The history of cognitive science is exceedingly involved, and the part played by artificial intelligence in it compared to the part played by the neurosciences has varied greatly over time.1 Only a piecemeal approach makes sense. I present here four short case studies that cover the whole period, from the beginnings in cybernetics to today's artificial intelligence (AI).In order to better situate these studies within a broader frame, I propose the diagram in Figure 1. To comment on it would require more time than available for my whole presentation. Let me just say the following. [End Page 1]It is essential to distinguish between two kinds of AI. The first to bear this name was launched by economist Herbert Simon and computer scientist Allan Newell at a Dartmouth conference in 1956. It was based on the premise that thinking is computing, with this computation bearing on sentences of a "language of thought" implementable in a digital computer. It turns out that this AI(1) was progressively substituted from the 1980s onward by an AI(2), which, to some extent, was a return to a fundamental result obtained by cybernetics in 1943. Neurophysiologist Warren McCulloch and mathematician Walter Pitts had constructed a mathematical model of a network of elementary calculators called "neurons" and explored its properties. The capacity to "think" was one of these. It was not situated at the elementary level, as was the case in AI(1), but it emerged at the collective level from the interactions between the neurons.This model was heavily criticized by the supporters of AI(1),2 and its first implementations, in the notorious "Perceptron" in particular (1957), were pitiful failures. However, the emergence of "second-order cybernetics" under the guidance of cybernetician Heinz von Foerster and the theory of complex, self-organizing systems that it helped develop, in cooperation and rivalry with similar efforts in the physical sciences, enabled the neural network model to come to a second life under different names: formal neurons, deep learning, big data, and the like. Together, they constitute AI(2).The following network of influences wouldn't have been possible without its stem, that is, the boxes containing the names of Kurt Gödel and Alan Turing. The former revolutionized logic by showing that reasoning about arithmetic and arithmetic are one and the same, insofar as it is possible to code in a 1-to-1 fashion propositions about integers (for instance, "7 is a prime number") by means of integers. The latter demonstrated that some mechanisms can self-transcend inasmuch as they generate an ensemble of outputs that cannot be defined mechanistically. Later, John von Neumann, who is credited along with Alan Turing with having invented the digital computer, would use this logical possibility to define complexity: A mechanism is complex if it is capable of generating one more complex than itself. The gate was open for the theories of complex, self-organizing systems to thrive and, by way of consequence, for AI(2) to emerge.fascination with modelsHerbert Simon (1916–2001), winner of the Nobel Prize in economics for his work on what he called "bounded rationality," is generally considered to be one [End Page 2] Click for larger view View full resolutionFigure 1.of the founders of artificial intelligence. Some cognitive scientists still rely on the computer program that he devised with Alan Newell to simulate the creative processes of human thought—a program aptly named "General Problem Solver." The title of one of his principal works, The Sciences of the... (shrink)

Standard semantic information processing models—information in; information processed; information out —lend themselves to standard models of the functioning of the brain in terms, e.g., of threshold-switch neurons connected via classical synapses. That is, in terms of sophisticated descendants of McCulloch and Pitts models. I argue that both the cognition and the brain sides of this framework are incorrect: cognition and thought are not constituted as forms of semantic information processing, and the brain does not function in terms of (...) passive input processing units organized as neural nets. An alternative framework is developed that models cognition and thought not in terms of semantic information processing, and, correspondingly, models brain functional processes also not in terms of semantic information processing. As alternative to such models: I outline a pragmatist oriented, interaction based, model of representation; derive from this model a fundamental framework of constraints on how the brain must function; show that such a framework is in fact found in the brain, and develop the outlines of a broader model of how mental processes can be realized within this alternative framework. Part I of this discussion focuses on some criticisms of standard modeling frameworks for representation and cognition, and outlines an alternative interactivist, pragmatist oriented, model. In part II, the focus is on the fact that the brain does not, in fact, function in accordance with standard passive input processing models—e.g., information processing models. Instead, there are multiple endogenously active processes at multiple spatial and temporal scales across multiple kinds of cells. A micro-functional model that accounts for, and even predicts, these multi-scale phenomena in generating emergent representation and cognition is outlined. That is, I argue that the interactivist model of representation outlined offers constraints on how the brain should function that are in fact empirically found, and, in reverse, that the multifarious details of brain functioning entail the pragmatist representational model—a very strong interrelationship. In the sequel paper, starting with part III, this model is extended to address macro-functioning in the CNS. In part IV, I offer a discussion of an approach to brain functioning that has some similarities with, as well as differences from, the model presented here: sometimes called the predictive brain approach. (shrink)

It is sometimes suggested that the history of computation in cognitive science is one in which the formal apparatus of Turing-equivalent computation, or effective computability, was exported from mathematical logic to ever wider areas of cognitive science and its environs. This paper, however, indicates some respects in which this suggestion is inaccurate. Computability theory has not been focused exclusively on Turing-equivalent computation. Many essential features of Turing-equivalent computation are not captured in definitions of computation as symbol manipulation. Turing-equivalent computation did (...) not play the role in McCulloch and Pitts’s early cybernetic work that is sometimes attributed to it. Finally, various segments of the neuroscientific community invoke a notion of computation that differs from the Turing-equivalent notion.Keywords: Circular causality; Computation; Cortical maps; Neural networks; Symbol manipulation; Turing-equivalent computation. (shrink)

One of the major values of animal ethical theory can be found in the light it sheds on practical ethical problems involving animals. McCulloch and Reiss’ paper does precisely this regarding the culling of badgers in England to limit the spread of tuberculosis. Perspicaciously realizing that societal ethics represents a combination of utilitarian and rights-based theorizing, the authors apply both of these perspectives to the issue, noting that both theoretical approaches generate a rejection of culling in the presence of (...) other viable alternatives. In addition, the authors suggest and defend the use of an Animal Welfare Impact Assessment tool to assess the impact of various management approaches on the animals, and demonstrate its congruence with both the ethical theories considered, and with societal moral attitudes. In this way, they show that their conclusion is directly compatible with the societal ethic, in my view a major prerequisite for effecting social change. (shrink)

This chapter describes the conceptual foundations of cognitive science during its establishment as a science in the 20th century. It is organized around the core ideas of individual agency as its basic explanans and information-processing as its basic explanandum. The latter consists of a package of ideas that provide a mathematico-engineering framework for the philosophical theory of materialism.

Bovine tuberculosis is the most economically important animal health policy issue in Britain. The problem of what to do about badgers has plagued successive governments since a dead badger was discovered with bovine TB in 1971. Successive Labour governments oversaw the Randomised Badger Culling Trial from 1998 to 2006. Despite the RBCT recommendation against culling, the 2010–2015 Coalition government implemented pilot badger culls. This paper provides an account of the evolution of bovine TB and badger control policy, focusing on the (...) 1997–2010 Labour, the 2010–2015 Coalition and the 2015-present Conservative governments. Interviews with bovine TB policy stakeholders supplement discussion of the development of bovine TB policy. The paper discusses the science and politics of bovine TB policy, in which there are different badger control policies in Westminster, Welsh and Scottish governments. Badger control is a highly polarised issue, and the Coalition and Conservative governments have been heavily criticised for a culling policy opposed by the independent scientific community. Recent governments have defended badger culling on the basis of veterinary advice and experience in countries such as New Zealand. The paper concludes with two key recommendations to inform controversial animal health and welfare policy issues such as bovine TB. First, mandatory Animal Welfare Impact Assessment provides objective data on the impacts of policy options on cows and badgers. Second, robust ethical analysis, conducted by independent experts using established moral frameworks, should be applied to animal health and welfare issues for the benefit of decision makers. (shrink)

An examination of the fundamental role cybernetics played in the birth of cognitive science and the light this sheds on current controversies. The conceptual history of cognitive science remains for the most part unwritten. In this groundbreaking book, Jean-Pierre Dupuy—one of the principal architects of cognitive science in France—provides an important chapter: the legacy of cybernetics. Contrary to popular belief, Dupuy argues, cybernetics represented not the anthropomorphization of the machine but the mechanization of the human. The founding fathers of cybernetics—some (...) of the greatest minds of the twentieth century, including John von Neumann, Norbert Wiener, Warren McCulloch, and Walter Pitts—intended to construct a materialist and mechanistic science of mental behavior that would make it possible at last to resolve the ancient philosophical problem of mind and matter. The importance of cybernetics to cognitive science, Dupuy argues, lies not in its daring conception of the human mind in terms of the functioning of a machine but in the way the strengths and weaknesses of the cybernetics approach can illuminate controversies that rage today—between cognitivists and connectionists, eliminative materialists and Wittgensteinians, functionalists and anti-reductionists. Dupuy brings to life the intellectual excitement that attended the birth of cognitive science sixty years ago. He separates the promise of cybernetic ideas from the disappointment that followed as cybernetics was rejected and consigned to intellectual oblivion. The mechanization of the mind has reemerged today as an all-encompassing paradigm in the convergence of nanotechnology, biotechnology, information technology, and cognitive science. The tensions, contradictions, paradoxes, and confusions Dupuy discerns in cybernetics offer a cautionary tale for future developments in cognitive science. (shrink)

Recent literature on the role of pictorial representation in the life sciences has focused on the relationship between detailed representations of empirical data and more abstract, formal representations of theory. The standard argument is that in both a historical and epistemic sense, this relationship is a directional one: beginning with raw, unmediated images and moving towards diagrams that are more interpreted and more theoretically rich. Using the neural network diagrams of Warren McCulloch and Walter Pitts as a case (...) study, I argue that while in the empirical sciences, pictorial representation tends to move from data to theory, in areas of the life sciences that are predominantly theoretical, when abstraction occurs at the outset, the relationship between detail and abstraction in pictorial representations can be of a different character. (shrink)

The conceptual history of cognitive science remains for the most part unwritten. In this groundbreaking book, Jean-Pierre Dupuy--one of the principal architects of cognitive science in France--provides an important chapter: the legacy of cybernetics. Contrary to popular belief, Dupuy argues, cybernetics represented not the anthropomorphization of the machine but the mechanization of the human. The founding fathers of cybernetics--some of the greatest minds of the twentieth century, including John von Neumann, Norbert Wiener, Warren McCulloch, and Walter Pitts--intended to (...) construct a materialist and mechanistic science of mental behavior that would make it possible at last to resolve the ancient philosophical problem of mind and matter. The importance of cybernetics to cognitive science, Dupuy argues, lies not in its daring conception of the human mind in terms of the functioning of a machine but in the way the strengths and weaknesses of the cybernetics approach can illuminate controversies that rage today--between cognitivists and connectionists, eliminative materialists and Wittgensteinians, functionalists and anti-reductionists. Dupuy brings to life the intellectual excitement that attended the birth of cognitive science sixty years ago. He separates the promise of cybernetic ideas from the disappointment that followed as cybernetics was rejected and consigned to intellectual oblivion. The mechanization of the mind has reemerged today as an all-encompassing paradigm in the convergence of nanotechnology, biotechnology, information technology, and cognitive science. The tensions, contradictions, paradoxes, and confusions Dupuy discerns in cybernetics offer a cautionary tale for future developments in cognitive science. (shrink)

Roughly speaking, computationalism says that cognition is computation, or that cognitive phenomena are explained by the agent‘s computations. The cognitive processes and behavior of agents are the explanandum. The computations performed by the agents‘ cognitive systems are the proposed explanans. Since the cognitive systems of biological organisms are their nervous 1 systems (plus or minus a bit), we may say that according to computationalism, the cognitive processes and behavior of organisms are explained by neural computations. Some people might prefer to (...) say that cognitive systems are ―realized‖ by nervous systems, and thus that—according to computationalism—cognitive computations are ―realized‖ by neural processes. In this paper, nothing hinges on the nature of the relation between cognitive systems and nervous systems, or between computations and neural processes. For present purposes, if a neural process realizes a computation, then that neural process is a computation. Thus, I will couch much of my discussion in terms of nervous systems and neural computation.1 Before proceeding, we should dispense with a possible red herring. Contrary to a common assumption, computationalism does not stand in opposition to connectionism. Connectionism, in the most general and common sense of the term, is the claim that cognitive phenomena are explained (at some level and at least in part) by the processes of neural networks. This is a truism, supported by most neuroscientific evidence. Everybody ought to be a connectionist in this general sense. The relevant question is, are neural processes computations? More precisely, are the neural processes to be found in the nervous systems of organisms computations? Computationalists say ―yes‖, anti-computationalists say ―no‖. This paper investigates whether any of the arguments on offer against computationalism have a chance at knocking it off.2 Ever since Warren McCulloch and Walter Pitts (1943) first proposed it, computationalism has been subjected to a wide range of objections.. (shrink)

A friend, correspondent and intellectual successor to David Ricardo, John Ramsay McCulloch forged his reputation in the emerging field of political economy by publishing deeply researched articles in Scottish periodicals and the Encyclopaedia Britannica. From 1828 he spent nearly a decade as professor of political economy at the newly founded University of London, thereafter becoming comptroller of the Stationery Office. Perhaps the first professional economist, McCulloch had become internationally renowned by the middle of the century, recognised for sharing (...) his ideas through lucid lecturing and writing. The present reference work, first published in 1832 and later revised, expanded and updated multiple times, made McCulloch considerable sums of money. His critical and analytical treatment of the data he had largely compiled himself made this much more than a mere book of facts. Several other works written or edited by McCulloch are also reissued in the Cambridge Library Collection. (shrink)

Examines Bergson's work from the perspectives of critical philosophy of race and decolonial theory, placing it in conversation with theorists from Africa, the African Diaspora, and Latin America.

Feminists today are re-imagining nature, biology, and matter in feminist thought and critically addressing new developments in biology, physics, neuroscience, epigenetics and other scientific disciplines. Mattering, edited by noted feminist scholar Victoria Pitts-Taylor, presents contemporary feminist perspectives on the materialist or ‘naturalizing’ turn in feminist theory, and also represents the newest wave of feminist engagement with science. The volume addresses the relationship between human corporeality and subjectivity, questions and redefines the boundaries of human/non-human and nature/culture, elaborates on the entanglements (...) of matter, knowledge, and practice, and addresses biological materialization as a complex and open process. This volume insists that feminist theory can take matter and biology seriously while also accounting for power, taking materialism as a point of departure to rethink key feminist issues. The contributors, an international group of feminist theorists, scientists and scholars, apply concepts in contemporary materialist feminism to examine an array of topics in science, biotechnology, biopolitics, and bioethics. These include neuralplasticity and the brain-machine interface; the use of biometrical identification technologies for transnational border control; epigenetics and the intergenerational transmission of the health effects of social stigma; ADHD and neuropharmacology; and randomized controlled trials of HIV drugs.A unique and interdisciplinary collection, Mattering presents in grounded, concrete terms the need for rethinking disciplinary boundaries and research methodologies in light of the shifts in feminist theorizing and transformations in the sciences. (shrink)

This article analyses Constant's largest work - De la Religion - in an attempt to clarify the ethical foundations of his political thought. The book presents his most fully developed ideas on history and society. A number of themes are discussed: Constant's theism; his belief in the growing authenticity of religious belief as a driving force in human history; the important role played by Rousseau's thought in his understanding of liberty. A study of De la Religion reveals that his enthusiasm (...) for commercial society was in no sense that of a simple individualist. (shrink)

A dramatic shift in British and French ideas about empire unfolded in the sixty years straddling the turn of the nineteenth century. As Jennifer Pitts shows in A Turn to Empire, Adam Smith, Edmund Burke, and Jeremy Bentham were among many at the start of this period to criticize European empires as unjust as well as politically and economically disastrous for the conquering nations. By the mid-nineteenth century, however, the most prominent British and French liberal thinkers, including John Stuart (...) Mill and Alexis de Tocqueville, vigorously supported the conquest of non-European peoples. Pitts explains that this reflected a rise in civilizational self-confidence, as theories of human progress became more triumphalist, less nuanced, and less tolerant of cultural difference. At the same time, imperial expansion abroad came to be seen as a political project that might assist the emergence of stable liberal democracies within Europe. Pitts shows that liberal thinkers usually celebrated for respecting not only human equality and liberty but also pluralism supported an inegalitarian and decidedly nonhumanitarian international politics. Yet such moments represent not a necessary feature of liberal thought but a striking departure from views shared by precisely those late-eighteenth-century thinkers whom Mill and Tocqueville saw as their forebears. Fluently written, A Turn to Empire offers a novel assessment of modern political thought and international justice, and an illuminating perspective on continuing debates over empire, intervention, and liberal political commitments. (shrink)

Since Leibniz's time, Cartesian mental causation has been criticized for violating the conservation of energy and momentum. Many dualist responses clearly fail. But conservation laws have important neglected features generally undermining the objection. Conservation is _local_, holding first not for the universe, but for everywhere separately. The energy in any volume changes only due to what flows through the boundaries. Constant total energy holds if the global summing-up of local conservation laws converges; it probably doesn't in reality. Energy conservation holds (...) if there is symmetry, the sameness of the laws over time. Thus, if there are time-places where symmetries fail due to nonphysical influence, conservation laws fail there and then, while holding elsewhere, such as refrigerators and stars. Noether's converse first theorem shows that conservation laws imply symmetries. Thus conservation trivially nearly entails the causal closure of the physical. But expecting conservation to hold in the brain simply assumes the falsehood of Cartesianism. Hence Leibniz's objection begs the question. Empirical neuroscience is another matter. So is Einstein's General Relativity: far from providing a loophole, General Relativity makes mental causation _harder_. (shrink)

Change and local spatial variation are missing in Hamiltonian general relativity according to the most common definition of observables as having 0 Poisson bracket with all first-class constraints. But other definitions of observables have been proposed. In pursuit of Hamiltonian–Lagrangian equivalence, Pons, Salisbury and Sundermeyer use the Anderson–Bergmann–Castellani gauge generator G, a tuned sum of first-class constraints. Kuchař waived the 0 Poisson bracket condition for the Hamiltonian constraint to achieve changing observables. A systematic combination of the two reforms might use (...) the gauge generator but permit non-zero Lie derivative Poisson brackets for the external gauge symmetry of General Relativity. Fortunately one can test definitions of observables by calculation using two formulations of a theory, one without gauge freedom and one with gauge freedom. The formulations, being empirically equivalent, must have equivalent observables. For de Broglie-Proca non-gauge massive electromagnetism, all constraints are second-class, so everything is observable. Demanding equivalent observables from gauge Stueckelberg–Utiyama electromagnetism, one finds that the usual definition fails while the Pons–Salisbury–Sundermeyer definition with G succeeds. This definition does not readily yield change in GR, however. Should GR’s external gauge freedom of general relativity share with internal gauge symmetries the 0 Poisson bracket, or is covariance sufficient? A graviton mass breaks the gauge symmetry, but it can be restored by parametrization with clock fields. By requiring equivalent observables, one can test whether observables should have 0 or the Lie derivative as the Poisson bracket with the gauge generator G. The latter definition is vindicated by calculation. While this conclusion has been reported previously, here the calculation is given in some detail. (shrink)

A friend, correspondent and intellectual successor to David Ricardo, John Ramsay McCulloch forged his reputation in the emerging field of political economy by publishing deeply researched articles in Scottish periodicals and the Encyclopaedia Britannica. From 1828 he spent nearly a decade as professor of political economy at the newly founded University of London, thereafter becoming comptroller of the Stationery Office. Perhaps the first professional economist, McCulloch had become internationally renowned by the middle of the century, recognised for sharing (...) his ideas through lucid lecturing and writing. First published in 1825, this textbook was an expanded version of an article originally written in 1822 for the Encyclopaedia Britannica. Reissued here is the 1830 enlarged second edition. In Britain and America the work reached many students, and was translated into multiple European languages. Several other works written or edited by McCulloch are also reissued in the Cambridge Library Collection. (shrink)

According to Brentano in a much-quoted passage,Every psychological phenomenon is characterized by…intentional inherent existence of … an object… In the idea something is conceived, in the judgement something is recognized or discovered, in loving loved, in hating hated, in desiring desired, and so on.

James L. Anderson analyzed the novelty of Einstein's theory of gravity as its lack of "absolute objects." Michael Friedman's related work has been criticized by Roger Jones and Robert Geroch for implausibly admitting as absolute the timelike 4-velocity field of dust in cosmological models in Einstein's theory. Using the Rosen-Sorkin Lagrange multiplier trick, I complete Anna Maidens's argument that the problem is not solved by prohibiting variation of absolute objects in an action principle. Recalling Anderson's proscription of "irrelevant" variables, I (...) generalize that proscription to locally irrelevant variables that do no work in some places in some models. This move vindicates Friedman's intuitions and removes the Jones-Geroch counterexample: some regions of some models of gravity with dust are dust-free and so naturally lack a timelike 4-velocity, so diffeomorphic equivalence to is spoiled. Torretti's example involving constant curvature spaces is shown to have an absolute object on Anderson's analysis, viz., the conformal spatial metric density. The previously neglected threat of an absolute object from an orthonormal tetrad used for coupling spinors to gravity appears resolvable by eliminating irrelevant fields. However, given Anderson's definition, GTR itself has an absolute object : a change of variables to a conformal metric density and a scalar density shows that the latter is absolute. (shrink)

Bipartism is the common view that the nature of an intentional state can be wholly explained in terms of (a) its horizontal relations with other such states (as well as peripheral inputs and outputs); and (b) its vertical relations with the world. Extrapolating from Nagel, I try to show that bipartism is fundamentally mistaken. Some intentional states are conscious states, and thus there is something it is like to be in them. This phenomenology is of a piece with such states’ (...) interpretability: to know what it is like to be X at least involves being able to interpret X’s conscious intentional states. But a bi‐partist account of an intentional state is not, by itself, interpretational. So bipartist accounts, at least of conscious intentional states, are incomplete: they fail to capture their phenomenology. (shrink)

Reflective equilibrium between physics and philosophy, and between GR and particle physics, is fruitful and rational. I consider the virtues of simplicity, conservatism, and conceptual coherence, along with perturbative expansions. There are too many theories to consider. Simplicity supplies initial guidance, after which evidence increasingly dominates. One should start with scalar gravity; evidence required spin 2. Good beliefs are scarce, so don't change without reason. But does conservatism prevent conceptual innovation? No: considering all serious possibilities could lead to Einstein's equations. (...) GR is surprisingly intelligible. Energy localization makes sense if one believes Noether mathematics: an infinity of symmetries shouldn't produce just one energy. Hamiltonian change results from Lagrangian-equivalence. Causality poses conceptual questions. For GR, what are canonical 'equal-time' commutators? For massive spin 2, background causality exists but is violated. Both might be cured by engineering a background null cone respected by a gauge groupoid. Perturbative expansions can enlighten. They diagnose Einstein's 1917 'mass'-Lambda analogy. Ogievetsky-Polubarinov invented an infinity of massive spin 2 gravities---including ghost-free de Rham-Gabadadze-Tolley theories!---perturbatively, and achieved the impossible : spinors in coordinates. (shrink)

It is a commonplace in the philosophy of physics that any local physical theory can be represented using arbitrary coordinates, simply by using tensor calculus. On the other hand, the physics literature often claims that spinors \emph{as such} cannot be represented in coordinates in a curved space-time. These commonplaces are inconsistent. What general covariance means for theories with fermions, such as electrons, is thus unclear. In fact both commonplaces are wrong. Though it is not widely known, Ogievetsky and Polubarinov constructed (...) spinors in coordinates in 1965, enhancing the unity of physics and helping to spawn particle physicists' concept of nonlinear group representations. Roughly and locally, these spinors resemble the orthonormal basis or "tetrad" formalism in the symmetric gauge, but they are conceptually self-sufficient and more economical. The typical tetrad formalism is de-Ockhamized, with six extra field components and six compensating gauge symmetries to cancel them out. The Ogievetsky-Polubarinov formalism, by contrast, is Ockhamized, with most of the fluff removed. As developed nonperturbatively by Bilyalov, it admits any coordinates at a point, but "time" must be listed first. Here "time" is defined in terms of an eigenvalue problem involving the metric components and the matrix $diag$, the product of which must have no negative eigenvalues in order to yield a real symmetric square root that is a function of the metric. Thus even formal general covariance requires reconsideration; the atlas of admissible coordinate charts should be sensitive to the types and \emph{values} of the fields involved. Apart from coordinate order and the usual spinorial two-valuedness, Ogievetsky-Polubarinov spinors form, with the metric, a nonlinear geometric object, for which important results on Lie and covariant differentiation are recalled. Such spinors avoid a spurious absolute object in the Anderson-Friedman analysis of substantive general covariance. They also permit the gauge-invariant localization of the infinite-component gravitational energy in General Relativity. Density-weighted spinors exploit the conformal invariance of the massless Dirac equation to show that the volume element is absent. Thus instead of an arbitrary nonsingular matrix with 16 components, 6 of which are gauged away by a new local $O$ gauge group and one of which is irrelevant due to conformal covariance, one can, and presumably should, use density-weighted Ogievetsky-Polubarinov spinors coupled to the 9-component symmetric square root of the part of the metric that fixes null cones. Thus $\frac{7}{16}$ of the orthonormal basis is eliminated as surplus structure. Greater unity between spinors and tensors and the like is achieved, such as regarding conservation laws. Regarding the conventionality of simultaneity, an unusually wide range of $\epsilon$ values is admissible, but some extreme values are inadmissible. Standard simultaneity uniquely makes the spinor transformation law linear and independent of the metric, because transformations among the standard Cartesian coordinate systems fall within the conformal group, for which the spinor transformation law is linear. The surprising mildness of the restrictions on coordinate order as applied to the Schwarzschild solution is exhibited. (shrink)

Conceptual atomists argue that most of our concepts are primitive. I take up three arguments that have been thought to support atomism and show that they are inconclusive. The evidence that allegedly backs atomism is equally compatible with a localist position on which concepts are structured representations with complex semantic content. I lay out such a localist position and argue that the appropriate position for a non-atomist to adopt is a pluralist view of conceptual structure. I show several ways in (...) which conceptual pluralism provides an advantage in satisfying the empirical and philosophical demands on a theory of conceptual structure and content. (shrink)

The conservation of energy and momentum have been viewed as undermining Cartesian mental causation since the 1690s. Modern discussions of the topic tend to use mid-nineteenth century physics, neglecting both locality and Noether’s theorem and its converse. The relevance of General Relativity has rarely been considered. But a few authors have proposed that the non-localizability of gravitational energy and consequent lack of physically meaningful local conservation laws answers the conservation objection to mental causation: conservation already fails in GR, so there (...) is nothing for minds to violate. This paper is motivated by two ideas. First, one might take seriously the fact that GR formally has an infinity of rigid symmetries of the action and hence, by Noether’s first theorem, an infinity of conserved energies-momenta. Second, Sean Carroll has asked how one should modify the Dirac–Maxwell–Einstein equations to describe mental causation. This paper uses the generalized Bianchi identities to show that General Relativity tends to exclude, not facilitate, such Cartesian mental causation. In the simplest case, Cartesian mental influence must be spatio-temporally constant, and hence 0. The difficulty may diminish for more complicated models. Its persuasiveness is also affected by larger world-view considerations. The new general relativistic objection provides some support for realism about gravitational energy-momentum in GR. Such realism also might help to answer an objection to theories of causation involving conserved quantities, because energies-momenta would be conserved even in GR. (shrink)

A thematic priority of the European Union’s Framework V research and development programme was the creation of a user-friendly information society which met the needs of citizens and enterprises. In practice, though, for example in the case of on-line digital music, the needs of citizens and enterprises may be in conflict. This paper proposes to leverage the appearance of ‘intelligence’ in the platform layer of a layered communications architecture to avoid such conflicts in similar applications in the future. The key (...) idea is that if the intelligence is encapsulated in an agent, then the agents should be organized as a society, and then the rules of the society can be used to ensure ‘responsible’ behaviour. We discuss how an agent society can be used to regulate behaviour in future information trading scenarios, and conclude that this approach offers a ‘third way’ which can satisfy the (reasonable) needs of both citizens and enterprises in the user-friendly information society. (shrink)

Let $\Omega $ be a complex lattice which does not have complex multiplication and $\wp =\wp _\Omega $ the Weierstrass $\wp $ -function associated with it. Let $D\subseteq \mathbb {C}$ be a disc and $I\subseteq \mathbb {R}$ be a bounded closed interval such that $I\cap \Omega =\varnothing $. Let $f:D\rightarrow \mathbb {C}$ be a function definable in $(\overline {\mathbb {R}},\wp |_I)$. We show that if f is holomorphic on D then f is definable in $\overline {\mathbb {R}}$. The proof of (...) this result is an adaptation of the proof of Bianconi for the $\mathbb {R}_{\exp }$ case. We also give a characterization of lattices with complex multiplication in terms of definability and a nondefinability result for the modular j-function using similar methods. (shrink)

The questions of what represents space-time in GR, the status of gravitational energy, the substantivalist-relationalist issue, and the exceptional status of gravity are interrelated. If space-time has energy-momentum, then space-time is substantival. Two extant ways to avoid the substantivalist conclusion deny that the energy-bearing metric is part of space-time or deny that gravitational energy exists. Feynman linked doubts about gravitational energy to GR-exceptionalism, as do Curiel and Duerr; particle physics egalitarianism encourages realism about gravitational energy. In that spirit, this essay (...) proposes a third possible view about space-time, one involving a particle physics-inspired non-perturbative split that characterizes space-time with a constant background _matrix_, a sort of vacuum value, thus avoiding the inference from gravitational _energy to substantivalism. On this proposal, space-time is, where eta=diag is a spatio-temporally constant numerical signature matrix, a matrix already used in GR with spinors. The gravitational potential, to which any gravitational energy can be ascribed, is g_{\mu\nu}- eta, an _affine_ geometric object with a tensorial Lie derivative and a vanishing covariant derivative. This non-perturbative split permits strong fields, arbitrary coordinates, and arbitrary topology, and hence is pure GR by almost any standard. This razor-thin background, unlike more familiar backgrounds, involves no extra gauge freedom and so lacks their obscurities and carpet lump-moving. After a discussion of Curiel's GR exceptionalist denial of the localizability of gravitational energy and his rejection of energy conservation, the two traditional objections to pseudotensors, coordinate dependence and nonuniqueness, are explored. Both objections are inconclusive and getting weaker. A literal interpretation involving infinitely many energies corresponding by Noether's first theorem to the infinite symmetries of the _action_ largely answers Schroedinger's false-negative coordinate dependence problem. Bauer's false-positive objection has multiple answers. Non-uniqueness might be handled by Nester et al.'s finding physical meaning in multiplicity in relation to boundary conditions, by an optimal candidate, or by Bergmann's identifying the non-uniqueness and coordinate dependence ambiguities as one. (shrink)

This note gives a new proof of the 'operational extensionality' property of Abramsky's lazy lambda calculus-namely the coincidence of contextual equivalence with a co-inductively defined notion of 'applicative bisimilarity'. This purely syntactic results is here proved using a logical relation between the syntax and its denotational semantics. The proof exploits a mixed inductive/coinductive characterisation of the logical relation recently discovered by the author.