Maxwell et al. [Maxwell, J. P., Masters, R. S. W., Kerr, E., & Weedon, E. . The implicit benefit of learning without errors. The Quarterly Journal of Experimental Psychology, 54A, 1049–1068. The implicit benefit of learning without errors. The Quarterly Journal of Experimental Psychology, 54A, 1049–1068] suggested that, following unsuccessful movements, the learner forms hypotheses about the probable causes of the error and the required movement adjustments necessary for its elimination. Hypothesis testing is an explicit process that places demands (...) on cognitive resources. Demands on cognitive resources can be identified by measuring probe reaction times and movement times. Lengthened PRT and movement times reflects increased cognitive demands. Thus, PRT and movement times should be longer following errors, relative to successful, movements. This hypothesis was tested using a motor skill . Furthermore, the association between error processing and the preparation and execution phases of movement was examined. The data confirmed that cognitive demand is greater for trials following an error, relative to trials without an error. This effect was apparent throughout learning and in both the preparatory and execution phases of the movement. Cognitive effort also appeared to be higher during movement preparation, relative to movement execution. (shrink)

Dijkerman & de Haan (D&dH) propose a somatosensory perceptual pathway that informs a consciously accessible body image, and an action pathway that provides information to a body schema, which is not consciously accessible. We argue that the body schema may become accessible to consciousness in some circumstances, possibly resulting from cross talk, but that this may be detrimental to skilled movement production.

Implicit processes almost certainly preceded explicit processes in our evolutionary history, so they are likely to be more resistant to disruption according to the principles of evolutionary biology [Reber, A. S. . The cognitive unconscious: An evolutionary perspective. Consciousness and Cognition, 1, 93–133.]. Previous work . Knowledge, nerves and know-how: The role of explicit versus implicit knowledge in the breakdown of a complex motor skill under pressure. British Journal of Psychology, 83, 343–358.]) has shown that implicitly learned motor skills remain (...) stable under psychological pressure and concurrent cognitive demands, and recently [Poolton, J. M., Masters, R. S. W., & Maxwell, J. P. . Passing thoughts on the evolutionary stability of implicit motor behaviour: Performance retention under physiological fatigue. Consciousness and Cognition, 16, 456–468.] showed that they also remain stable under conditions of anaerobic fatigue that would have significantly challenged the survival skills of our ancestors. Here we examine the stability of an implicitly learned motor skill under fatigue conditions that primarily tax a different physiological system , but which have equally strong evolutionary connotations. Participants acquired a throwing task by means of an errorless learning method or an errorful method. Motor performance in the errorless condition, but not the errorful condition, remained stable following an exhaustive VO2 max. running test. Our findings replicate and extend the work of Poolton et al., providing further support for Reber’s evolutionary distinction between implicit and explicit processes. (shrink)

Participants struck 500 golf balls to a concealed target. Outcome feedback was presented at the subjective or objective threshold of awareness of each participant or at a supraliminal threshold. Participants who received fully perceptible feedback learned to strike the ball onto the target, as did participants who received feedback that was only marginally perceptible . Participants who received feedback that was not perceptible showed no learning. Upon transfer to a condition in which the target was unconcealed, performance increased in both (...) the subjective and the objective threshold condition, but decreased in the supraliminal condition. In all three conditions, participants reported minimal declarative knowledge of their movements, suggesting that deliberate hypothesis testing about how best to move in order to perform the motor task successfully was disrupted by the impoverished disposition of the visual outcome feedback. It was concluded that sub-optimally perceptible visual feedback evokes implicit processes. (shrink)

In El Salvador from 1978 to 1988, contraceptive use among married women 15–44 years of age increased from 34% to 47%, and the total fertility rate declined from 6·3 to 4·6 children per woman. Most of this change took place from 1978 to 1985. Sterilization is the most prevalent method used, but nearly one-half of the women who are sterilized did not use any contraception before their operation. Few young couples use reversible methods of contraception to space births or delay (...) the start of childbearing. On average, women wait 8 years after marriage and have nearly three children before they use contraception. (shrink)

Mario Bunge wrote his classic Causality and Modern Science more than 60 years ago, and a third revised edition was published by Dover in 1979. With its impressive scope and historical perspective it was a long way ahead of its time. But many of its insights still have not been sufficiently appreciated by physicists and philosophers alike. These include Bunge’s distinction between causation and other types of determination, his critique of the still-dominant Humean accounts of causality as leaving out the (...) productive aspect of determination, his critique of the conflation of determination with predictability, his insistence on the fictional character of isolated causal chains, and his demonstration that “causal connectability” depends only on the principle of retarded action, not causation. It will be argued that there is a degree of agreement between his views on determinism and causality and those of Leibniz, and a comparison between the two thinkers’ views is used to throw further light on these matters. (shrink)

This treatise presents thoughts on the divide that exists in chemistry between those who seek their understanding within a universe wherein the laws of physics apply and those who prefer alternative universes wherein the laws are suspended or ‘bent’ to suit preconceived ideas. The former approach is embodied in the quantum theory of atoms in molecules (QTAIM), a theory based upon the properties of a system’s observable distribution of charge. Science is experimental observation followed by appeal to theory that, upon (...) occasion, leads to new experiments. This is the path that led to the development of the molecular structure hypothesis—that a molecule is a collection atoms with characteristic properties linked by a network of bonds that impart a structure—a concept forged in the crucible of nineteenth century experimental chemistry. One hundred and fifty years of experimental chemistry underlie the realization that the properties of some total system are the sum of its atomic contributions. The concept of a functional group, consisting of a single atom or a linked set of atoms, with characteristic additive properties forms the cornerstone of chemical thinking of both molecules and crystals and Dalton’s atomic hypothesis has emerged as the operational theory of chemistry. We recognize the presence of a functional group in a given system and predict its effect upon the static, reactive and spectroscopic properties of the system in terms of the characteristic properties assigned to that group. QTAM gives physical substance to the concept of a functional group. (shrink)

Darwinian Evolution and Classical Liberalism brings together a collection of new essays that examine the multifaceted ferment between Darwinian biology and classical liberalism.

This paper consists in a study of Leibniz’s argument for the infinite plurality of substances, versions of which recur throughout his mature corpus. It goes roughly as follows: since every body is actually divided into further bodies, it is therefore not a unity but an infinite aggregate; the reality of an aggregate, however, reduces to the reality of the unities it presupposes; the reality of body, therefore, entails an actual infinity of constituent unities everywhere in it. I argue that this (...) depends on a generalized notion of aggregation, according to which a thing may be an aggregate of its constituents if every one of its actual parts presupposes such constituents, but is not composed from them. One of the premises of this argument is the reality of bodies. If this premise is denied, Leibniz’s argument for the infinitude of substances, and even of their plurality, cannot go through. (shrink)

Three experiments explore the role of working memory in motor skill acquisition and performance. Traditional theories postulate that skill acquisition proceeds through stages of knowing, which are initially declarative but later procedural. The reported experiments challenge that view and support an independent, parallel processing model, which predicts that procedural and declarative knowledge can be acquired separately and that the former does not depend on the availability of working memory, whereas, the latter does. The behaviour of these two processes was manipulated (...) by providing or withholding visual (and auditory) appraisal of outcome feedback. Withholding feedback was predicted to inhibit the use of working memory to appraise success and, thus, prevent the formation of declarative knowledge without affecting the accumulation of procedural knowledge. While the first experiment failed to support these predictions, the second and third experiments demonstrated that procedural and declarative knowledge can be acquired independently. It is suggested that the availability of working memory is crucial to motor performance only when the learner has come to rely on its use. (shrink)

This book is a collection of secondary essays on America's most important philosophic thinkers—statesmen, judges, writers, educators, and activists—from the colonial period to the present. Each essay is a comprehensive introduction to the thought of a noted American on the fundamental meaning of the American regime.

In contrast with some recent theories of infinitesimals as non-Archimedean entities, Leibniz’s mature interpretation was fully in accord with the Archimedean Axiom: infinitesimals are fictions, whose treatment as entities incomparably smaller than finite quantities is justifiable wholly in terms of variable finite quantities that can be taken as small as desired, i.e. syncategorematically. In this paper I explain this syncategorematic interpretation, and how Leibniz used it to justify the calculus. I then compare it with the approach of Smooth Infinitesimal Analysis, (...) as propounded by John Bell. I find some salient differences, especially with regard to higher-order infinitesimals. I illustrate these differences by a consideration of how each approach might be applied to propositions of Newton’s Principia concerning the derivation of force laws for bodies orbiting in a circle and an ellipse. “If the Leibnizian calculus needs a rehabilitation because of too severe treatment by historians in the past half century, as Robinson suggests (1966, 250), I feel that the legitimate grounds for such a rehabilitation are to be found in the Leibnizian theory itself.”—(Bos 1974–1975, 82–83). (shrink)

Recovering Reason: Essays in Honor of Thomas L. Pangle is a collection of essays composed by students and friends of Thomas L. Pangle to honor his seminal work and outstanding guidance in the study of political philosophy. These essays examine both Socrates' and modern political philosophers' attempts to answer the question of the right life for human beings, as those attempts are introduced and elaborated in the work of thinkers from Homer and Thucydides to Nietzsche and Charles Taylor.

It is well known that Leibniz advocated the actual infinite, but that he did not admit infinite collections or infinite numbers. But his assimilation of this account to the scholastic notion of the syncategorematic infinite has given rise to controversy. A common interpretation is that in mathematics Leibniz’s syncategorematic infinite is identical with the Aristotelian potential infinite, so that it applies only to ideal entities, and is therefore distinct from the actual infinite that applies to the actual world. Against this, (...) I argue in this paper that Leibniz’s actual infinite, understood syncategorematically, applies to any entities that are actually infinite in multitude, whether numbers, actual parts of matter, or monads. It signifies that there are more of them than can be assigned a number, but that there is no infinite number or collection of them, which notion involves a contradiction. Similarly, to say that a magnitude is actually infinitely small in the syncategorematic sense is to say that no matter how small a magnitude one takes, there is a smaller, but there are no actual infinitesimals. In geometry one may calculate with expressions apparently denoting such entities, on the understanding that they are fictions, standing for variable magnitudes that can be made arbitrarily small, so as to produce demonstrations that there is no error in the resulting expressions. (shrink)

In the transition to Einstein’s theory of Special Relativity (SR), certain concepts that had previously been thought to be univocal or absolute properties of systems turn out not to be. For instance, mass bifurcates into (i) the relativistically invariant proper mass m0, and (ii) the mass relative to an inertial frame in which it is moving at a speed v = βc, its relative mass m, whose quantity is a factor γ = (1 – β2) -1/2 times the proper mass, (...) m = γm0. (shrink)

In this paper I offer a fresh interpretation of Leibniz’s theory of space, in which I explain the connection of his relational theory to both his mathematical theory of analysis situs and his theory of substance. I argue that the elements of his mature theory are not bare bodies (as on a standard relationalist view) nor bare points (as on an absolutist view), but situations. Regarded as an accident of an individual body, a situation is the complex of its angles (...) and distances to other co-existing bodies, founded in the representation or state of the substance or substances contained in the body. The complex of all such mutually compatible situations of co-existing bodies constitutes an order of situations, or instantaneous space. Because these relations of situation change from one instant to another, space is an accidental whole that is continuously changing and becoming something different, and therefore a phenomenon. As Leibniz explains to Clarke, it can be represented mathematically by supposing some set of existents hypothetically (and counterfactually) to remain in a fixed mutual relation of situation, and gauging all subsequent situations in terms of transformations with respect to this initial set. Space conceived in terms of such allowable transformations is the subject of Analysis Situs. Finally, insofar as space is conceived in abstraction from any bodies that might individuate the situations, it encompasses all possible relations of situation. This abstract space, the order of all possible situations, is an abstract entity, and therefore ideal. (shrink)

Before establishing his mature interpretation of infinitesimals as fictions, Gottfried Leibniz had advocated their existence as actually existing entities in the continuum. In this paper I trace the development of these early attempts, distinguishing three distinct phases in his interpretation of infinitesimals prior to his adopting a fictionalist interpretation: (i) (1669) the continuum consists of assignable points separated by unassignable gaps; (ii) (1670-71) the continuum is composed of an infinity of indivisible points, or parts smaller than any assignable, with no (...) gaps between them; (iii) (1672- 75) a continuous line is composed not of points but of infinitely many infinitesimal lines, each of which is divisible and proportional to a generating motion at an instant (conatus). In 1676, finally, Leibniz ceased to regard infinitesimals as actual, opting instead for an interpretation of them as fictitious entities which may be used as compendia loquendi to abbreviate mathematical reasonings. (shrink)

In this paper, we endeavour to give a historically accurate presentation of how Leibniz understood his infinitesimals, and how he justified their use. Some authors claim that when Leibniz called them “fictions” in response to the criticisms of the calculus by Rolle and others at the turn of the century, he had in mind a different meaning of “fiction” than in his earlier work, involving a commitment to their existence as non-Archimedean elements of the continuum. Against this, we show that (...) by 1676 Leibniz had already developed an interpretation from which he never wavered, according to which infinitesimals, like infinite wholes, cannot be regarded as existing because their concepts entail contradictions, even though they may be used as if they exist under certain specified conditions—a conception he later characterized as “syncategorematic”. Thus, one cannot infer the existence of infinitesimals from their successful use. By a detailed analysis of Leibniz’s arguments in his De quadratura of 1675–1676, we show that Leibniz had already presented there two strategies for presenting infinitesimalist methods, one in which one uses finite quantities that can be made as small as necessary in order for the error to be smaller than can be assigned, and thus zero; and another “direct” method in which the infinite and infinitely small are introduced by a fiction analogous to imaginary roots in algebra, and to points at infinity in projective geometry. We then show how in his mature papers the latter strategy, now articulated as based on the Law of Continuity, is presented to critics of the calculus as being equally constitutive for the foundations of algebra and geometry and also as being provably rigorous according to the accepted standards in keeping with the Archimedean axiom. (shrink)

Russell’s most important source for his book on Leibniz was C. I. Gerhardt’s seven-volume Die philosophischen Schriften von Gottfried Wilhelm Leibniz. Russell heavily annotated his copy of this important edition of Leibniz’s works. The present paper records all Russell’s marginalia, with the exception of passages marked merely by vertical lines in the margin, and provides explanatory commentary.

Heuristics of evolutionary biology dictate that phylogenetically older processes are inherently more stable and resilient to disruption than younger processes. On the grounds that non-declarative behaviour emerged long before declarative behaviour, Reber argues that implicit learning is supported by neural processes that are evolutionarily older than those supporting explicit learning. Reber suggested that implicit learning thus leads to performance that is more robust than explicit learning. Applying this evolutionary framework to motor performance, we examined whether implicit motor learning, relative to (...) explicit motor learning, conferred motor output that was resilient to physiological fatigue and durable over time. In Part One of the study a fatigued state was induced by a double Wingate Anaerobic test protocol. Fatigue had no affect on performance of participants in the implicit condition; whereas, performance of participants in the explicit condition deteriorated significantly. In Part Two of the study a convenience sample of participants was recalled following a one-year hiatus. In both the implicit and the explicit condition retention of performance was seen and, contrary to the findings in Part One, so was resilience to fatigue. The resilient performance in the explicit condition after one year may have resulted from forgetting or from consolidation of declarative knowledge as implicit memories. In either case, implicit processes were left to more effectively support motor performance. (shrink)

In preparation for his lectures on Leibniz delivered in Cambridge in Lent Term 1899, Russell started in the summer of 1898 to keep notes on writings by and about Leibniz in a large notebook of the type he commonly used for notetaking at this time. This article prints, with annotation, all the material on Leibniz in that notebook.

Following the lead of Hans Reichenbach in the early twentieth century, many authors have attributed a causal theory of time to Leibniz. My exposition of Leibniz’s theory of time in a paper of 1985 has been interpreted as a version of such a causal theory, even though I was critical of the idea that Leibniz would have tried to reduce relations among monadic states to causal relations holding only among phenomena. Since that time previously unpublished texts by Leibniz have become (...) available in which he himself explains temporal precedence in terms of causal precedence, and these texts have been given careful scrutiny by other scholars, such as Jan Cover, Stefano Di Bella and Michael Futch. In this paper I respond to their analyses, and try to make precise the way in which Leibniz’s views on time and on causality fit together in his metaphysics. (shrink)

In this paper I try to sort out a tangle of issues regarding time, inertia, proper time and the so-called “clock hypothesis” raised by Harvey Brown's discussion of them in his recent book, Physical Relativity. I attempt to clarify the connection between time and inertia, as well as the deficiencies in Newton's “derivation” of Corollary 5, by giving a group theoretic treatment original with J.-P. Provost. This shows how both the Galilei and Lorentz transformations may be derived from the relativity (...) principle on the basis of certain elementary assumptions regarding time. I then reflect on the implications of this derivation for understanding proper time and the clock hypothesis. (shrink)

We consider evidence for ritualized behavior in the sporting domain, noting that such behavior appears commonplace both before a competitive encounter and as part of pre-performance routines. The specific times when ritualized behaviors are displayed support the supposition that they provide temporary relief from pre-competition anxiety and act as thought suppressors in the moments preceding skill execution. (Published Online February 8 2007).

In this paper I attempt to throw new light on Leibniz's apparently conflicting remarks concerning the continuity of matter. He says that matter is "discrete" yet "actually divided to infinity" and (thus dense), and moreover that it fills (continuous) space. I defend Leibniz from the charge of inconsistency by examining the historical development of his views on continuity in their physical and mathematical context, and also by pointing up the striking similarities of his construal of continuity to the approach taken (...) by 20th century Combinatorial Topology. (shrink)

We sought to gain more insight into the effects of attention focus and time constraints on skill learning and performance in novices and experts by means of two complementary experiments using a table tennis paradigm. Experiment 1 showed that skill-focus conditions and slowed ball frequency disrupted the accuracy of experts, but dual-task conditions and speeded ball frequency did not. For novices, only speeded ball frequency disrupted accuracy. In Experiment 2, we extended these findings by instructing novices either explicitly or by (...) analogy . Explicitly instructed novices were less accurate in skill-focused and dual-task conditions than in single-task conditions. Following analogy instruction novices were less accurate in the skill-focused condition, but maintained accuracy under dual-task conditions. Participants in both conditions retained accuracy when ball frequency was slowed, but lost accuracy when ball frequency was speeded, suggesting that not attention, but motor dexterity, was inadequate under high temporal constraints. (shrink)

Descartes' allusions, in the Meditations and the Principles, to the individual moments of duration, has for some years stirred controversy over whether this commits him to a kind of time atomism. The origins of Descartes' way of treating moments as least intervals of duration can be traced back to his early collaboration with Isaac Beeckman. Where Beeckman (in 1618) conceived of moments as (mathematically divisible) physical indivisibles, corresponding to the durations of uniform motions between successive impacts on a body by (...) microscopic particles, Descartes was able to give a mathematical treatment of the problem of fall in which moments were rendered mathematical minima of motion that were necessarily devoid of extension. This achievement, coupled with his innovation of conceiving force as instantaneous tendency to motion, subsequently led him to disdain Beeckman's discretist physics with its extended indivisible moments. Nevertheless, he was not able to eradicate a fundamental tension in his philosophy between force as a quantity of motion, and force as an instantaneous tendency to motion. For by his principles, action, motion, quantity of motion, and indeed existence, all require some minimal interval of duration. This explains his need to refer to moments as least conceivable parts of duration, and this is what has given rise to the impression that he supposed duration to be composed of such parts, contrary to his commitment to continuous creation. (shrink)

G. E. Moore attended Russell’s lectures on Leibniz in 1899 and kept detailed notes which have been preserved among his papers. The present article prints his notes in their entirety with annotations.

Richard Arthur’s _Natural Deduction_ provides a wide-ranging introduction to logic. In lively and readable prose, Arthur presents a new approach to the study of logic, one that seeks to integrate methods of argument analysis developed in modern “informal logic” with natural deduction techniques. The dry bones of logic are given flesh by unusual attention to the history of the subject, from Pythagoras, the Stoics, and Indian Buddhist logic, through Lewis Carroll, Venn, and Boole, to Russell, Frege, and Monty Python.

G. E. Moore attended Russell’s lectures on Leibniz in 1899 and kept detailed notes which have been preserved among his papers. The present article prints his notes in their entirety with annotations.