Global properties of canonical derivability predicates in Peano Arithmetic) are studied here by means of a suitable propositional modal logic GL. A whole book [1] has appeared on GL and we refer to it for more information and a bibliography on GL. Here we propose a sequent calculus for GL and, by exhibiting a good proof procedure, prove that such calculus admits the elimination of cuts. Most of standard results on GL are then easy consequences: completeness, decidability, finite model property, (...) interpolation and the fixed point theorem. (shrink)

In the curve fitting problem two conflicting desiderata, simplicity and goodness-of-fit pull in opposite directions. To solve this problem, two proposals, the first one based on Bayes's theorem criterion (BTC) and the second one advocated by Forster and Sober based on Akaike's Information Criterion (AIC) are discussed. We show that AIC, which is frequentist in spirit, is logically equivalent to BTC, provided that a suitable choice of priors is made. We evaluate the charges against Bayesianism and contend that AIC (...) approach has shortcomings. We also discuss the relationship between Schwarz's Bayesian Information Criterion and BTC. (shrink)

In the curve fitting problem two conflicting desiderata, simplicity and goodness-of-fit, pull in opposite directions. To this problem, we propose a solution that strikes a balance between simplicity and goodness-of-fit. Using Bayes' theorem we argue that the notion of prior probability represents a measurement of simplicity of a theory, whereas the notion of likelihood represents the theory's goodness-of-fit. We justify the use of prior probability and show how to calculate the likelihood of a family of curves. We diagnose the (...) relationship between simplicity of a theory and its predictive accuracy. (shrink)

In the curve fitting problem two conflicting desiderata, simplicity and goodness-of-fit, pull in opposite directions. To this problem, we propose a solution that strikes a balance between simplicity and goodness-of-fit. Using Bayes' theorem we argue that the notion of prior probability represents a measurement of simplicity of a theory, whereas the notion of likelihood represents the theory's goodness-of-fit. We justify the use of prior probability and show how to calculate the likelihood of a family of curves. We diagnose the (...) relationship between simplicity of a theory and its predictive accuracy. (shrink)

In the curve fitting problem two conflicting desiderata, simplicity and goodness-of-fit, pull in opposite directions. To this problem, we propose a solution that strikes a balance between simplicity and goodness-of-fit. Using Bayes’ theorem we argue that the notion of prior probability represents a measurement of simplicity of a theory, whereas the notion of likelihood represents the theory’s goodness-of-fit. We justify the use of prior probability and show how to calculate the likelihood of a family of curves. We diagnose the (...) relationship between simplicity of a theory and its predictive accuracy. (shrink)

It is shown how mathematical discoveries such as De Moivre's theorem can result from patterns among the symbols of existing formulae and that significant mathematical analogies are often syntactic rather than semantic, for the good reason that mathematical proofs are always syntactic, in the sense of employing only formal operations on symbols. This radically extends the Lakatos approach to mathematical discovery by allowing proof-directed concepts to generate new theorems from scratch instead of just as evolutionary modifications to some existing (...) theorem. The emphasis upon syntax and proof permits discoveries to go beyond the limits of any prevailing semantics. It also helps explain the shortcomings of inductive AI systems of mathematics learning such as Lenat's AM, in which proof has played no part in the formation of concepts and conjectures. (shrink)

Roger Penrose's original and provocative ideas about the large-scale physics of the Universe, the small-scale world of quantum physics and the physics of the mind have been the subject of controversy and discussion. These ideas were set forth in his best-selling books The Emperor's New Mind and Shadows of the Mind. In this book, he summarises and brings up to date his current thinking in these complex areas. He presents a masterful summary of those areas of physics in which he (...) feels there are major unsolved problems. Through this, he introduces radically new concepts which he believes will be fruitful in understanding the workings of the brain and the nature of the human mind. These ideas are then challenged by three distinguished experts from different backgrounds - Abner Shimony and Nancy Cartwright as Philosophers of Science and Stephen Hawking as a Theoretical Physicist and Cosmologist. Finally, Roger Penrose responds to their thought-provoking criticisms. This volume provides an accessible, illuminating and stimulating introduction to Roger Penrose's vision of theoretical physics for the 21st Century. His enthusiasm, insight and good humour shine through this brilliant account of the problems of modern physics. (shrink)

This article examines not only how events are verbally reported in everyday and institutional storytelling episodes, but also how the actions witnessed are enacted by participants. This is particularly important to not only the believability of what occurred and is being discussed, but also how ordinary audience members react to stories and how they believe the truthfulness of them. As is seen in data analyzed from multiple sources, the way in which something is both reported and enacted has major implications (...) for not only the telling of stories, but what we know about the world around us. Questions about the idea of ‘direct reported actions’ are also considered. (shrink)

Many mathematicians have cited depth as an important value in their research. However, there is no single widely accepted account of mathematical depth. This article is an attempt to bridge this gap. The strategy is to begin with a discussion of Szemerédi's theorem, which says that each subset of the natural numbers that is sufficiently dense contains an arithmetical progression of arbitrary length. This theorem has been judged deep by many mathematicians, and so makes for a good case (...) on which to focus in analyzing mathematical depth. After introducing the theorem, four accounts of mathematical depth will be considered. (shrink)

Remarks on the Foundations of Mathematics, Wittgenstein, despite his official 'mathematical nonrevisionism', slips into attempting to refute Gödel's theorem. Actually, Wittgenstein could have used Gödel's theorem to good effect, to support his view that proof, and even truth, are 'family resemblance' concepts. The reason that Wittgenstein did not see all this is that Gödel's theorem had become an icon of mathematical realism, and he was blinded by his own ideology. The essay is a reply to Juliet Floyd's (...) work on Gödel: what she says Wittgenstein said, I say he should have said, but didn't (couldn't). (shrink)

It has been proposed that performance in the think – no think task represents a laboratory analogue of the voluntary form of memory repression. The central prediction of this repression hypothesis is that performance in the TNT task will be influenced by emotional characteristics of the material to be remembered. This prediction was tested in two experiments by asking participants to learn paired associates in which the first item was either emotionally positive or emotionally negative . The second word was (...) always emotionally neutral . Consistent with the repression hypothesis, significant memory suppression was observed in both experiments following ‘no think’ instructions for memories associated with emotionally negative material. No suppression was observed for memories associated with emotionally positive information. Implications of these findings for the relationship between performance in the TNT task and the controversial notion of memory repression are considered. (shrink)

In 1969, De Jongh proved the “maximality” of a fragment of intuitionistic predicate calculus forHA. Leivant strengthened the theorem in 1975, using proof-theoretical tools (normalisation of infinitary sequent calculi). By a refinement of De Jongh's original method (using Beth models instead of Kripke models and sheafs of partial combinatory algebras), a semantical proof is given of a result that is almost as good as Leivant's. Furthermore, it is shown thatHA can be extended to Higher Order Heyting Arithmetic+all trueΠ 2 (...) 0 -sentences + transfinite induction over primitive recursive well-orderings. As a corollary of the proof, maximality of intuitionistic predicate calculus is established wrt. an abstract realisability notion defined over a suitable expansion ofHA. (shrink)

From the concrete experience of war, Michael S. Yandell constructs a phenomenology of “negative revelation” in which false or distorted claims of goodness and justice disintegrate and become meaningless, adding depth to the term moral injury.

Elliott Sober''s selection for/selection of distinction has been widely used to clarify the idea that some properties of organisms are side-effects of selection processes. It has also been used, however, to choose between different descriptions of an evolutionary product when assigning biological functions to that product. We suggest that there is a characteristic error in these uses of the distinction. Complementary descriptions of function are misrepresented as mutually excluding one another. This error arises from a failure to appreciate that selection (...) processes can be described at several different theoretical levels. (shrink)

In arguing that Nietzsche's _Thus Spoke Zarathustra_ is a philosophical explanation of the possibility of modernism—that is, of the possibility of radical cultural change through the creation of new values—the author shows that literary fiction can do the work of philosophy. Nietzsche takes up the problem of modernism by inventing Zarathustra, a self-styled cultural innovator who aspires to subvert the culture of modernity by creating new values. By showing how Zarathustra can become a creator of new values, notwithstanding the forces (...) that hinder his will to innovate, Nietzsche answers the skeptic who proclaims that new-values creation is impossible. _Zarathustra_ is a story of repeated clashes between Zarathustra's avant-garde, modernist intentions and figures of doubt who condemn those intentions. Through a close reading of _Zarathustra_, the author reconstructs Nietzsche's explanation of the possibility of modernism. Showing how parody, irony, and plot organization frame that explanation, he also demonstrates the central significance of Zarathustra's speeches on the body and the will to power. The author argues that Nietzsche's critique of the modern philosophy of the subject revises Kant's concept of the dynamical sublime and makes allegorical use of the myth of Theseus, Ariadne, and Dionysus. He also proposes an original interpretation of the thought of eternal recurrence. Breaking with conventional Nietzsche scholarship, the author conceptualizes the thought not as a theoretical or a practical doctrine that Nietzsche endorses, but as a developing drama that Zarathustra performs. (shrink)

Contributors; Preface; Introduction; Part I. Instruments in Experiments: 1. Scientific instruments: models of brass and aids to discovery; 2. Glass works: Newton’s prisms and the uses of experiment; 3. A viol of water or a wedge of glass; Part II. Experiment and Argument: 4. Galileo’s experimental discourse; 5. Fresnel, Poisson and the white spot: the role of successful predictions in the acceptance of scientific theories; 6. The rhetoric of experiment; Part III. Representing and Realising: 7. ’Magnetic curves’ and the magnetic (...) field: experimentation and representation in the history of a theory; 8. Artificial clouds, real particles; 9. Living in the material world; 10. Justification and experimentation; Part IV. The Constituency of Experiment: 11. Extraordinary experiment: electricity and the creation of life in Victorian England; 12. Why did Britain join CERN?; Part V. Hallmarks of Experiment: 13. From Kwajalein to Armageddon? Testing and the social construction of missile accuracy; 14. The epistemology of experiment; Select bibliography; Name index; Subject index. (shrink)

1.1 In 1955, John Harsanyi proved a remarkable theorem:1 Suppose n agents satisfy the assumptions of von Neumann/Morgenstern (1947) expected utility theory, and so does the group as a whole (or an observer). Suppose that, if each member of the group prefers option a to b, then so does the group, or the observer (Pareto condition). Then the group’s utility function is a weighted sum of the individual utility functions. Despite Harsanyi’s insistence that what he calls the Utilitarian (...) class='Hi'>Theorem embeds utilitarianism into a theory of rationality, the theorem has fallen short of having the kind of impact on the discussion of utilitarianism for which Harsanyi hoped. Yet how could the theorem influence this discussion? Utilitarianism is as attractive to some as it is appalling to others. The prospects for this dispute to be affected by a theorem seem dim. Yet a closer look shows how the theorem could make a contribution. To fix ideas, I understand by utilitarianism the following claims: (1) Consequentialism: Actions are evaluated in terms of their consequences only. (2) Bayesianism: An agent's beliefs about possible outcomes are captured probabilistically. (3) Welfarism: The judgement of the relative goodness of states of affairs is based.. (shrink)

Many political theorists and philosophers use Condorcet's Jury Theorem to defend democracy. This paper illustrates an uncomfortable implication of Condorcet's Jury Theorem. Realistically, when the conditions of Condorcet’s Jury Theorem hold, even in very high stakes elections, having more than 100,000 citizens vote does no significant good in securing good political outcomes. On the Condorcet model, unless voters enjoy voting, or unless they produce some other value by voting, then the cost to most voters of voting exceeds (...) the expected epistemic benefits to the common good of their casting a vote. Anyone who is committed to democracy on the basis of the Jury Theorem ought also to hold that widespread voting is wasteful, at least unless she can provide some further justification of mass democratic participation. (shrink)

A hippocampal patient is described who shows preserved item recognition and simple recognition-based recollection but impaired recall and associative recognition. These data and other evidence suggest that contrary to Aggleton & Brown's target article, Papez circuit damage impairs only complex item-item-context recollection. A patient with perirhinal cortex damage and a delayed global memory deficit, apparently inconsistent with A&B's framework, is also described.

A layman's guide to the mechanics of Gödel's proof together with a lucid discussion of the issues which it raises. Includes an essay discussing the significance of Gödel's work in the light of Wittgenstein's criticisms.

This paper considers W.E.B. Du Bois’s short story, “Jesus Christ in Texas,” in the perspective of his analysis of the concept of beauty in Darkwater (1920); his exposition of the idea that “all art is propaganda” in “Criteria of Negro Art” (1926); and his moral psychology of white supremacy. On my account, Du Bois holds that beautiful art can help to undermine white supremacy by using representations of moral goodness to expand the white supremacist’s ethical horizons. To defend this thesis, (...) he relies on an image of “the cross and the lynching tree” to revise imagery that he draws from Albrecht Dürer’s 1504 painting, “The Adoration of Kings.”. (shrink)

: Faraday is often described as an experimentalist, but his work is a dialectical interplay of concrete objects, visual images, abstract, theoretically-informed visual models and metaphysical precepts. From phenomena described in terms of patterns formed by lines of force he created a general explanation of space-filling systems of force which obey both empirical laws and principles of conservation and economy. I argue that Faraday's articulation of situated experience via visual models into a theory capable of verbal expression owed much to (...) his strategy of moving—via conjectural visual models—between the phenomenology of particulars (often displayed as patterns) and the general features of dynamical phenomena which he depicted as structures. (shrink)

This study demonstrates that Dewey did not reject Hegelianism during the 1890s, as scholars maintain, but developed a humanistic/historicist reading that was indebted to an American Hegelian tradition. Scholars have misunderstood the "permanent Hegelian deposit" in Dewey's thought because they have not fully appreciated this American Hegelian tradition and have assumed that his Hegelianism was based primarily on British neo-Hegelianism. ;The study examines the American reception of Hegel in the nineteenth-century by intellectuals as diverse as James Marsh and Frederic Henry (...) Hedge and how it flowered in late nineteenth-century St. Louis. The St. Louis Hegelians read Hegel as a particularly practical and politically liberal philosopher whose social philosophy promoted both social diversity and unity. Led by W. T. Harris, they studied Hegel in German and published their own scholarship, as well as translations of German scholarship, in their Journal of Speculative Philosophy. Their efforts to make "Hegel talk English" and to base the St. Louis public schools on Hegel's philosophy of education won them national, and even, international attention. The St. Louis Hegelians sought to adapt Hegel's thought to their American context by assuaging elitist elements within it; Dewey's intellectual development was profoundly shaped by their appropriation of his philosophy. ;Dewey drew upon Hegel's argument that humans form societies because of their differences, not in spite of them. Hegel's rejection of the self-sufficient, atomistic individual entailed that the individual is dependent upon others for the satisfaction of material needs. Moreover, like Hegel, Dewey rejected the hedonistic basis of the British political tradition by arguing that humans seek recognition from their equals as well as satisfaction of material needs. Dewey believed Hegel's emphasis upon equality and diversity provided a model of society in which there was fertile ground for the individual to conceive and articulate cultural criticism. The study ends by comparing recent Hegel scholarship to Dewey's, demonstrating that American Hegelianism has returned, in important ways, to a Deweyan reading of Hegel. (shrink)

From 1882 to 1903, Dewey explicitly espoused a Hegelian philosophy. Until recently, scholars agreed that he broke from Hegel no later than 1903, but never adequately accounted for what he called the "permanent deposit" that Hegel left in his mature thought. I argue that Dewey never made a clean break from Hegel. Instead, he drew on the work of the St. Louis Hegelians to fashion a non-metaphysical reading of Hegel, similar to that championed by Klaus Hartmann and other Hegel scholars (...) since the 1970s. This reading of Hegel is remarkably consistent with Dewey's mature philosophy. Although Dewey abruptly repudiated Hegel during World War I, I contend this reflected the exigencies of war rather than philosophical concerns. (shrink)

SummaryFaraday's concept of force is described by six assumptions. These specify a concept that is quite distinct from ‘mechanical’ conceptions of his contemporaries and interpreters. Analysis of the role of these assumptions clarifies Faraday's weighting of experimental evidence and shows how closely-linked Faraday's chemistry and physics were to his theology. It is argued that Faraday was unable to secularize his concept of force by breaking the ties between his physics and his theology of nature. Examination of his basic assumptions also (...) explains Faraday's failure to quantify his principle of conservation of force, his rejection of mechanical concepts of force and energy, and his early attempt to develop a wave-model for the conversion and transmission of electricity, magnetism, light and heat. (shrink)

This paper attempts to define Exploratory Data Analysis (EDA) more precisely than usual, and to produce the beginnings of a philosophy of this topical and somewhat novel branch of statistics. A data set is, roughly speaking, a collection of k-tuples for some k. In both descriptive statistics and in EDA, these k-tuples, or functions of them, are represented in a manner matched to human and computer abilities with a view to finding patterns that are not "kinkera". A kinkus is a (...) pattern that has a negligible probability of being even partly potentially explicable. A potentially explicable pattern is one for which there probably exists a hypothesis of adequate "explicativity", which is another technical probabilistic concept. A pattern can be judged to be probably potentially explicable even if we cannot find an explanation. The theory of probability understood here is one of partially ordered (interval-valued), subjective (personal) probabilities. Among other topics relevant to a philosophy of EDA are the "reduction" of data; Francis Bacon's philosophy of science; the automatic formulation of hypotheses; successive deepening of hypotheses; neurophysiology; and rationality of type II. (shrink)

The work of the French Lithuanian Jewish philosopher, Emmanuel Levinas, describes a perceptive rethinking of the possibility of concrete acts of goodness in the world, a rethinking never more necessary than now, in the wake of the cruel realities of the twentieth century—ten million dead in the First World War, forty million dead in the Second World War, Hiroshima, Nagasaki, the Soviet gulags, the grand slaughter of Mao’s “Great Leap Forward,” the pointless and gory Vietnam War, the Cambodian self-genocide and (...) many an attempted extermination from the face of the earth of entire nations of indigenous peoples. The list of horrors goes on and on—daily holocausts that do not distinguish between the civilian and the soldier, the guilty and the innocent, those deserving of life and those less deserving. (shrink)

I respond to the comments by Larry Hickman and Thomas Alexander about my book, A Search for Unity in Diversity: The “Permanent Hegelian Deposit” in the Philosophy of John Dewey . I focus on four issues: 1) Precisely how do I prefer to characterize Dewey’s debt to Hegel? 2) How do I justify my admittedly controversial reading of Dewey’s World War I criticisms of Hegel? 3) Where do I believe Dewey found ideas in Hegel that led him to articulate the (...) historical fallacy? 4) How do I respond to Alexander’s concern that I have underestimated the influence of William James’s Principles of Psychology (1890) on Dewey? (shrink)

In the remarks that follow I concentrate on Lorenzo Simpson's two books, Technology, Time and the Conversations of Modernity and The Unfinished Project: Toward a Postmetaphysical Humanism. Common to both works — what unites them, I believe — is a philosophical orientation that has been deeply influenced by Gadamerian hermeneutics. I begin with a discussion of UP.