In the context of continuous first-order logic, special attention is often given to theories that are somehow continuous in an ‘essential’ way. A common feature of such theories is that they do not interpret any infinite discrete structures. We investigate a stronger condition that is easier to establish and use it to give an example of a strictly simple continuous theory that does not interpret any infinite discrete structures: the theory of richly branching [Formula: see text]-forests with generic binary predicates. (...) We also give an example of a superstable theory that fails to satisfy this stronger condition but nevertheless does not interpret any infinite discrete structures. (shrink)

We give a formalism for approximate isomorphism in continuous logic simultaneously generalizing those of two papers by Ben Yaacov [2] and by Ben Yaacov, Doucha, Nies, and Tsankov [6], which are largely incompatible. With this we explicitly exhibit Scott sentences for the perturbation systems of the former paper, such as the Banach‐Mazur distance and the Lipschitz distance between metric spaces. Our formalism is simultaneously characterized syntactically by a mild generalization of perturbation systems and semantically by certain elementary classes of two‐sorted (...) structures that witness approximate isomorphism. As an application, we show that the theory of any ‐tree or ultrametric space of finite radius is stable, improving a result of Carlisle and Henson [8]. (shrink)

Journal of Mathematical Logic, Ahead of Print. In the context of continuous first-order logic, special attention is often given to theories that are somehow continuous in an ‘essential’ way. A common feature of such theories is that they do not interpret any infinite discrete structures. We investigate a stronger condition that is easier to establish and use it to give an example of a strictly simple continuous theory that does not interpret any infinite discrete structures: the theory of richly branching (...) [math]-forests with generic binary predicates. We also give an example of a superstable theory that fails to satisfy this stronger condition but nevertheless does not interpret any infinite discrete structures. (shrink)

This book offers a re-examination of the evidence about citizens' capacity for self-governance and what it means for the future of democratic politics, from both empirical and normative perspectives. Are ordinary citizens capable of governing themselves? For more than three decades, social scientists have accumulated evidence of the undemocratic propensities of many ordinary citizens. This has caused some to worry about the stability of existing democratic institutions, while others argue that the institutions themselves are the problem: politics needs to be (...) democratized further, giving citizens more opportunities to practice democratic politics and acquire democratic values. The thirty-three contributors to this volume enter this debate with new evidence on citizens' capacity for deliberative politics. They argue that previous methods of investigation significantly underestimate people's ability to govern themselves, and that the prospects for democracy are better than conventional wisdom suggests. Realization of these prospects will depend on citizens grasping the interplay of emotions and reason in political life, creating new opportunities for citizen deliberation, and reinvigorating the institutions of representative government. Theories of democracy in turn will have to accommodate this changing reality as citizens show themselves to be self-determining in their political activities. (shrink)

We explore approximate categoricity in the context of distortion systems, introduced in our previous paper (Hanson in Math Logic Q 69(4):482–507, 2023), which are a mild generalization of perturbation systems, introduced by Yaacov (J Math Logic 08(02):225–249, 2008). We extend Ben Yaacov’s Ryll-Nardzewski style characterization of separably approximately categorical theories from the context of perturbation systems to that of distortion systems. We also make progress towards an analog of Morley’s theorem for inseparable approximate categoricity, showing that if there is (...) some uncountable cardinal $$\kappa $$ such that every model of size $$\kappa $$ is ‘approximately saturated,’ in the appropriate sense, then the same is true for all uncountable cardinalities. Finally we present some examples of these phenomena and highlight an apparent interaction between ordinary separable categoricity and inseparable approximate categoricity. (shrink)

We explore approximate categoricity in the context of distortion systems, introduced in our previous paper (Hanson in Math Logic Q 69(4):482–507, 2023), which are a mild generalization of perturbation systems, introduced by Yaacov (J Math Logic 08(02):225–249, 2008). We extend Ben Yaacov’s Ryll-Nardzewski style characterization of separably approximately categorical theories from the context of perturbation systems to that of distortion systems. We also make progress towards an analog of Morley’s theorem for inseparable approximate categoricity, showing that if there is (...) some uncountable cardinal $$\kappa $$ such that every model of size $$\kappa $$ is ‘approximately saturated,’ in the appropriate sense, then the same is true for all uncountable cardinalities. Finally we present some examples of these phenomena and highlight an apparent interaction between ordinary separable categoricity and inseparable approximate categoricity. (shrink)

Conducting or overseeing research in correctional settings requires knowledge of specific federal rules and regulations designed to protect the rights of individuals in incarceration. To investigate the extent to which relevant groups possess this knowledge, using a 10-item questionnaire, we surveyed 885 IRB prisoner representatives, IRB members and chairs with and without experience reviewing HIV/AIDS correctional protocols, and researchers with and without correctional HIV/AIDS research experience. Across all groups, respondents answered 4.5 of the items correctly. Individuals who have overseen or (...) conducted correctional research had the highest scores; however, even these groups responded correctly only to slightly more than half of the items. These findings emphasize the need for ongoing training in federal guidelines governing correctional research, particularly for those individuals who are embarking on this type of research. (shrink)

Language plays a role in the genocide of the Rohingya people in Myanmar and continues to shape their experiences in displacement, yet their linguistic rights are rarely discussed in relation to their human rights and humanitarian concerns. International human rights standards offer important foundations for conceptualizing the “right to language” and identifying how linguistic rights can be violated both in situ and in displacement. The Rohingya case highlights how language policies are weaponized to oppress unwanted minorities; their outsider status is (...) reinforced by the country’s language education policy and they face additional rights challenges in displacement—including obstacles to effectively accessing humanitarian aid. Moving forward, norms associated with self-determination and language rights offer a conceptual foundation for shifting attitudes and altering negative perceptions of Rohingya identity. (shrink)

Generic language (e.g., “tigers have stripes”) leads children to assume that the referenced category (e.g., tigers) is inductively informative and provides a causal explanation for the behavior of individual members. In two preregistered studies with 4- to 7-year-old children (N = 497), we considered the mechanisms underlying these effects by testing how correcting generics might affect the development of these beliefs about novel social and animal kinds (Study 1) and about gender (Study 2). Correcting generics by narrowing their scope to (...) a single individual limited beliefs that the referenced categories could explain what their members would be like while broadening the scope to a superordinate category (Study 2) uniquely limited endorsement of gender norms. Across both studies, correcting generics did not alter beliefs about feature heritability and had mixed effects on inductive inferences, suggesting that additional mechanisms (e.g., causal reasoning about shared features) contribute to the development of full-blown essentialist beliefs. These results help illuminate the mechanisms by which generics lead children to view categories as having rich inductive and causal potential; in particular, they suggest that children interpret generics as signals that speakers in their community view the referenced categories as meaningful kinds that support generalization. The findings also point the way to concrete suggestions for how adults can effectively correct problematic generics (e.g., gender stereotypes) that children may hear in daily life. (shrink)

The current studies (N = 255, children ages 4–5 and adults) explore patterns of age‐related continuity and change in conceptual representations of social role categories (e.g., “scientist”). In Study 1, young children's judgments of category membership were shaped by both category labels and category‐normative traits, and the two were dissociable, indicating that even young children's conceptual representations for some social categories have a “dual character.” In Study 2, when labels and traits were contrasted, adults and children based their category‐based induction (...) decisions on category‐normative traits rather than labels. Study 3 confirmed that children reason based on category‐normative traits because they view them as an obligatory part of category membership. In contrast, adults in this study viewed the category‐normative traits as informative on their own (not only as a cue to obligations). Implications for continuity and change in representations of social role categories will be discussed. (shrink)

How do people gather samples of evidence to learn about the world? Adults often prefer to sample evidence from diverse sources—for example, choosing to test a robin and a turkey to find out if something is true of birds in general. Children below age 9, however, often do not consider sample diversity, instead treating non‐diverse samples (e.g., two robins) and diverse samples as equivalently informative. The current study (N = 247) found that this discontinuity stems from developmental changes in standards (...) for evaluating evidence—younger children chose to learn from samples that best approximate idealized views of what category members are supposed to be like (e.g., the fastest cheetahs), with a gradual shift across age toward samples that cover more within‐category variation (e.g., cheetahs of varying speeds). These findings have implications for the relation between conceptual structure and inductive reasoning, and for the mechanisms underlying inductive reasoning more generally. (shrink)

: Can pragmatism account for the private aspect of the self? The classical pragmatists - Peirce, James, Mead, and Dewey - mount various attacks on the Cartesian view of the self, and they offer varied and attractive positive accounts of the person. But does pragmatism adequately acknowledge privacy or personal "inwardness"? I explore here the pragmatic picture of the self, drawing on all the classical sources, and I assess the adequacy of pragmatic resources for describing and explaining the puzzles of (...) personal privacy.Resumo: Pode o pragmatismo dar conta do aspecto privado do self? Os pragmatistas clássicos - Peirce, James, Mead e Dewey - desferem diversos ataques à visão cartesiana do self, e oferecem versões positivas, variadas e atrativas da pessoa. Mas pode o pragmatismo adequadamente reconhecer a privacidade ou a 'interioridade' pessoal? Eu exploro aqui a figura pragmática do self, bebendo em todas as fontes clássicas, e avalio a adequação dos recursos pragmáticos para descrever e explicar os quebra-cabeças da privacidade pessoal. (shrink)

Humanity seems to have a bright future, i.e., a non-trivial chance of expanding to fill the universe with lasting life. But the fact that space near us seems dead now tells us that any given piece of dead matter faces an astronomically low chance of begating such a future. There thus exists a great filter between death and expanding lasting life, and humanity faces the ominous question: how far along this filter are we?

The average, general readings in philosophy anthology have five to seven readings on necessary truth. This volume has fourteen. The old workhorses are here: Kant on synthetic and analytic propositions, Mill on necessary truths, Ayer on the a priori, Quine, Grice, and Strawson on dogmas of empiricism. In addition, Pap has two items, one in the middle of an exchange with Putnam over reds, greens, and the synthetic a priori. There is a tough logical analysis by Hintikka, contributions by Jonathan (...) Bennett and Hanson, and a final exchange between Katz and Quine. The selections are by no means comprehensive, but, as the editors note, this would have been impossible. A seventeen-page bibliography comes closer to fulfilling the completeness criterion. The editors include a short introduction, which really should have been expanded, since it raises some of the ontological issues that implicitly guide the debate that takes place among the selections.--E. A. R. (shrink)

Even outside of games, a wide range of otherwise puzzling common intuitions about fairness can be understood if the fundamental "game" of life is seen as wooing, i.e., attracting mates by showing that you have fit genes. The fairest social institutions are then those in which success correlates as much as possible with genetic fitness.

Prediction markets are low volume speculative markets whose prices offer informative forecasts on particular policy topics. Observers worry that traders may attempt to mislead decision makers by manipulating prices. We adapt a Kyle-style market microstructure model to this case, adding a manipulator with an additional quadratic preference regarding the price. In this model, when other traders are uncertain about the manipulator’s target price, the mean target price has no effect on prices, and increases in the variance of the target price (...) can increase average price accuracy, by increasing the returns to informed trading and thereby incentives for traders to become informed. (shrink)

Humans have slowly built more productive societies by slowly acquiring various kinds of capital, and by carefully matching them to each other. Because disruptions can disturb this careful matching, and discourage social coordination, large disruptions can cause a “social collapse,” i.e., a reduction in productivity out of proportion to the disruption. For many types of disasters, severity seems to follow a power law distribution. For some of types, such as wars and earthquakes, most of the expected harm is predicted to (...) occur in extreme events, which kill most people on Earth. So if we are willing to worry about any war or earthquake, we should worry especially about extreme versions. If individuals varied little in their resistance to such disruptions, events a little stronger than extreme ones would eliminate humanity, and our only hope would be to prevent such events. If individuals vary a lot in their resistance, however, then it may pay to increase the variance in such resistance, such as by creating special sanctuaries from which the few remaining humans could rebuild society. (shrink)

A simple exogenous growth model gives conservative estimates of the economic implications of machine intelligence. Machines complement human labor when they become more productive at the jobs they perform, but machines also substitute for human labor by taking over human jobs. At first, expensive hardware and software does only the few jobs where computers have the strongest advantage over humans. Eventually, computers do most jobs. At first, complementary effects dominate, and human wages rise with computer productivity. But eventually substitution can (...) dominate, making wages fall as fast as computer prices now do. An intelligence population explosion makes per-intelligence consumption fall this fast, while economic growth rates rise by an order of magnitude or more. These results are robust to automating incrementally, and to distinguishing hardware, software, and human capital from other forms of capital. (shrink)

If we are not to conclude that most planets like Earth have evolved life as intelligent as we are, we must presume Earth is not random. This selection effect, however, also implies that the origin of life need not be as easy as the early appearance of life on Earth suggests. If a series of major evolutionary transitions were required to produce intelligent life, selection implies that a subset of these were “critical steps,” with durations that are similarly distributed. The (...) time remaining from now until simple life is no longer possible on Earth must also be similarly distributed. I show how these results provide timing tests to constrain models of critical evolutionary transitions. (shrink)

In a simple model of conflict, two agents fight over a fixed prize, and how hard they fight depends on what they believe about their abilities. To this model I add “preagents,” representing parents, leaders, or natural selection, who choose each agent’s confidence in his ability. Depending on the reason for such confidence, I find five different patterns in how confidence varies with ability. Agents who estimate their ability with error have under-confidence when ability is high and over-confidence when ability (...) is low, while strategic commitment incentives induce the opposite pattern. Agents who misjudge their value for the prize, relative to their cost of effort, induce an overor under-confidence that is independent of ability, while cooperating pre-agents choose extreme under-confidence. Agents who use confidence to signal ability have a relatively uniform over-confidence. (shrink)

Since utilities and probabilities jointly determine choices, event-dependent utilities complicate the elicitation of subjective event probabilities. However, for the usual purpose of obtaining the information embodied in agent beliefs, it is sufficient to elicit objective probabilities, i.e., probabilities obtained by updating a known common prior with that agent’s further information. Bayesians who play a Nash equilibrium of a certain insurance game before they obtain relevant information will afterward act regarding lottery ticket payments as if they had event-independent risk-neutral utility and (...) a known common prior. Proper scoring rules paid in lottery tickets can then elicit objective probabilities. (shrink)

Perhaps some simple change will do the trick, like relying less on insurance and employers as middlemen. But if we are willing to consider radical change, let me offer a different suggestion. We are buying the wrong thing. What we want is health, i.e., a long healthy life, but when we sit down and draw up a contract, what we buy is health care, i.e., a certain degree of attention from health care specialists.

This explains how to smoothly integrate booked orders with a combinatorial market maker, all for the general case of bets on E[x|A] for arbitrary random variables x and sets A.

1. The philosophical version of the primary-secondary distinction concerns (a) the 'real' properties of matter, (b) the epistemology of sensation, and (c) a contrast challenged by Berkely as illusory. The scientific version of the primary-secondary distinction concerns (a') the physical properties of matter, (b') a contrast essential within the history of atomism, and (c') a contrast challenged by 20th century microphysics as de facto untenable. 2. The primary-secondary distinction within physics can be interpreted in two ways: a. it can refer (...) to content; e.g. 'Matter has the properties of mass, shape, density... etc. -- it only appears to have the properties of warmth, fragrance, etc.' Or, b. it can refer to form; e.g. 'Whatever properties our best theories accord to primary matter, e.g., electrons, these are by definition primary. All other properties of, e.g., macromatter, are derivative.' Concerning 2.a., this interpretation is simply false when 17th, 18th, or 19th century values for the property-variables are introduced. Concerning 2.b., this either uninformative or misleading. It is uninformative when it constitutes no more than a decision to use the word 'primary' as an umbrella-word for all the properties contemporary micro-physics accords to fundamental material particles, whatever these may be. It is misleading when it turns on an implicit contrast between certain properties particles may be said to have when 'harnessed' to a detector, and certain other properties these particles have when free and unharnessed to any detector. This contrast does not exist. Quantum-theoretic information is always about particles-and-their-detectors-in-combination. Dissolve this combination and you destroy any possible knowledge of the particle. Hence the notion of 'completely objectifiable properties of particles' is in principle unsound. (shrink)

Given a finite state space and common priors, common knowledge of the identity of an agent with the minimal (or maximal) expectation of a random variable implies ‘consensus’, i.e., common knowledge of common expectations. This ‘extremist’ statistic induces consensus when repeatedly announced, and yet, with n agents, requires at most log2 n bits to broadcast.

Prediction markets are increasingly being considered as methods for gathering, summarizing and aggregating diffuse information by governments and businesses alike. Critics worry that these markets are susceptible to price manipulation by agents who wish to distort decision making. We study the effect of manipulators on an experimental market, and find that manipulators are unable to distort price accuracy. Subjects without manipulation incentives compensate for the bias in offers from manipulators by setting a different threshold at which they are willing to (...) accept trades. (shrink)

What is the nature of lexical meanings such that they can both compose with others and also appear boundless? We investigate this question by examining the compositional properties of for-time adverbial as in “Ana jumped for an hour.” At issue is the source of the associated iterative reading which lacks overt morphophonological support, yet, the iteration is not disconnected from the lexical meanings in the sentence. This suggests an analysis whereby the iterative reading is the result of the interaction between (...) lexical meanings under a specific compositional configuration. We test the predictions of two competing accounts: Mismatch-and-Repair and Partition-Measure. They differ in their assumptions about lexical meanings: assumptions that have implications for the possible compositional mechanisms that each can invoke. Mismatch-and-Repair assumes that lexical meaning representations are discrete, separate from the conceptual system from which they originally emerged and brought into sentence meaning through syntactic composition. Partition-Measure assumes that lexical meanings are contextually salient conceptual structures substantially indistinguishable from the conceptual system that they inhabit. During comprehension, lexical meanings construe a conceptual representation, in parallel, morphosyntactic and morphophonological composition as determined by the lexical items involved in the sentence. Whereas both hypotheses capture the observed cost in the punctual predicate plus for-time adverbial composition (e.g., jump (vs. swim) for an hour), their predictions differ regarding iteration with durative predicates; for example, swim for a year (vs. for an hour). Mismatch-and-Repair predicts contrasting processing profiles and nonoverlapping activation patterns along punctuality differences. Partition-Measure predicts overlapping processing and cortical distribution profiles, along the presence of iterativity. Results from a self-paced reading and an functional Magnetic Resonance Imaging (fMRI) studies bear out the predictions of the Partition-Measure account, supporting a view of linguistic meaning composition in line with an architecture of language whereby combinatoriality and generativity are distributed, carried out in parallel across linguistic and nonlinguistic subsystems. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:388 HISTORY OF PHILOSOPHY Beyond the Edge of Certainty: Essays in Contemporary Science and Philosophy. Edited with an Introduction by Robert G. Colodny. (Englewood Cliffs, New Jersey: Prentice-Hall, Inc., 1965.) This is the second volume of lectures on various current topics in the philosophy of the physical, biological, and social sciences which has been published under the auspices of the Center for Philosophy of Science at the University of (...) Pittsburg. Volume I, Frontiers o] Science and Philosophy, also edited by Professor Colodny, appeared in 1962. Five of the seven lectures contained in this volume treat topics which fall within the philosophy of physics. The persistent student who is without a technical background in either logic or physics will find these for the most part quite readable. Considering this, it is worthy of note that, while the lectures are not of uniform quality in this respect, several problems are treated with sufficient freshness of insight to justify the interest of the philosopher of science as such. Since I cannot discuss all of the lectures, I will restrict my comments, for the most part, to those the significance of which I think I understand best and which deal significantly with some aspect of the history of philosophy. In "Newton's First Law: A Philosopher's Door into Natural Philosophy," Norwood Russell Hanson exhibits what has become a widely accepted analysis of Newton's First Law as a model to be applied to theories in science which must be regarded as, in some sense, true, but which, in principle, are not empirically demonstrable. Briant Ellis, in "The Origin and Nature of Newton's Laws of Motion," deals in a somewhat parallel way with all three of Newton's laws of motion. It is argued that these laws are primarily conceptual in origin. Evidence is marshalled that they were derived from Cartesian physics. That no amount of empirical work could establish or provide support for a principle of natural motion is held by Ellis to be due to the fact that "force" is conceived as something that exists only in order to explain effects. "Since we are at liberty to choose to regard whatever changes or states we please as natural (i.e., as not being effects) it follows that the forces which we should say are operative in nature depend upon the choices we actually make" (65). It would, I think be difficult to show that any one of the points Ellis makes, with the exception of his interesting historical note on the probable origin of Newton's laws of motion, has not previously been made. All, or nearly all, of these points were set forth, at least in outline, for example, by William Werkmeister in A Philosophy o] Science. The approach Ellis makes to his development of the concept of "force," however, is both fresh and incisive and worthy of careful study. In "A Philosopher looks at Quantum Mechanics," Hillary Putnam exhibits the Copenhagen interpretation of quantum mechanics of Bohr and Heisenberg, viewed in historical perspective, as the most adequate of several unsatisfactory theories. He finds the locus of the problem to lie in a suitable definition of "measurement." Noting that Heisenberg's definition (improperly) appeals to the macrocosm conceived in terms of classical mechanics, he seeks to clarify some of the issues that must follow the attempt to define measurement within the context of quantum mechanics. Putnam holds the relative sharpness of macroobservables for Bohr and Heisenberg to be an underived assumption of their theory. Since the quantities of which macro-observables are supposed to be averages are not (in quantum mechanics) required always to exist, this assumption cannot be derived from a plausible definition of macro-observables together with a suitable formulation of the laws of quantum mechanics. Moving from Bohr and Heisenberg's conclusion that measurement requires interaction of a system (or part of a system) measured with respect to an outside system, and that macroobservables do not exist unless measured, measurement for quantum mechanics is defined as "an interaction in which a system A (the 'measured' system), which was previously isolated, interacts with a system B (the 'measuring' system) in such a way as to cause a... (shrink)

When in May 1930, the Council of Trinity College, Cambridge, had to decide whether to renew Wittgenstein's research grant, it turned to Bertrand Russell for an assessment of the work Wittgenstein had been doing over the past year. His verdict: "The theories contained in this new work... are novel, very original and indubitably important. Whether they are true, I do not know. As a logician who likes simplicity, I should like to think that they are not, but from what I (...) have read of them I am quite sure that he ought to have an opportunity to work them out, since, when completed, they may easily prove to constitute a whole new philosophy." "[Philosophical Remarks] contains the seeds of Wittgenstein's later philosophy of mind and of mathematics. Principally, he here discusses the role of indispensable in language, criticizing Russell's The Analysis of Mind. He modifies the Tractatus's picture theory of meaning by stressing that the connection between the proposition and reality is not found in the picture itself. He analyzes generality in and out of mathematics, and the notions of proof and experiment. He formulates a pain/private-language argument and discusses both behaviorism and the verifiability principle. The work is difficult but important, and it belongs in every philosophy collection."—Robert Hoffman, Philosophy "Any serious student of Wittgenstein's work will want to study his Philosophical Remarks as a transitional book between his two great masterpieces. The Remarks is thus indispensible for anyone who seeks a complete understanding of Wittgenstein's philosophy."—Leonard Linsky, American Philosophical Association. (shrink)

In the past decade, the notion of a neural correlate of consciousness has become a focal point for scientific research on consciousness. A growing number of investigators believe that the first step toward a science of consciousness is to discover the neural correlates of consciousness. Indeed, Francis Crick has gone so far as to proclaim that ‘we need to discover the neural correlates of consciousness. For this task the primate visual system seems especially attractive. No longer need one spend time (...) attempting to endure the tedium of philosophers perpetually disagreeing with each other. Consciousness is now largely a scientific problem’. Yet the question of what it means to be a neural correlate of consciousness is actually far from straightforward, for it involves fundamental empirical, methodological, and philosophical issues about the nature of consciousness and its relationship to the brain. Even if one assumes, as we do, that states of consciousness causally depend on states of the brain, one can nevertheless wonder in what sense there is, or could be, such a thing as a neural correlate of consciousness. (shrink)

THEODORE KISIEL Date of birth: October 30,1930. Place of birth: Brackenridge, Pennsylvania. Date of institution of highest degree: PhD., Duquesne University, 1962. Academic appointments: University of Dayton; Canisius College; Northwestern University; Duquesne University; Northern Illinois University. I first left the university to pursue a career in metallurgical research and nuclear technology. But I soon found myself drawn back to the uni versity to 'round out' an overly specialized education. It was along this path that I was 'waylaid' into philosophy by (...) teachers like H. L. Van Breda and Bernard Boelen. The philosophy department at Duquesne University was then (1958-1962) a veritable "little Louvain," and the Belgian-Dutch connection exposed me to (among other visiting scholars) Jean Ladriere and Joe Kockelmans, who planted the seeds which eventually led me to the hybrid discipline of a hermeneutics of natural science, and prompted me soon after graduation to make the first of numerous extended visits to Belgium and Germany. The endeavor to learn French and German led me to the task of translating the phenomenological literature bearing especially on natural science and on Heidegger. The talk in the sixties was of a "continental divide" in philosophy between Europe and the Anglo-American world. But in designing my courses in the philosophy of science, I naturally gravitated to the works of Hanson, Kuhn, Polanyi and Toulmin without at first fully realizing why I felt such a strong kinship with them, beyond their common anti positivism. (shrink)

In order to understand the rise of runaway solutions in the radiation reaction problem a mechanical model is used. An alternative demonstration of Daboul’s theorem, through Hurwitz’s criterion, is given. The origin of runaway solutions in electrodynamics is discussed. They arise when the particle has a negative mechanical mass or when approximations are used in the equation of motion. In the 1-dimensional mechanical model an exact and linear equation of motion for the particle is obtained, the corresponding exact solution is (...) again runaway when the mechanical mass is negative. The exact solution is not runaway when the mechanical mass is positive. However, the use of approximations leads to an equation of motion which has runaway solutions. It is exhibited that the use of approximations in the 3-dimensional mechanical model is completely necessary because the general equation of motion for the particle is non-linear. The analysis of this case proceeds in a very similar way to the one carried out in electrodynamics. This means that the number of dimensions also plays an important role in the analysis. (shrink)

Published in 1987: The following essays form, as their title-page shows, only the first half of a collection which the writer hopes to complete in the course of a few months. Even when completed the whole work is designed to be merely preparatory to another on the interpretation of the Platonic Philosophy, and the materials brought together in the following pages, as well as those which, it is trusted, will form their continuation, were originally intended to appear in the Introduction (...) to that projected work. (shrink)

A common ethical code for everybody involved in health care is desirable, but there are important limitations to the role such a code could play. In order to understand these limitations the approach to ethics using principles and their application to medicine is discussed, and in particular the implications of their being prima facie. The expectation of what an ethical code can do changes depending on how ethical properties in general are understood. The difficulties encountered when ethical values are applied (...) reactively to an objective world can be avoided by seeing them as a more integral part of our understanding of the world. It is concluded that an ethical code can establish important values and describe a common ethical context for health care but is of limited use in solving new and complex ethical problems. (shrink)

It is a point of some interest to the historian of the social and intellectual development of Athens to determine, if possible, the exact dates between which the philosopher Anaxagoras made that city his home. As everyone knows, the tradition of the third and later centuries was not uniform. The dates from which the Alexandrian chronologists had to arrive at their results may be conveniently summed up under three headings, date of Anaxagoras' arrival at Athens, date of his prosecution and (...) escape to Lampsacus, length of his residence at Athens, The received account , was that Anaxagoras was twenty years old at the date of the invasion of Xerxes and lived to be seventy-two. This was apparently why Apollodorus placed his birth in Olympiad 70 and his death in Ol. 88. I, thus giving the years 500–428 B.C. of our reckoning, The further statement of Apollodorus that Anaxagoras xs1F24ρξατο xs03D5ιλοσοxs03D5εxs1FD6ν xs22EFπxs22EF Καλλίον has given rise to discussion; but when we remember that Demetrius of Phalerum had made what ‘Diogenes’ regards as an equivalent statement in his register of archons, and had said that Anaxagoras was twenty years old at the time, I think there can be no doubt of the meaning. Demetrius had clearly mentioned something about Anaxagoras which was looked on as giving the date at which he ‘began to philosophize,’ and had given his age at the time. The natural interpretation is that Demetrius mentioned the year of Anaxagoras’ arrival at Athens, and that this was taken as the time at which he ρξαtο φιλοσοφεlσ And it is further reasonable to suppose that this date was the source of the further statement of Demetrius, that Anaxagoras was born in or about 500 B.C. We may, I think, infer that Demetrius recorded the arrival of Anaxagoras in Athens under the year 480, giving his approximate age at that time. (shrink)