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)

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 (...) (SIA), as propounded by John Bell. Despite many parallels between SIA and Leibniz’s approach —the non-punctiform nature of infinitesimals, their acting as parts of the continuum, the dependence on variables (as opposed to the static quantities of both Standard and Non-standard Analysis), the resolution of curves into infinitesided polygons, and the finessing of a commitment to the existence of infinitesimals— I find some salient differences, especially with regard to higher-order infinitesimals. These differences are illustrated by a consideration of how each approach might be applied to Newton’s Proposition 6 of the Principia, and the derivation from it of the v2/r law for the centripetal force on a body orbiting around a centre of force. It is found that while Leibniz’s syncategorematic approach is adequate to ground a Leibnizian version of the v2/r law for the “solicitation” ddr experienced by the orbiting body, there is no corresponding possibility for a derivation of the law by nilsquare infinitesimals; and while SIA can allow for second order differentials if nilcube infinitesimals are assumed, difficulties remain concerning the compatibility of nilcube infinitesimals with the principles of SIA, and in any case render the type of infinitesimal analysis adopted dependent on its applicability to the problem at hand. (shrink)

Arthur E. Lean’s irreverent and con­troversial essays represent the distillation of many ideas about education—ideas developed during most of a lifetime spent in and about schools. In the second edition of this popular work, to which he has added eight new essays, he presents his latest observations on current ele­ments and programs in education—such as the grading system, academic rank, the teaching process, assessment of edu­cational progress—concluding that many of them are not only unnecessary but actually harmful to the (...) very process which they are supposed to serve. Covering a broad spectrum of current issues in its criticism of American edu­cation at all levels, _And Merely Teach _is a book to be read by veteran educator, beginning teacher, and lay citizen alike. Though critical of the teaching profes­sion, Arthur Lean also offers constructive suggestions in the form of practical solu­tions that are urgently needed to save our ailing educational system. (shrink)

The structure of the Lorentz transformation depends intimately on the conventional operations for measurement of lengths (L) and time intervals (T). The prescription for length measurement leads to justifiable utilization of Euclidean geometry over finite values of the coordinates. Then T-values can be regarded as ratios of length measurements within a suitably defined clock. In certain cases the synchronization process should be supplemented by measurements providing position certification. The Lorentz transformation emerges from three specific symmetry statements, assured by the nature (...) of the L and T operations: (1) one-one correspondence of finite values of the coordinates of two inertial frames, (2) frame reciprocity, and (3) spatial isotropy. (Light signaling is not needed in this derivation. Afterward, it is assumed that light is indeed an agent moving with the common speed revealed by the transformation.) When rest masses have been determined in the conventional fashion, the conservation of momentum and of energy follow from the kinematics—a result due to Einstein. (shrink)

In this paper, we use the risk apportionment technique of Eeckhoudt, Rey and Schlesinger (2007) to study higher order risk preferences for others’ health as well as ex-ante and ex-post inequality preferences for social risky distributions, and their interaction. In an experiment on a sample of university students acting as impartial spectators, we observe risk aversion towards social health losses and a dislike of ex-ante inequality. In addition, evidence for ex-post inequality seeking is much weaker than evidence for ex-ante inequality (...) aversion. Because ex-ante inequality aversion is unrelated to risk aversion, we conclude that simple forms of utilitarianism are not relevant for individual judgment of social risk over health. Last, our investigation of precautionary distribution, which would occur when one particular group in the society suffers from background health risk, shows substantial polarization of preferences. (shrink)

Le positivisme, de Comte à Carnap, a marqué une étape dans le développement d’une science spéciale en dehors des sujets traités jusque là par la philosophie. Cette communication montre que la « syntaxe logique » de Carnap comme la « synthèse subjective » de Comte est un hybride, — une tranche de la philosophie en train de devenir science, et essayant, à l’étape intermédiaire de son processus, d’être à la fois science et philosophie.

BackgroundThe outbreak of COVID-19 has been a major interrupting event, challenging how societies and individuals deal with risk. An essential determinant of the virus’ spread is a series of individual decisions, such as wearing face masks in public space. Those decisions depend on trade-offs between costs and risks, and beliefs are key to explain these.MethodsWe elicit beliefs about the COVID-19 pandemic during lockdown in France by means of surveys asking French citizens about their belief of the infection fatality ratio for (...) COVID-19, own risk to catch the disease, risk as perceived by others, and expected prevalence rate. Those self-assessments were measured twice during lockdown: about 2 weeks after lockdown started and about 2 weeks before lockdown ended. We also measured the quality of these beliefs with respect to available evidence at the time of the surveys, allowing us to assess the calibration of beliefs based on risk-related socio-demographics. Finally, comparing own risk to expected prevalence rates in the two successive surveys provides a dynamic view of comparative optimism with respect to the disease.ResultsThe risk perceptions are rather high in absolute terms and they increased between the two surveys. We found no evidence for an impact of personal experience with COVID-19 on beliefs and lower risk perceptions of the IFR when someone in the respondent’s family has been diagnosed with a disease. Answers to survey 1 confirmed this pattern with a clear indication that respondents were optimistic about their chances to catch COVID-19. However, in survey 2, respondents revealed comparative pessimism.ConclusionThe results show that respondents overestimated the probabilities to catch or die from COVID-19, which is not unusual and does not necessarily reflect a strong deviation from rational behavior. While a rational model explains why the own risk to catch COVID-19 rose between the two surveys, it does not explain why the subjective assessment of the IFR remained stable. The comparative pessimism in survey 2 was likely due to a concomitant increase in the respondents’ perceived chances to catch the disease and a decreased expected prevalence rate. (shrink)

This essay develops a theory of natural signs in order to show how evolutionary theory breathes new life into teleology. An argument to the contrary presented by Richard Taylor is refuted. The essay defends the view that the concept of negative feedback explicates purposiveness and that symbiotic evolution explains the occurrence of naturally adapted feedback systems. But evolution itself is not a teleological process, nor is it a negative feedback system. There is an exploration of the nature of the dissatisfaction (...) we feel with an evolutionary account of purposiveness from which the fortuitous cannot be eliminated. (shrink)

The failure of the critics of corporate governance to agree on what should be done to improve the governance process can, in most cases, be traced to a different understanding of the role of corporate directors in that process. This article analyzes and contrasts the obligations of directors under two legal theories, the fictional person theory and the organic theory, of the corporation. A comparison of the director's obligations under each theory indicates that the organic theory provides a better basis (...) for assessing the performance of directors and initiating reform.Among the boards of directors of Fortune 500 companies, I estimate that 95% are not fully doing what they are legally, morally, and ethically supposed to do. And they couldn't, even if they wanted to. (shrink)

This work examines the nature of what philosophers call de re mental attitudes, paying close attention to the controversies over the nature of these and allied...