On the equivalence of Goodman’s and Hempel’s paradoxes

Historically, Nelson Goodman’s paradox involving the predicates ‘grue’ and ‘bleen’ has been taken to furnish a serious blow to Carl Hempel’s theory of confirmation in particular and to purely formal theories of confirmation in general. In this paper, I argue that Goodman’s paradox is no more serious of a threat to Hempel’s theory of confirmation than is Hempel’s own paradox of the ravens. I proceed by developing a suggestion from R. D. Rosenkrantz into an argument for the conclusion that these paradoxes are, in fact, equivalent. My argument, if successful, is of both historical and philosophical interest. Goodman himself maintained that Hempel’s theory of confirmation was capable of handling the paradox of the ravens. And Hempel eventually conceded that Goodman’s paradox showed that there could be no adequate, purely syntactical theory of confirmation. The conclusion of my argument entails, by contrast, that Hempel’s theory of confirmation is incapable of handling Goodman’s paradox if and only if it is incapable of handling the paradox of the ravens. It also entails that for any adequate solution to one of these paradoxes, there is a corresponding and equally adequate solution to the other.     

The motion of the moon in the Romaka Siddhānta

Summary Formulae are fitted to the different sets of values, given by the translators, for the equation of centre for the motion of the moon according to the Romaka Siddhnta, as found in the Pañcasiddhntik of Varha Mihira.     

Autobiography and ‘The Two Cultures’ in the novels of C. P. Snow

That C. P. Snow had first-hand experience both in science and writing was taken for granted in the years of controversy over ‘the two cultures’, but neither the quality of his experience nor the circumstances of his eventual adoption of a literary career was given close enough consideration. Snow's own statements on these two points are often misleading. Yet the autobiographical nature of his fiction throws significant light on the subject. An examination of the autobiographical elements in Snow's novels in the light of his conception of the novel raises the question of whether his shift from science to literature was exactly the result of a genuine choice and also reveals that the two cultures dichotomy is embedded in his personal experience.     

A further analysis of Cardano’s main tool in the De Regula Aliza: on the origins of the splittings

Archive for History of Exact Sciences - In the framework of the De Regula Aliza (1570), Cardano paid much attention to the so-called splittings for the family of equations $$x^3 = a_1x + a_0$$ ; my...     

For the Glory of Athens: Xenophon’s Hipparchikos <Logos>, a technical treatise and instruction manual on ideal leadership

Xenophon’s Peri hippikes <technees>, “On Horsemanship,” and the Hipparchikos <logos>, “the Cavalry Commander”, writings which can be regarded as technical works with a didactic purpose, are almost unknown. Xenophon was interested in problems of leadership and the exercise of power (For the titles of the both writings and the analogous supplementary terms “technees” and “logos” compare Breitenbach, 1966, 1761. Angled brackets are used by modern editors of ancient texts as text-critical signs and are inserted here because “peri hippikes” and “hipparchikos” are adjectives and cannot stand alone; “technees” and “logos” are supplied as absent, but implied, substantives. The conventional signs “<>” clarify this supplementary act for the modern reader.). The “Cavalry Commander” (ca. 365 B.C.) intended for the instruction of potential hipparchs (calvary commanders) is simultaneously political and didactic and technical; in this text, categories of leadership that had been developed in earlier works are combined in a powerful manner. Xenophon constructed “leaders” as exempla (“examples”) of correct behaviour; military and political theory are synthesised. The Hipparchikos logos, as a didactic work, aims to produce specialists who master their techné (“art” or “skill”), to develop their ideal qualities. Both texts are directed at an Athenian society, in which the cavalry had lost their significance and pride as a result of recent political turbulence. Xenophon hoped to reform the cavalry for the benefit of Athens. The basic question of the didactic work is: how can I become the best hipparch, how can I go beyond simply filling the office, and instead develop it for the well-being of the polis and thus serve the city? The art of leadership consists in dealing with subordinates in such a manner that they obey and follow voluntarily—still an innovative and modern approach today.     

The foundational aspects of Gauss’s work on the hypergeometric,factorial and digamma functions

In his writings about hypergeometric functions Gauss succeeded in moving beyond the restricted domain of eighteenth-century functions by changing several basic notions of analysis. He rejected formal methodology and the traditional notions of functions, complex numbers, infinite numbers, integration, and the sum of a series. Indeed, he thought that analysis derived from a few, intuitively given notions by means of other well-defined concepts which were reducible to intuitive ones. Gauss considered functions to be relations between continuous variable quantities while he regarded integration and summation as appropriate operations with limits. He also regarded infinite and infinitesimal numbers as a façon de parler and used inequalities in order to prove the existence of certain limits. He took complex numbers to have the same legitimacy as real quantities. However, Gauss’s continuum was linked to a revised form of the eighteenth-century notion of continuous quantity: it was not reducible to a set of numbers but was immediately given.     

Characterization of the role of the antioxidant proteins metallothioneins 1 and 2 in an animal model of Alzheimer’s disease

Alzheimer’s disease (AD) is by far the most commonly diagnosed dementia, and despite multiple efforts, there are still no effective drugs available for its treatment. One strategy that deserves to be pursued is to alter the expression and/or physiological action of endogenous proteins instead of administering exogenous factors. In this study, we intend to characterize the roles of the antioxidant, anti-inflammatory, and heavy-metal binding proteins, metallothionein-1?+?2 (MT1?+?2), in a mouse model of Alzheimer’s disease, Tg2576 mice. Contrary to expectations, MT1?+?2-deficiency rescued partially the human amyloid precursor protein-induced changes in mortality and body weight in a gender-dependent manner. On the other hand, amyloid plaque burden was decreased in the cortex and hippocampus in both sexes, while the amyloid cascade, neuroinflammation, and behavior were affected in the absence of MT1?+?2 in a complex manner. These results highlight that the control of the endogenous production and/or action of MT1?+?2 could represent a powerful therapeutic target in AD.     

Borelli’s edition of books V–VII of Apollonius’s Conics,and Lemma 12 in Newton’s Principia

To solve the direct problem of central forces when the trajectory is an ellipse and the force is directed to its centre, Newton made use of the famous Lemma 12 (Principia, I, sect. II) that was later recognized equivalent to proposition 31 of book VII of Apollonius’s Conics. In this paper, in which we look for Newton’s possible sources for Lemma 12, we compare Apollonius’s original proof, as edited by Borelli, with those of other authors, including that given by Newton himself. Moreover, after having retraced its editorial history, we evaluate the dissemination of Borelli's edition of books V-VII of Apollonius’s Conics before the printing of the Principia.

     

The natures of numbers in and around Bombelli’s L’algebra

The purpose of this article is to analyse the mathematical practices leading to Rafael Bombelli’s L’algebra (1572). The context for the analysis is the Italian algebra practiced by abbacus masters and Renaissance mathematicians of the fourteenth to sixteenth centuries. We will focus here on the semiotic aspects of algebraic practices and on the organisation of knowledge. Our purpose is to show how symbols that stand for underdetermined meanings combine with shifting principles of organisation to change the character of algebra.     

A summary of Euler’s work on the pentagonal number theorem

In this article, we give a summary of Leonhard Euler’s work on the pentagonal number theorem. First we discuss related work of earlier authors and Euler himself. We then review Euler’s correspondence, papers and notebook entries about the pentagonal number theorem and its applications to divisor sums and integer partitions. In particular, we work out the details of an unpublished proof of the pentagonal number theorem from Euler’s notebooks. As we follow Euler’s discovery and proofs of the pentagonal number theorem, we pay attention to Euler’s ideas about when we can consider a mathematical statement to be true. Finally, we discuss related results in the theory of analytic functions.     

Boyle’s teleological mechanism and the myth of immanent teleology

According to recent commentators, medieval natural philosophers endorsed immanent teleology, the view that natural agents possess immanent active powers to achieve certain ends. Moreover, some scholars have argued that Robert Boyle, despite his intentions, failed to eliminate immanent teleology from his natural philosophy. I argue in this paper that it is not at all clear that immanent teleology was widely endorsed in the medieval period. Moreover, I argue that a proper understanding of immanent teleology, and why it was rejected by mainstream medieval natural philosophers, reveals that Boyle did not fail to eliminate immanent teleology from his natural philosophy. I conclude that any attempt to describe the break between medieval and early modern natural philosophy in terms of a break with immanent teleology is likely not on target.     

Two cell types in monoamine-containing ‘liquor contacting’ neuron system on the frog brain

Summary By means of an immunofluorescent technique, liquor contacting neurons, serotonergic in nature were demonstrated in the paraventricular organ and in the nucleus infundibularis dorsalis, and neurons catecholaminergic in nature were noted in the preoptic recess organ and in the caudal part of the 4th ventricle.     

Clearance of cerebral Aβ in Alzheimer’s disease: reassessing the role of microglia and monocytes

Deficiency in cerebral amyloid β-protein (Aβ) clearance is implicated in the pathogenesis of the common late-onset forms of Alzheimer’s disease (AD). Accumulation of misfolded Aβ in the brain is believed to be a net result of imbalance between its production and removal. This in turn may trigger neuroinflammation, progressive synaptic loss, and ultimately cognitive decline. Clearance of cerebral Aβ is a complex process mediated by various systems and cell types, including vascular transport across the blood–brain barrier, glymphatic drainage, and engulfment and degradation by resident microglia and infiltrating innate immune cells. Recent studies have highlighted a new, unexpected role for peripheral monocytes and macrophages in restricting cerebral Aβ fibrils, and possibly soluble oligomers. In AD transgenic (ADtg) mice, monocyte ablation or inhibition of their migration into the brain exacerbated Aβ pathology, while blood enrichment with monocytes and their increased recruitment to plaque lesion sites greatly diminished Aβ burden. Profound neuroprotective effects in ADtg mice were further achieved through increased cerebral recruitment of myelomonocytes overexpressing Aβ-degrading enzymes. This review summarizes the literature on cellular and molecular mechanisms of cerebral Aβ clearance with an emphasis on the role of peripheral monocytes and macrophages in Aβ removal.     

Neuroprotective effects of the gliopeptide ODN in an in vivo model of Parkinson’s disease

Parkinson’s disease (PD) is a neurodegenerative disorder characterized by a progressive loss of dopamine (DA) neurons through apoptotic, inflammatory and oxidative stress mechanisms. The octadecaneuropeptide (ODN) is a diazepam-binding inhibitor (DBI)-derived peptide, expressed by astrocytes, which protects neurons against oxidative cell damages and apoptosis in an in vitro model of PD. The present study reveals that a single intracerebroventricular injection of 10 ng ODN 1 h after the last administration of 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP) prevented the degeneration of DA neurons induced by the toxin in the substantia nigra pars compacta of mice, 7 days after treatment. ODN-mediated neuroprotection was associated with a reduction of the number of glial fibrillary acidic protein-positive reactive astrocytes and a strong inhibition of the expression of pro-inflammatory genes such as interleukins 1β and 6, and tumor necrosis factor-α. Moreover, ODN blocked the inhibition of the anti-apoptotic gene Bcl-2, and the stimulation of the pro-apoptotic genes Bax and caspase-3, induced by MPTP in the substantia nigra pars compacta. ODN also decreased or even in some cases abolished MPTP-induced oxidative damages, overproduction of reactive oxygen species and accumulation of lipid oxidation products in DA neurons. Furthermore, DBI knockout mice appeared to be more vulnerable than wild-type animals to MPTP neurotoxicity. Taken together, these results show that the gliopeptide ODN exerts a potent neuroprotective effect against MPTP-induced degeneration of nigrostriatal DA neurons in mice, through mechanisms involving downregulation of neuroinflammatory, oxidative and apoptotic processes. ODN may, thus, reduce neuronal damages in PD and other cerebral injuries involving oxidative neurodegeneration.