Cauchy's infinitesimals, his sum theorem, and foundational paradigms

Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy's proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy's proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy's proof closely and show that it finds closer proxies in a different modern framework. Keywords: Cauchy's infinitesimal; sum theorem; quantifier alternation; uniform convergence; foundational paradigms.Comment: 42 pages; to appear in Foundations of Scienc

Digital Art as ‘Monetised Graphics:’ Enforcing Intellectual Property on the Blockchain

In a global economic landscape of hyper-commodification and financialisation, efforts to assimilate digital art into the high-stakes commercial art market have so far been rather unsuccessful, presumably because digital art works cannot easily assume the status of precious object worthy of collection. This essay explores the use of blockchain technologies in attempts to create proprietary digital art markets in which uncommodifiable digital art works are financialised as artificially scarce commodities. Using the decentralisation techniques and distributed database protocols underlying current cryptocurrency technologies, such efforts, exemplified here by the platform Monegraph, tend to be presented as concerns with the interest of digital artists and with shifting ontologies of the contemporary work of art. I challenge this characterisation, and argue, in a discussion that combines aesthetic theory, legal and philosophical theories of intellectual property, rhetorical analysis, and research in the political economy of new media, that the formation of proprietary digital art markets by emerging commercial platforms such as Monegraph constitutes a worrisome amplification of long-established, on-going efforts to fence in creative expression as private property. As I argue, the combination of blockchain-based protocols with established ambitions of intellectual property policy yields hybrid conceptual-computational financial technologies (such as self-enforcing smart contracts attached to digital artefacts) that are unlikely to empower artists, but which serve to financialise digital creative practices as a whole, curtailing the critical potential of the digital as an inherently dynamic and potentially uncommodifiable mode of production and artistic expression

The economics of debt clearing mechanisms

We examine the evolution of decentralized clearinghouse mechanisms from the 13th to the 18th century; in particular, we explore the clearing of non- or limitedtradable debts like bills of exchange. We construct a theoretical model of these clearinghouse mechanisms, similar to the models in the theoretical matching literature, and show that specific decentralized multilateral clearing algorithms known as rescontre, skontrieren or virement des parties used by merchants were efficient in specific historical contexts. We can explain both the evolutionary self-organizing emergence of late medieval and early modern fairs, and its robustness during the 17th and 18th century

School Effects on the Wellbeing of Children and Adolescents

Well-being is a multidimensional construct, with psychological, physical and social components. As theoretical basis to help understand this concept and how it relates to school, we propose the Self-Determination Theory, which contends that self-determined motivation and personality integration, growth and well-being are dependent on a healthy balance of three innate psychological needs of autonomy, relatedness and competence. Thus, current indicators involve school effects on children’s well-being, in many diverse modalities which have been explored. Some are described in this chapter, mainly: the importance of peer relationships; the benefits of friendship; the effects of schools in conjunction with some forms of family influence; the school climate in terms of safety and physical ecology; the relevance of the teacher input; the school goal structure and the implementation of cooperative learning. All these parameters have an influence in promoting optimal functioning among children and increasing their well-being by meeting the above mentioned needs. The empirical support for the importance of schools indicates significant small effects, which often translate into important real-life effects as it is admitted at present. The conclusion is that schools do make a difference in children’s peer relationships and well-being