The Philosophy of the Cosmonomic Idea and the Philosophical Foundations of Mathematics

Since the discovery of the paradoxes of Zeno, the problem of infinity was dominated by the meaning of endlessness—a view also adhered to by Herman Dooyeweerd. Since Aristotle, philosophers and mathematicians distinguished between the potential infinite and the actual infinite. The main aim of this article is to highlight the strengths and limitations of Dooyeweerd’s philosophy for an understanding of the foundations of mathematics, including Dooyeweerd’s quasi-substantial view of the natural numbers and his view of the other types of numbers as functions of natural numbers. Dooyeweerd’s rejection of the actual infinite is turned upside down by the exploring of an alternative perspective on the interrelations between number and space in support of the idea of infinite totalities, or infinite wholes. No other trend has succeeded in justifying the mathematical use of the actual infinite on the basis of an analysis of the intermodal coherence between number and space.

Necessity of Religion

‘Necessity of Religion’ means that in the nature of man as an intelligent self-conscious being there is a necessary spiritual urge which forces him to rise above what is material and finite and to find rest nowhere short of an Infinite and Absolute Mind. This does not mean that each and every man is religious and the fact that there are men who are not religious does not disprove the necessity of religion. Rather in the very notion of a spiritual self-conscious being there is involved what may be called a virtual or potential infinite. True it is that Nature and man are both finite. But it is the characteristic of a spiritual intelligent being to transcend its individual limitations and realize itself in that which lies beyond itself.

More of the Same – On Spotify Radio

Spotify Radio allows users to find new music within Spotify’s vast back-catalogue, offering a potential infinite avenue of discovery. Nevertheless, the radio service has also been disliked and accused of playing the same artists over and over. We decided to set up an experiment with the purpose to explore the possible limitations found within “infinite archives” of music streaming services. Our hypothesis was that Spotify Radio appears to consist of an infinite series of songs. It claims to be personalised and never-ending, yet music seems to be delivered in limited loop patterns. What would such loop patterns look like? Are Spotify Radio’s music loops finite or infinite? How many tracks (or steps) does a normal loop consist of? To answer these research questions, at Umeå University’s digital humanities hub, Humlab, we set up an intervention using 160 bot listeners. Our bots were all Spotify Free users. They literally had no track record and were programmed to listen to different Swedish music from the 1970s. All bots were to document all subsequent tracks played in the radio loop and (inter)act within the Spotify Web client as an obedient bot listener, a liker, a disliker, and a skipper. The article describes different research strategies when dealing with proprietary data. Foremost, however, it empirically recounts the radio looping interventions set up at Humlab. Essentially, the article suggests a set of methodologies for performing humanist inquiry on big data and black-boxed media services that increasingly provide key delivery mechanisms for cultural materials. Spotify serves as a case in point, yet principally any other platform or service could be studied in similar ways. Using bots as research informants can be deployed within a range of different digital scholarship, so this article appeals not only to media or software studies scholars, but also to digitally inclined cultural studies such as the digital humanities.

More of the Same – On Spotify Radio

Spotify Radio allows users to find new music within Spotify’s vast back-catalogue, offering a potential infinite avenue of discovery. Nevertheless, the radio service has also been disliked and accused of playing the same artists over and over. We decided to set up an experiment with the purpose to explore the possible limitations found within “infinite archives” of music streaming services. Our hypothesis was that Spotify Radio appears to consist of an infinite series of songs. It claims to be personalised and never-ending, yet music seems to be delivered in limited loop patterns. What would such loop patterns look like? Are Spotify Radio’s music loops finite or infinite? How many tracks (or steps) does a normal loop consist of? To answer these research questions, at Umeå University’s digital humanities hub, Humlab, we set up an intervention using 160 bot listeners. Our bots were all Spotify Free users. They literally had no track record and were programmed to listen to different Swedish music from the 1970s. All bots were to document all subsequent tracks played in the radio loop and (inter)act within the Spotify Web client as an obedient bot listener, a liker, a disliker, and a skipper. The article describes different research strategies when dealing with proprietary data. Foremost, however, it empirically recounts the radio looping interventions set up at Humlab. Essentially, the article suggests a set of methodologies for performing humanist inquiry on big data and black-boxed media services that increasingly provide key delivery mechanisms for cultural materials. Spotify serves as a case in point, yet principally any other platform or service could be studied in similar ways. Using bots as research informants can be deployed within a range of different digital scholarship, so this article appeals not only to media or software studies scholars, but also to digitally inclined cultural studies such as the digital humanities.

Ockham on the Parts of the Continuum

This paper argues that, for Ockham, the parts of the continuum exist in act in the continuum: they are already there before any division of the continuum. Yet, they are infinitely many in that no division of the continuum will exhaust all the existing parts of the continuum taken conjointly. This reading of Ockham takes into account the crucial place of his new concept of the infinite in his analysis of the infinite divisibility of the continuum. Like many of his fellow anti-atomists, Ockham stresses that the concept of a potential infinite seems to contradict Aristotle’s modal logic, in particular the central assumption that there is no potency that will never be realized. Ockham, like other fourteenth-century anti-atomists, tried not only to refute atomism, but also to propose an analysis of the infinite divisibility of the continuum that is not incompatible with their modal logic.

A Study of Unrestricted Abstract Argumentation Frameworks

Research in abstract argumentation typically per-tains to finite argumentation frameworks (AFs). Ac-tual or potential infinite AFs frequently occur if theyare used for the purpose of nonmonotonic entail-ment, so-called instantiation-based argumentation,or if they are involved as modeling tool for dia-logues, n-person-games or action sequences. Apartfrom these practical cases a profound analysis yieldsa better understanding of how the nonmonotonic the-ory of abstract argumentation works in general. Inthis paper we study a bunch of abstract propertieslike SCC-recursiveness, expressiveness or intertrans-latability for unrestricted AFs.

Universales Morales: la ciencia de la naturaleza humana y el enfoque de la Ética cognitiva

<p><strong>Abstract</strong>: Recent trends in Cognitive Ethics have emphasized the conceptual debts with the development of the Science of Human Nature in the late 1600s and early 1700s. The paper deals mainly with two major theoretical approaches in the cognitive revolution, (1) that is possible to offer an explanation of the cognitive mechanisms involved in moral decision processes in terms of abstract principles allegedly embedded in human nature; and (2) that there might be substantive reasons to assume a moral faculty to account for the capacity to issue a potential infinite number of considered moral judgments.</p><p><strong>Keywords</strong>: Cognitive Ethics, Science of Human Nature, Universal Moral Grammar.</p><p> </p><p><strong>Resumen</strong>: Investigaciones recientes en la Ética Cognitiva han puesto de manifiesto algunas de la deudas teóricas con el desarrollo de la Ciencia de la Naturaleza Humana a finales del siglo XVII y a comienzos del siglo XVIII. El trabajo trata específicamente sobre dos asunciones teóricas específicas dentro de la revolución cognitiva, (1) que es posible ofrecer una explicación de las mecanismos cognitivos responsables de los procesos de decisión moral en términos de principios abstractos que supuestamente están incorporados en la naturaleza humana, y (2) podría ser razonable suponer que existe una cierta facultad moral humana que podría explicar la capacidad de emitir un número potencialmente infinito de juicios morales considerados.</p><p> </p>

Konsep Ketakhinggaan dalam Matematika

Ketakhinggaan adalah sebuah konsep penting yang tidak hanya digunakan dalam matematika, tetapi juga dalam bidang lainnya. Ketakhinggaan melambangkan realitas yang menunjukkan kekuasaan Tuhan yang tak terbatas. Dalam tulisan ini dibahas sejarah konsep ketakhinggaan (infinity) dan contoh penerapan dalam bidang komputer.Kata Kunci : Infinity, Paradoks, Aleph Null, Potential Infinite.

Concentration of solutions of equations of nonlinear Schrödinger type with vector potential: infinite-bump solutions and non-degeneracy

The equation –ε2Δu+F(V(x),u) = 0 is studied over all of ℝn, and solutions are constructed that concentrate at an infinite set asε→ 0. The functionV(x) is vector valued. This advances previous studies in whichV(x) was scalar valued.