The paper presents a formal model of the system of number representations as a multiplicity of mental number axes with a hierarchical structure. The hierarchy is determined by the mind as it acquires successive types of mental number axes generated by virtue of some algebraic mechanisms. Three types of algebraic structures, responsible for functioning these mechanisms, are distinguished: BASAN-structures, CASAN-structures and CAPPAN-structures. A foundational order holds between these structures. CAPPAN-structures are derivative from CASAN-structures which are (...) extensions of BASAN-structures. The constructed formal model unifies two competitive conceptions of cognitive arithmetic: namely, the conception of the mental number line and the conception of parallel individuation. The paper is the continuation of a paper entitled Representational structures of arithmetical thinking, in which rich empirical evidence supporting the model is presented. The main result achieved in the present paper may be philosophically interpreted as an attempt to formalize the Kantian conception of the pure idea of time, understood as the a priori form of human arithmetical thinking. In this way, our theory may be comprehended as a result of applying the hard method of logical reconstruction of fundamental epistemological categories. (shrink)

The third century of the hegira represents an extremely important period in terms of the formation process of Islamic sciences and the acquirement of the identity of a systematic school of fiqh madhhabs. In terms of the Zaydiyya madhhab, this century has an identity that affects the next period in terms of both political and scientific studies. Because in this period, the scholars of the madhhab like Kāsim al-Rassî (d. 246/860), Ahmad b. Isā (d. 247/861) and Yahyā b. al-Husayn (d. (...) 298/911), who were in a leading position both in politics and in sciences such as kalām, hadith and fiqh, emerged. Kāsim al-Rassî, who was accepted as the star of the Ahl al-Bayt by Zaydî sources in the first period, was presented as the Plato of Muslims by orientalists in modern studies. The main reason why today's studies on him are mostly about the history of sects and theology, most of Rassî's works are about kalām. However, Kāsim al-Rassî is an important name in the science of fiqh and İslamic legal theory as well as in the science of kalām. According to Abī Tālib Nātik bi’l-Hakk (d. 424/1033), one of the important jurists of the Zaydiyya madhhab, Rassî was a scholar who came to the fore with his ability in fiqh issues; in order to see his ijtihād method, his skill in furû al-fiqh, his mastery in using hadiths and knowing the disagreements of scholars, ‘‘Masā’il al-Dja’far b. Muhammad and Abd Allah b. Hasan” should be consulted. Rassi's epistles named Kitab al-Nāsikh wa’l-Mansūkh, Kitab al-tahāra, Kitab al-salāt al-yevm ve al-Laylā and Kitab al-menāsik are important studies on fiqh that have survived to the present day. In addition, Mueyyed-Billah (d. 411/1021) compiled Kāsim al-Rassî’s and Yahya b. al-Husayn's views on fiqh in his work named al-Tecrîd. Kāsim al-Rassî's views on fiqh are also determinative in later fiqh books such as Tahrîr, al-Cāmi' al-Kāfi, al-Intisār and al-Azhar. In time, the emergence of a jurisprudence sect named Kāsimiyya in Zaydiyya, referring to his name, is also important in terms of revealing his position. Although Rassî's views on fiqh have been referred to a number of studies in our country, no independent study has been found that deals with his views on fiqh. However, considering both of his works on fiqh that have survived to the present day and the early works in which his views are compiled, it is obvious that Kāsim al-Rassî's views on fiqh deserve an independent works. The aim of this study is to reveal Ressî's position within the madhhabs and his perspective on fiqh in general. In this context, in the study, the period in which Ressî lived, his life and works were briefly mentioned, and then the basic views of the fiqh, especially in the field of worship, were discussed in outline. (shrink)

The paper undertakes three interdisciplinary tasks. The first one consists in constructing a formal model of the basic arithmetic competence, that is, the competence sufficient for solving simple arithmetic story-tasks which do not require any mathematical mastery knowledge about laws, definitions and theorems. The second task is to present a generalized arithmetic theory, called the arithmetic of indexed numbers (INA). All models of the development of counting abilities presuppose the common assumption that our simple, folk arithmetic encoded linguistically in the (...) mind is based on the linear number representation. This classical conception is rejected and a competitive hypothesis is formulated according to which the basic mature representational system of cognitive arithmetic is a structure composed of many numerical axes which possess a common constituent, namely, the numeral zero. Arithmetic of indexed numbers is just a formal tool for modelling the basic mature arithmetic competence. The third task is to develop a standpoint called temporal pluralism, which is motivated by neo-Kantian philosophy of arithmetic. (shrink)

This paper is an amalgam of physics and mathematical logic. It contains an elementary axiomatization of spacetime in terms of the primitive concepts of particle, signal, and transmission and reception. In the elementary language formed with these predicates we state AxiomsE, C, andU, which are naturally interpretable as basic physical properties of particles and signals. We then determine all mathematical models of this axiom system; these represent certain generalizations of the standard model. Also, the automorphism groups of the models are (...) determined. Finally we give another physical model and discuss the philosophical implications. (shrink)

This article comments on Sylvia Walby’s critique of the politics of difference and the relativist tendencies she sees represented in some contemporary feminist positions. While the general direction of Walby’s intervention is not disputed, the theoretical architecture of her text as well as the way she develops her argumentation are critically assessed. Problems in the architecture of the text concern the unclear interconnection between epistemological questions, questions of moral philosophy/political theory and practical politics. The critique focuses on three aspects: on (...) problems connected with Walby’s use of the Habermasian notion of ‘argumentation’, on difficulties related to an incoherent use of the notion of ‘difference’ and on the inadequate way in which she constructs oppositions between theories. The article lays out some of the theoretical backgrounds of the debates Walby refers to, in order to enhance a more specific comparison and critique of positions. (shrink)

This axiomatization is based on the observation that ifG is the group of automorphisms of the states (induced, e.g., by suitable evolutions), then we can define a spherical function by mapping each element ofG to the matrix of its transition probabilities. Starting from five physically conservative axioms, we utilize the correspondence between spherical functions and representations to apply the structure theory for compact Lie groups and their orbits in representation spaces to arrive at the standard complex Hilbert space structure of (...) quantum mechanics. (shrink)

***Angaben zur beteiligten Person Kann: Christoph Kann ist Professor für Philosophie an der Universität Düsseldorf.

The article focuses on the temporal and epistemic economy connected to the transatlantic travels of the categorical triad of ‘race-class-gender’. It looks at conditions and forces that have fuelled the dynamics of the discourse on differences and inequality among women and analyses feminist discourse and its aporias as a particular environment for the travels of theories. Furthermore, it follows the changes the triad of ‘race-class-gender’ undergoes on its transatlantic route from the United States to a German-speaking context and it outlines (...) the theoretical challenges connected to an intersectional perspective that aims to overcome a theoretical stagnation that itself finds symptomatic expression in the ritual citing of ‘race-class-gender’. (shrink)

Charles Darwin's Origin of Species, published in 1859, was a revolutionary attempt “to overthrow the dogma of separate creations,” a declaration that provoked different reactions among the religious, ranging from mild enthusiasm to anger. Christians sympathetic to Darwin's effort sought to make Darwinism appear compatible with their religious beliefs. Two of Darwin's most prominent defenders in the United States were the Calvinists Asa Gray, a Harvard botanist, and George Frederick Wright, a cleric-geologist. Gray, who long favored a “special origination” in (...) connection with the evolution of humans and questioned whether natural selection can account for the formation of organs, the making of eyes, etc., embraced natural selection as the primary mechanism underlying the production of most species. He also went so far as to invoke divine providence, rather than randomness, to explain the variations on which natural selection acted. This chapter discusses creationism, intelligent design, and modern biology. (shrink)

Over the course of human history, the sciences, and biology in particular, have often been manipulated to cause immense human suffering. For example, biology has been used to justify eugenic programs, forced sterilization, human experimentation, and death camps—all in an attempt to support notions of racial superiority. By investigating the past, the contributors to _Biology and Ideology from Descartes to Dawkins_ hope to better prepare us to discern ideological abuse of science when it occurs in the future. Denis R. Alexander (...) and Ronald L. Numbers bring together fourteen experts to examine the varied ways science has been used and abused for nonscientific purposes from the fifteenth century to the present day. Featuring an essay on eugenics from Edward J. Larson and an examination of the progress of evolution by Michael J. Ruse, _Biology and Ideology_ examines uses both benign and sinister, ultimately reminding us that ideological extrapolation continues today. An accessible survey, this collection will enlighten historians of science, their students, practicing scientists, and anyone interested in the relationship between science and culture. (shrink)

As the crusade to outlaw the teaching of evolution changed to a battle for equal time for creationism, the ideological defenses of that doctrine also shifted from primarily biblical to more scientific grounds. This essay describes the historical development of “scientific creationism” from a variety of late–nineteenth– and early–twentieth–century creationist reactions to Charles Darwin's theory of evolution, through the Scopes trial and the 1960s revival of creationism, to the current spread of strict creationism around the world.

Belief in the divine origin of the universe began to wane most markedly in the nineteenth century, when scientific accounts of creation by natural law arose to challenge traditional religious doctrines. Most of the credit - or blame - for the victory of naturalism has generally gone to Charles Darwin and the biologists who formulated theories of organic evolution. Darwinism undoubtedly played the major role, but the supporting parts played by naturalistic cosmogonies should also be acknowledged. Chief among these was (...) the nebular hypothesis proposed by Pierre Simon Laplace in 1796, which explained the origin of the solar system as a natural development over extended periods of time. Ronald Numbers focuses on Laplace's theory as it affected American scientific thought. he first traces the history of Laplace's cosmogony chronologically, from its European inception to its demise about 1900. the last three chapters explore some of the theological and scientific consequences resulting from the acceptance of this cosmogony. Most significant was the change in the status of supernatural doctrine. When the nebular hypothesis lost credence at the end of the nineteenth century, those who had before tried to accommodate natural theory with supernatural doctrine no longer felt compelled to do so when faced with succeeding theories. The nebular hypothesis, it seems, had established natural law in the heavens. (shrink)

As past president of both the History of Science Society and the American Society of Church History, Ronald L. Numbers is uniquely qualified to assess the historical relations between science and Christianity. In this collection of his most recent essays, he moves beyond the clichés of conflict and harmony to explore the tangled web of historical interactions involving scientific and religious beliefs. In his lead essay he offers an unprecedented overview of the history of science and Christianity from the perspective (...) of the ordinary people who filled the pews of churchesor loitered around outside. Unlike the elite scientists and theologians on whom most historians have focused, these vulgar Christians cared little about the discoveries of Copernicus, Newton, and Einstein. Instead, they worried about the causes of the diseases and disasters that directly affected their lives and about scientists preposterous attempts to trace human ancestry back to apes. Far from dismissing opinion-makers in the pulpit, Numbers closely looks at two the most influential Protestant theologians in nineteenth-century America: Charles Hodge and William Henry Green. Hodge, after decades of struggling to harmonize Gods two revelationsin nature and in the Biblein the end famously described Darwinism as atheism. Green, on the basis of his careful biblical studies, concluded that Ussher's chronology was unreliable, thus opening the door for Christian anthropologists to accommodate the subsequent discovery of human antiquity. In Science without God Numbers traces the millennia-long history of so-called methodological naturalism, the commitment to explaining the natural world without appeals to the supernatural. By the early nineteenth century this practice was becoming the defining characteristic of science; in the late twentieth century it became the central point of attack in the audacious attempt of intelligent designers to redefine science. Numbers ends his reassessment by arguing that although science has markedly changed the world we live in, it has contributed less to secularizing it than many have claimed. Taken together, these accessible and authoritative essays form a perfect introduction to Christian attitudes towards science since the 17th century. (shrink)

Like other English-speaking peoples around the world, New Zealanders began debating Darwinism in the early 1860s, shortly after the publication of Charles Darwin's Origin of Species. Despite the opposition of some religious and political leaders – and even the odd scientist – biological evolution made deep inroads in a culture that increasingly identified itself as secular. The introduction of pro-evolution curricula and radio broadcasts provoked occasional antievolution outbursts, but creationism remained more an object of ridicule than a threat until the (...) last decades of the twentieth century, when first American and then Australian creationists began fomenting antievolutionism among New Zealanders. Although Stephen Jay Gould assured them in 1986 that they had little to fear from so-called scientific creationism, because it was a ‘peculiarly American’ phenomenon, scientific creationism by the mid-1990s had captured the allegiance of an estimated five per cent of the country and proved especially attractive to Maori and Pacific Islanders. In 1992 New Zealand creationists formed their own antievolution society, Creation Science. (shrink)

Originally published in 1995, Creation-Evolution Debates is the second volume in the series, Creationism in Twentieth Century America, reissued in 2021. The volume comprises eight debates from the early 1920s and 1930s between prominent evolutionists and creationists of the time. The original sources detail debates that took place either orally or in print, as well as active debates between creationists over the true meaning of Genesis I. The essays in this volume feature prominent discussions between the likes of Edwin Grant (...) Conklin, Henry Fairfield Osbourne and William Jennings Bryan, John Roach Francis and Charles Francis Potter, George McCready Price and Joseph McCabe and William Bell Riley versus Charles Smith, amongst many others. The collection will be of especial interest to natural historians, and theologians as well as academics of philosophy, and history. (shrink)