This article outlines the work of a group of US mathematicians called the American Postulate Theorists and their influence on Tarski's work in the 1930s that was to be foundational for model theory. The American Postulate Theorists were influenced by the European foundational work of the period around 1900, such as that of Peano and Hilbert. In the period roughly from 1900???1940, they developed an indigenous American approach to foundational investigations. This made use of interpretations of precisely formulated axiomatic theories (...) to prove such metatheoretic properties as independence, consistency, categoricity and, in some cases, completeness of axiom sets. This approach to foundations was in many respects similar to that later taken by Tarski, who frequently cites the work of American Postulate Theorists. Their work served as paradigm examples of the theories and concepts investigated in model theory. The article also examines the possibility of a more specific impetus to Tarski's model theoretic investigation, arising from his having studied in 1927???1929 a paper by C. H. Langford proving completeness for various axiom sets for linear orders. This used the method of elimination of quantifiers. The article concludes with an examination of one example of Langford's methods to indicate how their correct formulation seems to call for model-theoretic concepts. (shrink)

The theme of the second declamation of Calpurnius Flaccus is ‘Matrona Aethiopem peperit. Arguitur adulterii’. In one of the excerpts , the accuser is arguing that for a white woman with a white husband to produce a black child is certain proof of adultery, for individual races have fixed physical characteristics to distinguish them. I give the text as argued for by W. S. Watt.

THE NATURE OF POLITEIA AND ITS CANDIDACY FOR STATUS as the best regime in the doctrine of Aristotle remains a disputable question. Some scholars insist that whatever the best regime may be, it must be a kind of polity. Others, however, firmly contend that the best must be a variety of aristocracy, with a significant number arguing that the best may be a monarchy should a suitable candidate be available. Moreover, it has been argued that since the ancients did not (...) desire the establishment of “polities” and hence pluralistic politics, but that this has been a concern of the moderns, one must conclude that an understanding of politeia as being a “mixed regime” would be “a contradiction in terms, because a regime proper cannot. (shrink)

In the great kingdoms of ancient Mesopotamia, the king’s power was often evoked by means of lion symbolism. This has led scholars to conclude that lion motifs, and especially that of the lion-slaying hero, in early Greek art and literature were cultural borrowings from the more populous and urbanised civilisations to the east. Yet it is also notable that the Greek tradition, at least from the time of the Homeric poems, tended to problematise the ethics of the leonine man. This (...) article explores the function of lion imagery in narratives of elite masculinity in western Asia and early Greece respectively. It will argue that Greek myth and epic reflect on and problematise any potential equation between lions and kingly prestige, power and masculinity, instead drawing attention to the savagery and social isolation of the lion-like man-of-power, and his difficulty in conforming to the expectations of civilised society. (shrink)

We question the plausibility of Fincher & Thornhill's (F&T's) argument that localised pathogen-host coevolution leads to out-groups having pathogens more damaging than those infecting one's own family or religious group.

International political, social, economic and religious developments influence how local communities operate. The South African church society is influenced by such developments taking place globally and which clearly influence how local churches function. This article explores the role of the contemporary church as a ‘reformation agency’ in enhancing a socially transformative agenda in South Africa. A qualitative research approach – an interpretative phenomenology design – was employed to negotiate a shared understanding through conversation and intersubjective meaning-making with church ministers, with (...) the primary focus being their subjective experience of the changing role of the church in enhancing a transformative agenda in a South African context. A purposive sampling consisted of local church leaders who participated in the face-to-face and telephonic semi-structured interviews to achieve the purpose of the study. The findings clearly show that deliberate and intentional actions by churches allow them to become a voice for the marginalised, to create spaces for searching for excellence and to increase the quality of servant leadership, all as vehicles for transforming church society. Furthermore, servant leadership is a social phenomenon, a philosophy-in-practice aimed at leading by example to achieve a common goal. To accomplish this, church ministers are required to spearhead the challenge as a prerequisite to creating ‘lived experienced’ opportunities for members as an inward-outward spiritual journey. Finally, church leaders believed that transformation is a secular dimension, but that it can also be aligned towards God’s redemption plan and enhancing a socially just transformation agenda. Ultimately, this study proposed several recommendations to allow the local church to be relevant in practicing and promoting stronger unity and reconciliation amongst all churches nationally and globally. (shrink)

E. Beltrami in 1868 did not intend to prove the consistency of non-euclidean plane geometry nor the independence of the euclidean parallel postulate. His approach would have been unsuccessful if so intended. J. Hoüel in 1870 described the relevance of Beltrami's work to the issue of the independence of the euclidean parallel postulate. Hoüel's method is different from the independence proofs using reinterpretation of terms deployed by Peano about 1890, chiefly in using a fixed interpretation for non-logical terms. Comparing the (...) work of Beltrami and Hoüel with the treatment of non-euclidean geometry after the development of the axiomatic method in the 1890s indicates an important shift in mathematicians? attitudes towards mathematical theories. (shrink)

Henry Sheffer’s 1908 Harvard Ph.D. thesis contains an interesting appendix on a central feature of the logical work of his thesis advisor, Josiah Royce. This is the claim in Royce’s 1905 article “The Relations of the Principles of Logic to the Foundations of Geometry” that an unsymmetric ordering relation can be defined on the single symmetric O-relation for which he gives postulates in that paper. Sheffer criticizes Royce’s specific definition from the point of view of the evolving twentieth century conception (...) of axiomatic method and also shows more generally that an unsymmetric1 order relation cannot be defined in the system of the 1905 paper based on the O-relation. In this article I wish to consider the nature.. (shrink)

We present a memorial summary of the professional life and contributions to logic of John Corcoran. We also provide a full list of his many publications.Courtesy of Lynn Corcoran.

Articles by two American mathematicians, E. V. Huntington and Oswald Veblen, are discussed as examples of a movement in foundational research in the period 1900-1930 called American postulate theory. This movement also included E. H. Moore, R. L. Moore, C. H. Langford, H. M. Sheffer, C. J. Keyser, and others. The articles discussed exemplify American postulate theorists' standards for axiomatizations of mathematical theories, and their investigations of such axiomatizations with respect to metatheoretic properties such as independence, completeness, and consistency.

Articles by two American mathematicians, E. V. Huntington and Oswald Veblen, are discussed as examples of a movement in foundational research in the period 1900-1930 called American postulate theory. This movement also included E. H. Moore, R. L. Moore, C. H. Langford, H. M. Sheffer, C. J. Keyser, and others. The articles discussed exemplify American postulate theorists' standards for axiomatizations of mathematical theories, and their investigations of such axiomatizations with respect to metatheoretic properties such as independence, completeness, and consistency.

Jonathan Lear has suggested that Aristotle attempts to demonstrate a proof-theoretic analogue of a compactness theorem in Posterior analyticsI, chs. 19?22. Aristotle argues in these chapters that there cannot be in finite series of predications of terms. Lear's analysis of Aristotle's arguments are shown to be based on confusions about the nature of infinite orderings. Three distinct confusions are identified. In final remarks, it is suggested that a compactness claim is irrelevant to the issues which motivate Aristotle's arguments.

Research on cultural transmission among Americans has established a bias for transmitting stories that have disgusting elements. Conceived of as a cultural evolutionary force, this phenomenon is one type of emotional selection. In a series of online studies with Americans and Indians we investigate whether there are cultural differences in emotional selection, such that the transmission process favours different kinds of content in different countries. The first study found a bias for disgusting content among Americans but not among Indians. Four (...) subsequent studies focused on how country interacts with kind of emotional content in reactions to transmission of stories or information. Whereas Indian participants, compared to Americans, tended to be less interested in, and excited by, transmission of stories and news involving common disgust-elicitors, the opposite pattern held for transmission of happy surprises and good news. We discuss various possible explanations and implications. (shrink)