This essay examines the quantitative aspects of Greco-Roman science, represented by a group of established disci¬plines, which since the fourth century BC were called mathēmata or mathē¬ma¬tikai epistē¬mai. In the group of mathēmata that in Antiquity normally comprised mathematics, mathematical astronomy, harmonics, mechanics and optics, we have also included geography. Using a dataset based on The Encyclopaedia of Ancient Natural Scientists, our essay considers a community of mathēmatikoi (as they called themselves), or ancient scientists (as they are defined (...) for the purposes of the present paper) from a sociological point of view, focusing on the size of the scientific population known to us and its disciplinary, temporal and geographical distribution. A diachronic comparison of neighboring and partly overlapping communities, ancient scientists and philosophers, allows the pattern of their interrelationship to be traced. An examination of centers of science throughout ancient history reveals that there were five major centers – Athens, Alexandria, Rhodes, Rome and Byzantium/Constantinople – that appear and replace one another in succession as leaders. These conclusions serve to reopen the issue of the place of mathēmata and mathēmatikoi in ancient society. (shrink)

We present an approach in which ancient Greek mathematical proofs by Hippocrates of Chios and Euclid are addressed as a form of (guided) intentional reasoning. Schematically, in a proof, we start with a sentence that works as a premise; this sentence is followed by another, the conclusion of what we might take to be an inferential step. That goes on until the last conclusion is reached. Guided by the text, we go through small inferential steps; in each one, (...) we go through an autonomous reasoning process linking the premise to the conclusion. The reasoning process is accompanied by a metareasoning process. Metareasoning gives rise to a feeling-knowing of correctness. In each step/cycle of the proof, we have a feeling-knowing of correctness. Overall, we reach a feeling of correctness for the whole proof. We suggest that this approach allows us to address the issues of how a proof functions, for us, as an enabler to ascertain the correctness of its argument and how we ascertain this correctness. (shrink)

In Intimations of Christianity Among the Ancient Greeks , Simone Weil discusses precursors to Christian religious ideas which can be found in ancient Greek mythology, literature and philosophy. She looks at evidence of "Christian" feelings in Greek literature, notably in Electra, Orestes, and Antigone , and in the Iliad , going on to examine God in Plato, and divine love in creation, as seen by the ancient Greeks.

This chapter contains sections titled: Socrates and Dialectical Method Plato Aristotle Hellenistic Methodology.

Born in a small town in Lithuania, Rabbi Reuven Agushewitz emigrated to the United States in 1929. A Talmudic genius and an autodidact in philosophy, Rabbi Agushewitz published three philosophical works in Yiddish. Ancient Greek Philosophy, the first published but the last to be translated into English, offers a unique blend of clear philosophical principles and a flavorful Yiddish style, which Mark Steiner's translation preserves. Rabbi Agushewitz not only explains what the early Greek philosophers said, he also (...) amplifies their arguments with creative proofs that the ancients themselves did not offer. His attempts to correlate ancient philosophical statements with monotheism will resonate with the modern religious reader. In addition to the present volume, R. Agushewitz's philosophical books are Faith and Heresy and Principles of Philosophy, both published in translation under the auspices of the Michael Scharf Publication Trust of Yeshiva University Press. His volume of Talmudic novellae on Bava Kamma, "Bi'ur Reuven," was published with approbation from both Rabbi Aharon Kotler and Rabbi Joseph B. Soloveitchik. These Talmudic giants differed sharply on their attitude toward the study of philosophy, but they concurred wholeheartedly on the scholarship of R. Agushewitz. (shrink)