Mathematical Generality, Letter-Labels, and All That

Phronesis ◽  
2020 ◽  
Vol 65 (1) ◽  
pp. 27-75
Author(s):  
F. Acerbi

AbstractThis article focusses on the generality of the entities involved in a geometric proof of the kind found in ancient Greek treatises: it shows that the standard modern translation of Greek mathematical propositions falsifies crucial syntactical elements, and employs an incorrect conception of the denotative letters in a Greek geometric proof; epigraphic evidence is adduced to show that these denotative letters are ‘letter-labels’. On this basis, the article explores the consequences of seeing that a Greek mathematical proposition is fully general, and the ontological commitments underlying the stylistic practice.

2017 ◽  
Vol 5 (2) ◽  
Author(s):  
Anne Lykke

AbstractThe article explores aspects of the monetization of the Greek sanctuaries, more specifically how space was created to accommodate coins as objects and their use within the sacred sphere. Except in a limited number of cases, our understanding is still quite fragmented. Where most research has focused on analyzing the coin material or the epigraphic evidence, the intention here is to look more widely at the archaeological evidence connected with coins and coin-related material. This is done in an attempt to appreciate the significance of the progressing monetization and ritualization of the use of coins and in extension to develop an understanding of the possible changes in human behavior in the sanctuaries based on this evidence.


2012 ◽  
Vol 22 (02) ◽  
pp. 1230007
Author(s):  
OTTO E. RÖSSLER

The pre-history of chaos in a rationalist context is taken as a point of departure, starting out with ancient China. The related ancient-Greek "unmixing theory" then leads over to two simple formally 2-body Hamiltonian systems exhibiting chaotic behavior. When the two masses involved are unequal, "pseudoattractors" are formed. Deterministic statistical "thermodynamics" with its dissipative behavior arises when the potential is repulsive. Deterministic statistical "cryodynamics" arises when the potential is attractive. The latter class of Newtonian systems is characterized by "antidissipative" behavior. A geometric proof is sketched in the footsteps of Sinai and Bunimovich. Antidissipative behavior is known empirically from Hubble's law which was so far explained in less fundamental terms. Three experimental examples are proposed.


2017 ◽  
Vol 71 (3) ◽  
pp. 907-957 ◽  
Author(s):  
Johannes Thomann

Abstract In the fourth/tenth century a great number of new intellectual centers appeared in the Islamic world, and an increase in the number of persons involved in production of written works on mathematics and astronomy took place. One such new center was Aleppo under the Ḥamdanid ruler Sayf al-Dawla. According to al-Qabīṣī the generosity of Sayf al-Dawla led to the situation that ignorant people pretended to be astronomers or astrologer. Therefore, al-Qabīṣī argued, exams should be established for testing the level of competence and the completeness of knowledge of a candidate. Al-Qabīṣī was engaged in teaching by giving lectures based on a textbook, the Fuṣūl of al-Farghānī. This was a novelty in teaching astronomy, since before memorizing didactic poems and operating with astronomical instruments was the preferred method. While al-Qabīṣī’s aim in teaching astronomy was to train future professional astronomers and astrologers, in other contexts astronomy was a propaedeutic subject as part of the quadrivium. The philosopher Muḥammad Ibn al-Haytham (not to be confused with the mathematician al-Ḥasan Ibn al-Haytham) wrote a commentary of the Almagest, in which his intention was “to elucidate subtle ideas for the benefit of students”, and not to go into technical details of calculation. Obviously his aim was to educate future philosophers in the “philosophical sciences” (mathematics, natural sciences and metaphysics). Some generations earlier, al-Fārābī wrote a commentary on the Almagest with similar intentions. His preferred subject was the geometric proof, while observations and calculations were of little interest. Astronomy was incorporated into a curriculum of general scientific knowledge, – similar to the curriculum of the Alexandrian schools in late antiquity –, and ancient Greek texts on astronomy were preferred. This development was indeed a renaissance in the sense Jacob Burckhardt used the term.


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