In this paper which consists of two parts (Teil I and Teil II) we champion Diophantus of Alexandria and Isabella BaÅ¡makova against Norbert Schappacher. In two publications ([Schappacher 1998a] and [Schappacher 1998b]) he puts forward inter alia two propositions: Questioning Diophantus’ originality he considers affirmatively the possibility that the Arithmetica are the joint work of a team of authors like Bourbaki. And he calls BaÅ¡makova’s claim (in [BaÅ¡makova 1972]) that Diophantus uses negative numbers, a nonsense , reproaching her for her (...) thoughtlessness . Teil I: First, we disprove Schappacher’s Bourbaki thesis. Second, we investigate the semantic meaning and historical significance of Diophantus’ keywords $ λvarepsilon tildeιψιζ and ὕπαρξιζ. Next, we discuss Schappacher’s epistemology of the history of mathematics and defend BaÅ¡makova’s methods. Finally we analyse in detail three problems from Diophantus’ Arithmetica (and their solutions) given by Thomas Heath and Helmuth Gericke as proof of the their claim that Diophantus did not use negative numbers. Teil II: In this Part, we give 33 places where Diophantus uses negative quantities as intermediate results; they appear as differences a − b of positive rational numbers, the subtrahend b being bigger than the minuend a; they each represent the (negative) basis ( πλvarepsilonυρacuteα ) of a square number ( τvarepsilonτρacuteαγω ν o ζ ), which is afterwards computed by the formula (a - b) 2 = a 2 + b 2 - 2ab $ . Finally, we report how the topic Diophantus and the negative numbers has been dealt with by translators and commentators from Maximus Planudes onwards. Und er kommt zu dem Ergebnis: ≪Nur ein Traum war das Erlebnis. Weil≫, so schlieβt er messerscharf, ≪nicht sein k a n n, was nicht sein d a r f.≫ CHRISTIAN MORGENSTERN: Palmstrm. (shrink)

The first book-length philosophical study on the Presocratic influences in Plotinus’ Enneads.

_The first book-length philosophical study on the Presocratic influences in Plotinus’ Enneads._.

Theurgy, the religious magic practised by the later Neoplatonists, has been commonly regarded as the point at which Neoplatonism degenerates into magic, superstition and irrationalism.1 A superficial glance at the ancient lives of the Neoplatonists, and in particular at Eunapius’ Lives of the Sophists, reveals a group of people interested in animating statues, favoured with visions of gods and demons, and skilled in rain-making. But when we look more closely at the works of the Neoplatonists themselves, rather than the stories (...) biographers tell about them, we find a considerable diversity of attitudes towards theurgy and a number of attempts to fit theurgy into their philosophical system. (shrink)

Theurgy, the religious magic practised by the later Neoplatonists, has been commonly regarded as the point at which Neoplatonism degenerates into magic, superstition and irrationalism.1 A superficial glance at the ancient lives of the Neoplatonists, and in particular at Eunapius’ Lives of the Sophists, reveals a group of people interested in animating statues, favoured with visions of gods and demons, and skilled in rain-making. But when we look more closely at the works of the Neoplatonists themselves, rather than the stories (...) biographers tell about them, we find a considerable diversity of attitudes towards theurgy and a number of attempts to fit theurgy into their philosophical system. (shrink)

In his Life of Plotinus , Porphyry makes reference to certain gnostic ‘revelations’ under the names of ‘Zoroaster and Zostrianos and Nicotheus and Allogenes and Messos and many others of this kind’ which were circulated in Plotinus' school and refuted by Plotinus and his students, including Porphyry himself. Porphyry claims to have made ‘several refutations against the book of Zoroaster’ while Amelius apparently wrote some ‘forty volumes against the book of Zostrianos’. The surprising discovery of Coptic gnostic texts in the (...) Nag Hammadi Library under the specific names of Allogenes and Zostrianos and the close relation of these texts to The Three Steles of Seth and Marsanes has led to the general consensus that we now possess some of the actual texts mentioned by Porphyry. (shrink)

In his Life of Plotinus, Porphyry makes reference to certain gnostic ‘revelations’ under the names of ‘Zoroaster and Zostrianos and Nicotheus and Allogenes and Messos and many others of this kind’ which were circulated in Plotinus' school and refuted by Plotinus and his students, including Porphyry himself. Porphyry claims to have made ‘several refutations against the book of Zoroaster’ while Amelius apparently wrote some ‘forty volumes against the book of Zostrianos’. The surprising discovery of Coptic gnostic texts in the Nag (...) Hammadi Library under the specific names of Allogenes and Zostrianos and the close relation of these texts to The Three Steles of Seth and Marsanes has led to the general consensus that we now possess some of the actual texts mentioned by Porphyry. (shrink)

Is the Dionysian God, or an experience of the Dionysian God, absolutely ineffable? Does the Dionysian corpus assert or perform such ineffability? This paper will argue that the answer to each of these questions is no. The Dionysian God is known hyper-nous as the hyper-ousia cause of all. And the Dionysian corpus unambiguously refers to, asserts of, and metaphorizes about this God just so. In arguing these points, this paper will call upon both the speech act theory of John Searle (...) and the metaphor theory of George Lakoff and Mark Johnson. More particularly, it will look to Searle’s rules of reference and predication and conditions of illocutionary acts, as well as Lakoff and Johnson’s schematization of metaphor gestalt and entailment to show how Dionysian expressions of inexpressibility are rule-governed and the Dionysian God is thereby effable. (shrink)