This paper focuses on the exegetical proposal of the Tractatus de sex dierum operibus by Thierry of Chartres and it is tasked with analyzing the twofold interpretative framework adopted by the Cancelor: first, the accordance between the narration of Genesis and the heuristic models of physical and cosmological causality; second, the mathematical theology, which revises the work of creation according to an arithmological approach. The study is divided into two parts which follow the structure of the Tractatus. In the first (...) part, I analyse the physical plausibility of Christian cosmogony and subsequently the conception of matter with regard to both William of Conches’ inordinatum and the hermetic locus mundi. In the second part, I examine how the numerical discourse interprets the creatural unfolding and dependence on God, as well as the creation per verbum and the individuality of each created being. My purpose is threefold: first, to test the inner philosophical coherence of the Tractatus; second, to interpret specific theoretical points at the light of Thierry’s commentaries on Boethius’ De Trinitate, and finally, to relate the arithmetical issues of the Tractatus to Thierry's Commentum super Arithmeticam Boethii. (shrink)

Nikolai Bugaev was a mathematician keenly interested in philosophy. He stressed the role of discontinuity in his mathematical research that he called arithmology. He also emphasized the importance of discontinuity in nature which he embodied in his version of monadology. The article discusses the viability of his philosophical investigations.

The prevailing narrative in the history of science maintains that the ancient Greeks did not have a concept of a ‘law of nature’. This paper overturns that narrative and shows that some ancient Greek philosophers did have an idea of laws of nature and, moreover, they referred to them as ‘laws of nature’. This paper analyzes specific examples of laws of nature in texts by Plato, Aristotle, Philo of Alexandria, Nicomachus of Gerasa, and Galen. These examples emerged out of the (...) closely intertwined Platonic and Pythagorean traditions, and these philosophers’ texts make reference to laws of nature when describing arithmetical methods, arithmological doctrines, or medical theories. Nicomachus’ laws of nature are especially noteworthy, because they have features that historians look for in the search for the origin of the modern concept of laws of nature. Nicomachus’ laws of nature are mathematical, universal, and necessary. This paper raises the possibility that the ancient Platonic and Pythagorean traditions influenced the subsequent development of the idea of laws of nature in medieval and early modern Europe, including the conception of laws of nature deployed by Johannes Kepler and Isaac Newton. (shrink)

This essay examines the links between the soul and number in Renaissance thought, from the sixteenth to the early seventeenth century, a period in which ancient philosophy was fully accepted and modern science gradually asserted itself. Thanks to the influences of Kabbalistic thought, Pythagoreanism and Neoplatonism - in particular the works of Porphyry, Iamblichus and Proclus - the study of arithmology, a discipline concerned with the symbolic properties of numbers, spread throughout the Renaissance. By examining largely unpublished treatises such (...) as those of Fabio Paolini (1535-1605) and Francesco Patrizi (1529-1597), these pages offer new perspectives on the interpretation of Renaissance thought and sixteenth-century Platonic philosophy. -/- Il saggio indaga i legami tra anima e numero nell’ambito del pensiero rinascimentale, dal XVI secolo agli esordi del XVII secolo, epoca nella quale la filosofia antica viene pienamente recepita e la scienza moderna si afferma progressivamente. Grazie alle influenze esercitate dal pensiero cabalistico, dal pitagorismo e dal neoplatonismo – in particolare dalle opere di Porfirio, Giamblico e Proclo – durante il Rinascimento si diffonde lo studio dell’aritmologia, disciplina che si occupa delle proprietà simboliche dei numeri. Attraverso l’esame di trattati in larga parte inediti, come i lavori di Fabio Paolini (1535-1605) e di Francesco Patrizi (1529-1597), queste pagine offrono nuove prospettive sull’interpretazione del pensiero rinascimentale e della filosofia platonica del Cinquecento. (shrink)

Though widely known and frequently put forward since Nicomachus of Gerasa (2nd century AD), the arithmological doctrine of “perfect”, “abundant”, and “deficient” num­bers is newly illustrated in a medieval gloss to Martianus Capella’s De Nuptiis Philologiae et Mercurii, Book VII, where mythology is replaced by ethics and theology, and the perfect num­ber is compared to eternal justice.

Pour parler de la chute ou de la déclinaison de l’Âme dans le cadre des récits cosmogoniques gnostiques, Plotin a recours, en sus du terme νεῦσις, au substantif σφάλμα, comme s’il s’agissait d’un synonyme de νεῦσις. L’enquête que nous avons menée montre le bien-fondé de cet usage, puisque le terme σφάλμα est, de fait, utilisé par les hérésiologues pour décrire, dans un langage hérité du néo-pythagorisme et donc rythmé par le nombre, la chute de Sophia, laquelle incarne le douzième éon (...) de la Dodécade en même temps que le trentième et dernier éon de l’ensemble du Plérôme. Rapporté à la métaphysique pythagoricienne dont il relève, le récit gnostique perd toute apparence d’arbitraire et révèle enfin sa véritable structure, commandée de bout en bout par le nombre. Il est raisonnable de penser que l’arithmologie rivale du traité 34 de Plotin est là pour y couper court. When speaking of the fall or decline of the Soul within the context of the Gnostic cosmogonic narratives, Plotinus, in addition to the term νεῦσις, resorts to the substantive σφάλμα, as if it were a synonym of νεῦσις. The following investigation demonstrates the validity of this usage, as the term σφάλμα is, in fact, used by the heresiologists to describe, in a language inherited from Neopythagoreanism, and therefore structured by number, the fall of Sophia, which embodies both the twelfth aeon of the Dodecade as well as the thirtieth and final aeon of the entire Pleroma. Related back to the Pythagorean metaphysics whence it is stems, the Gnostic narrative loses any appearance of arbitrariness and finally reveals its true structure, ordered from start to finish by number. It is reasonable to think that the rival arithmology of Plotinus’ Treatise 34 was created in order to undermine this very narrative. (shrink)

In both ancient tradition and modern research Pythagoreanism has been understood as a religious sect or as a philosophical and scientific community. Numerous attempts have been made to reconcile these pictures as well as to analyze them separately. The most recent scholarship compartmentalizes different facets of Pythagorean knowledge, but this offers no context for exploring their origins, development, and interdependence. This collection aims to reverse this trend, addressing connections between the different fields of Pythagorean knowledge, such as eschatology, metempsychosis, metaphysics, (...) epistemology, arithmology and numerology, music, dietetics and medicine as well as politics. In particular, the contributions discuss how the Pythagorean way of life related to more doctrinal aspects of knowledge, such as Pythagorean religion and science. The volume explores the effects of this interdependence between different kinds of knowledge both within the Pythagorean corpus and in its later reception. Chapters cover historical periods from the Archaic Period (6th century BC) to Neoplatonism, Early Christianity, the European and Arabic Middle Ages, and the Renaissance through to the Early Modern Period (17th century AD). (shrink)

The reputation Theologoumena Arithmeticae has acquired is largely that of being an odd, and frequently opaque, compilation of arithmological lore. As a sourcebook for this aspect of the Pythagorean tradition it is, of course, invaluable. However, its poor reputation is increased, and its historical value lessened, by the depredations time has wrought on the text. ThA was never great prose: it is a compilation, largely from the lost Theologoumena Arithmeticae of Nicomachus of Gerasa and from Anatolius' Peri Dekados; and the (...) text which cannot be safely or conjecturally assigned to these two sources often reads like little more than the written-up notes of some student. However, the treatise contains passages of considerable lucidity, within the context of its peculiar framework. (shrink)

This essay considers the origins of the arithmological genre, the first specimen of which was an anonymous Neopythagorean treatise of the first century BCE. Arithmology as a special genre of philosophical writings dealing with the properties of the first ten numbers should be distinguished from number symbolism, which is a universal cultural phenomenon related to individual significant numbers. As our analysis shows, the philosophical foundations of arithmology were laid down in the treatise of Plato’s successor Speusippus On Pythagorean (...) Numbers, who relied on the Platonic doctrine of the ten ideal numbers, whereas in ancient Pythagoreanism arithmological notions, unlike number symbolism, are not attested. In the first century BCE, an epoch of revival of Platonism and Aristotelianism, Speusippus’ ideas received a second birth, thus marking the beginning of arithmology as a popular genre. (shrink)