Just as the period of dominance of Aristotelian philosophy in antiquity was succeeded by the rise to dominance of Stoicism and Epicureanism, as I documented in the fifth episode of the series, so they too began to lose their hold on the world of thought in late antiquity. From the middle of the third till the middle of the seventh century CE thought in the ancient world was dominated by Neoplatonism. The term Neoplatonism is a neologism created to describe a renaissance of nominally Platonic thought that took place in this period. The term itself is to some extent misleading, whereas the terms Stoic, Peripatetic or Platonic signify a single school founder by a single philosopher with a set of doctrines developed by that founder, Neoplatonism doesn’t. To quote the Stanford Encyclopedia of Philosophy:
Late antique philosophers now counted among “the Neoplatonists” did not think of themselves as engaged in some sort of effort specifically to revive the spirit and the letter of Plato’s dialogues. To be sure, they did call themselves “Platonists” and held Plato’s views, which they understood as a positive system of philosophical doctrine, in higher esteem than the tenets of the pre-Socratics, Aristotle, or any other subsequent thinker. However, and more importantly, their signature project is more accurately described as a grand synthesis of an intellectual heritage that was by then exceedingly rich and profound. In effect, they absorbed, appropriated, and creatively harmonized almost the entire Hellenic tradition of philosophy, religion, and even literature—with the exceptions of Epicureanism, which they roundly rejected, and the thoroughgoing corporealism of the Stoics. The result of this effort was a grandiose and powerfully persuasive system of thought that reflected upon a millennium of intellectual culture and brought the scientific and moral theories of Plato, Aristotle, and the ethics of the Stoics into fruitful dialogue with literature, myth, and religious practice. In virtue of their inherent respect for the writings of many of their predecessors, the Neoplatonists together offered a kind of meta-discourse and reflection on the sum-total of ideas produced over centuries of sustained inquiry into the human condition.
Plotinus (c. 204/5–270 CE) is regarded as the first of the Neoplatonists. Central to his philosophy and in fact to all of the Neoplatonists is monism expressed through the concepts of the One and Henosis.
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Plotinus taught that there is a supreme, totally transcendent “One”, containing no division, multiplicity, or distinction; beyond all categories of being and non-being. His “One” “cannot be any existing thing”, nor is it merely the sum of all things (compare the Stoic doctrine of disbelief in non-material existence), but “is prior to all existents”. Plotinus identified his “One” with the concept of ‘Good’ and the principle of ‘Beauty’. (Wikipedia)
Henosis is the word for mystical “oneness”, “union”, or “unity” in classical Greek. In Platonism, and especially Neoplatonism, the goal of henosis is union with what is fundamental in reality: the One the Source, or Monad. (Wikipedia)
Plotinus was succeeded by his pupil Porphyry of Tyre (c. 234–c. 305 CE),
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who was in turn succeeded by his pupil Iamblichus (c. 245–c. 325 CE).
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Both Theon of Alexandria (c. 335–c. 405 CE) and his daughter Hypatia (c. 360–c. 415 CE) were Neoplatonists but their philosophy differed from that of the acolytes of Iamblichus, which dominated Neoplatonic thought in Alexandria during their time.
The Neoplatonic philosopher-mathematicians produced commentaries on and annotated editions of the major Greek mathematical works. Theon was a textbook editor, who produced annotated edition of Euclid’s Elements, Euclid’s Data, his Optics and Ptolemaios’ Mathēmatikē Syntaxis. Theon’s edition of the Elements was, until the nineteenth century, the only surviving edition.
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We have no surviving works by Hypatia but the Suda, a tenth-century Byzantine encyclopaedia of the ancient Mediterranean world lists three mathematical works for her, which it states have all been lost. The Suda credits her with commentaries on the Conic Sections of the third-century BCE Apollonius of Perga, the “Astronomical Table” and the Arithemica of the second- and third-century CE Diophantus of Alexandria. Alan Cameron, however, argues convincingly that she in fact edited the surviving text of Ptolemaeus’ Handy Tables, (the second item on the Suda list) normally attributed to her father Theon as well as a large part of the text of the Almagest her father used for his commentary. Only six of the thirteen books of Apollonius’ Conic Sections exist in Greek; historians argue that the additional four books that exist in Arabic are from Hypatia, a plausible assumption. So once again, what we have is that Hypatia was like her father a textbook editor.
Proclus Lycius (412–185) wrote a commentary on Euclid’s Elements. According to Thomas Heath in volume one of his edition of The Thirteen Books of Euclid’s Elements:
It is well known that the commentary of Proclus on Eucl. Book I is one of the two main sources of information as to the history of Greek geometry which we possess, the other being the Collection of Pappus.
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Pappus of Alexandria (fl. 320) produced an encyclopaedic compendium of ancient Greek geometry, astronomy , and mechanics in eight books entitled, Synagoge (Συναγωγή) or Collection. This work, whilst highly important as a record of the history of Greek mathematics, remained virtually unknown until the sixteenth century when it was translated and published by Federico Commandino (1509–1575) in 1588. It became influential in the seventeeth century. The Suda credits him with a commentary on the first four books of Ptolemaios’ Mathēmatikē Syntaxis, now lost. He also wrote commentaries on Euclid’s Elements fragments of which are preserved in Proclus and on Ptolemaios’ Ἁρμονικά (Harmonika), now lost.
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Apart from small odds and ends, such as Pappus’ hexagon theorem in projective geometry, these Neoplatonic philosopher-mathematicians produced very little original work. However, their role in recording and conserving Greek mathematical works should not be underestimated.
The non-mathematical Neoplatonic philosophers also contributed almost nothing new to the roots of the discipline of physics that I have sketched in the previous episodes of this series but their obsessively inclusive, eclectic agglomeration of the works of earlier Greek philosophers, in particular Plato and Aristotle, meant that these works that had slid into the background during the dominance of Stoicism and Epicureanism was once again brought into the foreground and passed on down to future generations.
All three of the monotheistic religions, Judaism, Christianity, and Islam took a strong interest in Neoplatonism because of its strongly monist core and often became first acquainted with the works of Plato, Aristotle, and other earlier Greek philosophers through Neoplatonic sources rather than through the originals. In the history of science transmission of sources often takes indirect roots.
Above I said that Neoplatonic philosophers also contributed almost nothing new to the roots of the discipline of physics, however, there is one very notable exception, the sixth century Christian, Neoplatonist John Philoponus (c. 490–c. 570) of Alexandria. Philoponus was a pupil and sometime amanuensis of the Neoplatonist philosopher Ammonius Hermiae (C. 440–c. 520),who was also from Alexandria but had studied in Athens under Proclus before returning to Alexandria to teach. He lectured on Plato, Aristotle and Porphyry of Tyre, as well as on astronomy and geometry. As is often the case most of his supposed numerous writings have not survived. He is known to have lectured and written extensively over Aristotle as did Philoponus his pupil. However, whereas Ammonius seems to have been positive in his assessments of Aristotle, Philoponus was highly critical.
Amongst his voluminous writings Philoponus wrote extensive critiques of almost all of Aristotle’s texts of which in our context a couple are of great importance. As a Christian Philoponus rejected Aristotle’s concept of an eternal cosmos, replacing it with a cosmos created by God in its entirety in one moment. Because his cosmos was a single unified whole he rejected Aristotle’s division of the cosmos into supralunar and sublunar regions. The cosmos was overall the same and subject to the same laws. In this he was following the Stoics, and his philosophy is heavily influenced by Stoic concepts. Philoponus also anticipates Descartes in stating that bodies have extension in space.
Most important in the history of physics Philoponus rejects both Aristotle’s concept of fall and his concept of projectile motion. It seems that, unlike Galileo, Philoponus really did drop objects of differing weight from a tower and concluded that they fall almost at the same speed:
“if one lets fall simultaneously from the same height two bodies differing greatly in weight, one will find that the ratio of their times of motion does not correspond does not correspond to the ration of their weights, but that the difference in time is a very small one” (In Physica, 683, 17).[1]
He dismisses Aristotle’s theory of projectile motion and produces what would later become known as the theory of impetus an important precursor to the theory of inertia.
“some incorporeal kinetic power is imparted by the thrower to the object thrown “and that” if an arrow or a stone is projected by force in a void, the same things will happen much more easily, nothing being necessary except the thrower” (ibid, 641, 29).
Denying Aristotle’s distinction between sublunar and supralunar motion, Philoponus also applied his impetus concept to the motion of the planets.
Because of his deviant religious views on the nature of the Trinity, Philoponus was declared anathema at the Third Council of Constantinople, which limited the reception of his anti-Aristotelian dynamics in late antiquity, but his works were translated into Syriac and Arabic where they would have a significant influence as we shall see in future episodes.
Philoponus was the first philosopher to go beyond the dynamics of Aristotle and his concepts are the beginnings of the path that would eventually lead to the modern theories of that branch of physics.
[1] In Physica, H. Vitelli, ed. (Berlin, 1887)