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Proclus

Proclus is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Proclus rather than just read about it. In short: Proclus Lycius (; 8 February 412 CE – 17 April 485 CE), called Proclus the Successor (Ancient Greek: Πρόκλος ὁ Διάδοχος, Próklos ho Diádokhos), was a Greek Neoplatonic philosopher, one of the last major classical philosophers of late antiquity. He set forth one of the most elaborate and fully developed systems of Neoplatonism and, through later interpreters and translators, exerted an influence on Byzantine philosop…

Proclus — main illustration
Proclus — illustration

Key takeaways

  • Proclus belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Proclus to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Proclus from memory before moving on to harder problems.

Reference excerpt

Proclus Lycius (; 8 February 412 CE – 17 April 485 CE), called Proclus the Successor (Ancient Greek: Πρόκλος ὁ Διάδοχος, Próklos ho Diádokhos), was a Greek Neoplatonic philosopher, one of the last major classical philosophers of late antiquity. He set forth one of the most elaborate and fully developed systems of Neoplatonism and, through later interpreters and translators, exerted an influence on Byzantine philosophy, early Islamic philosophy, scholastic philosophy, and German idealism, especially G. W. F. Hegel, who called Proclus's Platonic Theology "the true turning point or transition from ancient to modern times, from ancient philosophy to Christianity."

Biography

The primary source for the life of Proclus is the eulogy Proclus, or On Happiness that was written for him upon his death by his successor, Marinus. Marinus's biography set out to prove that Proclus reached the peak of virtue and attained eudaimonia. There are also a few details about the time in which he lived in the similarly structured Life of Isidore written by the philosopher Damascius in the following century. According to Marinus, Proclus was born in 412 AD in Constantinople to a family of high social status from Lycia, and raised in Xanthus. He studied rhetoric, philosophy and mathematics in Alexandria, with the intent of pursuing a judicial position like his father. Before completing his studies, he returned to Constantinople when his rector, his principal instructor (one Leonas), had business there. Proclus became a successful practicing lawyer. However, the experience of the practice of law made Proclus realize that he truly preferred philosophy. He returned to Alexandria, and began determinedly studying the works of Aristotle under Olympiodorus the Elder. He also began studying mathematics during this period as well with a teacher named Heron (no relation to Hero of Alexandria, who was also known as Heron). As a gifted student, he eventually became dissatisfied with the level of philosophical instruction available in Alexandria, and went to Athens, philosophical center of the day, in 431 to study at the Neoplatonic successor of the New Academy, where he was taught by Plutarch of Athens (not to be confused with Plutarch of Chaeronea), Syrianus, and Asclepigenia; he succeeded Syrianus as head of the Academy in 437, and would in turn be succeeded on his death by Marinus of Neapolis. He lived in Athens as a vegetarian bachelor, prosperous and generous to his friends, until the end of his life, except for a one-year exile, to avoid pressure from Christian authorities. Marinus reports that he was writing seven hundred lines each day.

Philosophy

One challenge with determining Proclus' specific doctrines is that the Neoplatonists of his time did not consider themselves innovators; they believed themselves to be the transmitters of the correct interpretations of Plato himself. Although the neoplatonic doctrines are much different from the doctrines in Plato's dialogues, it's often difficult to distinguish between different Neoplatonic thinkers and determine what is original to each one. For Proclus, this is largely only possible with Plotinus, the only other Neoplatonic writer for whom a significant amount of writings survive. Proclus, like Plotinus and many of the other Neoplatonists, agreed on the three hypostases of Neoplatonism: The One (hen), The Intellect (nous) and The Soul (psyche), and wrote a commentary on the Enneads, of which only fragments survive. At other times he criticizes Plotinus' views, such as the prime mover. Unlike Plotinus, Proclus also did not hold that matter was evil, an idea that caused contradictions in the system of Plotinus. It is difficult to determine what, if anything, is different between the doctrines of Proclus and Syrianus: for the latter, only a commentary on Aristotle's Metaphysics survives, and Proclus never criticizes his teacher in any of his preserved writings. The particular characteristic of Proclus's system is his elaboration of a level of individual ones, called henads, between the One which is before being and intelligible divinity. The henads exist "superabundantly", also beyond being, but they stand at the head of chains of causation (seirai) and in some manner give to these chains their particular character. He identifies them with the Greek gods, so one henad might be Apollo and be the cause of all things apollonian, while another might be Helios and be the cause of all sunny things. Each henad participates in every other henad, according to its character. What appears to be multiplicity is not multiplicity at all, because any henad may rightly be considered the center of the polycentric system. According to Proclus, philosophy is the activity which can liberate the soul from a subjection to bodily passions, remind it of its origin in Soul, Intellect, and the One, and prepare it not only to ascend to the higher levels while still in this life, but to avoid falling immediately back into a new body after death. Because the soul's attention, while inhabiting a body, is turned so far away from its origin in the intelligible world, Proclus thinks that we need to make use of bodily reminders of our spiritual origin. In emphasizing the importance of an embodied practice of philosophy, he agrees with the doctrines of theurgy put forward by Iamblichus. Theurgy is possible because the powers of the gods (the henads) extend through their series of causation even down to the material world. And by certain power-laden words, acts, and objects, the soul can be drawn back up the series, so to speak. Proclus himself was a devotee of many of the religions in Athens, considering that the power of the gods could be present in these various approaches.

Works

… excerpt ends here. Continue reading the full article.

Illustrations

Proclus illustration
Proclus illustration

Worked examples

Example 1 — a first encounter with Proclus

Start with the simplest possible case. Write down what Proclus claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Proclus before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Proclus ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Proclus

In research
Proclus appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Proclus in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Proclus is common in secondary-school and first-year university syllabi. It links to neighbouring topics 412 births, 485 deaths, 5th-century Byzantine scientists, so understanding it makes those chapters shorter.
In everyday life
Look for Proclus outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.
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How to study Proclus in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Proclus means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Proclus out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Proclus in simple terms?

Proclus Lycius (; 8 February 412 CE – 17 April 485 CE), called Proclus the Successor (Ancient Greek: Πρόκλος ὁ Διάδοχος, Próklos ho Diádokhos), was a Greek Neoplatonic philosopher, one of the last major classical philosophers of late antiquity. He set forth one of the most elaborate and fully devel…

Why does Proclus matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Proclus?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Proclus.

Tags

  • 412 births
  • 485 deaths
  • 5th-century Byzantine scientists
  • 5th-century Byzantine writers
  • 5th-century Greek philosophers
  • 5th-century Greek poets
  • 5th-century mathematicians
  • Ancient Greek mathematicians
  • Epigrammatists of the Greek Anthology
  • Greek-language commentators on Plato
  • Late-Roman-era pagans
  • Neoplatonists in Athens

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