The ''Anonymous Commentary on Plato's Theaetetus'' is a partially extant

Ancient Greek Ancient Greek (, ; ) includes the forms of the Greek language used in ancient Greece and the classical antiquity, ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Greek ...

philosophical commentary A philosophical commentary is a written exposition and analysis of an authoritative philosophical text.Andrea Falcon (2005)"Commentators on Aristotle" ''Stanford Encyclopedia of Philosophy''.Han Baltussen (2018), "Philosophical Commentary", in Scot ...

from the early

Roman era In modern historiography, ancient Rome is the Roman people, Roman civilisation from the founding of Rome, founding of the Italian city of Rome in the 8th century BC to the Fall of the Western Roman Empire, collapse of the Western Roman Em ...

that contains an exposition on

Plato Plato ( ; Greek language, Greek: , ; born BC, died 348/347 BC) was an ancient Greek philosopher of the Classical Greece, Classical period who is considered a foundational thinker in Western philosophy and an innovator of the writte ...

's '' Theaetetus.'' The composition of the text has been dated to some time between the late 1st century BCE through the middle of the 2nd century CE, making it one of the few surviving historical examples of

Middle Platonist Middle Platonism is the modern name given to a stage in the development of Platonic philosophy, lasting from about 90 BC – when Antiochus of Ascalon rejected the scepticism of the new Academy – until the development of neoplatoni ...

literature. In the surviving portion of the commentary, the anonymous commentator discusses major themes of Plato's theories of knowledge such as

Definitions of knowledge Definitions of knowledge aim to identify the essential features of knowledge. Closely related terms are conception of knowledge, theory of knowledge, and analysis of knowledge. Some general features of knowledge are widely accepted among philosoph ...

Justified true belief Definitions of knowledge aim to identify the essential features of knowledge. Closely related terms are conception of knowledge, theory of knowledge, and analysis of knowledge. Some general features of knowledge are widely accepted among philosoph ...

, and the

Problem of the criterion In the field of epistemology, the problem of the criterion is an issue regarding the starting point of knowledge. This is a separate and more fundamental issue than the regress argument found in discussions on justification of knowledge. In W ...

, and compares the account of knowledge in the Theaetetus to the ''

Meno ''Meno'' (; , ''Ménōn'') is a Socratic dialogue written by Plato around 385 BC., but set at an earlier date around 402 BC. Meno begins the dialogue by asking Socrates whether virtue (in , '' aretē'') can be taught, acquired by practice, o ...

'', ''

Protagoras Protagoras ( ; ; )Guthrie, p. 262–263. was a pre-Socratic Greek philosopher and rhetorical theorist. He is numbered as one of the sophists by Plato. In his dialogue '' Protagoras'', Plato credits him with inventing the role of the professional ...

'' and the ''

Sophist (dialogue) The ''Sophist'' (; Henri Estienne (ed.), ''Platonis opera quae extant omnia'', Vol. 1, 1578p. 217) is a Platonic dialogue from the philosopher's late period, most likely written in 360 BC. In it the interlocutors, led by Eleatic Stranger employ ...

''. In addition, the commentator provides a summary of other interpretations of the dialogue during his time and presents a number of arguments against rival philosophical schools, especially

Stoicism Stoicism is a school of Hellenistic philosophy that flourished in ancient Greece and Rome. The Stoics believed that the universe operated according to reason, ''i.e.'' by a God which is immersed in nature itself. Of all the schools of ancient ...

Academic skepticism Academic skepticism refers to the philosophical skepticism, skeptical period of the Platonic Academy, Academy dating from around 266 BCE, when Arcesilaus became scholarch, until around 90 BCE, when Antiochus of Ascalon rejected skepticism, altho ...

, and

Pyrrhonism Pyrrhonism is an Ancient Greek school of philosophical skepticism which rejects dogma and advocates the suspension of judgement over the truth of all beliefs. It was founded by Aenesidemus in the first century BCE, and said to have been inspired ...

. The commentator also provides an in-depth analysis of the mathematical proof given by

Theodorus of Cyrene Theodorus of Cyrene (; 450 BC) was an ancient Greek mathematician. The only first-hand accounts of him that survive are in three of Plato's dialogues: the '' Theaetetus'', the ''Sophist'', and the ''Statesman''. In the first dialogue, he posits ...

and adds background historical detail on many of the people in the story and speculations on Plato's intentions in composition of the work. The commentary was lost along with the majority of

Commentaries on Plato Commentaries on Plato refers to the great mass of literature produced, especially in the ancient and medieval world, to explain and clarify the works of Plato. Many Platonist philosophers in the centuries following Plato sought to clarify and summ ...

and did not survive to the Medieval era in any known manuscript tradition. It was entirely unknown until the chance discovery in 1901 of a single papyrus roll dating to the middle of the 2nd century CE. The very beginning of the work is missing and the work cuts off partway through the dialogue. Its publication in 1905 attracted little interest at the time, as the commentators were not seen as original philosophers by classical scholarship of the time. In the second half of the 20th century, however, renewed interest in

Ancient Roman philosophy Ancient Roman philosophy is philosophy as it was practiced in the Roman Republic and its successor state, the Roman Empire. Roman philosophy includes not only philosophy written in Latin, but also philosophy written in Greek in the late Republic ...

and the philosophy of the ancient commentators has elevated it to one of the most important primary sources documenting the historical developments of

Platonism Platonism is the philosophy of Plato and philosophical systems closely derived from it, though contemporary Platonists do not necessarily accept all doctrines of Plato. Platonism has had a profound effect on Western thought. At the most fundam ...

and the commentary tradition in the early centuries of the

Roman empire The Roman Empire ruled the Mediterranean and much of Europe, Western Asia and North Africa. The Roman people, Romans conquered most of this during the Roman Republic, Republic, and it was ruled by emperors following Octavian's assumption of ...

Style, dating and authorship

Style

In addition to original philosophical works, many philosophers in antiquity wrote commentaries, most commonly on the works of other philosophers such as Plato and Aristotle, but also interpretive commentaries on religious or literary texts. Rather than simply reviewing or summarizing a philosophical or religious text, these works went through a line-by-line, highlighting specific passages and providing background or expositions. Many philosophical commentaries were intended as school notes, that expanded on the details of a philosophical work for students and clarified the meanings of obscure words, while others were more complex expositions and interpretations that were intended for a more advanced audience within a philosophical school. The Theaetetus commentary contains elements of both kinds of commentary. The Anonymous Theaetetus commentary is the earliest surviving commentary on a work of Plato. Philosophical commentaries had been written long prior, the earliest evidence of any philosophical commentary is on the works of

Homer Homer (; , ; possibly born ) was an Ancient Greece, Ancient Greek poet who is credited as the author of the ''Iliad'' and the ''Odyssey'', two epic poems that are foundational works of ancient Greek literature. Despite doubts about his autho ...

, and one of the earliest surviving philosophical commentaries on any type of work is the

Derveni papyrus The Derveni papyrus is an Ancient Greek papyrus roll that was discovered in 1962 at the archaeological site of Derveni, near Thessaloniki, in Central Macedonia. A philosophical treatise, the text is an allegorical commentary on an Orphic poem, a ...

, a 4th century BCE papyrus that contains an allegorical philosophical commentary on an

Orphic Orphism is the name given to a set of religious beliefs and practices originating in the ancient Greek and Hellenistic world, associated with literature ascribed to the mythical poet Orpheus, who descended into the Greek underworld and returned ...

cosmogony Cosmogony is any model concerning the origin of the cosmos or the universe. Overview Scientific theories In astronomy, cosmogony is the study of the origin of particular astrophysical objects or systems, and is most commonly used in ref ...

that dates to the middle of the 5th century BCE. The first known commentary on a work of

specifically was written in the third century BCE by Crantor of Soli, the last

scholarch A scholarch (, ''scholarchēs'') was the head of a school in ancient Greece. The term is especially remembered for its use to mean the heads of schools of philosophy, such as the Platonic Academy in ancient Athens. Its first scholarch was Plato h ...

of the

Old Academy The Academy (), variously known as Plato's Academy, or the Platonic Academy, was founded in Athens by Plato '' circa'' 387 BC. The academy is regarded as the first institution of higher education in the west, where subjects as diverse as biolo ...

, which has been lost, but many later works written by

Neoplatonists Neoplatonism is a version of Platonic philosophy that emerged in the 3rd century AD against the background of Hellenistic philosophy and religion. The term does not encapsulate a set of ideas as much as a series of thinkers. Among the common i ...

from the 3rd through 6th centuries CE have been preserved.

Dating

The commentary is generally believed to date from 45 BCE to 150 CE, although attempts to establish a more exact dating have proven contentious. The fragmentary nature of the work make questions of the date and authorship of the work difficult to answer more exactly, as few other philosophical works from the period have survived. Based on its content, the commentary must date from the 1st century BCE or later; as a work of Middle Platonism that ascribes positive doctrines to Plato and disputes the

Academic Skepticism Academic skepticism refers to the philosophical skepticism, skeptical period of the Platonic Academy, Academy dating from around 266 BCE, when Arcesilaus became scholarch, until around 90 BCE, when Antiochus of Ascalon rejected skepticism, altho ...

that was dominant in the

Hellenistic period In classical antiquity, the Hellenistic period covers the time in Greek history after Classical Greece, between the death of Alexander the Great in 323 BC and the death of Cleopatra VII in 30 BC, which was followed by the ascendancy of the R ...

and synthesizes the doctrines of the Stoics. The commentary must also have been written at the latest in the first half of the second century CE, when the papyrus that the surviving copy of the text has been dated to.

Authorship

Although no part of the work survives which would allow a definitive identification of its author, the author can be identified as a Middle Platonist on the basis of doctrinal content within the text. The Middle Platonists, beginning with

Antiochus of Ascalon Antiochus of Ascalon (; ; ) was a 1st-century BC Platonist philosopher. He rejected skepticism, blended Stoic doctrines with Platonism, and was the first philosopher in the tradition of Middle Platonism. Antiochus moved to Athens early in his li ...

, had rejected the skepticism of the

Platonic Academy The Academy (), variously known as Plato's Academy, or the Platonic Academy, was founded in Classical Athens, Athens by Plato ''wikt:circa, circa'' 387 BC. The academy is regarded as the first institution of higher education in the west, where ...

that had been dominant in

Hellenistic philosophy Hellenistic philosophy is Ancient Greek philosophy corresponding to the Hellenistic period in Ancient Greece, from the death of Alexander the Great in 323 BC to the Battle of Actium in 31 BC. The dominant schools of this period were the Stoics, the ...

, advocating a more dogmatic form of Platonism. Many Middle Platonists attempted to synthesize Platonic doctrines with either

Aristotelianism Aristotelianism ( ) is a philosophical tradition inspired by the work of Aristotle, usually characterized by Prior Analytics, deductive logic and an Posterior Analytics, analytic inductive method in the study of natural philosophy and metaphysics ...

; Antiochus had preferred the Stoics, while the Anonymous Commentator prefers

Aristotle Aristotle (; 384–322 BC) was an Ancient Greek philosophy, Ancient Greek philosopher and polymath. His writings cover a broad range of subjects spanning the natural sciences, philosophy, linguistics, economics, politics, psychology, a ...

while criticizing the Stoics. There have been attempts to identify the author with known Middle Platonists;

John M. Dillon John Myles Dillon (; born 15 September 1939) is an Irish classicist and philosopher who was Regius Professor of Greek (Trinity), Regius Professor of Greek in Trinity College, Dublin between 1980 and 2006. Prior to that he taught at the Universit ...

, seeing a similarity with the School of Gaius the Platonist, identifies him with the mid 2nd century CE philosopher Albinus, while Harold Tarrant says the best known candidate is the much earlier Eudorus of Alexandria, in the late 1st century BCE.

Content

The commentary is on Plato's '' Theaetetus'', one of his major works of

epistemology Epistemology is the branch of philosophy that examines the nature, origin, and limits of knowledge. Also called "the theory of knowledge", it explores different types of knowledge, such as propositional knowledge about facts, practical knowle ...

. In the dialogue, Socrates and an Athenian youth named Theaetetus, investigate the nature of knowledge (''

episteme In philosophy, (; ) is knowledge or understanding. The term ''epistemology'' (the branch of philosophy concerning knowledge) is derived from . History Plato Plato, following Xenophanes, contrasts with : common belief or opinion. The ter ...

''). Like many of the characters in Plato's dialogues, Theaetetus is a historical figure who is known to us independently of Plato. Both Theaetetus and his mentor,

were

Ancient Greek mathematicians Ancient Greek mathematics refers to the history of mathematical ideas and texts in Ancient Greece during classical and late antiquity, mostly from the 5th century BC to the 6th century AD. Greek mathematicians lived in cities spread around the s ...

who are known through citation of their work in theorems proved in

Euclid's Elements The ''Elements'' ( ) is a mathematics, mathematical treatise written 300 BC by the Ancient Greek mathematics, Ancient Greek mathematician Euclid. ''Elements'' is the oldest extant large-scale deductive treatment of mathematics. Drawing on the w ...

by later mathematicians. After a more general discussion of knowledge and understanding where they work through a mathematics problem Socrates and Theaetetus then discuss three potential definitions - knowledge as

perception Perception () is the organization, identification, and interpretation of sensory information in order to represent and understand the presented information or environment. All perception involves signals that go through the nervous syste ...

, knowledge as true belief (''

pistis In Greek mythology, ''Pistis'' (; Ancient Greek: Πίστις) was the personification of good faith, trust and reliability. In Christianity and in the New Testament, ''pistis'' is typically translated as "faith". The word is mentioned together ...

''), and knowledge as "''justified'' true belief," although the dialogue ultimately ends in

aporia In philosophy, an aporia () is a conundrum or state of puzzlement. In rhetoric, it is a declaration of doubt, made for rhetorical purpose and often feigned. The notion of an aporia is principally found in ancient Greek philosophy, but it also p ...

as this definition, too, is shown to be unsatifactory. The commentary is only partially preserved, starting in the middle of the introduction to the commentary itself and cutting off partway through. The extant portion covers only the beginning 15% of the dialogue which begins its coverage of the ''Theaetetus'' at the end of the prelude, a brief

frame story A frame story (also known as a frame tale, frame narrative, sandwich narrative, or intercalation) is a literary technique that serves as a companion piece to a story within a story, where an introductory or main narrative sets the stage either fo ...

. In this portion of the Theaetetus covered by the dialogue, Socrates asks Theodorus if he has any promising

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

students, and Theodorus introduces him to Theaetetus. Socrates challenges Theaetetus to explain to him the nature of knowledge, and they proceed to discuss the difference between knowledge and wisdom and the differences between examples of knowledge and knowledge itself. Theaetetus gives an example of a mathematical proof, and Socrates explains his philosophical method for bringing out ideas, which he compares to midwifery ( Maieutics). Socrates and Theaetetus then begin to discuss knowledge gained from sense-perception and examine

' famous maxim "Man is the measure of all things," and

Heraclitus Heraclitus (; ; ) was an Ancient Greece, ancient Greek Pre-Socratic philosophy, pre-Socratic philosopher from the city of Ephesus, which was then part of the Achaemenid Empire, Persian Empire. He exerts a wide influence on Western philosophy, ...

' theory of flux, although the commentary cuts off partway through this discussion. The commentator follows along the dialogue, adding explication of the readings of certain parts of the dialogue, giving cultural or historical background, and occasionally going into in-depth explication of certain philosophical arguments.

Introduction

Most ancient commentaries on Plato and Aristotle begin with an introductory preface explaining the work being commented on. However, the first column of text from the papyrus this commentary is very fragmentary, rendering it unreadable, so the surviving portion of the text begins in the middle of this introduction. The surviving text opens at the end of an explanation of the purpose (skopos) of the Theaetetus dialogue, which the commentator claims is

catharsis Catharsis is from the Ancient Greek word , , meaning "purification" or "cleansing", commonly used to refer to the purification and purgation of thoughts and emotions by way of expressing them. The desired result is an emotional state of renewal an ...

against the relativist doctrine of

, a

Sophist A sophist () was a teacher in ancient Greece in the fifth and fourth centuries BCE. Sophists specialized in one or more subject areas, such as philosophy, rhetoric, music, athletics and mathematics. They taught ''arete'', "virtue" or "excellen ...

from the 5th century BCE who taught that "Man is the measure of all things" and whose work ''On Truth'' the commentator claims Theaetetus had recently read. The commentator then states that some other Platonists believe that the purpose of the dialogue is to outline the

, to give an argument in the ''Theaetetus'' about what knowledge is not (i.e. sense perception) in order to follow it up in the ''

,'' with what knowledge is (i.e.

the forms The Theory of Forms or Theory of Ideas, also known as Platonic idealism or Platonic realism, is a philosophical theory credited to the Classical Greek philosopher Plato. A major concept in metaphysics, the theory suggests that the physical w ...

). However, the commentator says that these people are mistaken, and that the true purpose of the dialogue is to explain what the

essence Essence () has various meanings and uses for different thinkers and in different contexts. It is used in philosophy and theology as a designation for the property (philosophy), property or set of properties or attributes that make an entity the ...

(

ousia ''Ousia'' (; ) is a philosophical and theological term, originally used in ancient Greek philosophy, then later in Christian theology. It was used by various ancient Greek philosophers, especially Aristotle, as a primary designation for philoso ...

) of knowledge is. The commentator then discusses the content of the prologue, which relates a

in which the dialogue between Theaetetus and Socrates is being recounted from a book by

Euclid of Megara Euclid of Megara (; ; c. 435 – c. 365 BC) was a Greek Socratic philosopher who founded the Megarian school of philosophy. He was a pupil of Socrates in the late 5th century BC, and was present at his death. He held the supreme good to be o ...

, a Socratic philosopher who founded the

Megarian school The Megarian school of philosophy, which flourished in the 4th century BC, was founded by Euclides of Megara, one of the pupils of Socrates. Its ethical teachings were derived from Socrates, recognizing a single good, which was apparently combine ...

. The commentator interprets the prologue as a propaedeutic demonstration of

practical ethics Applied ethics is the practical aspect of moral considerations. It is ethics with respect to real-world actions and their moral considerations in private and public life, the professions, health, technology, law, and leadership. For example, bio ...

; Euclid, as a distinguished Socratic philosopher, is being used as a model for how one ought to behave. This is in opposition to the Stoic doctrine of

kathekon Kathēkon () (plural: ''kathēkonta'' ) is a Greek concept, forged by the founder of Stoicism, Zeno of Citium. It may be translated as "appropriate behaviour", "befitting actions", or "convenient action for nature",

Difference between Cyrene and Athens

In the dialogue,

and

Socrates Socrates (; ; – 399 BC) was a Ancient Greek philosophy, Greek philosopher from Classical Athens, Athens who is credited as the founder of Western philosophy and as among the first moral philosophers of the Ethics, ethical tradition ...

discuss the youth of Athens, and Socrates begins with remark about how he cares more for the youth of Athens than the youth of Cyrene. The commentator states that Socrates surely also cares for the Cyreneans, but that as an Athenian he naturally cares more for the youth of his own city due to the phenomenon of ''

Oikeiôsis In Stoic ethics, ''oikeiôsis'' (, ) is a technical term variously translated as "appropriation," "orientation," "familiarization," "affinity," "affiliation," and "endearment."Richter, Daniel S, ''Cosmopolis: Imagining Community in Late Classical ...

'', often translated as "''appropriation''." The commentator then goes on to discuss the Stoic and

Epicurean Epicureanism is a system of philosophy founded 307 BCE based upon the teachings of Epicurus, an ancient Greek philosopher. Epicurus was an atomist and materialist, following in the steps of Democritus. His materialism led him to religious s ...

doctrine of appropriation, which bases justice on this intuitive feeling. The commentator argues that, because we naturally have more intense feelings of ''appropriation'' towards ourselves and our own neighbors rather than strangers, people who based their notion of justice on appropriation will preferentially act in their own interest rather than acting justly. Then the commentator cites an example of a shipwreck, the

Plank of Carneades In ethics, the plank of Carneades is a thought experiment first proposed by the Academic Skeptic philosopher Carneades of Cyrene. It explores the concept of self-defense in relation to murder. In the thought experiment, there are two shipwrecked ...

, where someone who based their morality on these intuitive feelings would choose to save a friend or neighbor over a stranger, and that even if this never occurs, the claim is still refuted. The commentator then relates an argument from the Academic skeptics against the Stoics and Epicureans, where he argues that those who fail to preserve justice in equal measure must necessarily fail to preserve it at all. The commentator says that Plato did not base justice on appropriation, but on "becoming like a God" referring to a later part of the Theaetetus, which he states that his commentary will discuss at that point, which is however not in the extant portion of the text.

Nature of the soul

In the dialogue, Theodorus mentions one Athenian youth in particular who shows promise, Theaetetus. The commentator points out different virtues mentioned by the dialogue and associates them with the divisions of the soul made by Plato in the Republic: rational, spirited, and appetitive. The commentator contrasts the idea "of the ancients" of different virtues occurring in different people according to their natures with the Stoic idea that there is a single unified concept of virtue that manifests in different people in different amounts. The commentator discusses the "wax argument", that this fixed amount of virtue is inherently malleable, which he attributes to Aristo of Chios, a Stoic philosopher. Socrates states that he wants to investigate Theaetetus for himself, to see if he really possesses the virtue and wisdom that Theodorus claims. The commentator contrasts Theodorus, who is a mathematical expert, with someone able to judge the quality of someone's soul, stating that Theodorus' expertise should be examined in further detail, to see if the claim is actually true.

Different types of knowledge

Simple vs complex knowledge

Socrates asks Theaetetus if he is learning "a bit" of geometry. The commentator highlights this "a bit" as an opportunity to contrast simple knowledge, which consists of individual theorems in geometry or music, with composite systematic knowledge that is constructed from these such as the field of

, and provides three different examples of "simple" knowledge: # Plato's ''

'', which defines it as "right opinion with an explanation" #

, who defines it as "supposition with proof" #

Zeno Zeno may refer to: People * Zeno (name), including a list of people and characters with the given name * Zeno (surname) Philosophers * Zeno of Elea (), philosopher, follower of Parmenides, known for his paradoxes * Zeno of Citium (333 – 264 B ...

the Stoic, who states that it is "disposition in the receipt of impressions which is not subject to argument."

Wisdom vs knowledge

Socrates and Theaetetus then discuss the difference between wisdom and knowledge. The commentator provides a lengthier exposition on the argument in a logic form: * P1: Someone who learns becomes wiser * P2: Someone who becomes wiser acquires wisdom * P3: wisdom is knowledge * C: Therefore, someone who learns acquires knowledge However, the commentator observes that Socrates draws a different conclusion "wisdom and knowledge are the same" that does not follow this logical structure. This is not because the same people who become wise are also knowledgeable, as grammarians and musicologists are not the same just because the same people study grammar and music, but because both knowledge and wisdom have the same concern, learning, while grammar and music do not. The commentator stresses that the lead-in to the discussion "about what you are learning" shows that this is true even for simple knowledge.

Genus vs. differentia

In the dialogue, Socrates then asks about the nature of knowledge, and Theaetetus gives him examples, such as geometry and music. This provokes a long discussion on the distinction between giving an example of something and describing the thing itself. The commentator states that Theaetetus failed to give the

of knowledge, and enumerated the

species A species () is often defined as the largest group of organisms in which any two individuals of the appropriate sexes or mating types can produce fertile offspring, typically by sexual reproduction. It is the basic unit of Taxonomy (biology), ...

rather than the

genus Genus (; : genera ) is a taxonomic rank above species and below family (taxonomy), family as used in the biological classification of extant taxon, living and fossil organisms as well as Virus classification#ICTV classification, viruses. In bino ...

, as if someone was asked what an animal was and said "a man or a horse."

Irrational numbers

In the dialogue, Theodorus and Theaetetus work through a mathematical problem related to irrational numbers using a geometrical construction now called the

Spiral of Theodorus In geometry, the spiral of Theodorus (also called the square root spiral, Pythagorean spiral, or Pythagoras's snail) is a spiral composed of right triangles, placed edge-to-edge. It was named after Theodorus of Cyrene. Construction The spiral ...

, though Plato does not describe the problem in full detail, leading a variety of interpreters from antiquity through the modern era to debate how to reconstruct the problem Plato was describing from his description. The anonymous commentator provides a lengthy exposition on the problem, that has also informed modern interpretations. In the dialogue, the roots of numbers up through 17 are shown to be irrational, however, the proof is stopped there. The commentator provides several explanations why he would have stopped at 17, rejecting the claim that it was arbitrary. First he states that because Theodorus was also a musician, the intent of the theorem is to show that tones are not divided into equal semitones, which he claims to have shown in his (lost) commentary on Plato's ''Timaeus.'' Second he considers the possibility that Theodorus stopped after 17 because it is the first non-square number after 16, which is the square for which the perimeter and the area are equal. In the dialogue, the idea of generating a procedure that allows one to create a procedure for generating arbitrary perfect squares is discussed. The commentator then discusses the partition of the natural numbers, and the paradoxical idea that, although there are infinite numbers, it is possible to split them into two groups without enumerating them all first, such as even and odd, or prime and composite, or, as shown here, square and "oblong" (not a perfect square).In the dialogue, plane numbers and solid numbers are mentioned briefly. The commentator then discusses plane, cube, and solid numbers at length, and discusses how the same principles used to find square and oblong numbers can be further applied to perfect square numbers can be extended to finding perfect cubes,

Pythagorean triples A Pythagorean triple consists of three positive integers , , and , such that . Such a triple is commonly written , a well-known example is . If is a Pythagorean triple, then so is for any positive integer . A triangle whose side lengths are a P ...

and Pythagorean quadruples, and then goes on to provide a classification of different types of plane and solid numbers that can be found. The commentator concludes with an explanation of how this mathematical passage shows how one ought to pursue knowledge. 1) It is better to proceed from something more clear to something less clear, as Socrates and Theaetetus proceeded from magnitudes to numbers. 2) It is better to proceed from the universal to the particular, which is why they discussed "lengths" and then "powers" before "squares." 3) that understanding is reinforced by applying what has been learned to a new domain, as with applying what was learned about magnitudes and plain numbers to square and cubic numbers.

Midwife analogy

In the dialogue, Theaetetus is unable to apply the lessons he has learned from mathematics to the nature of knowledge. Socrates states that Theaetetus is "pregnant" and in labor, and that Socrates' role is to be the midwife who will draw out the birth of understanding. The commentator relates this to the Platonic doctrine of recollection ( Anamnesis) outline in the Meno. According to this doctrine, all knowledge is already present in the soul, and that to learn something is the same as for it to be "remembered." The commentator then refers the reader to his (non-extant) work on the ''Phaedo'' for further exposition.

Sense perception

In the remaining extant part of the commentary, which is very lacunose, the commentator discusses the idea of knowledge based on sense perception. In the dialogue, Theaetetus gives a definition of knowledge as sense perception; the commentator notes that this is a shocking thing for a geometer to say, given the proof-based nature of mathematics, which leads into a discussion of how he must have developed this misconception, via Protagoras and his book ''On Truth''. The commentator then distinguishes the relativism of Protagoras from the skepticism of the

Pyrrhonists Pyrrho of Elis (; ; ) was a Greek philosopher of Classical antiquity, credited as being the first Greek skeptic philosopher and founder of Pyrrhonism. Life Pyrrho of Elis is estimated to have lived from around 365/360 until 275/270 BCE. Pyr ...

; Protagoras says Protagoras says that these sense-impressions are the truth, while the Pyrrhonists claim that dogmatic statements about the truth are impossible. Protagoras states that sense-impressions are relative due to the inherent flux of the universe; the Pyrrhonists reject the idea that the content of sense-organs themselves have any distinct reality. The commentator then distinguishes between Protagoras and the

Cyrenaics The Cyrenaics or Kyrenaics (), were a sensual hedonist Greek school of philosophy founded in the 4th century BCE, supposedly by Aristippus of Cyrene, although many of the principles of the school are believed to have been formalized by his gra ...

; Protagoras says that wind is cold or warm relative to who experiences it, while the Cyrenaics say that someone can observe that they are being burned by a fire, but cannot extrapolate that it is in the nature (

Physis Physis (; ; pl. physeis, φύσεις) is a Greek philosophical, theological, and scientific term, usually translated into English—according to its Latin translation "natura"—as "nature". The term originated in ancient Greek philosophy, a ...

) of fire to burn. The dialogue then discusses the Heraclitean idea that all entities are constantly in flux, and states that it is a credible view; a doctrine assented to by Protagoras, Heraclitus, Empedocles, and most of the sophists, and all wise men other than

Parmenides Parmenides of Elea (; ; fl. late sixth or early fifth century BC) was a Pre-Socratic philosophy, pre-Socratic ancient Greece, Greek philosopher from Velia, Elea in Magna Graecia (Southern Italy). Parmenides was born in the Greek colony of Veli ...

, cannot be dismissed easily. In order to refute the idea of flux, the commentator introduces the "growth" argument, which he attributes to Pythagoras, and also states that Plato used the same argument in the ''Symposium'', and that it was favored by the Academic skeptics in arguing against the Stoics. According to the commentator,

Epicharmus of Kos Epicharmus of Kos or Epicharmus Comicus or Epicharmus Comicus Syracusanus (), thought to have lived between c. 550 and c. 460 BC, was a Greek dramatist and philosopher who is often credited with being one of the first comedic writers ...

, a

Old Comedy Old Comedy is the first period of the ancient Greek comedy, according to the canonical division by the Alexandrian grammarians.Mastromarco (1994) p.12 The most important Old Comic playwright is Aristophanes – whose works, with their daring pol ...

poet known for philosophical themes in his plays, learned this argument from the

Pythagoreans Pythagoreanism originated in the 6th century BC, based on and around the teachings and beliefs held by Pythagoras and his followers, the Pythagoreans. Pythagoras established the first Pythagorean community in the Ancient Greece, ancient Greek co ...

, which he adapted into a play to illustrate the absurdity of the claim that humans do not persist over time: After this point in the text, the commentator further elaborates his own version of the growth argument, but the papyrus is too fragmentary at this point to reconstruct the exact argument being made by the commentator. The commentary then cuts off entirely in the midst of a discussion on knowledge of colors at Theaetetus 153d8, though four other papyrus fragments are extant, on 157b8-158a2, discussing false sense-impressions arising from dreams, diseases, and madness.Comm. fr. A to D in

Themes

The arguments on knowledge provide valuable historical context for the development of

Platonic epistemology In philosophy, Plato's epistemology is a theory of knowledge developed by the Greek philosopher Plato and his followers. Platonic epistemology holds that knowledge of Platonic Ideas is innate, so that learning is the development of ideas buri ...

, as well as preserving information on other philosophical traditions of the time which the commentator argues against, such as

, and

Epicureanism Epicureanism is a system of philosophy founded 307 BCE based upon the teachings of Epicurus, an ancient Greek philosopher. Epicurus was an atomist and materialist, following in the steps of Democritus. His materialism led him to religious s ...

. As a Middle Platonist, the commentator weighs the doctrines of both Academic Skepticism and Stoicism, sometimes arguing in favor of Skepticism against Stoicism. Anon mentions the Stoics four times by name in the commentary and discusses several of their doctrines including

and

Kathekon Kathēkon () (plural: ''kathēkonta'' ) is a Greek concept, forged by the founder of Stoicism, Zeno of Citium. It may be translated as "appropriate behaviour", "befitting actions", or "convenient action for nature",

Legacy

The influence of the commentary on later Middle Platonism is difficult to determine, due to the ambiguity in the date of composition. The Theaetetus commentary shows similarities with the works of

Alcinous In Greek mythology, Alcinous (also Alcinoüs; ; ''Alkínoos'' ) was a son of Nausithous and brother of Rhexenor. After the latter's death, he married his brother's daughter Arete who bore him Nausicaa, Halius, Clytoneus and Laodamas. In ...

in their exposition on Anamnesis, Plato's theory of "recollection" as outlined in the ''

'' and ''

Phaedo ''Phaedo'' (; , ''Phaidōn'') is a dialogue written by Plato, in which Socrates discusses the immortality of the soul and the nature of the afterlife with his friends in the hours leading up to his death. Socrates explores various arguments fo ...

''. Both the anonymous commentator and Alcinous treat recollection as a natural process of remembering that unfolds from memories of previous lives. Many of the surviving works of

Apuleius Apuleius ( ), also called Lucius Apuleius Madaurensis (c. 124 – after 170), was a Numidians, Numidian Latin-language prose writer, Platonist philosopher and rhetorician. He was born in the Roman Empire, Roman Numidia (Roman province), province ...

, also in the middle of the second century, show similarities to these works, as do the philosophical works of Galen. However, this exposition shows marked differences with the exposition of works of

Plutarch Plutarch (; , ''Ploútarchos'', ; – 120s) was a Greek Middle Platonist philosopher, historian, biographer, essayist, and priest at the Temple of Apollo (Delphi), Temple of Apollo in Delphi. He is known primarily for his ''Parallel Lives'', ...

Numenius of Apamea Numenius of Apamea (, ''Noumēnios ho ex Apameias''; ) was a Greek philosopher, who lived in Rome, and flourished during the latter half of the 2nd century AD. He was a Neopythagorean and forerunner of the Neoplatonists. Philosophy Statements ...

, and

Celsus Celsus (; , ''Kélsos''; ) was a 2nd-century Greek philosopher and opponent of early Christianity. His literary work '' The True Word'' (also ''Account'', ''Doctrine'' or ''Discourse''; Greek: )Hoffmann p.29 survives exclusively via quotati ...

, which treat Anamnesis as a more deep and intentional form of contemplation. The commentary did not survive through medieval manuscript transmission, and is unknown other than the sole surviving manuscript, a fragmentary papyrus which was discovered in 1901 in Egypt. The commentary was published in 1905 by

Hermann Diels Hermann Alexander Diels (; 18 May 1848 – 4 June 1922) was a German Classics, classical scholar, who was influential in the area of early Greek philosophy and is known for his standard work ''Die Fragmente der Vorsokratiker''. Diels helped to im ...

, and attracted little attention at first, as the arguments in it were seen as relatively undeveloped and historians of philosophy and classical scholars of the late 19th and early 20th centuries, such as

Eduard Zeller Eduard Gottlob Zeller (; ; 22 January 181419 March 1908) was a German philosopher and Protestant theologian of the Tübingen School of theology. He was well known for his writings on Ancient Greek philosophy, especially Pre-Socratic Philosophy, ...

dismissed the eclectism of the period, and generally the commentators on Plato were not seen as original philosophers in their own right. However, more recent scholarly interest in the historical developments of

and the commentary tradition in general have prompted more analysis as the commentary is both the only extant commentary on Plato from the period, and the earliest extant Ancient Greek commentary of a philosophical text.

Notes

References to the Theaetetus are given in

Stephanus pagination Stephanus pagination is a system of reference and organization used in modern editions and translations of Plato (and less famously, Plutarch) based on the three-volume 1578 edition''Platonis opera quae extant omnia'' edidit Henricus Stephanus, Ge ...

, while column numbers are given in

Roman numerals Roman numerals are a numeral system that originated in ancient Rome and remained the usual way of writing numbers throughout Europe well into the Late Middle Ages. Numbers are written with combinations of letters from the Latin alphabet, eac ...

for the commentary, based on the edition of

Editions and translations

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References

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External links

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Trismegistos record
* * {{Platonists Works about Platonism Middle Platonism Ancient Greek philosophical literature Ancient Roman philosophical literature Epistemology literature Works of unknown authorship 2nd-century manuscripts