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The third man argument (commonly referred to as TMA; Greek : τρίτος ἄνθρωπος), first appears in Plato's dialogue Parmenides . (132a–b) Parmenides (speaking to Socrates) uses the example of μέγεθος (mégethos; "greatness") in a philosophical criticism of the theory of Forms. The theory of forms is formulated based on the speeches of characters across various dialogues by Plato, although it is often attributed to Plato himself. The argument was furthered by Aristotle ( Metaphysics 990b17–1079a13, 1039a2; Sophistic Refutations 178b36 ff.) who, rather than using the example of "greatness" (μέγεθος), used the example of a man (hence the name of the argument) to explain this objection to the theory, which he attributes to Plato; Aristotle posits that if a man is a man because he partakes in the form of man, then a third form would be required to explain how man and the form of man are both man, and so on, ad infinitum .
Plato's theory of Forms, as it is presented in such dialogues as the Phaedo , Republic and the first part of the Parmenides, seems committed to the following principles:
"F" stands for any Form ("appearance, property")—forma is a Boethian translation for εἶδος (eidos), which is the word that Plato used. Plato, in the Parmenides, uses the example "greatness" (μέγεθος) for "F-ness"; Aristotle uses the example "man".
However, the TMA shows that these principles are mutually contradictory, as long as there is a plurality of things that are F:
(In what follows, μέγας [megas; "great"] is used as an example; however, the argumentation holds for any F.)
Begin, then, with the assumption that there is a plurality of great things, say (A, B, C). By one-over-many, there is a form of greatness (say, G1) by virtue of partaking of which A, B, and C are great. By self-predication, G1 is great.
But then we can add G1 to (A, B, C) to form a new plurality of great things: (A, B, C, G1). By one-over-many, there is a form of greatness (say, G2) by virtue of partaking of which A, B, C, and G1 are great. But in that case G1 partakes of G2, and by Non-Self-Partaking, G1 is not identical to G2. So there are at least two forms of greatness, G1 and G2. This already contradicts Uniqueness, according to which there is exactly one (and hence no more than one) form of greatness.
But it gets worse for the theory of Forms. For by Self-Predication, G2 is great, and hence G2 can be added to (A, B, C, G1) to form a new plurality of great things: (A, B, C, G1, G2). By One-Over-Many, there is a form of greatness (say, G3) by virtue of partaking of which A, B, C, G1, and G2 are great. But in that case G1 and G2 both partake of G3, and by Non-Self-Partaking, neither of G1 and G2 is identical to G3. So there must be at least three forms of greatness, G1, G2, and G3.
Repetition of this reasoning shows that there is an infinite hierarchy of forms of greatness, with each form partaking of the infinite number of forms above it in the hierarchy. According to Plato, anything that partakes of many things must itself be many. So each form in the infinite hierarchy of forms of greatness is many. But then, given Purity and One/Many, it follows that each form in the infinite hierarchy of forms of greatness is not one. This contradicts Oneness.
Some scholars (including Gregory Vlastos) believe that the TMA is a "record of honest perplexity". Other scholars think that Plato means us to reject one of the premises that produces the infinite regress (namely, One-Over-Many, Self-Predication, or Non-Self-Partaking). But it is also possible to avoid the contradictions produced by the TMA by rejecting Uniqueness and Purity (while accepting One-Over-Many, Self-Predication, and Non-Self-Partaking).
In philosophy, being means the material or immaterial existence of a thing. Anything that exists is being. Ontology is the branch of philosophy that studies being. Being is a concept encompassing objective and subjective features of reality and existence. Anything that partakes in being is also called a "being", though often this usage is limited to entities that have subjectivity. The notion of "being" has, inevitably, been elusive and controversial in the history of philosophy, beginning in Western philosophy with attempts among the pre-Socratics to deploy it intelligibly. The first effort to recognize and define the concept came from Parmenides, who famously said of it that "what is-is". Common words such as "is", "are", and "am" refer directly or indirectly to being.
In logic, the law of non-contradiction (LNC) states that contradictory propositions cannot both be true in the same sense at the same time, e. g. the two propositions "A is B" and "A is not B" are mutually exclusive. Formally this is expressed as the tautology ¬(p ∧ ¬p).
Ontology is the philosophical study of being. More broadly, it studies concepts that directly relate to being, in particular becoming, existence, reality, as well as the basic categories of being and their relations. Traditionally listed as a part of the major branch of philosophy known as metaphysics, ontology often deals with questions concerning what entities exist or may be said to exist and how such entities may be grouped, related within a hierarchy, and subdivided according to similarities and differences.
Plato was an Athenian philosopher during the Classical period in Ancient Greece, founder of the Platonist school of thought, and the Academy, the first institution of higher learning in the Western world.
Parmenides of Elea was a pre-Socratic Greek philosopher from Elea in Magna Graecia. "Parmenides of Elea was in his prime about 475 BC. His floruit is placed by Diogenes Laertius in 504-501 BC. But he visited Athens and met Socrates when the latter was still very young, and he himself was about sixty-five years old; so that if Socrates was about twenty, the meeting took place about 450 BC, making Parmenides’ floruit 475 BC."
In metaphysics, a universal is what particular things have in common, namely characteristics or qualities. In other words, universals are repeatable or recurrent entities that can be instantiated or exemplified by many particular things. For example, suppose there are two chairs in a room, each of which is green. These two chairs both share the quality of "chairness", as well as greenness or the quality of being green; in other words, they share a "universal". There are three major kinds of qualities or characteristics: types or kinds, properties, and relations. These are all different types of universals.
Zeno's paradoxes are a set of philosophical problems generally thought to have been devised by Greek philosopher Zeno of Elea to support Parmenides' doctrine that contrary to the evidence of one's senses, the belief in plurality and change is mistaken, and in particular that motion is nothing but an illusion. It is usually assumed, based on Plato's Parmenides (128a–d), that Zeno took on the project of creating these paradoxes because other philosophers had created paradoxes against Parmenides' view. Thus Plato has Zeno say the purpose of the paradoxes "is to show that their hypothesis that existences are many, if properly followed up, leads to still more absurd results than the hypothesis that they are one." Plato has Socrates claim that Zeno and Parmenides were essentially arguing exactly the same point.
Zeno of Elea was a pre-Socratic Greek philosopher of Magna Graecia and a member of the Eleatic School founded by Parmenides. Aristotle called him the inventor of the dialectic. He is best known for his paradoxes, which Bertrand Russell described as "immeasurably subtle and profound".
Ancient Greek philosophy arose in the 6th century BC and continued throughout the Hellenistic period and the period in which Greece and most Greek-inhabited lands were part of the Roman Empire. Philosophy was used to make sense out of the world in a non-religious way. It dealt with a wide variety of subjects, including astronomy, mathematics, political philosophy, ethics, metaphysics, ontology, logic, biology, rhetoric and aesthetics.
Melissus of Samos was the third and last member of the ancient school of Eleatic philosophy, whose other members included Zeno and Parmenides. Little is known about his life, except that he was the commander of the Samian fleet in the Samian War. Melissus’ contribution to philosophy was a treatise of systematic arguments supporting Eleatic philosophy. Like Parmenides, he argued that reality is ungenerated, indestructible, indivisible, changeless, and motionless. In addition, he sought to show that reality is wholly unlimited, and infinitely extended in all directions; and since existence is unlimited, it must also be one.
Parmenides is one of the dialogues of Plato. It is widely considered to be one of the more, if not the most, challenging and enigmatic of Plato's dialogues. The Parmenides purports to be an account of a meeting between the two great philosophers of the Eleatic school, Parmenides and Zeno of Elea, and a young Socrates. The occasion of the meeting was the reading by Zeno of his treatise defending Parmenidean monism against those partisans of plurality who asserted that Parmenides' supposition that there is a one gives rise to intolerable absurdities and contradictions.
Gregory Vlastos was a scholar of ancient philosophy, and author of several works on Plato and Socrates. A Christian, Vlastos also wrote about Christian faith. He is considered to be "a preeminent scholar on Socrates who transformed the analysis of classical philosophy."
Thomas Taylor was an English translator and Neoplatonist, the first to translate into English the complete works of Aristotle and of Plato, as well as the Orphic fragments.
Syrianus was a Greek Neoplatonist philosopher, and head of Plato's Academy in Athens, succeeding his teacher Plutarch of Athens in 431/432. He is important as the teacher of Proclus, and, like Plutarch and Proclus, as a commentator on Plato and Aristotle. His best-known extant work is a commentary on the Metaphysics of Aristotle. He is said to have written also on the De Caelo and the De Interpretatione of Aristotle and on Plato's Timaeus.
Mitchell H. Miller, Jr. is an American philosopher. He was, until his retirement in 2013, the Dexter Ferry Professor in Philosophy at Vassar College. The majority of his work concerns the late dialogues of Plato, but he has also written on Hesiod, Parmenides, and Hegel.
Metaphysics is one of the principal works of Aristotle and the first major work of the branch of philosophy with the same name. The principal subject is "being qua being," or being insofar as it is being. It examines what can be asserted about any being insofar as it is and not because of any special qualities it has. Also covered are different kinds of causation, form and matter, the existence of mathematical objects, and a prime-mover God.
The Sophist is a Platonic dialogue from the philosopher's late period, most likely written in 360 BC. Its main theme is to identify what a sophist is and how a sophist differs from a philosopher and statesman. Because each seems distinguished by a particular form of knowledge, the dialogue continues some of the lines of inquiry pursued in the epistemological dialogue, Theaetetus, which is said to have taken place the day before. Because the Sophist treats these matters, it is often taken to shed light on Plato's Theory of Forms and is compared with the Parmenides, which criticized what is often taken to be the theory of forms.
The theory of Forms or theory of Ideas is a philosophical theory, concept, or world-view, attributed to Plato, that the physical world is not as real or true as timeless, absolute, unchangeable ideas. According to this theory, ideas in this sense, often capitalized and translated as "Ideas" or "Forms", are the non-physical essences of all things, of which objects and matter in the physical world are merely imitations. Plato speaks of these entities only through the characters of his dialogues who sometimes suggest that these Forms are the only objects of study that can provide knowledge. The theory itself is contested from within Plato's dialogues, and it is a general point of controversy in philosophy. Whether the theory represents Plato's own views is held in doubt by modern scholarship. However, the theory is considered a classical solution to the problem of universals.
On Ideas is a philosophical work which deals with the problem of universals with regards to Plato's Theory of Forms. The work is supposedly by Aristotle, but there is not universal agreement on this point. It only survives now as fragments in quotations by Alexander of Aphrodisias in his commentary of Aristotle's Metaphysics.
Many Plato interpreters held that his writings contain passages with double meanings, called 'allegories' or 'symbols', that give the dialogues layers of figurative meaning in addition to their usual literal meaning. These allegorical interpretations of Plato were dominant for more than fifteen hundred years, from about the first century CE through the Renaissance and into the Eighteenth Century, and were advocated by major figures such as Plotinus, Proclus, and Ficino. Beginning with Philo of Alexandria, these views influenced Jewish, Christian and Islamic interpretation of their holy scriptures. They spread widely in the Renaissance and contributed to the fashion for allegory among poets such as Dante, Spenser, and Shakespeare.