Parmenides of Elea (/pɑːrˈmɛnɪdiːz ... ˈɛliə/; Greek: Παρμενίδης ὁ Ἐλεάτης; fl. late sixth or early fifth century BC) was a pre-Socratic Greek philosopher from Elea in Magna Graecia (Greater Greece, which included Southern Italy). He was the founder of the Eleatic school of philosophy.
The single known work by Parmenides is a poem, On Nature, only fragments of which survive. In it, Parmenides prescribes two views of reality. In "the way of truth" (a part of the poem), he explains how reality (coined as "what is-is") is one, change is impossible, and existence is timeless, uniform, necessary, and unchanging. This is generally considered one of the first digressions into the philosophical concept of being, and has been contrasted with Heraclitus's statement that "No man ever steps into the same river twice" as one of the first digressions into the philosophical concept of becoming.
Parmenides and Heraclitus are therefore generally considered two of the founders of ontology. Scholars have generally believed that either Parmenides was responding to Heraclitus, or Heraclitus to Parmenides, though opinion on who was responding to whom changed over the course of the 20th century. In "the way of opinion", Parmenides explains the world of appearances, in which one's sensory faculties lead to conceptions which are false and deceitful. He has been considered the founder of metaphysics or ontology.
|Born||c. 515 BC|
|"Thought and being are the same"|
The truth–appearance distinction
Nothing comes from nothing
His dates are uncertain; according to Diogenes Laërtius, he flourished just before 500 BC, which would put his year of birth near 540 BC, but Plato has him visiting Athens at the age of 65, when Socrates was a young man, c. 450 BC, which, if true, suggests a year of birth of c. 515 BC. He was said to have been a pupil of Xenophanes, and regardless of whether they actually knew each other, Xenophanes' philosophy is the most obvious influence on Parmenides. Diogenes Laërtius also describes Parmenides as a disciple of "Ameinias, son of Diochaites, the Pythagorean"; but there are no obvious Pythagorean elements in his thought.
However, according to Sir William Smith, in Dictionary of Greek and Roman Biography and Mythology (1870):
Others content themselves with reckoning Parmenides as well as Zeno as belonging to the Pythagorean school, or with speaking of a Parmenidean life, in the same way as a Pythagorean life is spoken of; and even the censorious Timon allows Parmenides to have been a high-minded man; while Plato speaks of him with veneration, and Aristotle and others give him an unqualified preference over the rest of the Eleatics.
The first hero cult of a philosopher we know of was Parmenides' dedication of a heroon to his teacher Ameinias in Elea. Parmenides was the founder of the School of Elea, which also included Zeno of Elea and Melissus of Samos. Of his life in Elea, it was said that he had written the laws of the city. His most important pupil was Zeno, who according to Plato was 25 years his junior, and was regarded as his eromenos. Parmenides had a large influence on Plato, who not only named a dialogue, Parmenides, after him, but always wrote about him with veneration.
William Smith also wrote in Dictionary of Greek and Roman Biography and Mythology:
On the former reason is our guide; on the latter the eye that does not catch the object and re-echoing hearing. On the former path we convince ourselves that the existent neither has come into being, nor is perishable, and is entirely of one sort, without change and limit, neither past nor future, entirely included in the present. For it is as impossible that it can become and grow out of the existent, as that it could do so out of the non-existent; since the latter, non-existence, is absolutely inconceivable, and the former cannot precede itself; and every coming into existence presupposes a non-existence. By similar arguments divisibility, motion or change, as also infinity, are shut out from the absolutely existent, and the latter is represented as shut up in itself, so that it may be compared to a well-rounded ball; while thought is appropriated to it as its only positive definition. Thought and that which is thought of (Object) coinciding; the corresponding passages of Plato, Aristotle, Theophrastus, and others, which authenticate this view of his theory.
Cosmology originally comprised the greater part of his poem, him explaining the world’s origins and operations. John Palmer notes "Parmenides’ distinction among the principal modes of being and his derivation of the attributes that must belong to what must be, simply as such, qualify him to be seen as the founder of metaphysics or ontology as a domain of inquiry distinct from theology." Some idea of the sphericity of the Earth seems to have been known to both Parmenides and Empedocles.
Bright in the night with the gift of his light,
Round the earth she is erring,
Evermore letting her gaze
Turn towards Helios' rays
Of the cosmogony of Parmenides, which was carried out very much in detail, we possess only a few fragments and notices, which are difficult to understand, according to which, with an approach to the doctrines of the Pythagoreans, he conceived the spherical mundane system, surrounded by a circle of the pure light (Olympus, Uranus); in the centre of this mundane system the solid earth, and between the two the circle of the milkyway, of the morning or evening star, of the sun, the planets, and the moon; which circle he regarded as a mixture of the two primordial elements.
The fragments read:
You will know the aether’s nature, and in the aether all the/ signs, and the unseen works of the pure torch/ of the brilliant sun, and from whence they came to be,/ and you will learn the wandering works of the round-eyed moon/ and its nature, and you will know too the surrounding heaven,/ both whence it grew and how Necessity directing it bound it/ to furnish the limits of the stars. (Fr. 10)
…how the earth and sun and moon/ and the shared aether and the heavenly milk and Olympos/ outermost and the hot might of the stars began/ to come to be. (Fr. 11)
Parmenides is one of the most significant of the pre-Socratic philosophers. His single known work, a poem conventionally titled On Nature, has survived only in fragments. Approximately 160 verses remain today from an original total that was probably near 800. The poem was originally divided into three parts:
The proem is a narrative sequence in which the narrator travels "beyond the beaten paths of mortal men" to receive a revelation from an unnamed goddess (generally thought to be Persephone or Dikē) on the nature of reality. Aletheia, an estimated 90% of which has survived, and doxa, most of which no longer exists, are then presented as the spoken revelation of the goddess without any accompanying narrative.
Parmenides attempted to distinguish between the unity of nature and its variety, insisting in the Way of Truth upon the reality of its unity, which is therefore the object of knowledge, and upon the unreality of its variety, which is therefore the object, not of knowledge, but of opinion. In the Way of Opinion he propounded a theory of the world of seeming and its development, pointing out, however, that, in accordance with the principles already laid down, these cosmological speculations do not pretend to anything more than mere appearance.
In the proem, Parmenides describes the journey of the poet, escorted by maidens ("the daughters of the Sun made haste to escort me, having left the halls of Night for the light"), from the ordinary daytime world to a strange destination, outside our human paths. Carried in a whirling chariot, and attended by the daughters of Helios the Sun, the man reaches a temple sacred to an unnamed goddess (variously identified by the commentators as Nature, Wisdom, Necessity or Themis), by whom the rest of the poem is spoken. The goddess resides in a well-known mythological space: where Night and Day have their meeting place. Its essential character is that here all opposites are undivided, or one. He must learn all things, she tells him – both truth, which is certain, and human opinions, which are uncertain – for though one cannot rely on human opinions, they represent an aspect of the whole truth.
The section known as "the way of truth" discusses that which is real and contrasts with the argument in the section called "the way of opinion," which discusses that which is illusory. Under the "way of truth," Parmenides stated that there are two ways of inquiry: that it is, on the one side, and that it is not. on the other side. He said that the latter argument is never feasible because there is no thing that can not be: "For never shall this prevail, that things that are not are." (B 7.1)
There are extremely delicate issues here. In the original Greek the two ways are simply named "that Is" (ὅπως ἐστίν) and "that Not-Is" (ὡς οὐκ ἐστίν) (B 2.3 and 2.5) without the "it" inserted in our English translation. In ancient Greek, which, like many languages in the world, does not always require the presence of a subject for a verb, "is" functions as a grammatically complete sentence. Much debate has been focused on where and what the subject is. The simplest explanation as to why there is no subject here is that Parmenides wishes to express the simple, bare fact of existence in his mystical experience without the ordinary distinctions, just as the Latin "pluit" and the Greek huei (ὕει "rains") mean "it rains"; there is no subject for these impersonal verbs because they express the simple fact of raining without specifying what is doing the raining. This is, for instance, Hermann Fränkel's thesis. Many scholars still reject this explanation and have produced more complex metaphysical explanations. Since existence is an immediately intuited fact, non-existence is the wrong path because a thing cannot disappear, just as something cannot originate from nothing. In such mystical experience (unio mystica), however, the distinction between subject and object disappears along with the distinctions between objects, in addition to the fact that if nothing cannot be, it cannot be the object of thought either:
Thinking and the thought that it is are the same; for you will not find thinking apart from what is, in relation to which it is uttered. (B 8.34–36)
For to be aware and to be are the same. (B 3)
It is necessary to speak and to think what is; for being is, but nothing is not. (B 6.1–2)
Helplessness guides the wandering thought in their breasts; they are carried along deaf and blind alike, dazed, beasts without judgment, convinced that to be and not to be are the same and not the same, and that the road of all things is a backward-turning one. (B 6.5–9)
Thus, he concluded that "Is" could not have "come into being" because "nothing comes from nothing". Existence is necessarily eternal. That which truly is [x], has always been [x], and was never becoming [x]; that which is becoming [x] was never nothing (Not-[x]), but will never actually be. Parmenides was not struggling to formulate the laws of conservation of mass and conservation of energy; he was struggling with the metaphysics of change, which is still a relevant philosophical topic today. Moreover, he argued that movement was impossible because it requires moving into "the void", and Parmenides identified "the void" with nothing, and therefore (by definition) it does not exist. That which does exist is The Parmenidean One, which is timeless, uniform, and unchanging:
How could what is perish? How could it have come to be? For if it came into being, it is not; nor is it if ever it is going to be. Thus coming into being is extinguished, and destruction unknown. (B 8.20–22)
Nor was [it] once, nor will [it] be, since [it] is, now, all together, / One, continuous; for what coming-to-be of it will you seek? / In what way, whence, did [it] grow? Neither from what-is-not shall I allow / You to say or think; for it is not to be said or thought / That [it] is not. And what need could have impelled it to grow / Later or sooner, if it began from nothing? Thus [it] must either be completely or not at all. (B 8.5–11)
[What exists] is now, all at once, one and continuous... Nor is it divisible, since it is all alike; nor is there any more or less of it in one place which might prevent it from holding together, but all is full of what is. (B 8.5–6, 8.22–24)
And it is all one to me / Where I am to begin; for I shall return there again. (B 5)
Parmenides claimed that there is no truth in the opinions of the mortals. Genesis-and-destruction, as Parmenides emphasizes, is a false opinion, because to be means to be completely, once and for all. What exists can in no way not exist.
For this view, that That Which Is Not exists, can never predominate. You must debar your thought from this way of search, nor let ordinary experience in its variety force you along this way, (namely, that of allowing) the eye, sightless as it is, and the ear, full of sound, and the tongue, to rule; but (you must) judge by means of the Reason (Logos) the much-contested proof which is expounded by me. (B 7.1–8.2)
After the exposition of the arche (ἀρχή), i.e. the origin, the necessary part of reality that is understood through reason or logos (that [it] Is), in the next section, the Way of Appearance/Opinion/Seeming, Parmenides proceeds to explain the structure of the becoming cosmos (which is an illusion, of course) that comes from this origin.
The structure of the cosmos is a fundamental binary principle that governs the manifestations of all the particulars: "the aether fire of flame" (B 8.56), which is gentle, mild, soft, thin and clear, and self-identical, and the other is "ignorant night", body thick and heavy.
The mortals lay down and decided well to name two forms (i.e. the flaming light and obscure darkness of night), out of which it is necessary not to make one, and in this they are led astray. (B 8.53–4)
The structure of the cosmos then generated is recollected by Aetius (II, 7, 1):
For Parmenides says that there are circular bands wound round one upon the other, one made of the rare, the other of the dense; and others between these mixed of light and darkness. What surrounds them all is solid like a wall. Beneath it is a fiery band, and what is in the very middle of them all is solid, around which again is a fiery band. The most central of the mixed bands is for them all the origin and cause of motion and becoming, which he also calls steering goddess and keyholder and Justice and Necessity. The air has been separated off from the earth, vapourized by its more violent condensation, and the sun and the circle of the Milky Way are exhalations of fire. The moon is a mixture of both earth and fire. The aether lies around above all else, and beneath it is ranged that fiery part which we call heaven, beneath which are the regions around the earth.
The traditional interpretation of Parmenides' work is that he argued that the every-day perception of reality of the physical world (as described in doxa) is mistaken, and that the reality of the world is 'One Being' (as described in aletheia): an unchanging, ungenerated, indestructible whole. Under the Way of Opinion, Parmenides set out a contrasting but more conventional view of the world, thereby becoming an early exponent of the duality of appearance and reality. For him and his pupils, the phenomena of movement and change are simply appearances of a changeless, eternal reality. This interpretation could settle because of various wrong translations of the fragments. For example, it is not at all clear that Parmenides refuted that which we call perception. The verb noein, used frequently by Parmenides, could better be translated as 'to be aware of' than as 'to think'. Furthermore, it is hard to believe that 'being' is only within our heads, according to Parmenides.
Parmenides' philosophy is presented in the form of poetry. The philosophy he argued was, he says, given to him by a goddess, though the "mythological" details in Parmenides' poem do not bear any close correspondence to anything known from traditional Greek mythology:
Welcome, youth, who come attended by immortal charioteers and mares which bear you on your journey to our dwelling. For it is no evil fate that has set you to travel on this road, far from the beaten paths of men, but right and justice. It is meet that you learn all things — both the unshakable heart of well-rounded truth and the opinions of mortals in which there is not true belief. (B 1.24–30)
It is with respect to this religious/mystical context that recent generations of scholars such as Alexander P. Mourelatos, Charles H. Kahn, and the controversial Peter Kingsley have begun to call parts of the traditional, rational logical/philosophical interpretation of Parmenides into question (Kingsley in particular stating that Parmenides practiced iatromancy). It has been claimed that previous scholars placed too little emphasis on the apocalyptic context in which Parmenides frames his revelation. As a result, traditional interpretations have put Parmenidean philosophy into a more modern, metaphysical context to which it is not necessarily well suited, which has led to misunderstanding of the true meaning and intention of Parmenides' message. The obscurity and fragmentary state of the text, however, renders almost every claim that can be made about Parmenides extremely contentious, and the traditional interpretation has by no means been abandoned.
Parmenides' considerable influence on the thinking of Plato is undeniable, and in this respect Parmenides has influenced the whole history of Western philosophy, and is often seen as its grandfather. Even Plato himself, in the Sophist, refers to the work of "our Father Parmenides" as something to be taken very seriously and treated with respect. In the Parmenides, the Eleatic philosopher, which may well be Parmenides himself, and Socrates argue about dialectic. In the Theaetetus, Socrates says that Parmenides alone among the wise (Protagoras, Heraclitus, Empedocles, Epicharmus, and Homer) denied that everything is change and motion.
Parmenides is credited with a great deal of influence as the author of an "Eleatic challenge" that determined the course of subsequent philosophers' enquiries. For example, the ideas of Empedocles, Anaxagoras, Leucippus, and Democritus have been seen as in response to Parmenides' arguments and conclusions.
Parmenides' influence on philosophy reaches up till present times. The Italian philosopher Emanuele Severino has founded his extended philosophical investigations on the words of Parmenides. His philosophy is sometimes called Neo Parmenideism, and can be understood as an attempt to build a bridge between the poem on truth and the poem on opinion.
Parmenides made the ontological argument against nothingness, essentially denying the possible existence of a void. According to Aristotle, this led Democritus and Leucippus, and many other physicists, to propose the atomic theory, which supposes that everything in the universe is either atoms or voids, specifically to contradict Parmenides' argument. Aristotle himself reasoned, in opposition to atomism, that in a complete vacuum, motion would encounter no resistance, and "no one could say why a thing once set in motion should stop anywhere; for why should it stop here rather than here? So that a thing will either be at rest or must be moved ad infinitum, unless something more powerful get in its way." See also horror vacui.
Erwin Schrödinger identified Parmenides' monad of the "Way of Truth" as being the conscious self in "Nature and the Greeks". The scientific implications of this view have been discussed by scientist Anthony Hyman.
A shadow of Parmenides' ideas can be seen in the physical concept of Block time, which considers existence to consist of past, present, and future, and the flow of time to be illusory. In his critique of this idea, Karl Popper called Einstein "Parmenides". However, Popper did write:
Aletheia (Ancient Greek: ἀλήθεια) is truth or disclosure in philosophy. It was used in Ancient Greek philosophy and revived in the 20th century by Martin Heidegger.
It is a Greek word variously translated as "unclosedness", "unconcealedness", "disclosure" or "truth". The literal meaning of the word ἀ–λήθεια is "the state of not being hidden; the state of being evident." It also means factuality or reality. It is the opposite of lethe, which literally means "oblivion", "forgetfulness", or "concealment". According to Pindar's Olympian Ode, Aletheia is the daughter of Zeus, while Aesop in his Fables said that she was crafted by Prometheus.Becoming (philosophy)
In philosophy, becoming is the possibility of change in a thing that has being, that exists.
In the philosophical study of ontology, the concept of becoming originated in ancient Greece with the philosopher Heraclitus of Ephesus, who in the sixth century BC, said that nothing in this world is constant except change and becoming. This point was made by Heraclitus with the famous quote "No man ever steps in the same river twice." His theory stands in direct contrast to the philosophic idea of being, first argued by Parmenides, a Greek philosopher from the italic Magna Grecia, who believed that the change or "becoming" we perceive with our senses is deceptive, and that there is a pure perfect and eternal being behind nature, which is the ultimate truth of being. This point was made by Parmenides with the famous quote "what is-is". Becoming, along with its antithesis of being, are two of the foundation concepts in ontology. Scholars have generally believed that either Parmenides was responding to Heraclitus, or Heraclitus to Parmenides, though opinion on who was responding to who changed over the course of the 20th century.
In philosophy, the word "becoming" concerns a specific ontological concept which should not be confused with process philosophy as a whole or with the related study of process theology.Eleatics
The Eleatics were a pre-Socratic school of philosophy founded by Parmenides in the early fifth century BC in the ancient town of Elea. Other members of the school included Zeno of Elea and Melissus of Samos. Xenophanes is sometimes included in the list, though there is some dispute over this. Elea, whose modern-day appellation is Velia, was a Greek colony located in present-day Campania in southern Italy.Glaucon
Glaucon (; Greek: Γλαύκων; c. 445 BC – 4th century BC) son of Ariston, was an ancient Athenian and the philosopher Plato's older brother. He is primarily known as a major conversant with Socrates in the Republic, and the interlocutor during the Allegory of the Cave. He is also referenced briefly in the beginnings of two dialogues of Plato, the Parmenides and Symposium.List of speakers in Plato's dialogues
The following is a list of the speakers found in the dialogues traditionally ascribed to Plato, including extensively quoted, indirect and conjured speakers. Dialogues, as well as Platonic Epistles and Epigrams, in which these individuals appear dramatically but do not speak are listed separately.
Unnamed speakersMelissus of Samos
Melissus of Samos (; Greek: Μέλισσος ὁ Σάμιος; fl. 5th century BC) 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.Nothing
"Nothing", used as a pronoun subject, denotes the absence of a something or particular thing that one might expect or desire to be present ("We found nothing," "Nothing was there") or the inactivity of a thing or things that are usually or could be active ("Nothing moved," "Nothing happened"). As a predicate or complement "nothing" denotes the absence of meaning, value, worth, relevance, standing, or significance ("It is a tale/ Told by an idiot, full of sound and fury,/ Signifying nothing"; "The affair meant nothing"; "I'm nothing in their eyes"). "Nothingness" is a philosophical term that denotes the general state of nonexistence, sometimes reified as a domain or dimension into which things pass when they cease to exist or out of which they may come to exist, e.g., God is understood to have created the universe ex nihilo, "out of nothing."Nothing comes from nothing
Nothing comes from nothing (Latin: ex nihilo nihil fit) is a philosophical expression of a thesis first argued by Parmenides. It is associated with ancient Greek cosmology, such as is presented not just in the works of Homer and Hesiod, but also in virtually every internal system—there is no break in-between a world that did not exist and one that did, since it could not be created ex nihilo in the first place.Ontology
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.Parmenides (dialogue)
Parmenides (Greek: Παρμενίδης) 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.Philosophy in the Tragic Age of the Greeks
Philosophy in the Tragic Age of the Greeks (German: Philosophie im tragischen Zeitalter der Griechen) is an incomplete book by Friedrich Nietzsche. He had a clean copy made from his notes with the intention of publication. The notes were written around 1873. In it he discussed five Greek philosophers from the sixth and fifth centuries BC. They are Thales, Anaximander, Heraclitus, Parmenides, and Anaxagoras. He had, at one time, intended to include Democritus, Empedocles, and Socrates. The book ends abruptly after the discussion of Anaxagoras's cosmogony.Philosophy of motion
Philosophy of motion is a branch of philosophy concerned with exploring questions on the existence and nature of motion. The central questions of this study concern the epistemology and ontology of motion, whether motion exists as we perceive it, what is it, and, if it exists, how does it occur. The philosophy of motion is important in the study of theories of change in natural systems and is closely connected to studies of space and time in philosophy.
The philosophy of motion was of central concern to Ancient Greek and Roman philosophers, particularly the pre-Socratic philosophers such as Parmenides, Zeno of Elea, Heraclitus and Democritus. As such, it was influential in the development of the philosophy of science in general.Plato
Plato (; PLAY-toe Greek: Πλάτων Plátōn, pronounced [plá.tɔːn] PLOT-own in Classical Attic; 428/427 or 424/423 – 348/347 BC) was an Athenian philosopher during the Classical period in Ancient Greece and the founder of the Academy, the first institution of higher learning in the Western world. He is widely considered the pivotal figure in the history of Ancient Greek and Western philosophy, along with his teacher, Socrates, and his most famous student, Aristotle. Alfred North Whitehead once noted: "the safest general characterization of the European philosophical tradition is that it consists of a series of footnotes to Plato."Plato has also often been cited as one of the founders of Western religion and spirituality. The so-called Neoplatonism of philosophers like Plotinus and Porphyry influenced Saint Augustine and thus Christianity.
Plato was the innovator of the written dialogue and dialectic forms in philosophy. Plato also appears to have been the founder of Western political philosophy. His most famous contribution bears his name, Platonism (also ambiguously called either Platonic realism or Platonic idealism), the doctrine of the Forms known by pure reason to provide a realist solution to the problem of universals. He is also the namesake of Platonic love and the Platonic solids.
His own most decisive philosophical influences are usually thought to have been along with Socrates, the pre-Socratics Pythagoras, Heraclitus and Parmenides, although few of his predecessors' works remain extant and much of what we know about these figures today derives from Plato himself. Unlike the work of nearly all of his contemporaries, Plato's entire oeuvre is believed to have survived intact for over 2,400 years. Although their popularity has fluctuated over the years, the works of Plato have never been without readers since the time they were written.Pluralist school
The Pluralist school was a school of pre-Socratic philosophers who attempted to reconcile Parmenides' rejection of change with the apparently changing world of sense experience. The school consisted of Anaxagoras, Archelaus, and Empedocles. It can also be said to have included the Atomists, Leucippus and Democritus. The Pluralists rejected the idea that the diversity of nature can be reduced to a single principle (monism). Anaxagoras posited that nature contained an innumerable number of principles, while Empedocles reduced nature to four elements (fire, air, earth, and water) which could not be reduced to one another and which would be sufficient to explain change and diversity.Third man argument
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.Velia
Velia was the Roman name of an ancient city of Magna Graecia on the coast of the Tyrrhenian Sea. It was founded by Greeks from Phocaea as Hyele (Ancient Greek: Ὑέλη) around 538–535 BC. The name later changed to Ele and then Elea (; Ancient Greek: Ἐλέα) before it became known by its current Latin and Italian name during the Roman era. Its ruins are located in the Cilento region near the modern village Velia, which was named after the ancient city. The village is a frazione of the comune Ascea in the Province of Salerno, Campania, Italy.
The city was known for being the home of the philosophers Parmenides and Zeno of Elea, as well as the Eleatic school of which they were a part. The site of the acropolis of ancient Elea was once a promontory called Castello a Mare, meaning "castle on the sea" in Italian. It now lies inland and was renamed to Castellammare della Bruca in the Middle Ages.World
The world is the planet Earth and all life upon it, including human civilization. In a philosophical context, the "world" is the whole of the physical Universe, or an ontological world (the "world" of an individual). In a theological context, the world is the material or the profane sphere, as opposed to the celestial, spiritual, transcendent or sacred spheres. "End of the world" scenarios refer to the end of human history, often in religious contexts.
The history of the world is commonly understood as spanning the major geopolitical developments of about five millennia, from the first civilizations to the present. In terms such as world religion, world language, world government, and world war, the term world suggests an international or intercontinental scope without necessarily implying participation of every part of the world.
The world population is the sum of all human populations at any time; similarly, the world economy is the sum of the economies of all societies or countries, especially in the context of globalization. Terms such as "world championship", "gross world product", and "world flags" imply the sum or combination of all sovereign states.Zeno's paradoxes
Zeno's paradoxes are a set of philosophical problems generally thought to have been devised by Greek philosopher Zeno of Elea (c. 490–430 BC) 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.Some of Zeno's nine surviving paradoxes (preserved in Aristotle's Physics
and Simplicius's commentary thereon) are essentially equivalent to one another. Aristotle offered a refutation of some of them. Three of the strongest and most famous—that of Achilles and the tortoise, the Dichotomy argument, and that of an arrow in flight—are presented in detail below.
Zeno's arguments are perhaps the first examples of a method of proof called reductio ad absurdum also known as proof by contradiction. They are also credited as a source of the dialectic method used by Socrates.Some mathematicians and historians, such as Carl Boyer, hold that Zeno's paradoxes are simply mathematical problems, for which modern calculus provides a mathematical solution.
Some philosophers, however, say that Zeno's paradoxes and their variations (see Thomson's lamp) remain relevant metaphysical problems.The origins of the paradoxes are somewhat unclear. Diogenes Laërtius, a fourth source for information about Zeno and his teachings, citing Favorinus, says that Zeno's teacher Parmenides was the first to introduce the Achilles and the tortoise paradox. But in a later passage, Laërtius attributes the origin of the paradox to Zeno, explaining that Favorinus disagrees.Zeno of Elea
Zeno of Elea (; Greek: Ζήνων ὁ Ἐλεάτης; c. 495 – c. 430 BC) 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 has described as "immeasurably subtle and profound".