Parmenides of Elea
Parmenides of Elea was a pre-Socratic Greek philosopher whose surviving poem revolutionized Western metaphysics by arguing that reality is one, ungenerated, indestructible, and unchanging. Born in the Greek colony of Elea in Magna Graecia around 515 BCE, he stands at the center of the so‑called Eleatic school. Ancient reports link him with Xenophanes and Pythagorean circles, though details of his life remain sparse and partly legendary. Parmenides’ sole known work, a hexameter poem conventionally called "On Nature," frames philosophy as a revelatory journey: a youth is conveyed in a chariot to a goddess who discloses two paths of inquiry—the Way of Truth and the Way of Opinion. In the first, Parmenides offers rigorous arguments that genuine being cannot come to be, perish, or possess internal differences; in the second, he presents a cosmology he regards as merely plausible for mortal belief. His radical denial of change, multiplicity, and non‑being forced later philosophers to clarify concepts of existence, identity, and logical consistency. Plato, Aristotle, and many subsequent traditions wrestled with Parmenides’ challenge, making him a pivotal figure in the development of ontology, rational argumentation, and the distinction between knowledge and opinion.
At a Glance
- Born
- c. 515 BCE(approx.) — Elea (Velia), Magna Graecia (modern Campania, Italy)
- Died
- c. 450 BCE(approx.) — Elea (Velia), Magna GraeciaCause: Unknown (natural causes presumed)
- Floruit
- Early 5th century BCE (c. 500–450 BCE)Traditional floruit synchronized with the 69th Olympiad (504–501 BCE) and his reported visit to Athens.
- Active In
- Elea (Velia), Magna Graecia, Southern Italy, Greater Greek world
- Interests
- MetaphysicsOntologyLogicEpistemologyCosmologyPhilosophy of language and truth
Reality—what truly is—is a single, ungenerated, imperishable, indivisible, and unchanging being that admits no non‑being or internal difference; genuine knowledge arises only from following the rational "Way of Truth" that recognizes the logical impossibility of coming‑to‑be and ceasing‑to‑be, while all accounts based on sense perception belong to the deceptive "Way of Opinion."
Περὶ φύσεως (Perì phýseōs)
Composed: c. 500–480 BCE
"Come now, and I will tell you—and do you, when you have heard the tale, carry it away— the only ways of inquiry that can be thought of: the one, that it is and that it is not possible for it not to be; the other, that it is not and that it must not be."— Parmenides, Fragment B2 (DK 28 B2), from "On Nature"
The goddess introduces the two fundamental paths of inquiry, distinguishing the logically coherent affirmation of being from the incoherent path that denies it.
"It is necessary to say and to think that Being is; for it is to be, but nothing is not."— Parmenides, Fragment B6 (DK 28 B6), from "On Nature"
Parmenides links thought, speech, and being, insisting that intelligible discourse can only be about what is, never about non‑being.
"Nor was it ever, nor will it be, since it is now, all at once, one, continuous."— Parmenides, Fragment B8.5–6 (DK 28 B8), from "On Nature"
In the central argument of the Way of Truth, he denies temporal becoming and presents being as a timeless, unified whole.
"For the same thing is for thinking and for being."— Parmenides, Fragment B3 (DK 28 B3), from "On Nature"
This succinct formula expresses the tight correlation between what can be thought and what truly is, foundational for later epistemology and ontology.
"Thus according to opinion these things have been fashioned, and in this way, as it seems, they grew and now are, and from here mortals have given them names."— Parmenides, Fragment B19 (DK 28 B19), from "On Nature"
From the cosmological section, Parmenides distances himself from the world‑picture of mortals as merely a plausible arrangement of appearances, not ultimate truth.
Formative Period in Elea
During his youth and early adulthood in Elea, Parmenides is traditionally said to have encountered Xenophanes’ critique of anthropomorphic religion and possibly Pythagorean doctrines; this milieu likely shaped his distrust of sensory appearances and his orientation toward systematic, reason‑based inquiry.
Composition of the Poem "On Nature"
In his mature period, Parmenides composed his philosophical poem, articulating a strict contrast between the rationally necessary structure of being and the deceptive testimonies of sense, establishing the core Eleatic doctrines of the One and the rejection of becoming and non‑being.
Eleatic Leadership and Influence
Later ancient reports describe Parmenides as a respected figure in Elea’s civic life and as the teacher or intellectual predecessor of Zeno of Elea, suggesting a role as both philosophical founder and local statesman whose circle developed and defended Eleatic arguments.
Posthumous Reception and Systematization
After his death, Parmenides’ thought was recast and debated by Plato, Aristotle, Megarians, and later Neoplatonists, who mined his dense fragments for principles of logic and ontology, often interpreting or softening his radical monism while preserving his demand for strict rational justification.
1. Introduction
Parmenides of Elea is commonly regarded as a pivotal figure in early Greek philosophy whose surviving poem recasts inquiry into nature as a rigorous investigation into being (τὸ ἐόν) and non‑being (μὴ ἐόν). While earlier so‑called pre‑Socratic thinkers often focused on identifying basic physical constituents and processes, Parmenides’ work shifts attention to what can coherently be thought and said, and to the logical conditions under which anything can be said to exist at all.
The poem, conventionally titled On Nature, is preserved only in fragments, yet it offers one of the earliest extended arguments in Western philosophy. A mythic prologue presents a youth carried in a chariot to a goddess, who promises to reveal both the Way of Truth—a strict account of what is and must be—and the Way of Opinion, a plausible but ultimately deceptive account of the world of change and plurality. This two‑track structure underlies much of the later tradition’s understanding of the distinction between knowledge (of what is necessary and unchanging) and opinion (about changing appearances).
Across antiquity and modern scholarship, Parmenides has been interpreted variously as a radical monist who denies all change, as a sophisticated logician clarifying the concept of existence, as a religious or mystical seer casting metaphysics in revelatory terms, or as a theorist of language and thought. Subsequent sections of this entry examine his life and context, the poem’s textual state, the structure and content of the Way of Truth and Way of Opinion, and the wide range of interpretations and reactions his work has generated from Plato and Aristotle to contemporary analytic and continental philosophy.
2. Life and Historical Context
2.1 Biographical Outline
Little about Parmenides’ life is securely known. Ancient biographical traditions, especially in Diogenes Laertius, give approximate dates and a small set of anecdotes that modern scholars treat cautiously.
| Aspect | Information (traditional, with caveats) |
|---|---|
| Birth | c. 515 BCE in Elea (Velia) in Magna Graecia |
| Floruit | Early 5th century BCE, around the 69th Olympiad (504–501 BCE) |
| Death | c. 450 BCE, likely in Elea |
| Social role | Reported as a lawgiver or statesman in Elea |
| Intellectual circle | Associated with Xenophanes, Ameinias (a Pythagorean), and Zeno of Elea |
Sources describe Parmenides as coming from a distinguished family and credit him with authorship of Elea’s laws, which citizens allegedly swore to uphold annually. Many historians regard this as possible but not demonstrable.
2.2 Elea and Magna Graecia
Parmenides lived in Elea, a Greek colony in southern Italy founded by Phocaean refugees. Elea became a center of what later writers called the Eleatic school, including Parmenides, Zeno, and Melissus (though Melissus came from Samos). The western Greek colonies hosted diverse philosophical currents—Milesian naturalism, Pythagorean mathematics and religion, and Xenophanean theology—which likely formed the intellectual environment in which Parmenides’ ideas emerged.
2.3 Intellectual and Political Milieu
Historians typically situate Parmenides between earlier Ionian inquirers into nature (Thales, Anaximander, Heraclitus) and the classical Athenian philosophers. He thus stands at a juncture when:
| Broader context | Relevance to Parmenides |
|---|---|
| Persian Wars and Greek–Persian conflict | Promoted pan‑Hellenic identity and cultural exchange, facilitating the spread of ideas to Magna Graecia. |
| Rise of Pythagorean communities | May have influenced Elea’s intellectual climate with numerological and religious doctrines. |
| Early development of rational argumentation | Provided precedents for the kind of deductive reasoning found in Parmenides’ poem. |
Plato’s dialogue Parmenides depicts an elderly Parmenides visiting Athens and conversing with a young Socrates around 450 BCE. Modern scholars widely treat this as a literary construction, though it is often taken to reflect Parmenides’ high reputation in 4th‑century philosophical circles rather than as strict historical testimony.
3. Sources and Textual Transmission
3.1 Primary Evidence: The Fragments
Parmenides’ thought is known exclusively from quotations and testimonies in later authors. His poem On Nature survives as fragments (direct quotations) and testimonia (indirect reports).
| Type | Examples of sources | Content type |
|---|---|---|
| Fragments | Simplicius, Sextus Empiricus, Proclus | Direct lines or passages from the poem, especially on the Way of Truth |
| Testimonia | Plato, Aristotle, Theophrastus, Diogenes Laertius | Paraphrases, summaries, and characterizations of Parmenides’ doctrines |
Modern editions typically follow the Diels–Kranz (DK) numbering, where Parmenides is DK 28, with fragments labeled B1, B2, etc. Alternative arrangements (e.g., Laks–Most) propose different sequences or groupings.
3.2 Transmission History
The poem itself has not survived as a continuous text. Instead, it is reconstructed from:
- Late antique philosophical commentaries, especially Simplicius’ 6th‑century commentaries on Aristotle, which quote long stretches of Parmenides to discuss pre‑Socratic views.
- Quotations in doxographical works, such as Aetius (via later epitomes), summarizing early cosmologies.
- Citations in polemical or exegetical contexts, for instance in Sextus Empiricus, who uses Parmenides in skeptical arguments.
Scholars generally agree that Simplicius is the single most important source for the text of the Way of Truth, while the Way of Opinion is more fragmentary and dispersed.
3.3 Textual Reconstruction and Ordering
The original ordering of fragments is uncertain. Editors use internal cues (transitions, pronouns, thematic progression) and external testimonies to reconstruct the poem’s structure. Major points of debate include:
| Issue | Main positions |
|---|---|
| Length and exact division between Proem, Truth, Opinion | Some argue for a relatively compact poem; others posit extensive lost sections, particularly in the cosmology. |
| Placement of certain cosmological fragments | Disagreement over whether some fragments belong early or late in the doxastic section. |
| Integrity of key fragments (e.g., B8) | Scholarly discussion of whether Simplicius transmits an entire argumentative block or a composite of separate parts. |
Different reconstructions can significantly shape interpretations of Parmenides’ metaphysics and cosmology. Nonetheless, there is broad consensus about the existence of a three‑part structure (Proem, Way of Truth, Way of Opinion) and about the content of the central ontological argument.
4. Intellectual Development and Influences
4.1 Relationship to Xenophanes
Ancient sources sometimes present Xenophanes of Colophon as Parmenides’ teacher or influence. Modern scholars distinguish between:
| View | Description |
|---|---|
| Direct discipleship | Accepts ancient reports that Parmenides studied with Xenophanes, inheriting his critique of anthropomorphic gods and emphasis on a single divine reality. |
| Indirect influence | Treats Xenophanes as a background figure whose ideas circulated in Magna Graecia, shaping Parmenides’ environment without implying personal instruction. |
| Skeptical stance | Questions any firm biographical link, seeing the teacher‑student relation as a later construction to systematize early philosophy. |
Conceptual parallels often cited include Xenophanes’ emphasis on a single greatest god, immobile and all‑seeing, and Parmenides’ notion of a unique, unchanging being, though their projects differ in important respects.
4.2 Pythagorean Connections
Reports associate Parmenides with Ameinias, a Pythagorean, and with Pythagorean communities in southern Italy.
Proposed influences include:
- A shared interest in cosmic order and mathematical structure, especially in the cosmological section.
- Possible adaptation of Pythagorean ideas of opposites (limit/unlimited, light/dark) into Parmenides’ two‑principle cosmology in the Way of Opinion.
- Ascetic or religious practices that might underlie the poem’s mythic and initiatory Proem.
Some scholars emphasize these links, presenting Parmenides as transforming Pythagorean themes into a new logical and ontological framework; others stress the differences, noting his rejection of plural principles at the level of true being.
4.3 Engagement with Pre‑Socratic Natural Philosophy
Parmenides’ arguments respond implicitly or explicitly to earlier natural philosophers:
| Predecessor | Possible point of engagement |
|---|---|
| Milesians (Thales, Anaximander, Anaximenes) | Their accounts of cosmogony and elemental change may be targets of Parmenides’ critique of coming‑to‑be. |
| Heraclitus | His emphasis on flux is often read as a foil to Parmenides’ denial of change, though direct dependence is debated. |
| Early atomists (Leucippus, Democritus) | Later, their responses to Parmenides suggest that his denial of the void and of generation shaped their formulations. |
Some interpreters regard Parmenides as repudiating earlier cosmologies wholesale; others argue that he systematizes their assumptions about what is while relocating cosmology to the realm of mere opinion.
4.4 Internal Development
Given the lack of chronological data, reconstructing phases in Parmenides’ own intellectual development is speculative. A common hypothesis is that he began from interests in cosmology and physics, later arriving at the more radical metaphysical views articulated in the Way of Truth, and finally reworking cosmology within a doxastic framework. Critics of this hypothesis caution that it projects modern narratives of “progress” onto sparse evidence and may oversimplify the poem’s compositional unity.
5. The Poem On Nature: Form and Structure
5.1 Overall Architecture
Most reconstructions agree that the poem has three main parts:
| Part | Conventional name | Content focus |
|---|---|---|
| 1 | Proem (B1) | Mythic journey to the goddess; introduction of the two ways of inquiry |
| 2 | Way of Truth | Ontological and logical analysis of what is |
| 3 | Way of Opinion | Cosmology and account of the world as it appears to mortals |
The work is composed in dactylic hexameter, the traditional meter of Homeric epic, which Parmenides adapts to philosophical argument rather than heroic narrative.
5.2 The Proem
The opening lines (Fragment B1) describe a young man transported in a chariot beyond the paths of mortals to a goddess who greets him and promises to reveal:
“the only ways of inquiry that can be thought of:
the one, that it is and that it is not possible for it not to be;
the other, that it is not and that it must not be.”— Parmenides, On Nature (DK 28 B2, trans.)
The Proem thereby establishes both the revelatory framework and the rigorous distinction between admissible and inadmissible routes of thought, preparing the reader for the transition from narrative to argument.
5.3 The Way of Truth
In the central section, the goddess expounds the path “that it is,” laying out the necessary attributes of being: ungenerated, imperishable, whole, unique, continuous, and unchanging. The language shifts from journey imagery to dense, abstract reasoning. This section is relatively well preserved, especially in Simplicius, and includes the extended argument in Fragment B8.
5.4 The Way of Opinion
The goddess then turns to “the beliefs of mortals,” which she explicitly marks as deceptive, yet systematically ordered. Here Parmenides presents a cosmology based on two opposed principles (often identified as Light and Night or Fire and Night), explaining the origins of celestial bodies, the earth, and living beings. The structure and extent of this section are less certain, and modern reconstructions differ significantly in the ordering of fragments.
5.5 Poetic Form and Philosophical Content
Scholars debate the significance of Parmenides’ choice of epic verse. Some argue that the traditional form and mythic tropes serve as a deliberate contrast to the novel rational content, signaling a reorientation of wisdom from divine myth to demonstrative argument. Others see continuity with earlier didactic poetry (Hesiod, Xenophanes), suggesting that philosophy at this stage remained inseparable from poetic and religious modes of expression.
6. The Way of Truth: Ontology of Being
6.1 The Two Routes of Inquiry
At the heart of the Way of Truth stands a distinction between two conceivable “routes” (ὁδοί) for thought:
“that it is and that it is not possible for it not to be”
versus
“that it is not and that it must not be.”— Parmenides, On Nature (DK 28 B2)
The first path affirms being and excludes its non‑being; the second posits non‑being and is rejected as unsayable and unthinkable. The Way of Truth thus proceeds exclusively along the first route.
6.2 Attributes of Being
Following this methodological restriction, the goddess deduces the necessary properties of what is. In Fragment B8 and related lines, being is characterized as:
| Attribute | Description in the Way of Truth |
|---|---|
| Ungenerated and imperishable | It cannot come into being from nothing nor pass into nothing, since this would invoke non‑being. |
| Whole and complete | Lacks nothing; there is no “outside” into which it could grow or diminish. |
| One and continuous | No internal divisions or plurality, as division would require regions where being is and is not. |
| Immobile and unchanging | Movement or change would imply being in different states or places, again invoking non‑being. |
| Timeless (“now, all at once”) | It “was not, nor will be,” but simply “is,” suggesting a denial of temporal becoming. |
These attributes form what later thinkers term Parmenidean monism, though interpretations differ on how literal or rigorous the monism is.
6.3 Argumentative Strategy
Parmenides frequently reasons by reductio ad absurdum: assuming alternatives (e.g., that being came to be, that there are multiple beings) and deriving contradictions. He presents logical constraints on discourse—what can be said without contradiction—and infers from them metaphysical conclusions about reality’s structure.
Central to this is the link between thinking, speaking, and being:
“It is necessary to say and to think that Being is;
for it is to be, but nothing is not.”— Parmenides, On Nature (DK 28 B6)
Scholars differ on whether Parmenides primarily offers a metaphysical thesis about reality, or a thesis about the semantics and logic of the verb “to be” and related concepts.
6.4 Scope of Denial
Another point of debate concerns the scope of what Parmenides denies:
- Some interpreters see a rejection of all change and plurality in any sense.
- Others propose that his claims apply only to what is fully real or knowable, leaving room for a subordinate realm of appearances (later elaborated in the Way of Opinion) without according it genuine being.
7. The Way of Opinion: Cosmology and Appearances
7.1 Transition from Truth to Opinion
After outlining the necessary nature of being, the goddess announces a shift:
“Here I end my trustworthy account and thought about truth;
from here on learn the beliefs of mortals, listening to the deceptive order of my words.”— Parmenides, On Nature (paraphrasing DK 28 B8.50–52)
This marks a transition to a doxastic (opinion‑based) discourse. The goddess makes clear that what follows is not true in the strict sense but represents how mortals interpret appearances.
7.2 Dual Principles and Cosmological Scheme
In the Way of Opinion, the world is explained through two fundamental, contrasting principles. Fragments indicate a pair often identified as Light (or Fire) and Night (or Darkness):
| Principle | Typical attributes in the fragments |
|---|---|
| Light/Fire | Warm, fine, rare, active, associated with the divine and with knowledge. |
| Night/Dark | Cold, dense, passive, associated with mortality and ignorance. |
These opposites combine in different proportions to yield observable phenomena—heavenly bodies, earth, air, and living beings.
7.3 Cosmological Content
The surviving fragments suggest a structured cosmology:
- A cosmogony describing the formation of a spherical cosmos.
- Accounts of the sun, moon, stars, and possibly the Milky Way.
- Explanations of meteorological phenomena and the arrangement of the heavens.
- A theory of human generation and physiology, including a controversial fragment on the role of the “steering goddess” (sometimes linked to Aphrodite) in reproduction.
Because the text is incomplete, scholars reconstruct this system using doxographical testimonies and parallels in other early cosmologies.
7.4 Status of the Kosmos of Opinion
The epistemic and metaphysical status of this cosmology is heavily debated:
| Interpretation | Main idea |
|---|---|
| Concessive/Instrumental | Parmenides offers the cosmology as a “best possible” account for those who cannot follow strict reason, acknowledging its falsity at the level of being. |
| Didactic/Progressive | The cosmology functions as a pedagogical step, showing how to systematize appearances without confusing them with ultimate reality. |
| Dual‑level ontology | Some argue that Parmenides allows a subordinate kind of being for the world of change, distinct from the being analyzed in the Way of Truth. |
All readings agree that the Way of Opinion is clearly distinguished from the prior account in terms of truth‑status, even if its internal coherence and scientific ambition are noteworthy.
8. Metaphysics and Monism
8.1 Forms of Parmenidean Monism
Parmenides is often cited as the earliest and most radical proponent of monism—the view that reality is fundamentally one. Scholars distinguish several interpretations:
| Type of monism | Characterization in relation to Parmenides |
|---|---|
| Existential monism | Only one thing exists at all; plurality is illusory. |
| Predicational monism | There may be many things, but they do not differ in what‑it‑is to be; all share the same fundamental nature. |
| Priority monism | A single whole is metaphysically prior to its parts, which are dependent aspects. |
Many commentators attribute to Parmenides at least existential monism on the basis of his denial of division and plurality in Being; others argue he is better read as advancing a more nuanced predicational or priority monism.
8.2 Denial of Becoming and Change
Parmenides’ metaphysics famously denies genesis (coming‑to‑be) and phthora (passing‑away) at the level of true being. The reasoning is that any such process would require a transition between being and non‑being, which his arguments forbid. Similarly, qualitative change (e.g., from hot to cold) would imply that something both is and is not in certain respects, violating the constraint that non‑being is not.
Some interpreters extend this to a denial of spatial change or motion; others think his primary concern is with ontological rather than physical becoming.
8.3 Spatial and Temporal Features of Being
Fragment B8 invokes a series of spatial metaphors: being is “like the bulk of a well‑rounded sphere, equally balanced in every direction.” Scholars debate whether this imagery:
- Indicates that Being is literally spatially extended and spherical.
- Functions as an analogy for uniformity and lack of differentiation.
Temporally, Being “is now, all at once, one, continuous,” leading many to regard Parmenides as offering a proto‑eternalist or atemporal picture in which reality does not undergo temporal succession.
8.4 Relation to Cosmology and Plurality
The presence of an elaborate cosmology in the Way of Opinion raises questions about how Parmenides’ metaphysical monism relates to the pluralistic world described there. Competing views include:
- Strict eliminativism: the manifold world has no genuine reality whatsoever.
- Two‑level metaphysics: Being is one at the fundamental level, while a derivative or merely apparent level displays plurality and change.
- Methodological distinction: the monism applies to what can be known by strict reasoning, while cosmology is a separate, more empirical enterprise.
Subsequent philosophers, notably the atomists and pluralists (Empedocles, Anaxagoras), explicitly react to Parmenides’ monist challenge, devising ways to reconcile plurality and change with some of his constraints.
9. Epistemology: Truth, Thought, and Non‑Being
9.1 Thought–Being Correlation
Parmenides’ epistemology is crystallized in the formula:
“For the same thing is for thinking and for being.”
— Parmenides, On Nature (DK 28 B3)
This has been read in multiple ways:
| Interpretation | Emphasis |
|---|---|
| Ontological | Thought and being are coextensive; thinking succeeds only when it latches onto what truly is. |
| Semantic | Meaningful discourse requires a referent; speaking and thinking empty names is impossible. |
| Epistemic | Genuine knowledge is restricted to necessary truths about what cannot be otherwise. |
Most accounts converge on the view that Parmenides tightly connects cognition, language, and reality, excluding the possibility of genuinely thinking or speaking about what is not.
9.2 The Status of Non‑Being
The axiom “nothing is not” underwrites Parmenides’ rejection of non‑being as a legitimate object of thought or speech. This raises interpretive questions:
- Does he deny the concept of negation altogether?
- Or does he reject only the attempt to treat absolute non‑being as a subject of predication?
Some scholars argue that Parmenides is primarily concerned with existential negation (there is nothing that is not), not with all forms of logical negation. Others suggest that his view foreshadows later puzzles about negative existentials and empty reference.
9.3 Doxa vs. Alētheia
The poem distinguishes alētheia (truth) from doxa (opinion). Mortals, guided by the senses, produce accounts that mix being and non‑being, leading to contradictions. The goddess therefore cautions the listener to follow the path where “it is” and avoid deceptive mixtures.
| Aspect | Truth (Alētheia) | Opinion (Doxa) |
|---|---|---|
| Basis | Rational necessity | Sensory appearances |
| Object | What is one, unchanging | Changing world of opposites |
| Cognitive status | Knowledge | Belief, plausible but false in strict sense |
Debate persists over whether Parmenides allows gradations of cognitive value within opinion—for instance, whether some cosmological accounts are “less false” because more systematically ordered.
9.4 Sense Perception and Illusion
While Parmenides does not extensively theorize sense perception, his contrast between truth and opinion implies skepticism about the epistemic reliability of the senses. Later interpreters disagree about the extremity of this stance:
- Some read him as an early proponent of rationalism, sharply limiting the role of perception in acquiring knowledge.
- Others hold that he targets only uncritical reliance on sense data, not perception as such, and that the Way of Opinion provides a rationally structured account of appearances rather than rejecting them outright.
10. Logic, Argumentation, and the Two Ways
10.1 The Two Ways as a Logical Framework
The goddess’ initial division of inquiry into two ways functions as a primitive logical partition of possible theses:
- Way of “is”: Affirmation of being; internally coherent.
- Way of “is not”: Assertion of non‑being; rejected as unsayable.
This binary framework anticipates later logical distinctions between contradictory and contrary propositions and between necessary and impossible states of affairs.
10.2 Use of Reductio and Excluded Middle
Parmenides frequently uses arguments that resemble reductio ad absurdum, showing that alternative positions entail impossibilities. His reasoning presupposes a form of the law of non‑contradiction (it is not the case that something both is and is not) and something akin to the law of excluded middle (between being and non‑being there is no third option).
Scholars disagree on whether Parmenides consciously formulates such logical laws or whether they are retrospectively attributed on the basis of his argumentative practice.
10.3 The Copula and Existential “Is”
A major topic in modern scholarship concerns the different senses of “is” (ἐστι):
| Use of “is” | Example reconstruction | Debated status |
|---|---|---|
| Existential | “X is (exists)” | Central to the denial that “what is not” can be. |
| Predicative | “X is F” | Raises questions about how predication is possible if Being is undifferentiated. |
| Veridical | “It is so that p” | Connects to the notion of truth as what “is the case.” |
Some interpreters argue that Parmenides exploits all three uses without distinction, while others contend that careful attention to these senses is crucial for understanding his arguments and avoiding attributing to him unnecessary paradoxes.
10.4 Order and Method in the Poem
The structured progression—from eliminating the Way of “is not,” through deriving properties of Being, to presenting a subordinate cosmology—has been read as an early example of a systematic method in philosophy. Commentators differ on how programmatic this method is:
- One line of interpretation presents Parmenides as a proto‑logician, whose main contribution is clarifying the conceptual space of coherent discourse.
- Another emphasizes the role of revelation and authority, viewing the logic as embedded in a broader mythic and religious narrative rather than as a stand‑alone formal enterprise.
Despite disagreements, there is wide agreement that Parmenides’ argumentative rigor influenced later developments in Greek logic, especially as reported by Plato, Aristotle, and later dialecticians.
11. Physics and Cosmology in the Doxastic Section
11.1 Dual‑Element Theory
In the Way of Opinion, Parmenides develops a dual‑element or dual‑principle physics. The basic constituents are typically identified (from the fragments) as:
“on the one hand, the aetherial fire of flame,
gentle, very light, everywhere the same as itself;
on the other hand, night, dense in body and heavy.”— Parmenides, On Nature (paraphrasing DK 28 B8.56–59, B9)
From these two, the cosmological system is constructed by varying mixtures and proportions.
11.2 Structure of the Cosmos
Although the text is incomplete, testimonies and fragments suggest:
| Feature | Description in reconstructions |
|---|---|
| Spherical cosmos | The world is often taken to be arranged concentrically, with rings or zones of light and dark. |
| Central fire or earth | Some sources place a fiery or luminous element at the center; others stress a central earth encircled by rings. |
| Heavenly bodies | The sun, moon, fixed stars, and possibly the Milky Way are generated from condensations and rarefactions of the two basic elements. |
Interpretations diverge on details, partly because later doxographers might conflate Parmenides’ views with those of other early cosmologists.
11.3 Meteorology and Biological Accounts
Fragments and testimonies also attribute to Parmenides explanations of:
- Winds and weather, arising from movements and interactions of warm and cold exhalations.
- Human and animal generation, linked to mixtures of warm (light) and cold (dark) components in reproductive seed.
- The sex of offspring, possibly determined by the dominance of one principle over the other at conception.
These topics place Parmenides within the wider pre‑Socratic interest in natural explanation, even as he conceptually distances such accounts from ultimate truth.
11.4 Scientific Status and Coherence
Scholarly assessments of the doxastic physics vary:
| Assessment | Main claim |
|---|---|
| Highly systematic | Sees Parmenides as constructing a sophisticated two‑element theory comparable to later pluralist systems. |
| Deliberately flawed | Argues that the cosmology embodies contradictions (e.g., mixing being and non‑being) to show the ultimate inadequacy of all such accounts. |
| Best available science under constraints | Proposes that Parmenides offers a serious, rationalized cosmology operating under the constraints set by his ontological arguments, though granted only doxastic status. |
Whatever its precise status, the cosmological section influenced later natural philosophers who either adopted or modified its dualistic framework.
12. Religion, Myth, and the Goddess Narrative
12.1 The Proem as Initiatory Myth
The poem opens with a mythic journey: a youth is carried in a chariot, guided by maidens, through the gates of Night and Day to a goddess who takes his right hand in welcome. Many interpreters see in this an initiatory or mystery‑cult motif, where the protagonist is led from the realm of mortals to a higher revelation.
The goddess is unnamed; candidates proposed include Dike (Justice), Aletheia (Truth), Moira (Fate), or an amalgam of these. The ambiguity has allowed for multiple readings of her role.
12.2 Religious vs. Rational Dimensions
The blend of religious imagery and rigorous argument has generated contrasting interpretations:
| View | Characterization |
|---|---|
| Rationalizing myth | The religious framework is largely a literary device; the core is a rational metaphysics that supersedes traditional myth. |
| Philosophical revelation | The goddess represents a divine source of truth, suggesting that ultimate metaphysical insight is a kind of inspired revelation. |
| Continuity with didactic poetry | Parmenides continues the tradition of Hesiod and Xenophanes, where gods convey cosmological and theological knowledge in poetic form. |
No consensus exists on whether Parmenides meant to demythologize religious discourse or to elevate his philosophy by casting it as sacred teaching.
12.3 Gates, Night and Day, and Symbolism
The imagery of the gates of Night and Day has been interpreted symbolically:
- As marking the passage from ignorance to knowledge.
- As representing the boundary between appearance and reality.
- As echoing cosmological or underworld motifs in epic and Orphic traditions.
Some scholars detect Pythagorean or Orphic resonances, such as the idea of a soul’s journey or ascent; others caution against over‑systematizing the symbolism beyond what the text warrants.
12.4 The Goddess in the Doxastic Section
The same goddess who reveals the Way of Truth also articulates the Way of Opinion, explicitly labeling it deceptive. This dual role has prompted divergent interpretations:
- One view holds that the goddess, though divine, can present merely human beliefs for pedagogical reasons.
- Another suggests that the lower cosmological account is still in some sense sanctioned by the divine, though its content falls short of ultimate truth.
The coexistence of religious authority and fallible cosmology exemplifies the complex relationship between mythic revelation and philosophical reasoning in Parmenides’ work.
13. Parmenides and the Eleatic School
13.1 Defining the Eleatic Tradition
Ancient authors speak of an Eleatic school centered in Elea. Its principal figures are:
| Philosopher | Place | Connection to Parmenides |
|---|---|---|
| Parmenides | Elea | Foundational figure articulating monism and the denial of change. |
| Zeno of Elea | Elea | Described as Parmenides’ disciple or associate; famous for paradoxes defending Eleatic doctrine. |
| Melissus of Samos | Samos | Extends Eleatic arguments; often classified as Eleatic despite geographic distance. |
The extent to which these thinkers formed a self‑conscious “school” is debated; the label may partly reflect later systematization.
13.2 Zeno’s Paradoxes as Defense
Plato reports Zeno as composing arguments to defend Parmenides’ views by showing that assuming plurality leads to contradictions. Zeno’s paradoxes of motion, plurality, and space are widely interpreted as elaborations of Eleatic themes:
- If reality were many, it would be both finite and infinite, large and small, etc.
- If motion existed, it would involve traversing infinitely many points, which seems impossible.
Some scholars see Zeno as radicalizing Parmenides’ logic; others treat his arguments as clarifying the implications of Parmenides’ monism for everyday assumptions.
13.3 Melissus’ Systematization
Melissus applies Eleatic reasoning in a more overtly argumentative prose style, affirming that what is is:
- Unlimited in extent,
- Eternal,
- Unchangeable,
- One.
He departs from Parmenides at points—for example, stressing infinite rather than finite (spherical) extension. Interpretations vary on whether Melissus faithfully transmits Parmenidean doctrine or significantly reinterprets it.
13.4 Broader Eleatic Influence
Beyond these core figures, Eleatic ideas influenced:
- Sophists and Megarian logicians, who adopt strict criteria for meaningful statements.
- Later Stoics and Neoplatonists, who engage with Eleatic notions of unity and being.
Modern scholars dispute whether the Eleatic “school” had a unified doctrine or whether Parmenides’ legacy consisted primarily in setting a problematic—how to reconcile logic, being, and appearance—that subsequent thinkers addressed in diverse ways.
14. Engagement with Plato and Aristotle
14.1 Plato’s Dialogue Parmenides
Plato’s dialogue Parmenides portrays an elderly Parmenides examining the young Socrates’ theory of Forms. The dialogue includes:
| Part | Relevance to Parmenides |
|---|---|
| Critique of Forms | Uses Eleatic‑style objections (e.g., the “Third Man” regress) to probe the metaphysics of separate Forms. |
| Hypotheses about the One and Many | Explores consequences of affirming or denying that the One is, echoing Parmenidean concerns about being and multiplicity. |
Scholars debate the extent to which Plato faithfully represents historical Parmenides or rather appropriates Eleatic themes for his own dialectical purposes. Many treat the dialogue as evidence of Parmenides’ prestige and as a key source for the logical reception of his ideas.
14.2 Other Platonic Dialogues
Elsewhere Plato engages with Parmenidean themes:
- In the Sophist, the Eleatic Stranger wrestles with being and non‑being, seeking a way to speak of “what is not” without falling into Parmenidean contradictions.
- In the Theaetetus and Cratylus, Parmenides is juxtaposed with Heraclitus as representing the poles of stability and flux.
Interpretations differ on whether Plato ultimately overcomes, accommodates, or reinterprets Parmenides’ strictures on non‑being and change.
14.3 Aristotle’s Critique and Adaptation
Aristotle repeatedly discusses Parmenides in the Physics, Metaphysics, and On Generation and Corruption. He credits Parmenides with recognizing the importance of the principle of non‑contradiction and with framing the question of being, but criticizes him for:
- Treating being as a single genus or category.
- Failing to distinguish between substance, quality, and other categories.
- Denying change and plurality, which Aristotle regards as evident.
Aristotle offers alternative solutions, such as the doctrine of potentiality and actuality, that aim to explain change without invoking absolute non‑being, thereby responding to the Eleatic challenge.
14.4 Later Ancient Reception
Later Platonists and commentators, including Simplicius and Proclus, read Parmenides through the lens of Platonic metaphysics:
- Neoplatonists often treat Parmenides as anticipating the Platonic One or Intellect, integrating him into hierarchical ontologies.
- Commentators preserve extensive quotations of the poem while interpreting it within their own systems.
These engagements highlight the flexibility of Parmenides’ text, which could be taken as endorsing a strict monism, a metaphysics of intelligible being, or a logic of predication, depending on the interpreter’s framework.
15. Modern Interpretations and Scholarly Debates
15.1 Metaphysical vs. Logical Readings
Contemporary scholarship divides, broadly, between:
| Approach | Core emphasis |
|---|---|
| Metaphysical reading | Parmenides is primarily a theorist of reality, asserting that there exists exactly one unchanging entity and denying the real existence of the changing world. |
| Logical/semantic reading | His main concern is the logic of “is” and the impossibility of meaningful reference to non‑being, rather than a literal denial of plurality and change. |
Many recent commentators adopt intermediate positions, acknowledging both metaphysical and logical dimensions.
15.2 The Status of the Doxastic Cosmology
Another major debate focuses on how seriously to take the Way of Opinion:
- Dismissive interpretations regard it as a concession to traditional cosmology, deliberately undermined to highlight the superiority of the Way of Truth.
- Rehabilitative readings see it as an earnest attempt at a rationalized science of appearances, compatible with, though strictly subordinate to, the ontology of Being.
- Two‑world interpretations propose a layered ontology, where the cosmological world has a lesser degree or different kind of being.
Evidence for each view is drawn from the tone of the goddess’ warnings, the internal coherence of the cosmology, and comparative studies of pre‑Socratic physics.
15.3 Unity and Chronology of the Poem
Scholars also dispute:
- Whether the poem was composed as a single unified work or reflects stages in Parmenides’ own development.
- The order and completeness of the preserved fragments, especially in the cosmological section.
- The extent of editorial influence from ancient transmitters like Simplicius.
New papyrological discoveries have not significantly altered the text, so these debates largely hinge on close philological and philosophical analysis.
15.4 Parmenides in Contemporary Philosophy
In modern analytic and continental thought, Parmenides has been read in diverse ways:
- As a precursor to formal logic and to debates about reference, negative existentials, and the ontology of abstract objects.
- As an early exponent of ontological monism, inspiring contemporary discussions of priority monism and the metaphysics of the whole.
- As an exemplar of continental concerns with being and nothingness, influencing interpretations of Heidegger and others.
Despite divergent methodologies, modern interpreters generally agree that Parmenides sets a fundamental agenda: how to articulate a coherent relation between what is, what can be thought, and what appears.
16. Legacy and Historical Significance
16.1 Impact on Ancient Philosophy
Parmenides’ insistence that thought and being are coextensive and that non‑being is inexpressible exerted a lasting influence on Greek philosophy:
| Area | Influence |
|---|---|
| Metaphysics | Framed debates about unity vs. plurality, change vs. permanence, and the nature of substance. |
| Logic | Anticipated concerns with consistency, excluded middle, and the meaning of “is,” shaping later dialectical practices. |
| Epistemology | Helped crystallize the distinction between knowledge (alētheia) and opinion (doxa). |
Plato, Aristotle, the atomists, and the pluralists all position themselves in relation to the Eleatic challenge.
16.2 Influence Beyond Antiquity
In late antiquity and the Middle Ages, Parmenides was often read through Neoplatonic lenses, contributing to concepts of an immutable, perfect One or First Principle. Renaissance and early modern scholars, reviving Greek texts, incorporated him into narratives of the history of metaphysics, though often in highly schematic form.
16.3 Modern Philosophical Reception
From the 19th century onward, Parmenides has been a focal point for:
- Histories of philosophy, which frequently portray him as the founder of ontology.
- Heideggerian readings, which see in him an originary experience of Being later obscured by metaphysics.
- Analytic metaphysics, where his arguments are revisited in discussions of existence, identity over time, and modal necessity.
These receptions differ sharply, yet all treat Parmenides as a crucial reference point for fundamental questions about what it is to be.
16.4 Continuing Relevance
Parmenides’ legacy lies less in a set of doctrines universally accepted and more in a set of constraints and puzzles:
- How can we explain change without appealing to nothing?
- What is the relation between language and reality?
- Can there be meaningful talk of non‑existent objects or states?
By pressing such questions with unprecedented rigor, Parmenides helped inaugurate the tradition of systematic metaphysical and logical reflection that continues to shape philosophical inquiry.
Study Guide
intermediateThe entry assumes some familiarity with basic philosophical vocabulary and early Greek thought. Parmenides’ arguments about being and non‑being are conceptually demanding and use technical distinctions (e.g., truth vs. opinion, logical vs. metaphysical claims). However, the article explains historical context and major debates clearly enough for motivated learners beyond the absolute beginner level.
- Basic outline of ancient Greek history and geography (Archaic and Classical periods, Greek colonies such as Magna Graecia) — Parmenides lived in Elea in southern Italy and is situated between early Ionian natural philosophers and classical Athenian thinkers; knowing the basic historical and geographic setting helps you place him in context.
- Familiarity with pre-Socratic philosophy in general terms — Understanding that many early Greek thinkers were searching for the ‘principles of nature’ and offering cosmologies makes Parmenides’ shift to being and non‑being, and his critique of earlier cosmologies, much clearer.
- Introductory logic: contradiction, validity, and basic use of the verb ‘to be’ — Parmenides’ arguments turn on avoiding contradiction and on what can or cannot be said to ‘be’; a minimal sense of logical consistency and of existential vs. predicative ‘is’ will make his reasoning more intelligible.
- Pre-Socratic Philosophy — Gives a survey of early Greek thinkers and their main concerns, allowing you to see how Parmenides both inherits and radically transforms the pre-Socratic project.
- Xenophanes of Colophon — Clarifies the theological and poetic background (critique of anthropomorphic gods, idea of a single greatest god) that likely influenced Parmenides’ thinking about divine truth and unity.
- Heraclitus of Ephesus — Helps you appreciate Parmenides as a foil to philosophies of flux and becoming, and to understand later contrasts between ‘Eleatics’ and ‘Heracliteans’ in Plato and Aristotle.
- 1
Get oriented with Parmenides’ life, setting, and why he matters.
Resource: Sections 1–2: Introduction; Life and Historical Context
⏱ 25–35 minutes
- 2
Understand the poem’s structure and how we know its contents.
Resource: Sections 3–5: Sources and Textual Transmission; Intellectual Development and Influences; The Poem "On Nature": Form and Structure
⏱ 35–45 minutes
- 3
Study the core doctrine of Being and the distinction between truth and opinion.
Resource: Sections 6–7 and 9–10: The Way of Truth; The Way of Opinion; Epistemology; Logic, Argumentation, and the Two Ways
⏱ 60–80 minutes
- 4
Explore how Parmenides’ strict ontology relates to cosmology, myth, and the Eleatic school.
Resource: Sections 8, 11–13: Metaphysics and Monism; Physics and Cosmology in the Doxastic Section; Religion, Myth, and the Goddess Narrative; Parmenides and the Eleatic School
⏱ 60–75 minutes
- 5
See how later philosophers interpret and respond to Parmenides.
Resource: Sections 14–16: Engagement with Plato and Aristotle; Modern Interpretations and Scholarly Debates; Legacy and Historical Significance
⏱ 50–70 minutes
- 6
Consolidate your understanding by reviewing key terms and revisiting crucial fragments.
Resource: Glossary terms in the study guide (e.g., Being, Non‑being, Way of Truth, Way of Opinion, Doxa, Monism, Alētheia), plus the essential quotes listed in the main entry.
⏱ 30–45 minutes
Eleatic school
A cluster of pre-Socratic thinkers centered on Parmenides (including Zeno and Melissus) who argue that reality is one, unchanging, and indivisible, and who use rigorous argument to attack theories of plurality and change.
Why essential: Seeing Parmenides as part of an Eleatic tradition clarifies how his ideas were developed and defended by Zeno’s paradoxes and Melissus’ prose arguments, and how later philosophers understood ‘Eleatic’ positions.
Being (τὸ ἐόν, to eon)
For Parmenides, what truly and necessarily is: ungenerated, imperishable, whole, one, continuous, and unchanging; the only proper object of thought and speech.
Why essential: The entire Way of Truth is an investigation into the necessary features of Being; without grasping this notion, Parmenides’ monism and denial of becoming cannot be understood.
Non‑being (μὴ ἐόν, mē eon)
The supposed opposite of Being, which Parmenides argues is unthinkable and unsayable—“nothing is not”—so that appeals to coming‑to‑be from or passing‑away into nothing are incoherent.
Why essential: His rejection of non‑being underlies his denial of generation, destruction, and many forms of change, and forces later philosophers to find new ways of talking about absence, negation, and the void.
Way of Truth (ὁδὸς ἀληθείας, hodos alētheias)
The rational path of inquiry in the poem that follows the thesis ‘it is and it is not possible for it not to be,’ deriving the strict properties of Being and excluding contradiction.
Why essential: This section contains Parmenides’ core ontological arguments and his correlation of thinking, speaking, and Being; it defines what counts as genuine knowledge as opposed to mere opinion.
Way of Opinion (ὁδὸς δόξης, hodos doxēs)
The second path the goddess describes, presenting a dualistic cosmology based on Light and Night that systematizes appearances but is explicitly labeled deceptive and merely doxastic.
Why essential: Understanding this section is crucial for seeing how Parmenides re-situates cosmology as subordinate to ontology and for grasping later debates over whether he allows any legitimacy to empirical science.
Doxa (δόξα)
Opinion or belief founded on sensory appearances; for Parmenides, the shifting and often contradictory outlook of ‘mortals’ who mix Being and non‑being in their accounts.
Why essential: The sharp contrast between doxa and alētheia structures his epistemology and influences later distinctions between knowledge and belief in Plato and Aristotle.
Monism (Parmenidean monism)
The doctrine that reality in the strict sense is a single, unified Being without true plurality, internal differentiation, or change.
Why essential: Whether Parmenides is read as an existential, predicational, or priority monist shapes how we interpret his denial of change and multiplicity and how later pluralists and atomists respond to him.
Logical necessity and the two ways
The idea that only what avoids contradiction and non‑being is thinkable and sayable, embodied in the goddess’ division between the admissible way (‘it is’) and the inadmissible way (‘it is not’).
Why essential: This provides the logical backbone of Parmenides’ method, influencing the development of reductio arguments, the principle of non‑contradiction, and later Greek logic.
Parmenides simply denies that change and plurality exist in any sense at all, so he cannot possibly acknowledge the everyday world.
He denies that change and plurality belong to what is truly and necessarily Being, but he also provides an elaborate cosmology in the Way of Opinion that accounts for appearances at a lower epistemic and possibly ontological level.
Source of confusion: The stark rhetoric of the Way of Truth and later portrayals of Parmenides as an extreme monist can obscure the structured attention he gives to the world of experience in the doxastic section.
Because Parmenides speaks in poetic and religious language, his philosophy is primarily mystical or irrational.
Although he uses a mythic, goddess-revelation framework and epic verse, the content of the Way of Truth is highly rational and argumentative, relying on logical constraints rather than on religious authority alone.
Source of confusion: The presence of chariots, goddesses, and symbolic imagery in the Proem can lead readers to overlook the careful deductive structure embedded in the poem.
Parmenides’ arguments only concern abstract logic and language, not reality; he is just analyzing the word ‘is.’
While he does attend closely to the uses of ‘is’ and the impossibility of speaking of what is not, he uses these logical and semantic points to draw substantive conclusions about what reality must be like.
Source of confusion: Modern interest in logic and semantics can lead to over-reading Parmenides as a purely linguistic theorist and underplaying his own metaphysical aims.
The Way of Opinion is obviously incoherent, so Parmenides must be mocking cosmology rather than attempting a serious account.
The surviving fragments suggest a carefully structured dual-element physics; many scholars now think Parmenides offers the best systematic account of appearances available under Eleatic constraints, even while denying it ultimate truth.
Source of confusion: The goddess’ warning that the cosmology is ‘deceptive’ can be misread as implying sloppiness or satire, rather than as signaling a lower epistemic status.
There was a tightly unified ‘Eleatic school’ with a single, fixed doctrine directly handed down from Parmenides to Zeno and Melissus.
Although later authors group these thinkers as Eleatic, their doctrines differ in important ways (e.g., Melissus’ infinite Being vs. Parmenides’ sphere); ‘Eleatic school’ is partly a retrospective label.
Source of confusion: Ancient doxographies tend to organize philosophers into neat schools, and modern textbooks sometimes repeat this classification without emphasizing internal diversity.
How does Parmenides’ distinction between the Way of Truth and the Way of Opinion reshape the earlier pre-Socratic project of explaining nature?
Hints: Compare the roles cosmology plays for Milesians and Heraclitus with Parmenides’ three-part poem; focus on how he treats cosmology as doxastic rather than as ultimate truth.
What are the main steps in Parmenides’ argument that Being is ungenerated and imperishable, and how do they rely on the rejection of non‑being?
Hints: Look closely at the reasoning in the Way of Truth (especially B2, B6, B8): what happens if we say Being came to be or will perish? Where would it come from or go to, and why is that problematic?
In what sense does Parmenides link thinking and being in the claim that ‘the same thing is for thinking and for being’? Is this best read as an ontological, semantic, or epistemic thesis?
Hints: Identify how the article outlines multiple interpretations (Section 9.1). Ask yourself: Does Parmenides say that all thinking is automatically true, or that only what is can be truly thought? How does this constrain possible objects of thought?
Can Parmenides consistently maintain both a strict monism in the Way of Truth and a dualistic cosmology in the Way of Opinion, or is there a tension in his system?
Hints: Consider the different scholarly views on the status of the doxastic section (Section 7.4 and 15.2): Is the cosmology merely a concession, a pedagogical step, or part of a two-level ontology? How might each view handle possible contradictions?
How do Zeno’s paradoxes, as later reported, function as a defense of Parmenides’ claims about Being and plurality?
Hints: Relate Zeno’s arguments about motion and plurality (Section 13.2) to Parmenides’ denial of multiplicity and change. Ask what assumptions about space, time, or divisibility Zeno targets and how this supports Eleatic conclusions.
In what ways do Plato and Aristotle each accept, transform, or reject Parmenides’ restrictions on talking about non‑being?
Hints: Compare Plato’s Sophist (the problem of ‘what is not’) and Aristotle’s use of potentiality/actuality and the principle of non‑contradiction (Section 14). How do they try to allow meaningful negation and change without reintroducing absolute non‑being?
What role does the goddess-revelation framework play in interpreting the authority and character of Parmenides’ arguments?
Hints: Use Section 12: Does the mythic Proem undermine or enhance the rational force of the arguments? Consider views that see it as a literary device vs. a genuine religious framing of philosophical truth.
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@online{philopedia_parmenides_of_elea,
title = {Parmenides of Elea},
author = {Philopedia},
year = {2025},
url = {https://philopedia.com/philosophers/parmenides-of-elea/},
urldate = {December 11, 2025}
}Note: This entry was last updated on 2025-12-08. For the most current version, always check the online entry.