Clear and simple notes on Parmenides’ philosophy. These cover his three axioms, the seven key conclusions on being, his views on time and change, and his lasting influence on Democritus, Plato, Aristotle, and Zeno. Helpful revision guide for students learning about being, reality, and rationalist philosophy.
Table of Contents
Parmenides and His Philosophy
- Parmenides was from Elea, a city on the western coast of Italy.
- He was born around 515 BC and died around 450 BC (approximate dates).
- He was the founder of the Eleatic school of philosophy.
- Some sources suggest Parmenides knew Pythagorean ideas. His link with Heraclitus is debated. He opposed Heraclitus on change.
- His philosophy was completely opposite to Heraclitus.
- Plato’s dialogue Parmenides tells a story of him meeting young Socrates. This is literary, not confirmed history.
- Parmenides used logic in a very rigorous and powerful way, more than earlier philosophers.
- People did not accept his conclusions, but they were impressed by his logical reasoning style.
- His logical method influenced later philosophy and gave it a new direction.
- He expressed his philosophy in the form of a poem.
- In the poem, he says that his knowledge came from a goddess, meaning it was divine knowledge.
- The poem has two parts: the way of truth (what reality actually is) and the way of opinion (what ordinary people think reality is).
- He clearly distinguished between truth and opinion.
Summary:
Parmenides, founder of the Eleatic school, lived in Elea around 515–450 BC. He opposed Heraclitus, used rigorous logic, and deeply influenced philosophy. His poem presents divine knowledge in two parts: the way of truth (real reality) and the way of opinion (common belief).
Axiomatic Method in Greek Philosophy
- Before discussing Parmenides, it is important to understand the Axiomatic Method.
- During that time, many theories about the ultimate substance were being developed, and geometry was also progressing.
- Egyptians used geometry mainly as a practical tool to measure land after Nile floods.
- Greeks, however, were more curious about why geometry works and the reasoning behind its rules.
- At first, Greeks discovered separate proofs and theorems, but geometry was not a complete system because these theorems were unconnected.
- Later, they tried to combine all geometry theorems into a single Axiomatic System.
- An Axiomatic System is based on some first premises called axioms, which are self-evident and need no proof.
- From these axioms, all other rules of geometry can be logically proven.
- The oldest Greek book on geometry is Euclid’s Elements (around 300 BC), while in India the Shulba Sutra is much older.
- In Euclid’s Elements, fundamental axioms are given, such as:
- Two points make a straight line.
- A straight line can extend infinitely in both directions.
- With a point and radius, a circle can be drawn.
- Using these simple axioms, complex formulas of geometry can be demonstrated.
- This process of deriving complex truths from simple premises is called “demonstration.”
- The Axiomatic Method made geometry a complete system and remained unchallenged until the 19th century.
- Philosophers were deeply impressed by this reasoning method: from simple, self-evident truths, one can reach very complex conclusions.
Summary:
The Axiomatic Method began in Greek geometry, especially in Euclid’s Elements. It shows how self-evident axioms can prove complex formulas through logical reasoning. This method strongly influenced philosophers, including Parmenides, as it demonstrated how truth can be built step by step from simple premises.
Parmenides’ Three Axioms
- Greek geometry’s Axiomatic Method influenced many philosophers, including Parmenides.
- He also used this method to develop his philosophy, starting with three simple axioms.
- Unlike geometry, where results matched perception, Parmenides’ conclusions were the opposite of normal human experience.
- The main philosophical problem since Thales was change — how the one turns into many.
- Parmenides tried to solve the problem of change using the axiomatic method.
- His first axiom: the fundamental principle is one (monism).
- His second axiom: “what is, is.” This means being exists; existence is existence. It is a tautology (A is A).
- Here “is” means “to exist.” For Greeks, “being is being” was undeniable.
- His third axiom: “what is not, is not.” Non-existence cannot exist; nothingness is impossible.
- In short: whatever exists, exists; whatever does not exist, does not exist.
- These three axioms are self-evident and do not need proof.
- On the basis of these axioms, Parmenides developed seven conclusions about reality.
Summary:
Parmenides applied the axiomatic method to philosophy by proposing three self-evident axioms: reality is one, what exists exists, and non-existence does not exist. Using these, he aimed to solve the problem of change and later derived seven logical conclusions about reality.
Thought and Existence
- Parmenides’ first conclusion: whatever we think or speak about exists.
- We cannot think about “nothing,” because non-existence does not exist (based on the third axiom).
- Thinking always has an object; every thought is about something that exists.
- Example: imagining a metro on the moon still involves real things (moon and metro).
- Example: unicorns are combinations of real parts (horse, horn, wings, flying). The parts exist, even if the whole does not.
- A thought must have form; there is no thought without an object.
- What cannot be thought also cannot exist. For example, a “round square” cannot be imagined or exist because it is logically impossible.
- This links reason and reality: the rational is real, and the real is rational.
- Paradoxical or contradictory ideas (like a married bachelor, cold fire, or the Buddhist koan) show things that cannot exist because they cannot be rationally thought.
- The problem remains: composite thoughts (like unicorns) combine existing parts but do not exist as a whole. Parmenides left this unresolved, and it was addressed much later by Bertrand Russell’s theory of definite descriptions.
Summary:
Parmenides argued that we cannot think about “nothing,” since non-being does not exist. Every thought has an object, so whatever we think exists in some way. Impossible and irrational things (like a round square) cannot be thought and therefore cannot exist. This was Parmenides’ first conclusion, though it raised later problems about imaginary objects like unicorns.
Being is Uncreated
- Parmenides’ second conclusion: being is uncreated (what is, is uncreated).
- To prove this, he assumes the opposite: being is created.
- If being is created, it must come either from nothing or from something.
- Option 1: Being from nothing is impossible, because “nothing” does not exist (third axiom).
- Option 2: Being from something else is also impossible, because reality is one (monism, first axiom). There is no “something else” apart from being.
- Therefore, being cannot be created from nothing or from something.
- Conclusion: being always existed; it is uncreated.
- Second argument: If being were created at a particular time (T1), why only at T1 and not at T2 or T3?
- If nothing existed before being, then there was no reason for it to appear at one moment and not another.
- Thus, the idea of creation at a specific time is meaningless.
- Modern parallel: the Big Bang is often seen as the beginning of the universe, but questions about “before the Big Bang” are problematic because time itself began with the Big Bang.
Summary:
Parmenides reasoned that being cannot come from nothing or from something else. Therefore, it must always have existed. His second conclusion is that being is uncreated and eternal, with no beginning in time.
Hidden Principles in Parmenides’ Argument
- Parmenides proved that being is uncreated, but his reasoning also involved three hidden principles.
- Principle of Causality: every effect must have a cause. Parmenides assumed that if being were created, it must come from either something or nothing.
- Principle of Sufficient Reason: everything must have a reason why it is the way it is and not otherwise. Parmenides asked why being, if created, came into existence at time T1 and not at T2 or T3.
- These two principles sound similar but differ:
- Causality deals with the relation between two events (cause and effect).
- Sufficient reason deals with why one event happens in a specific way rather than another.
- Reductio ad Absurdum: a method of proof by assuming the opposite claim and showing it leads to absurdity.
- Parmenides used this when he assumed “being is created,” then showed it was impossible, leaving “being is uncreated” as the valid conclusion.
- Later philosophers developed and used these principles in detail.
Summary:
While proving that being is uncreated, Parmenides relied on three hidden principles: causality, sufficient reason, and reductio ad absurdum. These became important tools for later philosophers in both philosophy and science.
Being is Indestructible
- Parmenides’ third conclusion: being is indestructible (imperishable).
- Destruction means complete disappearance or turning into nothing.
- According to the third axiom, “what is not, is not.” Nothing does not exist.
- Therefore, being cannot change into non-being, since non-being is impossible.
- Conclusion: being can never be destroyed.
Summary:
Parmenides argued that destruction means turning into nothing, but nothing does not exist. Hence, being cannot be destroyed and is imperishable.
Being is Unchangeable
- Parmenides’ fourth conclusion: being is unchangeable (changeless).
- If being changes, it must change either into being or into non-being.
- Change into non-being is impossible, because non-being does not exist.
- Change into being is also meaningless, since being already exists.
- Therefore, being cannot undergo change and is changeless.
Summary:
Parmenides reasoned that being cannot change into non-being or even into itself. Thus, being is completely unchangeable and remains the same.
Being is Eternal
- Parmenides’ fifth conclusion: being is eternal.
- Eternal means always existing — without beginning and without end.
- Being is uncreated, so it has always existed.
- Being is indestructible, so it can never cease to exist.
- Therefore, being exists forever, past and future.
Summary:
Parmenides concluded that because being is uncreated and indestructible, it must be eternal. It has no beginning and no end, existing always.
Being is Indivisible
- Parmenides’ sixth conclusion: being is indivisible.
- Being has no holes, gaps, or empty spaces within it.
- Division can only happen by something else — either being or non-being.
- Dividing being with being is meaningless; it remains the same (like water cannot divide water).
- Dividing being with non-being is impossible, because non-being does not exist.
- Therefore, being cannot be divided and is indivisible.
Summary:
Parmenides argued that being cannot be divided either by itself or by non-being. Hence, it is whole and indivisible, without any gaps or emptiness.
Being is Motionless
- Parmenides’ seventh conclusion: being is motionless.
- Motion means moving from one place to another.
- Movement requires empty space for something to move into.
- Empty space means “nothing,” but nothing does not exist (third axiom).
- Therefore, being cannot move and must be motionless.
Summary:
Parmenides concluded that motion is impossible because it requires empty space, and empty space (nothing) does not exist. Thus, being is motionless.
Time is Unreal
- Parmenides argued that time is unreal; it is only an illusion.
- Present is seen as a point between past and future.
- Past does not exist anymore, and future has not yet come.
- According to the third axiom (“what is not, is not”), past and future do not exist.
- Therefore, only the present exists, and reality is “all at once” — everything is now.
- Later, Augustine used a similar argument in discussing God’s existence.
- Parmenides based all his reasoning on three axioms:
- Being is one (monism).
- What is, is.
- What is not, is not.
- From these, he derived several conclusions:
- Whatever we think exists.
- Being is uncreated.
- Being is indestructible.
- Being is unchangeable.
- Being is eternal.
- Being is indivisible.
- Being is motionless.
- Time is unreal (past and future do not exist).
Summary:
Parmenides concluded that only the present exists and time itself is unreal. Based on his three axioms, he developed a full system where being is one, uncreated, indestructible, changeless, eternal, indivisible, motionless, and beyond time.
Parmenides: Material or Idea?
- Some scholars argue that Parmenides’ “being” is not material but an idea.
- Materialism: reality is physical matter.
- Idealism: reality is created by thoughts or consciousness.
- Parmenides denied change and motion, which makes his claims hard to accept through sense experience.
- He sharply separated sense (illusion) from reason (truth).
- Unlike Thales or Heraclitus, where sense and reason are closer, in Parmenides the gap is extreme, making belief difficult.
- This led some scholars to think his reality is only an idea.
- But Parmenides actually spoke of material reality (monistic materialism).
- Denying change and motion does not mean reality becomes an idea.
- Earlier philosophers also said reason, not senses, reveals reality.
- Parmenides clearly described reality as finite and spherical in shape.
- For Greeks, infinite (boundless) was problematic; finite was seen as definable and meaningful.
- His reality is finite in space but eternal in time.
- Thus, Parmenides followed the tradition of earlier philosophers, speaking of a material, finite, and spherical reality.
Please Note: Ancient reports show Parmenides’ being as a finite, spherical plenum. Some scholars call this material. Others read it as abstract. The debate is open.
Summary:
Though some interpret Parmenides’ being as an idea, he actually described it as material reality. He called it one, finite in space, eternal in time, and spherical in shape, continuing the tradition of materialist philosophy.
Parmenides vs. Melissus on Reality
- Parmenides had two important students: Zeno and Melissus.
- Parmenides’ fragments describe reality as finite and ‘well-rounded.’
- Melissus argued reality is infinite. This explains why books mention both.
- His reasoning: if reality is finite, it must have a boundary.
- Beyond that boundary, either being or non-being must exist.
- Non-being cannot exist (third axiom), so only being can exist beyond the boundary.
- Therefore, Melissus concluded that reality is infinite, without limits.
- This created two different views:
- Parmenides → reality is finite and spherical.
- Melissus → reality is infinite and boundless.
- That is why books may mention both views, leading to confusion.
Summary:
Parmenides described reality as finite and spherical, but his student Melissus argued it must be infinite, since non-being cannot exist beyond any boundary. This difference explains why some sources present reality as finite and others as infinite.
Comparison: Thales, Heraclitus, and Parmenides
- Thales:
- Believed in both change and permanence (being and becoming).
- Reality is a permanent fundamental substance.
- This substance is water, the essence of reality.
- Heraclitus:
- Focused on change and becoming.
- Reality is not a substance but a fundamental process.
- This process is flux, symbolized by fire.
- For him, change and tension are necessary for reality to exist.
- Parmenides:
- Reality is being, which is changeless, motionless, indestructible, and eternal.
- Becoming (change and motion) is only an illusion.
- Opposites:
- Heraclitus: reality is change and flux.
- Parmenides: reality is static and unchanging.
- Similarities:
- Both said senses deceive us; true reality cannot be known through sense experience.
- True reality must be understood through reason.
- Heraclitus’ unchanging logos (cosmic principle) and Parmenides’ unchanging being show a common idea of permanence behind appearances.
- Both challenge normal experience and puzzle the reader.
Summary:
Thales, Heraclitus, and Parmenides offered different views of reality: substance (water), process (flux/fire), and static being. While Heraclitus and Parmenides seem completely opposite, both rejected sense experience and emphasized reason, each pointing to something changeless beyond appearances.
Influence and Legacy of Parmenides
- Parmenides deeply influenced later philosophers.
- Democritus: accepted Parmenides’ idea that being is indestructible, but explained change through the rearrangement of indestructible, indivisible atoms.
- Plato: tried to combine Heraclitus and Parmenides. He said objects of true knowledge must be stable and eternal like Parmenides’ being, not ever-changing like Heraclitean flux.
- Aristotle: later attempted to solve the problems raised by both.
- Parmenides is often often seen as the first rationalist philosopher.
- He insisted that knowledge must come from reasoning, not from the senses.
- His principle: follow the argument wherever it leads, even if it goes against common sense or experience.
- Socrates also echoed this idea in Plato’s dialogue Crito.
- Parmenides was often mocked, but philosophy requires philosophical rejection: one can reject a conclusion only with valid reasoning, not without argument.
- His student Zeno defended him, creating arguments that challenged trust in sense experience.
- Key philosophical themes from Parmenides’ work:
- One and Many: how unity relates to multiplicity.
- Appearance and Reality: what seems vs. what truly is.
- Sense and Reason: which can lead us to truth.
- Materialism and Idealism: is reality matter or idea?
- Being and Becoming: is reality fixed (Parmenides) or flux (Heraclitus)?
- Truth and Opinion: the difference between reasoned truth and common belief.
Summary:
Parmenides shaped philosophy by insisting on reason over senses and developing themes that influenced Democritus, Plato, Aristotle, and Zeno. His ideas sparked central debates about being and becoming, matter and idea, sense and reason — debates that gave direction to the entire history of philosophy.
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