Axiom vs. Postulate — What's the Difference?
By Tayyaba Rehman — Updated on October 16, 2023
"Axiom" is a statement accepted as true without proof; "Postulate" is an assumed truth requiring no explanation, used as a starting point in theory.
Difference Between Axiom and Postulate
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Key Differences
An "Axiom" is generally understood to be a foundational statement that is accepted as true without controversy or evidence. It's considered self-evident and doesn't require proof. Conversely, a "Postulate" is similar in that it’s a statement assumed to be true without proof, but it’s typically used as a starting point for a larger theory or system of beliefs, serving as a basis for logical reasoning.
"Axioms" are often used in mathematics and logic, where they serve as the starting points for a system of reasoning, and because they're accepted without proof, they're considered universally true within their system. "Postulates," while similar in nature, are more commonly used in the realm of geometry and are specific to the system or theory they're used in, meaning their acceptance might not be as universal as axioms.
Both "Axioms" and "Postulates" are fundamental in building theoretical frameworks, as they are statements accepted without proof. However, the term "Axiom" is often associated with a broader context and is perceived as more universal, whereas a "Postulate" is usually more context-specific, often used to build upon a particular theory.
When it comes to application, "Axioms" are considered the bedrock of logical systems, and their truth is not contingent upon evidence or external confirmation. On the other hand, "Postulates" can be seen as the building blocks within a system or a theory, providing a foundation from which complex theorems and hypotheses can be derived.
In terms of adaptability, "Axioms" are less flexible because they are viewed as universally true statements across various systems. In contrast, "Postulates" are more adaptable and can be replaced or modified based on new findings or the development of a theory, showcasing a degree of flexibility within the realm of scientific postulations.
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Comparison Chart
Basic Definition
A statement accepted as true without proof
An assumed truth used as a theory’s basis
Scope
Broader, more universal
More specific to a system or theory
Application
Foundational in logic and mathematics
Common in geometry, foundational for theories
Flexibility
Less flexible, considered universally true
More adaptable within its theory
Proof Requirement
None, it’s self-evident
None, but serves as a starting point
Compare with Definitions
Axiom
A universally accepted principle in a field of study.
In mathematics, it's an axiom that numbers don't lie.
Postulate
A statement accepted as true for the purpose of argument or investigation.
The theory's first postulate is that all objects fall at the same rate in a vacuum.
Axiom
A statement that forms the foundation of a theory or system.
Her economic theories are based on the axiom that the market is always right.
Postulate
An assumption used as a basis for mathematical reasoning.
We'll start our geometry lesson with the postulate that all right angles are equal.
Axiom
A proposition in logic or mathematics taken to be self-evident.
The axiom states that through any two points, there is exactly one straight line.
Postulate
Something taken as self-evident or assumed without proof as a basis for reasoning.
The scientist made a groundbreaking discovery using a postulate rejected by her peers.
Axiom
A self-evident truth that requires no proof.
The idea that the whole is greater than any of its parts is an ancient axiom.
Postulate
Suggest or assume the existence, fact, or truth of (something) as a basis for reasoning, discussion, or belief
She postulated that the environmentalists might have a case
His theory postulated a rotatory movement for hurricanes
Axiom
A principle widely accepted on its intrinsic merit.
The legal axiom 'innocent until proven guilty' underpins many judicial systems.
Postulate
(in ecclesiastical law) nominate or elect (someone) to an ecclesiastical office subject to the sanction of a higher authority
The chapter was then allowed to postulate the bishop of Bath
Axiom
An axiom, postulate or assumption is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Greek axíōma (ἀξίωμα) 'that which is thought worthy or fit' or 'that which commends itself as evident.'The term has subtle differences in definition when used in the context of different fields of study.
Postulate
A thing suggested or assumed as true as the basis for reasoning, discussion, or belief
Perhaps the postulate of Babylonian influence on Greek astronomy is incorrect
Axiom
A statement or proposition which is regarded as being established, accepted, or self-evidently true
The axiom that sport builds character
Postulate
To assume or assert the truth, reality, or necessity of, especially as a basis of an argument
"We can see individuals, but we can't see providence.
We have to postulate it" (Aldous Huxley).
Axiom
A self-evident or universally recognized truth; a maxim
“It is an economic axiom as old as the hills that goods and services can be paid for only with goods and services” (Albert Jay Nock).
Postulate
To propose as a hypothesis or explanation
Researchers now postulate that the disease is caused by a virus.
Axiom
An established rule, principle, or law.
Postulate
To assume as a premise or axiom; take for granted.
Axiom
A self-evident principle or one that is accepted as true without proof as the basis for argument; a postulate.
Postulate
(Archaic) To make claim for; demand.
Axiom
(philosophy) A seemingly self-evident or necessary truth which is based on assumption; a principle or proposition which cannot actually be proved or disproved.
Postulate
Something assumed without proof as being self-evident or generally accepted, especially when used as a basis for an argument
"the postulate that there is little moral difference between the superpowers" (Henry A. Kissinger).
Axiom
A fundamental assumption that serves as a basis for deduction of theorems; a postulate (sometimes distinguished from postulates as being universally applicable, whereas postulates are particular to a certain science or context).
Postulate
A fundamental element; a basic principle.
Axiom
An established principle in some artistic practice or science that is universally received.
The axioms of political economy cannot be considered absolute truths.
Postulate
(Mathematics) An axiom.
Axiom
A self-evident and necessary truth, or a proposition whose truth is so evident as first sight that no reasoning or demonstration can make it plainer; a proposition which it is necessary to take for granted; as, "The whole is greater than a part;" "A thing can not, at the same time, be and not be."
Postulate
(Archaic) A requirement; a prerequisite.
Axiom
An established principle in some art or science, which, though not a necessary truth, is universally received; as, the axioms of political economy.
Postulate
Something assumed without proof as being self-evident or generally accepted, especially when used as a basis for an argument. Sometimes distinguished from axioms as being relevant to a particular science or context, rather than universally true, and following from other axioms rather than being an absolute assumption.
Axiom
A saying that widely accepted on its own merits
Postulate
A fundamental element; a basic principle.
Axiom
(logic) a proposition that is not susceptible of proof or disproof; its truth is assumed to be self-evident
Postulate
(logic) An axiom.
Postulate
A requirement; a prerequisite.
Postulate
Postulated.
Postulate
To assume as a truthful or accurate premise or axiom, especially as a basis of an argument.
Postulate
To appoint or request one's appointment to an ecclesiastical office.
Postulate
To request, demand or claim for oneself.
Postulate
Something demanded or asserted; especially, a position or supposition assumed without proof, or one which is considered as self-evident; a truth to which assent may be demanded or challenged, without argument or evidence.
Postulate
The enunciation of a self-evident problem, in distinction from an axiom, which is the enunciation of a self-evident theorem.
The distinction between a postulate and an axiom lies in this, - that the latter is admitted to be self-evident, while the former may be agreed upon between two reasoners, and admitted by both, but not as proposition which it would be impossible to deny.
Postulate
Postulated.
Postulate
To beg, or assume without proof; as, to postulate conclusions.
Postulate
To take without express consent; to assume.
The Byzantine emperors appear to have . . . postulated a sort of paramount supremacy over this nation.
Postulate
To invite earnestly; to solicit.
Postulate
(logic) a proposition that is accepted as true in order to provide a basis for logical reasoning
Postulate
Maintain or assert;
He contended that Communism had no future
Postulate
Take as a given; assume as a postulate or axiom;
He posited three basic laws of nature
Postulate
Require as useful, just, or proper;
It takes nerve to do what she did
Success usually requires hard work
This job asks a lot of patience and skill
This position demands a lot of personal sacrifice
This dinner calls for a spectacular dessert
This intervention does not postulates a patient's consent
Postulate
A fundamental element accepted without proof in developing a theory.
Her hypothesis begins with the postulate that light travels faster than sound.
Postulate
A basic proposition that cannot be deduced from any other within a theory.
The postulate formed the undeniable base of his philosophical argument.
Common Curiosities
Are "Axioms" more universal than "Postulates"?
Generally, yes. "Axioms" are considered universally true within their system, while "Postulates" are often specific to a particular theory.
Can a "Postulate" be proven?
A "Postulate" is assumed to be true without proof, serving as a starting point for further reasoning within a theory.
Can "Axioms" and "Postulates" be used interchangeably?
They are similar, but "Axioms" are usually broader, while "Postulates" are more specific to a theory or system.
Is a "Postulate" a type of hypothesis?
It's similar, but a "Postulate" is generally accepted without the need for empirical testing, unlike a hypothesis.
How do "Axioms" aid in logical argumentation?
"Axioms" provide basic, accepted truths that serve as starting points for logical reasoning.
Are "Postulates" always scientific?
No, "Postulates" can be used in any field that requires a foundational statement for building a theory, including philosophy.
Why are "Axioms" important in mathematics?
"Axioms" form the foundational truths from which complex mathematical theorems and principles are derived.
Who decides an "Axiom"?
"Axioms" are generally established by consensus within a field of study, like mathematics or philosophy.
Is an "Axiom" always true?
An "Axiom" is accepted as true within its specific system of logic or mathematics without requiring proof.
Are all "Axioms" self-evident?
Within their systems, yes. "Axioms" are considered self-evident truths that don’t require proof.
Do "Postulates" have a role outside of geometry?
Yes, "Postulates" can be foundational statements in various scientific theories and logical systems.
Can an "Axiom" be questioned or disproven?
"Axioms" are accepted without proof within their system, so they're not typically disproven, but they can be questioned outside their system.
Can a "Postulate" evolve over time?
Yes, "Postulates" can be adapted or replaced as theories develop or new information emerges.
What happens if a "Postulate" is incorrect?
If a "Postulate" is incorrect, it can undermine the theories or conclusions drawn from it.
Can an "Axiom" exist outside of mathematics and logic?
Yes, "Axioms" can also be principles accepted as true in various fields, like ethics or economics.
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Written by
Tayyaba RehmanTayyaba Rehman is a distinguished writer, currently serving as a primary contributor to askdifference.com. As a researcher in semantics and etymology, Tayyaba's passion for the complexity of languages and their distinctions has found a perfect home on the platform. Tayyaba delves into the intricacies of language, distinguishing between commonly confused words and phrases, thereby providing clarity for readers worldwide.
