Mathematics
Given a line and a point not on the line, there is exactly one line parallel to the given line through the point
Axiomatic
It is not derived from other principles but serves as a fundamental assumption in Euclidean geometry
The speed of light in a vacuum is constant and is the same for all observers, regardless of the motion of the light source or observer
Axiomatic
In the context of Einstein's theory of relativity. This statement is treated as a postulate (an axiom-like foundation) for the theory of relativity.
It is a fundamental truth in the analysis of human actions that individuals seek to maximize their own benefit
Axiomatic
This statement is often treated as an axiom, forming the basis for models that explain and predict human behavior, in the context of classical economics and some social science theories.
Historical narratives are influenced by the perspectives of those who record them
Axiomatic
True, as it is widely accepted that historians' perspectives shape historical narratives. This serves as a foundational principle in historiography.
The morality of an action is determined solely by its consequences.
Non-Axiomatic
Not axiomatic because it is subject to extensive debate. Various ethical theories (e.g., deontology, virtue ethics) challenge this claim, showing it is not a universally self-evident or accepted truth.
There exists an infinite number of prime numbers
Non-Axiomatic
This is a theorem rather than an axiom.
Matter cannot be created or destroyed, only changed in form
Axiomatic
It is a fundamental principle that forms the basis for many physical laws. It is accepted without proof and used to explain a wide range of physical phenomena.
Humans are social animals
Axiomatic
It is more of a widely observed fact in social sciences.
Historical events are subject to interpretation
Axiomatic
This is true, as it is a fundamental principle of historical analysis that no event is understood without some degree of interpretation
The ends justify the means
Non-Axiomatic
This is not an axiom because it is not universally accepted or self-evident. It is false or debatable, depending on the ethical framework.
A whole is greater than any of its parts.
Axiomatic
It is a basic self-evident truth in mathematics, particularly in set theory and arithmetic, where the whole (e.g., a set) is always considered greater or equal to its individual parts.
Sun revolves around the Earth
Non-Axiomatic
It is not self-evident and requires observational proof, making it a non-axiomatic statement.
People behave the same way in all cultures
Non-Axiomatic
It is an empirical claim that can be tested and disproven.
History is written by the victors
Non-Axiomatic
Not a universally self-evident truth and can be challenged with multiple perspectives and sources.
Stealing is wrong in every situation
Non-Axiomatic
This statement is not universally accepted without debate. Different ethical frameworks and contexts (e.g., stealing to survive) challenge this statement, making it a matter of interpretation rather than a self-evident truth.