Definition:Axiom/Logical
Definition
A logical axiom is an axiom which does not stand in the context of a wider subject matter.
That is, it is a statement which is considered as self-evident.
Note, however, that there has been disagreement for as long as there have been logicians and philosophers as to whether particular statements are true or not.
For example, the Law of Excluded Middle is accepted as axiomatic by philosophers and logicians of the Aristotelian school but is denied by the intuitionist school.
Examples
Axioms of Propositional Logic
The Axioms of Propositional Logic are examples of logical axioms.
Law of Excluded Middle
The Law of Excluded Middle is an example of a logical axiom.
Also known as
The name primitive proposition can sometimes be found for logical axiom.
Also see
- Results about logical axioms can be found here.
Linguistic Note
The usual plural form of axiom is axioms.
However, the form axiomata can also sometimes be found, although it is sometimes considered archaic.
Sources
- 1910: Alfred North Whitehead and Bertrand Russell: Principia Mathematica: Volume $\text { 1 }$ ... (previous) ... (next): Chapter $\text{I}$: Preliminary Explanations of Ideas and Notations
- 1972: A.G. Howson: A Handbook of Terms used in Algebra and Analysis ... (previous) ... (next): $\S 1$: Some mathematical language: Axioms
- 1993: Richard J. Trudeau: Introduction to Graph Theory ... (previous) ... (next): $1$. Pure Mathematics: Games