Axioms are statements or principles that are accepted as being true without the need for proof or evidence. Axioms are often self-evident, fundamental ideas that serve as the basis for building more complex theories, arguments, or systems of thought. They are commonly used everywhere; from mathematics to making life decisions.
How we apply axioms in everyday life
Here's a few of the many ways axioms are used:
Foundations for reasoning
Axioms provide a starting point for logical reasoning, helping us build arguments and make sense of the world around us. For example, the axiom "things that are equal to the same thing are equal to each other" is a basic principle in mathematics and logic that we use to understand equality.
Shared understanding
Axioms are often universally accepted principles, which help create a shared understanding between people in discussions or problem-solving situations. This common ground makes it easier to communicate ideas and collaborate effectively.
Simplifying complex ideas
Axioms break down complex ideas into simpler, more manageable components. By accepting certain fundamental truths, we can focus on exploring new ideas and building upon existing knowledge without having to prove every single concept from scratch.
Guiding principles
Axioms can serve as guiding principles in our lives, shaping our beliefs, values, and decision-making processes. For example, the golden rule, "treat others as you would like to be treated," is an ethical axiom that many people follow to navigate social interactions.
Explore further
While axioms are generally accepted as true, it's important to recognise that they can sometimes be challenged or revised as new information or perspectives emerge.