Skip to content
Wellsprings
epistemology

First Principles & Axioms

ἀρχαί / ἀξιώματα

The bedrock starting points that every proof depends on yet none can prove — where the endless chain of 'why?' finally has to stop.

Archái and axiómata are the foundational assumptions from which all logical reasoning begins—the bedrock truths that cannot themselves be proven without circular reasoning. Aristotle developed the systematic account of first principles, arguing that every demonstration must start somewhere, and that starting point cannot be demonstrated. These are not opinions or guesses but necessary truths that serve as anchors for all knowledge that follows.

In practice, a mathematician might begin with the axiom that equals added to equals produce equals, then build theorems upon it without needing to justify that axiom itself. Similarly, in natural philosophy, Aristotle insists that first principles about causation and existence must be established as fact before we can properly explain anything else. The entire edifice of rational inquiry depends on identifying and agreeing upon these indemonstrable truths.

Where this idea shows up

41 Greek sources·1 Jewish-canon citation

Where to read it