Aristotle conceived first principles (Greek archai) as the basic building blocks of all knowledge – the ultimate starting points that cannot be derived from anything more fundamental. In his Metaphysics he famously notes that wisdom concerns “primary causes (aitia) and the starting-points (or principles, archai)” . In modern terms a first principle is simply “a basic proposition or assumption that cannot be deduced from any other proposition or assumption” . In other words, an archē is an irreducible axiom or fact on which further reasoning depends. For Aristotle, grasping first principles was the goal of true science and philosophy: these unquestioned truths underlie every deduction, definition, and discovery.
First Principles in Metaphysics: Ultimate Causes and Axioms
Aristotle’s Metaphysics (his “first philosophy”) seeks the most fundamental aspects of reality – the causes and principles of being as such. He explains that first philosophy deals with what is “better known in themselves” (even if less obvious to us) by studying things “qua beings” . For example, he holds that the Law of Non-Contradiction – “the same thing cannot at the same time both belong and not belong to the same thing and in the same respect” – is “the most certain of all principles” . Because every proof implicitly uses this law, it itself cannot be proved without circularity. Aristotle declares the non-contradiction to be a first principle, “not derived from anything more basic” . In Metaphysics Γ he argues that even to deny the law of non-contradiction is impossible without incoherence: one would negate the very act of meaning or discourse. Thus logical axioms like non-contradiction (and similarly the law of excluded middle) are examples of archai common to every inquiry . In sum, the metaphysical archai are the ultimate facts or causes (e.g. “what is substance?”) that must be assumed in any higher reasoning.
First Principles in Logic and Science: Demonstration and Definition
In Aristotle’s Posterior Analytics (his treatise on scientific knowledge), he shows how all demonstration rests on first principles. A demonstration is a syllogism that produces scientific knowledge, but its premises must satisfy special conditions: they must be true, primary, immediate, better known than and prior to the conclusion . Concretely, Aristotle insists that the premises must themselves be true, basic and indemonstrable . If a premise were demonstrable, we would regress infinitely looking for still more basic premises. Hence each science must “stop” at a set of immediate propositions or axioms that are taken as given. He writes: “The premises must be primary and indemonstrable; otherwise they will require demonstration… The premises must be the causes of the conclusion, better known than it, and prior to it.” . In other words, to know something scientifically we assume certain axioms whose truth we recognize intuitively (or by induction) and then deduce their consequences.
Aristotle further explains that these basic axioms often turn out to be definitions or essences. For example, in any demonstration about geometrical figures or natural kinds, one premise may simply assert the essential nature of the subject. He notes that “the basic premises of demonstrations are definitions, and… these will be found indemonstrable” . In practice Aristotle distinguishes: a proposition taken as an immediate starting premise is a thesis or axiom if it is accepted without proof. A definition – “laying down” what something is – is itself a kind of thesis. For instance, he notes that “to define what a unit is,” one simply lays it down that a unit “is quantitatively indivisible” . Such definitional statements are accepted as first principles rather than proved. Thus both mathematical postulates (e.g. about lines or numbers) and conceptual definitions serve as archai.
Crucially, Aristotle acknowledges that we must know these principles in some way before we can demonstrate anything. In Posterior Analytics he argues that knowledge of the immediate premises is “independent of demonstration,” since a regress of proofs must end in indemonstrable truths . How, then, do we grasp them? He proposes that human minds have a natural capacity of nous (intellect or insight) that becomes familiar with the archai. In fact, Aristotle insists that “intuition supplies the first principles (archai) of human knowledge” . Experience “actualizes” this innate potential: by sensing repeated instances we come to recognize the universal form (essence) and hence the defining premises of a science . To Aristotle, this “intuitive” apprehension is infallible at the foundational level – you cannot consistently doubt the very laws that make proof possible . He famously concludes that it is impossible to demonstrate absolutely everything, for that would demand an infinite regress without any starting point . In short, Aristotle’s logic shows that every discipline must rest on first principles – the undemonstrable axioms of that field – which our nous grasps as self-evident starting points. (He notes also that there are “common” first principles shared by all sciences, and “special” ones unique to each field .)
Examples of Aristotelian First Principles
Aristotle’s texts give many examples of archai in action. For instance, logical axioms are archetypal first principles: the non-contradiction principle that “the same attribute cannot both belong and not belong to the same subject at once” is assumed in every reasoning, never proved. In mathematics, simple geometric truths stand as starting points: Aristotle assumes that “the angles of every triangle are equal to two right angles,” a universal fact known prior to any particular proof . This universal was assumed even before identifying a specific triangle. Likewise in arithmetic the definition “a unit is quantitatively indivisible” is accepted axiomatically . More broadly, any discipline has its own first principles (e.g. physical laws in natural science). Euclid’s geometry offers a classic case: his whole system is built from a handful of postulates and primitive definitions – each one a first principle that “cannot be deduced from any other,” like “through any two points a straight line may be drawn” .
Each example shows how, in Aristotle’s system, knowledge is built upward from those first principles. You start with the axioms or essence of the subject, and then deduce further truths. Trying to prove the axiom itself is either impossible or circular.
First Principles and Modern Thought
Aristotle’s doctrine of archai resonates with contemporary “first principles thinking,” which enjoys popularity in science, engineering and philosophy today. The modern idea – to strip a problem down to its most basic axioms and reason up from there – echoes Aristotle’s insistence on foundational truths . In physics, for example, calculations “from first principles” (ab initio) start with fundamental laws rather than fitted models . In critical thinking, one is taught to question assumptions and ensure conclusions do not violate any basic laws of logic or nature . Aristotle essentially invented this approach: he believed that without solid first premises you can reach no true conclusions. As one modern commentator puts it, Aristotle viewed every science as requiring “certain indemonstrable first premises,” known by intuition, on which all further knowledge rests .
Today we still see Aristotle’s influence when we accept axioms in mathematics, or core principles in science. Even disciplines like biology or psychology ultimately rest on basic “given” facts (e.g. something exists, causality holds, logical consistency). Aristotle showed that knowing these archai is what makes knowledge possible – once grasped, “nothing except intuition can be truer than scientific knowledge” . For anyone passionate about deep ideas, Aristotle’s model is inspiring: to understand any subject, one strives to identify its simplest first principles and build knowledge upward. His example encourages us to probe assumptions, seek definitions of essence, and recognize the “self-evident” starting points that underlie our reasoning.
In summary, Aristotle’s first principles are the axiomatic foundations of reasoning in metaphysics, logic and science. They serve as both the goal (to find the ultimate causes and essences) and the basis (the premises of every proof) of philosophy. By elevating the archai to central importance, Aristotle bequeathed to us a timeless framework: to think rigorously, we must ground ourselves in the bedrock of first principles.
Sources: Aristotle’s own texts (Metaphysics, Posterior Analytics, Nicomachean Ethics), as well as expert commentary , support this overview. Each point above can be traced to these sources of Aristotelian scholarship.