Principle

For Plato, the search for first principles is the search for the ground of all being and knowing. In the Republic, the Form of the Good occupies this position. It is the "unhypothetical principle" (anarchos hypothesis) that dialectic reaches when it ascends beyond the assumptions of mathematics and the particular sciences. The Good is not one form among others; it is the source of the being and intelligibility of all the other Forms, as the sun is the source of both light and growth. Plato's analogy is precise: just as the eye sees because the sun illuminates visible objects, the mind knows because the Good illuminates intelligible objects. Without this first principle, the Forms would be unintelligible, and knowledge would lack an ultimate ground.

In the Phaedo, Plato illustrates a different method of reaching principles: the method of hypothesis. Socrates proposes that if one cannot reach the first principle directly, one should adopt the strongest hypothesis and test its consequences. If the consequences are consistent, the hypothesis stands provisionally. But the goal remains to reach a principle that needs no further support.

Plato establishes the aspiration that all knowledge should rest on a single self-grounding principle. Aristotle preserves the idea of first principles but rejects the single supreme Form. Plotinus restores it in the figure of the One.

Aristotle gives "principle" (arche) its systematic treatment. A principle is that from which something either is, comes to be, or is known. In the order of reality, the principles of natural things are matter, form, and privation. In the order of knowledge, the principles of demonstration are axioms, definitions, and hypotheses. The most important insight in the Posterior Analytics is that first principles cannot themselves be demonstrated. All demonstration proceeds from prior, better-known premises; but if every premise required demonstration, there would be an infinite regress and no knowledge at all. Therefore there must be immediate, indemonstrable starting points, grasped by nous (intellectual intuition), not by discursive reasoning.

Aristotle distinguishes common axioms (the law of contradiction, which applies to all beings) from proper principles (specific to each science). The law of contradiction, "the same attribute cannot at the same time belong and not belong to the same subject in the same respect," is the firmest of all principles. No one can genuinely believe its negation.

Aristotle's account of first principles as indemonstrable and known by nous shapes the entire Scholastic and early modern discussion. Aquinas builds his natural law theory on the parallel structure. Locke and Hume will challenge whether any principles are truly self-evident.

Plotinus identifies the first principle with the One (to hen), which stands beyond being, beyond intellect, beyond any determination. The One is not a thing among things; it is the source from which all things proceed by a kind of overflow or emanation. Intellect (Nous), the second hypostasis, arises when the One's overflow turns back upon its source and contemplates it. Soul, the third hypostasis, arises from Intellect's overflow in turn. The entire hierarchy of reality is generated by this procession from a single, simple principle.

Plotinus's argument for the One draws on Plato's Parmenides and Republic. If there is to be anything at all, there must be a principle of unity prior to all multiplicity. Multiplicity presupposes unity, for every plurality is a plurality of ones. But the One itself cannot be a plurality; it must be absolutely simple, without parts, without qualities, without self-consciousness (for consciousness implies the duality of knower and known). The One is known, if at all, not by thought but by a mystical union in which the distinction between knower and known dissolves.

Plotinus's One becomes the model for divine simplicity in Christian, Jewish, and Islamic theology. Augustine draws on it for his account of God as the source of all being, and Aquinas for the doctrine that God's essence is his existence.

Aquinas extends Aristotle's account of principles into two domains: speculative and practical. In the speculative order, the first principle is the law of contradiction, known immediately by the natural light of the intellect. No one needs to be taught it; it is grasped as soon as the terms are understood. In the practical order, the first principle of natural law occupies a parallel position: "good is to be done and pursued, and evil is to be avoided." This principle is self-evident in the same way that the law of contradiction is. Just as the speculative intellect naturally assents to "the same thing cannot be and not be," the practical intellect naturally assents to "good is to be pursued."

From this first practical principle, secondary precepts of natural law are derived by practical reasoning. Aquinas calls the habitual knowledge of first practical principles "synderesis." It is not acquired by experience or instruction but is a natural disposition of the human intellect, oriented to the good as the speculative intellect is oriented to truth. The parallel between speculative and practical principles gives Aquinas a unified theory of the foundations of both knowledge and morality.

Aquinas's natural law theory, grounded in self-evident practical principles, shapes Catholic moral theology and secular natural law traditions for centuries. Locke challenges the self-evidence of moral principles; Kant reconstructs practical philosophy on a different first principle.

Descartes seeks a first principle so certain that no doubt can touch it. His method is to doubt everything that admits the slightest uncertainty: the senses deceive, mathematics might be wrong if a malicious demon distorts our reasoning, even the external world might not exist. But one thing survives: the act of doubting itself. If I doubt, I think; if I think, I exist. "Cogito, ergo sum." This is the first principle of Descartes's philosophy, known by direct intellectual intuition rather than by inference. It is not a syllogism with a suppressed premise ("all thinking things exist; I think; therefore I exist") but an immediate awareness.

From the Cogito, Descartes attempts to rebuild the entire edifice of knowledge. The existence of God is proved next (because the idea of a perfect being could not originate in an imperfect mind), and God's perfection guarantees that clear and distinct ideas are true. The chain from first principle to recovered world depends entirely on the absolute certainty of the starting point. Descartes has shifted the locus of principles from the structure of being (as in Aristotle) to the structure of consciousness. What is first in the order of knowing replaces what is first in the order of being.

The Cogito becomes the paradigmatic first principle of modern philosophy. Locke challenges its necessity; Hume questions whether the self it reveals is anything more than a bundle of perceptions; Kant reinterprets it as a condition of experience rather than a substance discovered.

Locke devotes the entire first book of the Essay to demolishing innate principles. If the law of contradiction were truly innate, he argues, children and the unlearned would assent to it. But they do not. They cannot even frame the proposition, let alone assent to it. Universal assent, even if it existed, would not prove innateness; it could be explained by the common course of experience. Locke grants that certain propositions are self-evident in the sense that anyone who understands the terms will assent to them. But self-evidence is not innateness. The understanding of the terms comes from experience, and the assent follows from that understanding.

The same applies to supposed innate practical principles. "Do unto others as you would have them do unto you" is not universally observed, and many peoples live by opposite rules. There is no moral principle that commands universal, unreflective assent. Locke's critique does not deny that some propositions are foundational. It denies that they are written into the mind prior to experience. Principles are discovered, not pre-installed.

Locke's rejection of innate principles forces subsequent thinkers to explain how foundational knowledge arises from experience. Hume follows Locke's empiricism to its skeptical conclusion; Kant responds by arguing that while principles are not innate, they are a priori conditions of any possible experience.

Hume pushes the question of principles to its crisis. The principle of causation, that every event has a cause and similar causes produce similar effects, is the foundation of all empirical reasoning. But what justifies it? Not reason: the negation of any causal claim is perfectly conceivable. That fire might not burn, that bread might not nourish, involves no contradiction. Not experience: we observe constant conjunction (one event regularly following another) but never necessary connection. The impression of "cause" gives us sequence and contiguity, nothing more.

The principle of causation rests on custom or habit. After repeated experience of fire followed by heat, the mind automatically expects heat when it sees fire. This expectation is a psychological fact, not a rational insight. Hume does not say the principle is worthless; he says it has no rational foundation. Nature has equipped us with useful habits of expectation that serve survival perfectly well. But the philosopher who asks "why should the future resemble the past?" will find no answer in either reason or observation. The principle of causation, the most important of all principles, is itself ungrounded.

Hume's skeptical challenge to the principle of causation is the most consequential attack on foundationalism in the modern tradition. Kant credits it with waking him from "dogmatic slumber" and responds with the synthetic a priori. Mill tries to ground induction empirically.

Kant's answer to Hume is the synthetic a priori. Some principles are neither analytic (true by definition) nor a posteriori (known from experience). They are synthetic (their predicates are not contained in their subjects) and yet a priori (known independently of experience). "Every event has a cause" is such a principle. Its negation is conceivable (contra the analytic), and no amount of experience could establish its universality (contra the a posteriori). How are such principles possible? Kant's answer: they are the conditions under which experience itself is constituted. The understanding applies the categories (substance, cause, reciprocity, and others) to the manifold of intuition, and this application is governed by principles that structure all possible experience.

The principle of causation is not a generalization from observed regularities; it is the rule that makes the ordering of events into a temporal sequence possible at all. Without it, there would be no experience of succession, only a chaos of impressions. Kant thus rescues principles from Humean skepticism without relying on innateness or self-evidence. Principles are neither written into the mind from birth nor learned from experience; they are the architecture of cognitive experience itself.

Kant's synthetic a priori reshapes the entire question of first principles. It creates a new kind of foundationalism: principles are justified not by being self-evident or by resting on experience but by being constitutive of any coherent experience. This framework dominates nineteenth- and twentieth-century philosophy of science.

Mill completes the empiricist challenge to self-evident principles. Even the axioms of mathematics and logic, he argues, are not a priori truths known by rational intuition. They are very well-confirmed empirical generalizations. The law of contradiction holds because we have never encountered a counter-instance and cannot imagine one, but this psychological inability does not prove logical necessity. It reflects the uniform course of our experience. Similarly, "two plus three equals five" is true because every observed instance of combining two things with three things has yielded five things. If our experience had been different, our arithmetic might have been different.

Mill extends this analysis to the principle of induction itself. "The course of nature is uniform" is the ultimate major premise of all inductive reasoning, and it is itself an induction from experience. This creates a circularity that Mill acknowledges but does not regard as vicious. Induction justifies itself by its track record: it has worked, and that working is itself a fact of experience. Critics find this deeply unsatisfying, but Mill insists that the demand for a non-empirical foundation is the demand for something that does not and cannot exist.

Mill represents the most thoroughgoing empiricist position on principles. His claim that even mathematical axioms are empirical discoveries remains controversial, but his insistence that all principles face the tribunal of experience shapes the logical positivists and the philosophy of science.