Principle

For Plato the search for principles is a search for what is first both in being and in knowing. In the Republic the Form of the Good occupies that position. It is the unhypothetical principle at which dialectic arrives when it ascends beyond the assumptions with which mathematics and the particular sciences begin. The Good is not one Form among others but the source of the being and the intelligibility of all the rest, as the sun is the source both of light and of growth. The comparison holds at each point: as the eye sees because the sun illuminates visible things, so the mind knows because the Good illuminates intelligible things. Without such a principle the Forms would remain unintelligible, and knowledge would want an ultimate ground.

The Phaedo exhibits a different approach. Where the principle cannot be reached directly, Socrates proposes that one lay down the account which seems strongest and examine what follows from it, holding the hypothesis secure so long as its consequences agree with one another. The procedure is provisional. What has been assumed still requires a foundation, and the inquiry is not finished until it reaches something that needs no further support. In this respect the mathematical sciences, which begin from postulates they do not examine, stand below dialectic, which Plato calls the highest of the sciences precisely because it ascends to unhypothetical beginnings. The difference between an assumption and an axiom is considered more fully under the ideas of Hypothesis and Dialectic.

Principles are not for Plato confined to the order of knowledge. Soul is called the principle of life and of motion in the universe, and it is a principle of a peculiar kind, since it has an existence of its own within the realm of being. Here Plato may be contrasted with Aristotle, for whom matter and form are principles of changing substances without being substances themselves. Whether a principle must be an entity, an aspect of some entity, or a law stating a universal condition of whatever is or happens, is a question that recurs whenever the principles of reality are discussed, and it is treated further under Being, Cause, and Soul.

Plato leaves to the tradition the aspiration that knowledge should rest at last upon a single self-grounding principle. Aristotle keeps the demand for indemonstrable beginnings while rejecting the supreme Form; Plotinus restores a supreme principle under the name of the One. Whether the ascent to an unhypothetical beginning can be completed at all remains in dispute, and the denial that it can is pressed by Montaigne and, in another manner, by the later empiricists.

Aristotle's treatment of principle (arche) is the most systematic the tradition affords. A principle is that from which a thing is, or comes to be, or is known. In the order of reality he argues that the principles of change are three, matter, form, and privation, and that no more are necessary and no fewer will do. Their priority is priority in nature rather than in time, since a substance composite of matter and form does not exist before its components coexist. In the order of knowledge the principles of demonstration are definitions, axioms, and hypotheses. Aristotle is also among the few who dwell upon the relation of principle to element and to cause, observing that the same thing may be all three, and that privation is a principle which is neither.

The Posterior Analytics holds that first principles cannot themselves be demonstrated. All instruction by argument proceeds from knowledge already possessed, and if every premise required proof the regress would be endless and nothing would be known. That axioms are indemonstrable is on this view a virtue rather than a defect, for what is demonstrated cannot be the starting point of demonstration. Of first principles, Aristotle explains, we see some by induction, some by perception, and some by a certain habituation, and the faculty which apprehends them he calls intuitive reason. He distinguishes further between the common notions, such as the law of contradiction, which run through the several sciences, and the proper principles peculiar to a single subject matter.

In the practical order particular facts are counted among principles. We deliberate neither about the end to be sought nor about the circumstances perceived, and the judgment that this is bread, or that this bottle contains poison, is a starting point of the practical conclusion as truly as the most general proposition about the end. Against those who insist upon having everything demonstrated, Aristotle offers an indirect defense of the law of contradiction, inviting the objector to try denying it without reducing his own speech to absurdity. The region in which contrary assumptions may be argued with some reason on both sides he assigns to dialectic; science he confines to what rests upon axioms. That distinction is pursued under the ideas of Knowledge and Opinion.

The doctrine that first principles are indemonstrable and apprehended by intuitive reason governs the scholastic discussion and much of the modern one. Aquinas adopts it for the practical order as well as the speculative. Bacon retains the common notions while disputing whether the highest axioms are intuited immediately from the particulars of experience or reached only through intermediate stages of generalization, a question treated under Induction. Locke, Hume, and Mill in their turn ask whether any proposition possesses the self-evidence Aristotle claims for it.

Considering the principles of the universe as a whole, Plotinus enumerates three: the One, which is also the Good; the Intellectual Principle, or primal thinker; and Soul. Aristotle treats the three principles of change as coordinate with one another, but Plotinus places his three in an absolute order of first, second, and third. They are principles in the order of reality, and they are at the same time the ultimate grades or modes of reality, which distinguishes them from matter and form as Aristotle conceives these. The One stands beyond being and beyond intellect, without parts, qualities, or self-consciousness, since consciousness would introduce the duality of knower and known. Intellect arises as the overflow of the One turns back upon its source and contemplates it, and Soul in turn proceeds from Intellect.

The number of the primals is argued rather than assumed. Those who would hold to fewer must identify the Intellectual Principle with Soul, or with the First, and so collapse distinctions the account requires. Those who would add more, interposing a mediating reason-principle between Soul and the Supreme Mind, deny intellection to Soul itself, which would then derive its reason from an intermediate rather than from Intellect. Neither addition nor subtraction is admissible, and Plotinus concludes that no more than these three may be affirmed. The reasoning parallels Aristotle's argument that an infinite number of principles is incompatible with the notion of principle, though the two arrive at different enumerations.

Since the One is prior to all multiplicity, and every plurality is a plurality of ones, unity cannot itself be a plurality. It follows that the first principle admits no determination whatever, and that whatever is said of it is said improperly. Whether such a principle can be known at all becomes a question of some difficulty. Plotinus allows no approach to it by discursive thought, but only a union in which the distinction between knower and known is not maintained. The relation of unity to being, and the sense in which what is beyond being may still be called a principle, are considered under the ideas of Being, One, and God.

The Plotinian One furnishes the model of divine simplicity for Christian, Jewish, and Islamic theology. Augustine draws upon it in treating God as the source of all being, and Aquinas in the doctrine that God's essence is his existence. The hierarchical ordering of principles that Plotinus defends also bears on the question, raised under the ideas of Being and Cause, whether the principles of reality are themselves existing things or only aspects of the things that exist.

Aquinas carries the Aristotelian account of principles into two orders at once, the speculative and the practical. In the speculative order the first principle is the law of contradiction, whose truth is perceived as soon as the meaning of 'is' and 'not' is understood. In the practical order the first precept of natural law, that good is to be done and pursued and evil avoided, holds a parallel place, and is known in the same manner, as soon as the meaning of 'seek' and 'good' is understood. From this precept the secondary precepts follow by practical reasoning, as theorems follow from axioms. Aquinas gives the habit by which the mind holds the first practical principles the special name of synderesis.

That such truths are called natural does not mean, on this account, that they are innate, instinctive, or congenital. Aquinas denies innate ideas no less firmly than Locke does, and insists that sense-experience is the source of all human knowledge. The assent given to first principles he attributes to a natural habit of the mind, the intellectual virtue he calls understanding, which answers to what Aristotle calls intuitive reason. Truths are natural in the sense that reason, functioning normally, will come to recognize them. Where Aquinas parts from Locke is on the further point that such immediate truths hold for reality itself and not merely for the relations among our own ideas. The habitual possession of principles is discussed more fully under the idea of Habit.

Principles admit of other distinctions in his account. The same thing may be principle, element, and cause together, while privation is a principle that is neither cause nor element; and in the sphere of conduct an end is both a principle and a final cause without being an element, the last end being at once the highest final cause and the first principle, first in intention though last in attainment. The sciences themselves are ordered by the character of their principles, and sacred theology stands above the rest because its principles are articles of faith rather than axioms of reason. These matters belong also to the ideas of Cause, Element, and Theology.

The parallel Aquinas draws between speculative and practical first principles shapes the natural law tradition in theology and afterward in jurisprudence. Locke and Montaigne question whether any moral precept commands the universal assent that self-evidence would require, and Montaigne asks that a single such precept be produced. Kant retains the notion of first principles of the practical reason while placing their source in the transcendental structure of reason rather than in a natural habit, a difference examined under the idea of Law.

Descartes proposes to find a beginning that no doubt can reach. Whatever admits the least uncertainty is to be set aside: the senses, which have deceived; the reasonings of mathematics, which a deceiving power might distort; the existence of bodies and of the world itself. What withstands this procedure is the act of doubting. If I doubt, I think; if I think, I am. The proposition is not, in Descartes' understanding of it, a syllogism with a suppressed major premise, but something apprehended immediately by the intellect. It thus belongs to the class of immediate truths, though it differs from the axioms of the tradition in being a truth about a particular existence rather than a general proposition.

Upon this beginning the rest is to be rebuilt. The existence of God is demonstrated on the ground that the idea of a perfect being could not arise in an imperfect mind, and the divine perfection is then made the warrant that what is clearly and distinctly perceived is true. Whether the chain can bear the weight placed upon it has been disputed ever since; what is not disputed is the shift of emphasis it marks, from what is first in the order of being, where Aristotle and Aquinas locate principles, to what is first in the order of knowing. The relation between these two orders of priority is treated under the ideas of Being and Knowledge.

On the origin of axioms Descartes stands with those who allow their indemonstrability while denying that they are inductions from experience. Like Kant afterward, though on other grounds, he takes them to be prior to experience rather than gathered from it, holding them innate possessions of the intellect. He agrees with Plato, Aristotle, Aquinas, Bacon, and Spinoza in the further matter that self-evident truths describe the nature and existence of things outside the mind, and does not confine them, as Locke and Hume will, to the perception of agreement among our own ideas. Where axioms come from, and whether they are intuited or acquired, is considered under Idea and Induction.

The Cogito becomes the starting point against which later inquiries into principles are measured. Locke doubts that so much can be built upon it, and holds that our knowledge of our own existence, though immediate, yields no general maxims. Hume asks whether the self it discloses amounts to more than a succession of perceptions. Kant retains the thought that the 'I think' must accompany all representations, while treating it as a condition of experience rather than as a substance found by inspection.

The first book of the Essay is given over to the denial of innate principles. If the law of contradiction were stamped upon the mind at birth, Locke argues, children and the unlearned would assent to it; but they cannot so much as frame the proposition. Universal assent would not establish innateness even where it obtained, since the common course of experience would account for it equally well. Locke does not deny that certain propositions carry their evidence with them, so that whoever understands the terms must agree. He denies that such evidence argues an origin prior to experience. The terms are had from experience, and the assent follows upon the understanding of them.

Self-evidence is also, on Locke's account, narrower in its reach than the schools supposed. What is immediately perceived is the agreement or disagreement of ideas, and general maxims can accordingly express nothing about the real existence of things. Of real existence we have immediate knowledge only in particular cases: we know our own existence intuitively, the existence of God by demonstration resting upon it, and the existence of other things by the report of the senses. Locke is therefore not denying that some truths about reality are known without proof, but only that the truths so known are general propositions. He goes further and disputes that any science has in fact been built upon such maxims.

The same treatment is extended to practical principles. No rule of conduct is universally observed, and whole peoples live by contraries of what others hold sacred, so that no moral precept commands the unreflective assent that innateness would require. This does not leave morality without foundations in Locke's view, since he takes moral truths to be capable of demonstration; it removes them from the class of things given to the mind beforehand. Whether principles are gathered from experience, possessed by natural habit, or held a priori is disputed among Aquinas, Descartes, and Kant, and the several answers are considered under the ideas of Experience, Idea, and Judgment.

Locke's rejection of innate principles obliges those who come after him to explain how knowledge of first principles can arise from experience alone. Hume carries the position further, restricting demonstrable truth to mathematics and leaving the study of nature to probability. Kant grants Locke that principles are not innate, while holding them a priori conditions of any possible experience. William James later adopts Locke's restriction of intuitive truths to the relations among ideas and calls the vindication of the intuitionist position, so understood, a barren victory.

Hume asks what warrant belongs to the principle upon which all reasoning from experience proceeds, namely that like causes are followed by like effects. Reason does not supply it, since the contrary of any matter of fact remains conceivable and implies no contradiction; that fire should not burn or bread not nourish can be distinctly supposed. Neither does observation supply it, for what the senses report is the constant conjunction of one event with another, together with succession and contiguity, and never a necessary connection between them. The principle is thus neither demonstrable nor established by the very experience it is invoked to govern.

What remains, on Hume's account, is custom. The mind that has often seen heat follow fire comes to expect heat upon seeing fire, and the expectation is a fact about the mind rather than an insight into things. Hume does not conclude that the principle should be abandoned, since nature has furnished us with habits of expectation on which life proceeds well enough. He concludes that no rational foundation for it can be produced, and that whoever asks why the future should resemble the past will get no answer from either reasoning or observation. The connection between habit and belief is considered further under the ideas of Custom and Habit.

The consequence for the ordering of the sciences is considerable. Hume allows self-evident truths only where the mind compares its own ideas, which is to say in mathematics, and he denies that such truths concern real existence or matters of fact. Physics, being concerned with real existences, has no axioms available to it, and therefore cannot demonstrate its conclusions but must advance them as probabilities. The distinction between what may be known and what may only be opined thus runs along the line dividing the relations of ideas from matters of fact, a division treated under Knowledge, Opinion, and Hypothesis.

Hume's argument sets the terms in which the question of principles is afterward debated. Kant reports that it woke him from dogmatic slumber, and answers it by making the causal principle a condition under which experience is constituted rather than a generalization drawn from it. Mill accepts the empirical origin of the principle and undertakes to show that induction may be grounded without appeal to any truth prior to experience. The skeptical position itself has older forms, and its more thoroughgoing version, which allows no axioms of any kind, is set out by Montaigne.

Kant meets the Humean difficulty with the synthetic judgment a priori. Some propositions are neither analytic, their predicates being not contained in their subjects, nor derived from experience, since no accumulation of instances could yield the universality they claim. That every event has a cause is a proposition of this kind. How such judgments are possible is the question the first Critique undertakes to answer, and the answer proposed is that they state the conditions under which experience is constituted. The understanding applies its categories, among them substance, causality, and reciprocity, to the manifold given in intuition, and the application proceeds according to principles that hold for whatever can be experienced at all.

The word principle is used by Kant in a more restricted sense than by Aristotle. He reserves it for general propositions which may stand as major premises in reasoning, and among these he distinguishes ordinary general propositions, which are principles only relatively, from synthetic judgments a priori, which alone he counts principles without qualification. A further distinction separates the principles of the understanding, which are constitutive of experience, from the principles of reason, which are to be employed regulatively, determining the direction of thought beyond experience without pretending to constitute any object. The causal principle, so understood, is the rule by which events are ordered in a temporal series rather than a summary of regularities observed.

The principles of the pure practical reason legislate a priori for the realm of freedom as those of the speculative reason legislate for the realm of nature, and the parallel leads Kant to conceive a metaphysic of nature and a metaphysic of morals as twin disciplines. Aquinas draws a like parallel between the first principles of demonstration and the precepts of natural law, and the two accounts agree that morality must rest upon principles of the practical reason. They differ on how such principles are possessed, Aquinas assigning them to a natural habit of a mind furnished by experience, Kant to the transcendental structure of reason itself. The question belongs also to the ideas of Duty and Law.

Kant's account offers a third answer beside innateness and induction, justifying principles by their office in making coherent experience possible. It governs much of the later philosophy of science, and it does not go unchallenged. William James denies that the eternal verities which the structure of our mind lays hold of thereby lay hold on extramental being, or that they have, as he says Kant pretended, a legislating character for all possible experience. Mill, taking the opposite course, holds that even the axioms Kant treats as a priori are gathered from experience.

Mill carries the empirical account of principles to its furthest point. The axioms of mathematics and logic, on his view, are not truths of reason apprehended prior to experience but generalizations of very wide confirmation. The law of contradiction commands assent because no instance to the contrary has ever been met with and none can be imagined, and this inability of the imagination he takes to record the uniform course of experience rather than a necessity in things. So too with the propositions of arithmetic: two and three have been found to make five wherever the combination has been made, and had experience run otherwise, the reckoning would have run otherwise as well. Whether axioms are intuitive inductions or reached by stages of generalization is examined under the idea of Induction.

The same analysis is applied to the principle upon which induction itself proceeds. That the course of nature is uniform stands as the ultimate major premise of every inductive argument, and it is arrived at, Mill holds, by induction from experience. The circle is acknowledged, though he does not regard it as vicious, since the uniformity of nature is on his account a complex fact compounded of the several uniformities that particular inquiries establish, and the procedure is warranted by its results. Those who require a foundation outside experience will find the answer unsatisfying; Mill's reply is that what they require does not exist and could not be had.

The demand for first principles is not thereby abandoned in the practical order. Mill observes that the utilitarians, whatever else divides them from Kant, must agree with him that if there is to be a science of ethics morality must be deduced from principles, and ultimately from one, for where several are admitted a determinate order of precedence among them is needed. He adds that questions of ultimate ends do not admit of direct proof, and that incapacity of proof by reasoning belongs to all first principles alike, to the first premises of our knowledge as well as to those of our conduct. The remark stands close to what Aristotle says of the law of contradiction, and the matter is treated further under Good and Evil and Happiness.

Mill states the most thoroughgoing of the empiricist positions on principles. His claim that the axioms of mathematics are discoveries about the world rather than truths of reason has been much disputed, and the dispute continues in the later philosophy of science, where his insistence that every principle answers to experience is taken up by the logical positivists. The opposed view, that some principles are known independently of experience and hold for reality, is maintained by Descartes, Kant, and, on other grounds, by Aristotle and Aquinas.