Chapter 70: PRINCIPLE

INTRODUCTION

Of the three ways in which principles are considered in the tradition of the great books, the most familiar sense of the word is the one in which we speak of moral principles, principles of action, or political principles. The connotation of the word in this usage seems to be twofold. We think of principles as rules of conduct and we think of them as standards by which to measure and judge human acts or political events. Either conception attributes a certain generality to principles. Just as rules apply to an indefinite number of particular cases, so any principle we appeal to in order to decide a practical problem or to weigh the merits of an action undertaken, can be applied again and again in other circumstances.

In addition to this characteristic of generality, principles seem to have the quality of underlying or being the source of other things. In jurisprudence the search for principles consists in the attempt to discover those few most fundamental precepts from which the more detailed rules of law can be derived. The constitution of a state provides the principles which underlie its particular laws and sets the standards by which their legality is to be measured. Governments are judged by the principles they attempt to apply as well as by their success in putting these principles into practice. To say of a government that its acts are unprincipled is not to condemn the particular acts as wrong, but to accuse the government of having no uniform policy to serve as a foundation for its acts.

This aspect of the meaning of principle—as the source from which a set of consequences follows—seems to be more characteristic of the idea of principle than the aspect of generality. According to its Latin derivation and the equivalent root in Greek, “principle” means a beginning or a foundation. Sometimes it means that which comes first absolutely, in the sense of being before everything else; sometimes it means that which comes first only relatively, taking precedence over some things, but having others prior to itself. Since priority may be either absolute or relative—first without qualification or first only in a certain respect—the traditional phrase “first principle” does not have the redundancy of “first first” or “beginning beginning.”

If there are absolutely first beginnings, to which nothing else can be prior, they can legitimately be called “first principles” to distinguish them from principles which come first only in a certain respect. Only if there are first principles can regression to infinity be avoided in the search for origins. The propositions which lie at the foundation of a science may, for example, constitute its principles, but they may also be derived in turn from some prior science. Only the principles of a science which is prior to or independent of all others can be truly first principles.

THE FOREGOING example brings us to the other meaning of principle that is popularly recognized. It is the sense in which men speak of principles in relation to conclusions, or of principles as the foundations of a science.

The priority which belongs to principles in the domain of thought need not be temporal. Principles may or may not be first in the order of learning. But if they are not first in the temporal order, they must be first logically, as premises are logically prior to a conclusion, or, as in Euclid’s Elements, his principles—his definitions, postulates, and axioms—are logically prior to all the theorems he demonstrates by means of them.

It may be asked whether, among propositions related as premises and conclusions, the logical priority of one proposition to another is sufficient to make the prior proposition a principle. Can a proposition be a principle if, even though it is used as a premise in reasoning, it lacks generality? For example, is the particular proposition—that this bottle contains poison—a principle underlying the practical conclusion that its contents should not be swallowed?

Aristotle answers affirmatively. In the order of practical thinking, he holds, we deliberate neither about the end to be sought nor about the particular facts on which a choice of the means depends. “The end cannot be a subject of deliberation,” he writes, “but only the means; nor indeed can the particular facts be a subject of it, as whether this is bread or has been baked as it should; for these are matters of perception.” The perceived particulars thus function as principles along with the most general of all practical propositions, namely, what the end should be. Calling the faculty which apprehends first principles “intuitive reason,” Aristotle says that “the intuitive reason involved in practical reasonings grasps the last and variable fact, i.e., the minor premise. For these variable facts are the starting-points for the apprehension of the end, since the universals are reached from the particulars; of these therefore we must have perception, and this perception is intuitive reason.”

Perception, at least in the form of sense-perception, seems to be only one of the two ways in which we apprehend the particular facts which are principles in practical reasoning. Like Aristotle, Aquinas uses the judgment, that this is bread or iron, as an example of “facts received through the senses” which are “principles… accepted in the inquiry of counsel.” But the moral quality inherent in particular acts does not seem to be perceptible by the senses alone; and such particular moral judgments are also involved in moral reasoning. Aristotle suggests that habit (i.e., the moral habits or virtues) are the immediate source of such judgments, which can be called “perceptions of the particular” even though they are not simply sense-perceptions.

“Of first principles,” Aristotle explains, “we see some by induction, some by perception, some by a certain habituation.” By induction we see the general truths; by sense-perception, the sensible particulars; and by habituation, the moral particulars. Hence Aristotle insists that “anyone who is to listen intelligently to lectures about what is noble and just and, generally, about the subjects of political science must have been brought up in good habits. For the fact is the starting-point, and if this is sufficiently plain to him, he will not at the start need the reason as well; for the man who has been well brought up has or can easily get the starting-points.”

The word “principle” is used by Kant in a much more restricted sense. He reserves the status of principle to the general propositions which serve as the major premises in reasoning. In both the theoretic and the practical sciences, principles express reason’s understanding of universal and necessary relationships.

Kant differs from Aristotle in other respects. He differentiates between ordinary general propositions which merely serve as major premises in reasoning and the propositions he classifies as “synthetic judgments a priori.” He regards the former as principles only in a relative sense and treats the latter alone as principles absolutely. He also distinguishes between those principles of the understanding which he thinks are “constitutive of experience,” and those principles of the reason which should be used in what he calls a “regulative,” not a constitutive manner. They determine the direction and goals of thought beyond experience. But such differences concerning the nature and kinds of principles do not affect the commonly accepted meaning of principle as that from which, in the temporal order of learning, knowledge develops or that upon which, in the logical order, knowledge rests.

THE THIRD AND relatively unfamiliar sense in which principles are discussed in the great books does not refer to the sources of man’s moral decisions, political acts, or scientific conclusions. The discussion in question refers to reality apart from man. Just as men try to discover the elements of matter, or the causes of motion, so they try to discover the principles of existence and of change. The issues which arise from this concern with the principles of reality are discussed in such chapters as BEING, CAUSE, CHANGE, FORM, NATURE, and MATTER.

If the word “principle” always connotes a beginning, every special sense of principle should involve some kind of priority. As we have already observed, principles may be either prior in time or prior logically. But the principles of the universe or the principles of change are not usually thought to be prior in either of these ways. For them Aristotle specifies another kind of priority—priority in nature—to explain the primacy of those principles which constitute the nature of a thing. In his view, for example, matter and form are the principles of a physical substance. Since a substance composite of matter and form cannot exist until its matter and its form coexist, matter and form are not prior to the substance they compose. Their priority to substance consists only in the fact that that which has the nature of a composite substance results from the union of matter and form as its natural components. Because the substance is the natural resultant, matter and form can properly be called its natural principles.

This way of considering principles at once suggests a close relationship among principles, elements, and causes; and also indicates the connection between the present chapter and the chapters on CAUSE and ELEMENT. The ultimate parts into which a whole can be divided may be its principles as well as its elements. The form or matter of a substance may be, in Aristotle’s theory, not only one of its principles, but also a cause—a formal or a material cause. Among the great authors Aristotle and Aquinas alone seem to dwell upon the relationship of these three terms. They give instances in which the same thing is principle, element, and cause, as well as instances in which a principle is neither a cause nor an element, e.g., privation. In the sphere of human conduct, an end is both a principle and a final cause, but not an element. The last end is the highest final cause and the first principle—first in intention though last in attainment.

THE TRADITIONAL issues concerning this idea differ according to the general context in which the question of principles is raised. The main controversy, for example, with regard to principles in the order of reality is over their number and order.

Aristotle argues against an infinite number of principles as incompatible with the very notion of principle itself. In his analysis of change or motion, he tries to prove that no more than three principles are necessary, and no less will do. These are, as the chapter on CHANGE explains, matter, form, and privation. Considering the principles of the universe as a whole, Plotinus also enumerates three and tries to prove that none can be added or subtracted. But whereas Aristotle treats the three principles of change as coordinate, Plotinus places the cosmic principles in the absolute order of first, second, and third.

“We need not go seeking any other Principles,” writes Plotinus. “This—the One and the Good—is our First, next to it follows the Intellectual Principle, the Primal Thinker, and upon this follows Soul. Such is the order in nature. The intellectual realm allows no more than these and no fewer. Those who hold to fewer Principles must hold the identity of either Intellectual Principle and Soul, or of Intellectual Principle and The First… To increase the Primals by making the Supreme Mind engender the Reason-Principle, and this again engender in the Soul a distinct power to act as mediator between Soul and the Supreme Mind, this is to deny intellection to the Soul, which would no longer derive its Reason from the Intellectual Principle, but from an intermediate…. Therefore, we must affirm no more than these three Primals.”

In the sense in which Plotinus conceives the three primals, they are not only principles in the order of reality, but are themselves the ultimate grades or modes of reality. Similarly for Plato soul is not only the principle of life and thought in the universe, but it also has its own existence in the realm of being. For Aristotle, in contrast, the principles of change do not have existence in and of themselves. Matter, form, and privation are not substances, but aspects of substance. They are present in every changing substance and in every change, but they are only the principles of mutable being; they are not mutable beings in themselves.

Lucretius states two principles as the basic laws of nature. The first is that nothing comes into being out of nothing; the second, that nothing is ever completely reduced to nothingness. The word “principle” is obviously not being used in the same sense here as when it designates The One for Plotinus, soul for Plato, matter for Aristotle, or the atoms which Lucretius calls the “first beginnings.” Here it does not refer to an entity, or even to an aspect of some real being, but rather to a law—the statement of a universal and necessary condition which governs all that is or happens. It is in this sense that the proposition traditionally called “the law of contradiction”—that the same thing cannot both be and not be in the same respect at the same time—is said by Aristotle to be the first principle of being as well as of thought.

The conception of the law of contradiction and the related laws of identity and excluded middle as principles of thought raises problems about logical principles in general—whether they are axioms or postulates, whether they are merely rules of reasoning and demonstration or are themselves premises from which conclusions can be deduced. If, for example, the law of contradiction is only a rule of thought, which forbids the mind to affirm and deny the same proposition, then it is not a principle of knowledge in the sense in which the definitions and axioms of geometry function as premises in the demonstration of theorems. No conclusion can be drawn from it concerning the nature of things. But if, in addition to being a rule of thought, it is a metaphysical axiom, which states the most fundamental fact about existence, then like the axioms in geometry it may be the source of conclusions in metaphysics.

On this second point Locke seems to differ sharply from Aristotle and Aquinas. He denies that the laws of identity and contradiction are fruitful principles of knowledge. “These magnified maxims,” he writes, “are not the principles and foundations of all our other knowledge.” Nor have they been, he adds, “the foundations whereon any science hath been built. There is, I know, a great deal of talk, propagated from scholastic men, of sciences and the maxims on which they are built; but it has been my ill luck, never to meet with any such sciences, much less any one built upon these two maxims, ‘what is, is’ and ‘it is impossible for the same thing to be and not to be.’”

WE SHALL PRESENTLY consider the issue concerning axioms or postulates—whether the principles of the sciences are self-evident truths or are only provisional assumptions. Those who are willing to admit the existence of axioms do not all agree, however, that such truths refer to reality. Hume, for example, limits the content of axioms to knowledge of the relations between our own ideas. They are not truths about real existence or matters of fact.

Locke also grants self-evidence only to perceptions of the agreement or disagreement between ideas. “Concerning the real existence of all other beings” except ourselves and God, we have, he writes, “not so much a demonstrative, much less a self-evident, knowledge; and therefore concerning these there are no maxims.” But Locke does think that our demonstrative knowledge of God’s existence depends upon an intuitive knowledge of our own existence; and in addition to knowing our own existence directly or without proof, he also thinks we have through our senses an equally direct knowledge of the existence of other things. Such intuitive and sensitive knowledge of particular existences is, like the truth of axioms, immediate—that is, something known directly or without proof, without any appeal to prior propositions. Hence Locke is not denying that we know some immediate truths about reality, but only that such truths consist exclusively of propositions about particular existences. Since axioms, or what Locke calls “maxims,” are always general propositions, the self-evident truths which they express do not apply to reality.

William James uses the word “intuitive”—in a different sense from Locke—to characterize propositions that state “the necessary and eternal relations” which the mind “finds between certain of its ideal conceptions.” Intuitive propositions are for him, therefore, what maxims are for Locke; and like Locke, James also denies that such axioms of reason hold for reality. “Only hypothetically,” he says, “can we affirm intuitive truths of real things—by supposing, namely, that real things exist which correspond exactly with the ideal subject of the intuitive propositions… The intuitive propositions of Locke leave us as, regards outer reality none the better for their possession. We still have to ‘go to our senses’ to find what the reality is.

“The vindication of the intuitionist position,” James continues, “is thus a barren victory. The eternal verities which the very structure of our mind lays hold of do not necessarily themselves lay hold on extramental being, nor have they, as Kant pretended later, a legislating character for all possible experience. They are primarily interesting only as subjective facts. They stand waiting in the mind, forming a beautiful ideal network; and the most we can say is that we hope to discover outer realities over which the network may be flung so that ideal and real may coincide.”

The opposite view seems to be taken by Plato, Aristotle, Aquinas, Bacon, Descartes, Spinoza, and Kant. Though they are far from being in complete agreement concerning the principles of knowledge, the propositions which they call axiomatic, self-evident, intuitive, or a priori synthetic judgments, are not restricted by them to the mind’s perception of the relations between its own ideas. There are self-evident or immediate truths in physics and metaphysics, as well as in mathematics and logic. Whether these are inductions from experience or innate possessions of the mind, whether they are intuitive apprehensions of intelligible being or a priori judgments having a transcendental origin, these propositions are held to describe the world of experience, or the nature and existence of things outside the human mind.

THERE SEEM TO BE two degrees of skepticism with regard to principles in the order of knowledge. Complete skepticism would consist in denying principles in every sense. That would be the same as denying any beginning or basis for even the opinions which men hold. No one seems to go that far.

The issue with respect to the foundations of knowledge or opinion is therefore not between those who affirm and those who deny principles, but between different views of what the starting points are. It is sometimes said, for example, that sensations are the principles or beginnings of all human learning. This view is shared both by those who think that all our ideas or concepts are abstracted from the materials provided by the senses and by those who account for all the other contents of the mind—its memories and imaginations, its complex formations—in terms of the simple impressions originally received by the senses.

Concepts, as distinct from sense-perceptions, are also sometimes regarded as principles of knowledge by those who think that concepts originate by abstraction from sensory materials, as well as by those who think that ideas are primary principles, i.e., having no origin in any prior apprehensions. On either view, ideas or concepts function as principles insofar as they are the simples from which the more complex acts of the mind develop, such as the acts of judgment and reasoning. Just as on the level of language, words are the principles of all significant speech, out of which sentences and paragraphs are formed; just as, in the logical order, terms are said to be the principles of propositions and syllogisms; so concepts are the principles of judgments and reasonings. The definitions of Euclid, for example, state the notions of point, line, triangle, etc. which underlie his theorems and demonstrations.

One common characteristic of either sensations or concepts as principles of knowledge seems to be simplicity. Nothing more elementary, out of which they can be formed, is prior to them. Another characteristic is that they are principles of knowledge or opinion without being themselves acts of knowledge or opinion. This point is made by all who hold that only propositions—whether statements of opinion or of knowledge—can be true or false.

The terms which express the simple apprehensions of the mind—its sensations or concepts—cannot be true or false, because, unlike propositions, which are composed of terms, they do not assert anything. If sensations and concepts cannot be true or false in the sense in which propositions or judgments are, then they lack the distinctive property of knowledge or opinion. In contrast, propositions or judgments—which are supposed to be principles, whether axioms or assumptions—can be treated as themselves expressions of knowledge or opinion, not merely as its starting points or sources.

THE TWO DEGREES of skepticism previously mentioned apply only to those principles of knowledge which are themselves capable of being regarded as knowledge or opinion and hence as either true or false.

We have already considered the skepticism of those who, admitting that the truth of some propositions can be immediately recognized by the mind, nevertheless deny that such self-evident truths describe reality. This may or may not be accompanied by a further depreciation of axioms on the ground that they are merely analytical propositions and hence trifling, uninstructive, or tautological.

The chapter on JUDGMENT considers the issue which revolves around the derogatory use of such words as “tautology” or “truism” to designate self-evident truths. Though the invidious connotation of the word “truism” does not make the truth to which this epithet is applied any less true, the dignity of a truth does seem to be affected by the refusal to regard it as a statement of reality. Furthermore, a certain degree of skepticism results from such refusal. Hume exemplifies this. He holds that self-evident truths are possible only in mathematics, which deals not with matters of fact, but with the relations between our own ideas. In consequence, he denies to the study of nature the certitude or demonstrative character which he finds in mathematical science. Since physics is concerned with real existences, no axioms or self-evident principles are available to it; and so, according to Hume, it cannot demonstrate its conclusions, but must advance them as probabilities.

A more thorough-going skepticism seems to consist in holding that there are absolutely no matters at all about which men have axiomatic knowledge. This appears to be the position of Montaigne. No truths are self-evident. None commands the universal assent of mankind; none belongs to the nature of the mind so that all men must agree to it. Montaigne almost holds it to be axiomatic that there are no axioms, for if there were, he says, “there would be some one thing to be found in the world… that would be believed by men with an universal consent; but this, that there is no one proposition that is not debated and controverted amongst us, or that may not be, makes it very manifest that our natural judgment does not very clearly comprehend what it embraces.”

If it is objected that, in the absence of such principles, there is no starting point or foundation for science, Montaigne seems willing to accept the consequence. He does not flinch from an infinite regression of reasons. “No reason,” he writes, “can be established but upon the foundation of another reason; and so run back to all infinity.” To those who say that there is no disputing with persons who deny principles, he replies that “men can have no principles, if not revealed to them by the Divinity; of all the rest, the beginning, the middle, and the end are nothing but dream and vapor.”

If, however, for practical purposes, a beginning must be made somewhere, Montaigne suggests that it can be done by taking things for granted and then getting others to grant our presuppositions. “It is very easy,” he writes, “upon granted foundations to build whatever we please… By this way, we find our reason well-grounded and discourse at a venture; for our masters prepossess and gain beforehand as much room in our belief as is necessary for them towards concluding afterwards what they please, as geometers do by their postulates; the consent and approbation we allow them giving them power to draw us to the right and left, and to whirl us about at their own pleasure.”

IF THE ONLY principles upon which reasoning can be based or from which conclusions can be drawn are assumptions, postulates, or hypotheses rather than axioms, then everything is a matter of opinion and probability; nothing can have the certitude of knowledge. As indicated in the chapters on KNOWLEDGE and OPINION, one theory of that distinction makes knowledge an act of the mind independent of our wishes or will and treats opinion as a judgment voluntarily accepted or rejected. Accordingly, assumptions or postulates are perfectly representative of opinion, and axioms express the very essence of knowledge. To assume or postulate anything is to take it for granted—voluntarily! A postulate neither compels assent, nor does it ever exclude the possibility of taking the opposite for granted. Where men make postulates, there dispute is possible. But to assert something as an axiom is to command assent on the ground that its opposite can be immediately recognized as impossible. No proposition can be regarded as an axiom if its acceptance or rejection is in any way a matter of choice.

For Aristotle the area in which men can dispute with some reason on both sides belongs to what he calls “dialectic,” whereas what he calls “science” is the area from which dispute is excluded by demonstrations which rest on self-evident truths. One is the area of probability and opinion; the other, of certainty and knowledge. Contrary assumptions are the starting point of dialectical argument, whereas science begins with axioms. These may be the first principles which Aristotle and Bacon call “common notions” because they are common to diverse sciences; or they may be the axioms peculiar to a single subject matter.

The word “dialectic” is used by Plato in a quite different sense. It names the highest science. Whereas the mathematical sciences start from hypotheses which require further support, dialectic—in the conception of Plato—rises to the first principles of all knowledge. In the hierarchical ordering of the sciences, Plato’s dialectic, Aristotle’s metaphysics, and Bacon’s philosophia prima seem to occupy respectively the same primary position and to perform the same function in virtue of being the discipline which contemplates or considers the absolutely first or most universal principles. For Bacon, as for Aquinas, the only higher science is sacred theology, whose principles are articles of supernatural faith, not axioms of reason.

These matters are more fully discussed in the chapters on DIALECTIC, METAPHYSICS, and THEOLOGY; questions concerning different kinds of principles or the principles of different sciences are considered in HYPOTHESIS and LOGIC. The chapter on INDUCTION, furthermore, discusses the inductive origin of axioms, as well as the disagreement between Bacon and Aristotle on the point of whether the highest axioms or first principles are immediately intuited from the particulars of experience, or are reached only through intermediate stages of generalization.

Since axioms are indemonstrable, they cannot be derived by reasoning as conclusions from any truths prior to themselves. Their indemonstrability is regarded by Aristotle and Pascal as a virtue rather than a defect, for if they were demonstrable, they could not be the principles or starting points of demonstration. If there were no axioms, then nothing could be demonstrated, because everything in turn would require proof in an endless regression.

To the ancient counterparts of the skeptical Montaigne, Aristotle replies that unless the law of contradiction is an indisputable axiom, any form of reasoning, even probable reasoning from assumptions, is impossible. The principle which underlies all disputation cannot itself be disputed. To those who, with skeptical intent, insist upon having everything demonstrated before they will accept it, Aristotle offers an indirect defense of the law of contradiction by asking the questioner to try denying that self-evident principle without reducing himself to absurdity.

Those who acknowledge the existence of axioms generally agree that they are indemonstrable truths, but some, like Descartes and Kant, do not agree that they are inductions from experience. The alternatives seem to be that axioms are innate possessions of the intellect or that they are transcendental a priori principles of pure reason, independent of experience. Yet Locke, who denies innate ideas and principles, or anything prior to experience, does not treat what he calls self-evident maxims as inductions from experience. They are rather direct perceptions of agreement or disagreement among the ideas we have acquired through experience.

Aquinas, who, no less than Locke, denies innate ideas and insists upon sense-experience as the source of all human knowledge, refers to the assent we give first principles as a natural habit of the mind—the intellectual virtue he calls “understanding,” equivalent to what Aristotle calls “intuitive reason.” As the chapter on HABIT indicates, axioms are called “natural” truths, not in the sense of being innate, instinctive, or congenital, but only in the sense that if the human reason functions naturally or normally it will come to recognize these truths. Again, like Locke, Aquinas seems to be saying that the truth of axioms is perceived by the human understanding as soon as their terms are known, but he does not concur with Locke in thinking that therefore such truths hold only for relations between our own ideas.

THE THEORY OF the possession of principles by natural habit has, for Aquinas, more than a verbal connection with the theory of natural law. Of the various meanings of the phrase “natural law” which are distinguished in the chapter on LAW, we are here concerned with what both Kant and Aquinas conceive as the moral law whose precepts are the fundamental principles of human conduct. Both also speak of the precepts of the natural law or the moral law as the first principles of man’s practical reason.

For Aquinas, these principles are primary in the order of practical truth and the moral sciences, as metaphysical first principles are primary in the order of speculative truth and the theoretic sciences. “The precepts of the natural law,” he writes, “are to the practical reason what the first principles of demonstration are to the speculative reason, because both are self-evident principles.” As the proposition that “the same thing cannot be affirmed and denied at the same time” is the first principle of the speculative reason, so “the first precept of law, that good is to be done, and evil is to be avoided,” is the first principle of the practical reason.

For Kant, the principles of the pure practical reason, which legislate a priori for the realm of freedom, play an analogous role to the principles of the pure speculative reason, which legislate a priori for the realm of nature or experience. It is this parallelism between the two sets of principles which Kant seems to have in mind when he conceives a metaphysic of nature and a metaphysic of morals as twin disciplines founded on the speculative and the practical employment of the transcendental principles of pure reason.

The same fundamental issues which we have considered in connection with the axioms of theoretic knowledge occur here in connection with the first principles of moral knowledge. Aquinas and Kant disagree, for example, about the way in which we come into possession of these principles. For Kant, the principles of morality, like the principles of nature, belong to the transcendental structure of pure reason itself. For Aquinas, as already suggested, the precepts of the natural law are known in the same way as the axioms of the speculative reason. As the truth of the principle of contradiction is known when we understand the meaning of ‘is’ and ‘not,’ so the truth of the first command of natural law—‘Seek the good’—is known when we understand the meaning of ‘seek’ and ‘good.’ We hold such truths by the natural habit of our minds, which in the case of the natural law is given the special name of synderesis.

Just as we find a certain skepticism with regard to the principle of contradiction and other axioms, so we find doubts about the existence of natural law, or about indisputable and universally acceptable principles of morality. Referring to those who think that there are some laws “first, perpetual, and immutable, which they call natural that are imprinted in mankind by the condition of their own proper being,” Montaigne declares that “the only sign by which they can argue or infer some laws to be natural is the universality of approbation”; and he adds: “Let them produce me but one of this condition.”

The consequences of skepticism are here the same as before. Without first principles, moral science either fails entirely or is reduced to systems of belief based upon one set of assumptions or another. In either case, moral judgments express, not knowledge, but opinion. As John Stuart Mill observes, the utilitarians must, despite all other differences, agree with Kant that if there is to be a science of ethics, “morality must be deduced from principles,” and ultimately from one first principle, for “if there be several, there should be a determinate order of precedence among them.”

What Mill says concerning the self-evidence of the first principle of morality—which he formulates as a statement of the ultimate end of human conduct—closely resembles what Aristotle says about the self-evidence of the law of contradiction. “Questions of ultimate ends are not amenable to direct proof,” Mill writes. “To be incapable of proof by reasoning is common to all first principles: to the first premises of our knowledge, as well as to those of our conduct.”

OUTLINE OF TOPICS

Principles in the order of reality 1a. The differentiation of principle, element, and cause 1b. The being, number, and kinds of principles in the order of reality 1c. The metaphysical significance of the principles of thought
The kinds of principles in the order of knowledge 2a. The origin of knowledge in simple apprehensions (1) Sensations or ideas as principles (2) Definitions as principles (3) Indefinables as principles of definition 2b. Propositions or judgments as principles (1) Immediate truths of perception: direct sensitive knowledge of appearances; evident particular facts (2) Immediate truths of understanding: axioms or self-evident truths; a priori judgments as principles (3) Constitutive and regulative principles: the maxims of reason
First principles or axioms in philosophy, science, dialectic 3a. Principles and demonstration (1) The indemonstrability of axioms: natural habits of the mind (2) The indirect defense of axioms (3) The dependence of demonstration on axioms: the critical application of the principles of identity and contradiction 3b. Principles and induction: axioms as intuitive inductions from experience; stages of inductive generalization 3c. Axioms in relation to postulates, hypotheses, or assumptions (1) The distinction between first principles in general, or common notions, and the principles of a particular subject matter or science (2) The difference between axioms and assumptions, hypotheses and principles, as a basis for the distinction between knowledge and opinion, or science and dialectic (3) The distinction and order of the sciences according to the character of their principles
First principles in the practical order: the principles of action or morality; the principles of the practical reason 4a. Ends as principles, and last ends as first principles: right appetite as a principle in the practical order 4b. The natural moral law and the categorical imperative
The skeptical denial of first principles or axioms: the denial that any propositions elicit the universal assent of mankind

REFERENCES

To find the passages cited, use the numbers in heavy type, which are the volume and page numbers of the passages referred to. For example, in 4 Homer: Iliad, IX, 11 [265-283] 12d, the number 4 is the number of the volume in the set; the number 12d indicates that the passage is in section d of page 12.

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Author’s Divisions: One or more of the main divisions of a work (such as Part, Bk, Ch, Sect) are sometimes included in the reference; line numbers, in brackets, are given in certain cases; e.g., Iliad, Bk 11 [265-283] 12d.

Bible References: The references are to book, chapter, and verse. When the King James and Douay versions differ in title of books or in the numbering of chapters or verses, the King James version is cited first and the Douay, indicated by a (D), follows; e.g., OLD TESTAMENT: Nehemiah, 7:45—(D) I Esdras, 7:46.

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For additional information concerning the style of the references, see the Explanation of Reference Style; for general guidance in the use of The Great Ideas, consult the Preface.

1. Principles in the order of reality

1a. The differentiation of principle, element, and cause

7 Plato: Timaeus, 455d
8 Aristotle: Physics, Bk. I, Ch. 1 [184a10-16] 259a / Generation and Corruption, Bk. II, Ch. 1 [329a24-b2] 429a-b / Metaphysics, Bk. I, Ch. 6 [987b19-23] 505d; Bk. III, Ch. 3 [998b20-999a13] 517a-b; Bk. V, Ch. 1-3 533a-534d; Ch. 24 545a-b; Bk. VII, Ch. 16 [1040b18-23] 564d; Ch. 17 565a-566a,c esp [1041b26-33] 566a,c; Bk. VIII, Ch. 3 [1043b5-14] 567d-568a; Bk. XII, Ch. 1 598a-c; Ch. 4-5 599d-601a esp Ch. 4 [1070b22-35] 600b
19 Aquinas: Summa Theologica, Part I, Q. 33, A. 1, Rep. 1 180d-181c; Q. 42, A. 3, Ans. and Rep. 2 227a-d; Q. 105, A. 6, Ans. 543b-544a
31 Descartes: Objections and Replies, 159a
45 Lavoisier: Elements of Chemistry, Pref., 3d-4a

1b. The being, number, and kinds of principles in the order of reality

7 Plato: Phaedo, 240b-246c / Republic, Bk. III, 333c-d; Bk. VI, 383d-388a / Timaeus, 455c-458b / Sophist, 564d-574c / Philebus, 610d-613a; 615c-617d
8 Aristotle: Physics, Bk. I 259a-268d; Bk. III, Ch. 4 [203a2-14] 281b-c; Bk. IV, Ch. 1 [208b8-209a2] 287b-c; Bk. VI, Ch. 5 318a-319c / On the Heavens, Bk. I, Ch. 2 359d-360d; Bk. III, Ch. 3-5 393c-396a / Metaphysics, Bk. I, Ch. 3-10 501c-511d; Bk. III, Ch. 2 512b-513b; Ch. 1 [995b13-996a17] 514a-c; Ch. 2 [997a34]-Ch. 6 [1003a17] 516a-522a,c; Bk. V, Ch. 3-4 534c-535c; Bk. VII-XIV 550b,d-626d / On the Soul, Bk. I, Ch. 2 [404b30-405b31] 634a-635a
10 Galen: Natural Faculties, Bk. I, Ch. 3 168c-169a
12 Lucretius: On the Nature of Things, Bk. I [146-264] 2d-4b; [418-448] 6b-c
17 Plotinus: Second Ennead, Tr. IX, Ch. 1 65d-66d / Fourth Ennead, Tr. VII, Ch. 9 198b-d / Fifth Ennead, Tr. I, Ch. 4 209d-210c; Tr. III, Ch. 1 214c-215a; Tr. IV 226d-228b / Sixth Ennead, Tr. I-III 252a-297b; Tr. VIII, Ch. 7-8 345d-347a; Tr. IX 353d-360d passim
19 Aquinas: Summa Theologica, Part I, Q. 2, A. 3 12c-14a; Q. 3, A. 5, Ans. 17c-18b; Q. 6, Ans. and Rep. 2 18c-19a; Q. 14, A. 11, Rep. 1 84c-85c; Q. 25, A. 1 143d-144c; Q. 27 153a-157c; Q. 33, A. 1 180d-181c; A. 3, Rep. 1 182c-183c; Q. 42, AA. 2-3 225d-227d; Q. 44 238a-241d; Q. 49 264d-268a,c esp A. 3 266d-268a,c; Q. 75, A. 1, Ans. 378b-379c; Q. 77, A. 5, Rep. 1-2 403d-404c; A. 6 404c-405c; Q. 84, A. 2, Ans. and Rep. 3 442b-443c; A. 4, Rep. 1 444d-446b; Q. 115, A. 2 587c-588c
31 Descartes: Discourse on the Method, Part VI, 61d-62c
31 Spinoza: Ethics, Part II, Prop. 10, Schol. 376d-377a
34 Newton: Mathematical Principles of Natural Philosophy, 1b-2a; Law I-III 14a-b; Bk. III, General Scholium, 371b-372a / Optics, Bk. III, 541b-542a
42 Kant: Critique of Pure Reason, 66d-93c esp 68a-74b, 85d-88a; 108a-112d esp 110a-d / Critique of Judgement, 467d-470b; 565b-d; 566d-567a; 575b-578a
45 Lavoisier: Elements of Chemistry, Pref., 3b-4a
45 Fourier: Analytical Theory of Heat, 169a-b
53 James: The Principles of Psychology, 882a-884b

1c. The metaphysical significance of the principles of thought

7 Plato: Euthydemus, 72d-73b / Republic, Bk. IV, 350d-351b
8 Aristotle: On Interpretation, Ch. 13 [22a8-23a26] 34d-35c / Metaphysics, Bk. III, Ch. 1 [995b6-10] 514a; Ch. 2 [996b26-997a15] 515b-d; Bk. IV, Ch. 3 524b-525a; Bk. XI, Ch. 1 [1059a23-26] 587a
20 Aquinas: Summa Theologica, Part I-II, Q. 94, A. 2, Ans. 221d-223a
31 Descartes: Discourse on the Method, Part IV, 52a / Objections and Replies, Def. III 130b; Axiom V 131d-132a
31 Spinoza: Ethics, Part II, Prop. 10, Schol. 376d-377a; Prop. 37-40 386b-388b; Prop. 44, Corol. 2 390a
35 Locke: An Essay Concerning Human Understanding, Bk. IV, Ch. VII, Sect. 10-11 339b-342d
42 Kant: Critique of Pure Reason, 15c-16c; 59c-107b / Preface to the Metaphysical Elements of Ethics, 367d-368a / Critique of Judgement, 543d-544a; 560c; 562a-d; 600d-601d; 603b-c
46 Hegel: The Philosophy of Right, Pref., 6c
53 James: The Principles of Psychology, 302a-b; 671a-672a; 852a; 862a-866a; 873a-874a; 881b-886a esp 881b-882a, 884b-886a; 890a
54 Freud: New Introductory Lectures on Psycho-Analysis, 877b-c

2. The kinds of principles in the order of knowledge

2a. The origin of knowledge in simple apprehensions

2a(1) Sensations or ideas as principles

7 Plato: Symposium, 167a-b / Phaedo, 228a-230c / Republic, Bk. VII, 392b-393b / Theaetetus, 517b-536b / Seventh Letter, 810d
8 Aristotle: Posterior Analytics, Bk. I, Ch. 18 111b-c / Metaphysics, Bk. I, Ch. 1 [980a28-b24] 499a
12 Lucretius: On the Nature of Things, Bk. I [422-425] 6b; [693-700] 9c; Bk. II [434-436] 20c; Bk. IV [353-521] 48d-51a esp [469-521] 50b-51a
19 Aquinas: Summa Theologica, Part I, Q. 12, A. 12, Ans. 60d-61c; Q. 17, A. 1, Ans. 100d-101d; Q. 18, A. 2, Ans. 105c-106b; Q. 84, A. 6 447c-449a; A. 8, Ans. and Rep. 1 450b-451b; Part I-II, Q. 14, A. 6, Ans. 680c-681a
23 Hobbes: Leviathan, Part I, 49a
28 Gilbert: On the Loadstone, Bk. V, 105c
28 Harvey: On Animal Generation, 332a-335c esp 334c-d
35 Locke: An Essay Concerning Human Understanding, Bk. I, Ch. I, Sect. 15 98d-99a; Bk. II, Ch. I, Sect. 1-8 121a-123a esp Sect. 2 121b-c; Sect. 23-25 127b-d esp Sect. 24 127b-c; Ch. II, Sect. 2 128a-b; Ch. VII, Sect. 10 133a-b; Ch. XII, Sect. 1-6 148d-149d esp Sect. 2 149a; Ch. XIV, Sect. 2 155b-c; Sect. 27 160d-161a; Sect. 30-31 161c-162a; Ch. XV, Sect. 2-3 162c-d; Ch. XVII, Sect. 22-Ch. XVIII, Sect. 1 173d-174a; Ch. XVIII, Sect. 6 174c-d; Ch. XXI, Sect. 9 202c-203a; Bk. III, Ch. I, Sect. 5 252b-c; Ch. IV, Sect. 12-14 262b-263a
35 Berkeley: The Principles of Human Knowledge, Intro., 405a-412a,c passim, esp Sect. 4 405c-d, Sect. 17 409d-410a
35 Hume: An Enquiry Concerning Human Understanding, Sect. II 455b-457b; Sect. VII, Div. 49 471c-d
42 Kant: Critique of Pure Reason, 14a-22a,c; 66d-72c esp 69c-72c; 101b-107b
53 James: The Principles of Psychology, 452a-459b esp 453b-454a, 455a-457a; 480a
54 Freud: The Ego and the Id, 701d

2a(2) Definitions as principles

7 Plato: Phaedrus, 134b-d; 140a-b / Meno, 174a-179b / Theaetetus, 544c-549d / Seventh Letter, 809c-810d
8 Aristotle: Posterior Analytics 97a-137a,c passim, esp Bk. I, Ch. 3 [72b18-24] 99b-c, Ch. 10 [76b35-77a4] 105c-d, Ch. 22 [84a6-b2] 114d-115b, Ch. 23 [84b19-85a3] 115c-116a, Bk. II, Ch. 3-10 123c-128d / Topics, Bk. VII, Ch. 3 [153a6-11] 208a-b; Bk. VIII, Ch. 3 [158b31-159a2] 214d-215c / Metaphysics, Bk. III, Ch. 2 [996b18-21] 515b; Bk. IV, Ch. 7 [1012a18-24] 532a-b; Ch. 8 [1012b5-8] 532c; Bk. VII, Ch. 10 [1036a1-8] 559b-c; Bk. XIII, Ch. 4 [1078b17-30] 610b-c / On the Soul, Bk. I, Ch. 1 [402b15-403a2] 631d-632a
19 Aquinas: Summa Theologica, Part I, Q. 2, A. 2 Rep. 2 11d-12c; Q. 17, A. 3, Rep. 1-2 102d-103c; Q. 58, A. 5 303c-304c; Q. 85, A. 6 458d-459c
20 Aquinas: Summa Theologica, Part I-II, Q. 94, A. 2, Ans. 221d-223a
23 Hobbes: Leviathan, Part I, 56b-d; 58d-59c; 65d; Part IV, 269b-c
31 Descartes: Objections and Replies, 128c
33 Pascal: On the Geometrical Demonstration, 430b-431b
35 Locke: An Essay Concerning Human Understanding, Bk. III, Ch. IX, Sect. 15-16 288d-289c; Ch. XI, Sect. 15-17 303b-304a; Bk. IV, Ch. III, Sect. 20, 319b
42 Kant: Critique of Pure Reason, 215b-217a
46 Hegel: The Philosophy of Right, Intro., Par. 2 9b-10a
54 Freud: Instincts and Their Vicissitudes, 412a-b

2a(3) Indefinables as principles of definition

7 Plato: Theaetetus, 544c-547c
8 Aristotle: Metaphysics, Bk. I, Ch. 9 [992b24-993a1] 511a-b; Bk. III, Ch. 2 [994b16-27] 513a-b; Bk. V, Ch. 3 [1014b3-13] 534d; Bk. VIII, Ch. 3 [1043b28-33] 568b
33 Pascal: On the Geometrical Demonstration, 431b-434a; 442a-443b
35 Locke: An Essay Concerning Human Understanding, Bk. III, Ch. II, Sect. 2 128a-b; Ch. VII, Sect. 10 133a-b; Ch. XI 147b-148d; Ch. XVI, Sect. 1 174a; Sect. 6 174c-d; Bk. III, Ch. IV, Sect. 12-14 262b-263a
42 Kant: Critique of Pure Reason, 215d-216c
44 Boswell: The Life of Samuel Johnson, 82b

2b. Propositions or judgments as principles

2b(1) Immediate truths of perception: direct sensitive knowledge of appearances; evident particular facts

8 Aristotle: Posterior Analytics, Bk. I, Ch. 18 111b-c; Ch. 23 [84b19-85a1] 115c-116a; Bk. II, Ch. 2 [90a24-30] 123b-c; Ch. 19 136a-137a,c / On the Heavens, Bk. I, Ch. 7 [306a1-18] 397b-c / Metaphysics, Bk. I, Ch. 1 [981b10-13] 499d-500a; Ch. 9 [992b24-993a1] 511a-b; Bk. IV, Ch. 5 [1010b14-26] 530b-c; Bk. VII, Ch. 10 [1036a1-8] 559b-c; Bk. XI, Ch. 6 [1062b33-1063a9] 591a-b
9 Aristotle: Nicomachean Ethics, Bk. I, Ch. 4 [1095b30-1096a12] 340c-d; Ch. 7 [1098a35-b3] 343d; Bk. II, Ch. 9 [1109b20-23] 355c; Bk. III, Ch. 3 [1112b34-1113a2] 358d-359a; Bk. VI, Ch. 11 [1143a25-b6] 392d-393a; Bk. VII, Ch. 3 [1147a25-b6] 397c-d; Bk. X, Ch. 1 [1172a34-b9] 426b-c; Ch. 8 [1179a16-23] 433d-434a
12 Lucretius: On the Nature of Things, Bk. I [693-700] 9c; Bk. IV [469-521] 50b-51a
19 Aquinas: Summa Theologica, Part I-II, Q. 14, A. 6, Ans. 680c-681a
28 Harvey: On Animal Generation, 332a-335c
31 Descartes: Objections and Replies, 229d-230d
35 Locke: An Essay Concerning Human Understanding, Bk. I, Ch. I, Sect. 15-19 98d-100c esp Sect. 19 100b-c; Sect. 23 101b-102a; Bk. IV, Ch. I, Sect. 4 307b-c; Ch. II, Sect. 1 309b-d; Ch. III, Sect. 21 319c; Ch. VII, Sect. 4 337b-338b; Sect. 9-10 338d-340a; Sect. 11, 342c-d; Ch. XI 354c-358c; Ch. XII, Sect. 3 358d-359c
35 Hume: An Enquiry Concerning Human Understanding, Sect. V, Div. 37 465c-466a
42 Kant: Critique of Pure Reason, 66d-72c esp 67d-68a / Critique of Practical Reason, 351c
43 Mill: Utilitarianism, 445d-446a; 461c
53 James: The Principles of Psychology, 867a-868b

2b(2) Immediate truths of understanding: axioms or self-evident truths; a priori judgments as principles

8 Aristotle: Posterior Analytics, Bk. I, Ch. 2 [72a7-9] 98c; [72a15-19] 98c-d; Ch. 3 99b-100a; Ch. 15 109a-b; Bk. II, Ch. 9 128a-b / Metaphysics, Bk. III, Ch. 2 [996b26-997a14] 515b-d; Bk. IV, Ch. 3 [1005b23-34] 524d-525a
9 Aristotle: Nicomachean Ethics, Bk. VI, Ch. 6 389d; Ch. 8 [1142a25-29] 391b-c; Ch. 11 [1143a25-b13] 392d-393a / Rhetoric, Bk. I, Ch. 2 [1356a26-28] 596b
19 Aquinas: Summa Theologica, Part I, Q. 2, A. 1, Ans. 10d-11d; Q. 17, A. 3, Rep. 2 102d-103c; Q. 84, A. 3, Rep. 3 443d-444d; Q. 85, A. 6, Ans. 458d-459c; Q. 87, A. 1, Rep. 1 465a-466c; Q. 117, A. 1, Ans. and Rep. 1,3 595d-597c; Part I-II, Q. 1, A. 4, Rep. 2 612a-613a; A. 5, Ans. 613a-614a
20 Aquinas: Summa Theologica, Part I-II, Q. 57, A. 2 36a-37b; Q. 90, A. 2, Rep. 3 206b-207a; Q. 91, A. 3, Ans. 209d-210c; Q. 94, A. 2, Ans. 221d-223a; A. 4, Ans. 223d-224d; Part II-II, Q. 8, A. 1, Rep. 2 417a-d
25 Montaigne: Essays, 260c-261a
30 Bacon: The Advancement of Learning, 61d
31 Descartes: Rules for the Direction of the Mind, III, 4a-d; IV, 5c-d; 6d; VI, 8d-9a; VII, 13c-d; XII, 23c / Discourse on the Method, Part IV, 51b-52a / Meditations on First Philosophy, V, 95a-96a / Objections and Replies, 123a-b; 125a-b; 224b,d
33 Pascal: Pensées, 1 171a-172a
35 Locke: An Essay Concerning Human Understanding, Bk. I 95b,d-121a,c esp Ch. I, Sect. 15-19 98d-100c, Sect. 23 101b-102a, Ch. II, Sect. 21-27 111a-112c, Ch. III, Sect. 23 119b-120a; Bk. IV, Ch. I, Sect. 4 307b-c; Ch. II, Sect. 1 309b-d; Sect. 7-8 310d-311a; Ch. VII 337a-344d esp Sect. 1 337a, Sect. 10-11 339b-342d; Ch. IX, Sect. 2-3 349a-c; Ch. XII, Sect. 1-6 358c-360a; Sect. 12, 362b-c; Sect. 15 363a-b; Ch. XVII, Sect. 14-17 378c-379c; Ch. XX, Sect. 7-10 390d-392a
42 Kant: Critique of Pure Reason, 31a-d; 64d-93c esp 64d-66d, 68a-74b, 85d-88a; 211c-218d; 225a-227a / Fundamental Principles of the Metaphysic of Morals, 268b-d; 279c-d / Critique of Practical Reason, 295b-d; 329d-330c / Critique of Judgement, 542d-543a
43 Declaration of Independence: [7-15] 1a-b
43 The Federalist: Number 31, 103c-104a; Number 83, 244b-c
43 Mill: Utilitarianism, 445d-447a; 458d-459c
53 James: The Principles of Psychology, 319b-320a; 869a-879b passim, esp 869a-870a, 872b

2b(3) Constitutive and regulative principles: the maxims of reason

42 Kant: Critique of Pure Reason, 72c-74b esp 73c-74a; 109d-112d; 194b-c; 199c-209d esp 199c-200c, 201d-202a, 206a-207b / Critique of Practical Reason, 343a; 349b-355d / Introduction to the Metaphysic of Morals, 390b; 392b-d / Critique of Judgement, 550a-551a,c; 562a-d; 570b-572c; 577b; 578a-d

3. First principles or axioms in philosophy, science, dialectic

3a. Principles and demonstration

3a(1) The indemonstrability of axioms: natural habits of the mind

8 Aristotle: Prior Analytics, Bk. I, Ch. 16 [64b28-38] 85c / Posterior Analytics, Bk. I, Ch. 3 99b-100a / Metaphysics, Bk. III, Ch. 2 [996b26-997a14] 515b-d; Bk. IV, Ch. 4 [1005b35-1006a12] 525a-b; Bk. XI, Ch. 5 [1061b34-1062a5] 590a-b / On the Soul, Bk. I, Ch. 3 [407b22-30] 636d-637a
9 Aristotle: Nicomachean Ethics, Bk. VI, Ch. 3 388b-c; Ch. 6 389d; Ch. 11 [1143a25-b13] 392d-393a
19 Aquinas: Summa Theologica, Part I, Q. 14, A. 1, Rep. 2 75d-76c; Q. 16, A. 6, Rep. 1 98b-d; Q. 17, A. 3, Rep. 2 102d-103c; Q. 79, A. 12 425c-426b; Part I-II, Q. 1, A. 4, Rep. 2 612a-613a; A. 5, Ans. 613a-614a
20 Aquinas: Summa Theologica, Part I-II, Q. 53, A. 1, Ans. 19d-21a; Q. 57, A. 2, Ans. and Rep. 2 36a-37b; Q. 94, A. 1 221a-d
30 Bacon: The Advancement of Learning, 56c-59c
33 Pascal: On the Geometrical Demonstration, 440b
35 Locke: An Essay Concerning Human Understanding, Bk. I, Ch. I, Sect. 10-11 97c-98a; Ch. II, Sect. 23 119b-120a; Bk. IV, Ch. XI, Sect. 1-10 354c-357b passim, esp Sect. 10 357a-b
42 Kant: Critique of Pure Reason, 66d-72c esp 67c-69c; 211c-218d / Critique of Judgement, 542d-543a
43 The Federalist: Number 31, 103c-104a
43 Mill: Utilitarianism, 445d-447a; 461c; 465a-b
53 James: The Principles of Psychology, 851a-890a esp 851a-852a, 879b-882a, 889a-b

3a(2) The indirect defense of axioms

8 Aristotle: Metaphysics, Bk. IV, Ch. 4-8 525a-532d; Bk. XI, Ch. 5-6 590a-592b

3a(3) The dependence of demonstration on axioms: the critical application of the principles of identity and contradiction

7 Plato: Euthydemus, 72d-73b / Cratylus, 112a / Republic, Bk. IV, 350d-351b
8 Aristotle: Posterior Analytics, Bk. I, Ch. 1-3 97a-100a; Ch. 7 [75a38-b7] 103c; Ch. 11 105d-106b; Ch. 19-23 111c-116a; Ch. 32 [88a36-b4] 120d / Topics, Bk. VIII, Ch. 3 [158b31-159a4] 214d-215a / Metaphysics, Bk. III, Ch. 2 [996b26-997a14] 515b-d; Bk. IV, Ch. 3 [1005b18-27] 524b; Ch. 4 [1005b35-1006a12] 525a-b; Ch. 6 [1011b3-14] 530d; Bk. V, Ch. 5 [1015b6-9] 535d-536a; Bk. XI, Ch. 6 [1063b7-12] 591d
9 Aristotle: Nicomachean Ethics, Bk. VI, Ch. 3 388b-c; Ch. 6 389d; Ch. 11 [1143a25-b13] 392d-393a / Rhetoric, Bk. I, Ch. 2 [1356a26-28] 596b
11 Euclid: Elements, Bk. I, Common Notions 2a
19 Aquinas: Summa Theologica, Part I, Q. 14, A. 7 81d-82b; Q. 17, A. 3, Rep. 1-2 102d-103c; Q. 36, A. 3, Rep. 4 194c-195d; Q. 84, A. 3, Rep. 3 443d-444d; Q. 85, A. 6 458d-459c; Part I-II, Q. 1, A. 4, Rep. 2 612a-613a
20 Aquinas: Summa Theologica, Part I-II, Q. 90, A. 2, Rep. 3 206b-207a; Q. 94, A. 2, Ans. 221d-223a
28 Harvey: On Animal Generation, 333d-334d esp 334a
30 Bacon: The Advancement of Learning, 56c-59d
31 Descartes: Discourse on the Method, Part II, 46c-47a / Meditations on First Philosophy, III, 82b-d; V, 95b-96a / Objections and Replies, 123a-b; 125a-b; 224b,d
31 Spinoza: Ethics, Part II, Prop. 37-47 386b-391a esp Prop. 40, Schol. 1-2 387b-388b
35 Locke: An Essay Concerning Human Understanding, Bk. IV, Ch. I, Sect. 1, 309d; Sect. 7-8 310d-311a; Ch. VII 337a-344d esp Sect. 10-11 339b-342d
42 Kant: Critique of Pure Reason, 17d-18d; 64d-65c; 68a-69c; 174b-d; 211c-218d
43 The Federalist: Number 31, 103c-104a
44 Boswell: The Life of Samuel Johnson, 82b
46 Hegel: The Philosophy of Right, Additions, 3 116a

3b. Principles and induction: axioms as intuitive inductions from experience; stages of inductive generalization

8 Aristotle: Prior Analytics, Bk. II, Ch. 23 90a-c / Posterior Analytics, Bk. I, Ch. 18 111b-c; Bk. II, Ch. 2 [90a24-30] 123b-c; Ch. 7 [92a34-b1] 126b; Ch. 19 136a-137a,c
9 Aristotle: Nicomachean Ethics, Bk. VI, Ch. 3 388b-c; Ch. 6 389d; Ch. 11 [1143a25-b13] 392d-393a
28 Harvey: On Animal Generation, 333d-334d esp 334c-d
30 Bacon: The Advancement of Learning, 56c-59c; 96d-97a / Novum Organum 105a-195d esp Pref. 105a-106d, Bk. I, Aph. 11-26 107d-108d, Aph. 36-38 109b-c, Aph. 63 113d-114a, Aph. 66 114d-115c, Aph. 69-70 116a-117a, Aph. 94 126a-b, Aph. 103-106 127d-128c, Bk. II, Aph. 1-10 137a-140d, Aph. 15-16 149a-b, Aph. 20-22 150d-153c, Aph. 52 194c-195d
31 Descartes: Objections and Replies, 123a-b; 167c-d
35 Locke: An Essay Concerning Human Understanding, Bk. I, Ch. III, Sect. 25, 120d
35 Hume: An Enquiry Concerning Human Understanding, Sect. I, Div. 2 451b-c; Div. 9, 454d; Sect. IV, Div. 26 460b-c
42 Kant: Critique of Pure Reason, 66d-72c; 217a-c
43 Mill: Utilitarianism, 446a; 475b,d [fn 1]
46 Hegel: The Philosophy of History, Part IV, 361a-b

3c. Axioms in relation to postulates, hypotheses, or assumptions

3c(1) The distinction between first principles in general, or common notions, and the principles of a particular subject matter or science

7 Plato: Republic, Bk. VI, 383d-388a esp 386d-388a
8 Aristotle: Posterior Analytics, Bk. I, Ch. 10 104d-105d; Ch. 11 [77a26-35] 106b; Ch. 32 120c-121b / Topics, Bk. I, Ch. 2 [101a37-b4] 144a / On the Heavens, Bk. III, Ch. 7 [306a1-18] 397b-c / Metaphysics, Bk. IV, Ch. 3 [1005a15-18] 524d / On the Soul, Bk. I, Ch. 1 [402a17-23] 631b
9 Aristotle: Rhetoric, Bk. I, Ch. 2 [1358a3-33] 597d-598b
30 Bacon: The Advancement of Learning, 40a-48d esp 40a-41b, 43a-c, 44c-45a
35 Berkeley: The Principles of Human Knowledge, Sect. 118 436b-c
43 Mill: Utilitarianism, 445b-c

3c(2) The difference between axioms and assumptions, hypotheses and principles, as a basis for the distinction between knowledge and opinion, or science and dialectic

7 Plato: Republic, Bk. VI-VII, 383d-398c esp Bk. VII, 396d-398c
8 Aristotle: Posterior Analytics, Bk. I, Ch. 2 97d-99a; Ch. 11 [77a22-35] 106b / Topics, Bk. VIII, Ch. 3 [158b31-159a4] 214d-215a / Physics, Bk. VIII, Ch. 1 [252a23-b7] 336a-b / Metaphysics, Bk. IV, Ch. 2 [1004b18-27] 523d
9 Aristotle: Nicomachean Ethics, Bk. I, Ch. 3 [1094b11-28] 339d-340a / Rhetoric, Bk. I, Ch. 2 [1358a3-33] 597d-598b
19 Aquinas: Summa Theologica, Part I, Q. 12, A. 7, Ans. and Rep. 2 56a-57b; A. 13, Rep. 3 61c-62b; Q. 47, A. 1, Rep. 3 256a-257b; Q. 82, A. 2, Ans. 432d-433c; Q. 83, A. 1, Ans. 436d-438a
20 Aquinas: Summa Theologica, Part I-II, Q. 51, A. 3 14b-15a; Q. 67, A. 3, Ans. 83b-84d; Part II-II, Q. 1, A. 4, Ans. 382c-383b; Part III, Q. 9, A. 3, Rep. 2 765b-766b
23 Hobbes: Leviathan, Part I, 65b-d
25 Montaigne: Essays, 260c-261a
30 Bacon: The Advancement of Learning, 56c-59b
31 Descartes: Rules for the Direction of the Mind, I 2a-3b
34 Huygens: Treatise on Light, Pref., 551b-552a
35 Locke: An Essay Concerning Human Understanding, Bk. IV, Ch. XVII, Sect. 2 371d-372b; Sect. 15-17 378d-379c
42 Kant: Critique of Pure Reason, 217a-218c; 240b-243c / Critique of Judgement, 600d-604b

3c(3) The distinction and order of the sciences according to the character of their principles

7 Plato: Republic, Bk. VI, 386d-388a; Bk. VII, 391b-398c
8 Aristotle: Metaphysics, Bk. VI, Ch. 1 [1025b1-18] 547b,d; Bk. XI, Ch. 3 [1061a29-b4] 589c; Ch. 4 [1061b17-28] 589d-590a; Ch. 7 [1063b36-1064a9] 592b; Bk. XIII, Ch. 2 [1077a11]-Ch. 3 [1078a31] 609a-d
9 Aristotle: Nicomachean Ethics, Bk. I, Ch. 7 [1098a20-b8] 343c-344a / Rhetoric, Bk. I, Ch. 2 [1358a3-33] 597d-598b
19 Aquinas: Summa Theologica, Part I, Q. 1, A. 2, Ans. and Rep. 1 4a-c; A. 5 5c-6a; A. 6, Rep. 1-2 6b-7a
23 Hobbes: Leviathan, Part I, 71c-d; 72a-d; Part II, 163a-b
30 Bacon: The Advancement of Learning, 39d-41b
31 Descartes: Rules for the Direction of the Mind, II 2a-3b / Discourse on the Method, Part I, 43d-44a / Meditations on First Philosophy, I, 76c / Objections and Replies, 128d-129a / Geometry, Bk. I, 304a-b
35 Hume: An Enquiry Concerning Human Understanding, Sect. IV, Div. 20-21 458a-c; Div. 30, 462a
42 Kant: Critique of Pure Reason, 15c-16c; 17d-19a; 64d-65c; 68a-69c; 215d-217c / Fundamental Principles of the Metaphysic of Morals, 253a-d / Critique of Practical Reason, 351b-352c / Introduction to the Metaphysic of Morals, 388a-c / Critique of Judgement, 578a-b
43 The Federalist: Number 31, 103c-104a
43 Mill: Utilitarianism, 445b-c
53 James: The Principles of Psychology, xiiib-xiva; 884b-886a
54 Freud: On Narcissism, 400d-401a / Instincts and Their Vicissitudes, 412a-b

4. First principles in the practical order: the principles of action or morality; the principles of the practical reason

7 Plato: Gorgias, 262a-263c; 280c-d
9 Aristotle: Nicomachean Ethics, Bk. I, Ch. 3 339d-340b passim; Ch. 7 [1098a25-b8] 343d-344a; Bk. VI, Ch. 5 389a-c passim; Ch. 11 [1143a25-b13] 392d-393a; Bk. VII, Ch. 8 [1151a11-19] 401d-402a
12 Epictetus: Discourses, Bk. I, Ch. 22 127c-128c; Bk. II, Ch. 2 177c-178d; Ch. 10 185d-187a
12 Marcus Aurelius: Meditations, Bk. VII, Sect. 1 285a-b
18 Augustine: The City of God, Bk. VIII, Ch. 8 270a-d; Bk. XIX 507a-530a,c passim
20 Aquinas: Summa Theologica, Part I-II, Q. 91, A. 3, Ans. 209d-210c
23 Hobbes: Leviathan, Part I, 86c-96b; Part II, 140b; 153c-154a
31 Spinoza: Ethics, Part IV, Prop. 18, Schol. 429a-d
35 Locke: An Essay Concerning Human Understanding, Bk. I, Ch. II-III 103d-121a,c esp Ch. II, Sect. 3 104b-d, Sect. 21-27 111a-112c
38 Rousseau: A Discourse on… Inequality, 330d-331b; 343d-345c
42 Kant: Critique of Pure Reason, 190c-d; 234c-240b esp 235a-b, 238c-239a / Fundamental Principles of the Metaphysic of Morals 253a-287d esp 253d-254d, 256c-257d, 258d-259a, 260a-261d, 262a-265a, 266b-268a, 268d [fn 2], 269c, 270d-271a, 273d-280b, 280d-281a, 282b-283d, 286a-287d / Critique of Practical Reason 291a-361d esp 291b-293b, 293c-d [fn 3], 298a-300a, 304d-307d, 310b-311d, 318c-321b, 325a-328a, 329a-331a, 338c-355d / Preface to the Metaphysical Elements of Ethics, 365b-366d; 367c; 369c-373b / Introduction to the Metaphysic of Morals 383a-394a,c esp 386d-388a, 392b / The Science of Right, 397a-402a / Critique of Judgement, 463a-467a; 478a-479d; 584d-587a; 588b [fn 2]; 594c-596c
43 The Federalist: Number 31, 103c-104a
43 Mill: Utilitarianism 445a-476a,c passim, esp 445a-447b
49 Darwin: The Descent of Man, 316a-317a; 592d
53 James: The Principles of Psychology, 886b-888a
54 Freud: A General Introduction to Psycho-Analysis, 592d-593a / Beyond the Pleasure Principle, 639a-640c; 662c-663b esp 663a / Civilization and Its Discontents, 772a-b

4a. Ends as principles, and last ends as first principles: right appetite as a principle in the practical order

7 Plato: Gorgias, 262a-263c; 280c-d / Republic, Bk. VI-VII, 383d-398c esp Bk. VII, 397a-398c
8 Aristotle: Metaphysics, Bk. I, Ch. 2 [982b4-7] 500d; Bk. II, Ch. 2 [994a8-10] 512b; [994b9-16] 512d-513a; Bk. III, Ch. 2 [996a21-b13] 514d-515a; Bk. V, Ch. 1 [1013a20-24] 533b; Bk. VII, Ch. 7 [1032b28-29] 555b-d; Bk. IX, Ch. 8 [1050a3-6] 575d-576b; Bk. XII, Ch. 10 [1075a12-24] 605d-606a
9 Aristotle: Parts of Animals, Bk. I, Ch. 1 [639b10-640a12] 161d-162b / Movement of Animals, Ch. 6 [700b4]-Ch. 7 [701a39] 235d-236d / Nicomachean Ethics, Bk. I, Ch. 1-4 339a-340d esp Ch. 4 [1095b30-1096a12] 340c-d; Ch. 7 [1098a35-b8] 343d-344a; Ch. 12 [1101b34-1102a4] 347b; Bk. II, Ch. 9 [1109b20-23] 355c; Bk. III, Ch. 3 [1112b12-1113a2] 358c-359a; Bk. VI, Ch. 2 387d-388b; Ch. 5 389a-c passim; Ch. 8 [1142a12-31] 391b-c; Ch. 9 [1142b17-35] 391d-392b; Ch. 11 [1143a25-b13] 392d-393a; Ch. 12 [1144a31-37] 394a; Ch. 13 [1144b30-1145a6] 394c-d; Bk. VII, Ch. 3 [1147a25-b6] 397c-d; Ch. 8 [1151a15-19] 402a; Bk. X, Ch. 6-8 430d-434a / Politics, Bk. VII, Ch. 13 [1331b24-37] 536b-c / Rhetoric, Bk. I, Ch. 6-7 602d-607d
12 Epictetus: Discourses, Bk. III, Ch. 13-14 188b-190a
18 Augustine: The City of God, Bk. X, Ch. 1, 298b,d / On Christian Doctrine, Bk. I, Ch. 3-4 625b-c; Ch. 35 634c-d
19 Aquinas: Summa Theologica, Part I, Q. 18, A. 3, Ans. 106b-107c; Q. 19, A. 2, Rep. 2 109c-110b; A. 5, Ans. 112d-113c; Q. 22, A. 1, Rep. 3 127d-128d; Q. 25, A. 5, Ans. 147d-149a; Q. 60, A. 2, Ans. 311a-d; Q. 82, AA. 1-2 431d-433c; Q. 113, A. 1, Rep. 2 576a-d; Part I-II, Q. 1 609a-615c; Q. 8, A. 2, Ans. 656a-d; Q. 9, A. 3, Ans. 659c-660a; Q. 11, A. 3 667d-668d; Q. 12, AA. 2-4 670b-672a; Q. 13, A. 3, Ans. 674c-675a; A. 6, Rep. 1 676c-677b; Q. 14, A. 2 678b-c; A. 6, Ans. 680c-681a; Q. 15, A. 3 682c-683b; Q. 16, A. 3 685b-686a; Q. 34, AA. 3-4 770c-772b
20 Aquinas: Summa Theologica, Part I-II, Q. 56, A. 2, Rep. 3 30c-31a; A. 3, Ans. 31a-32b; A. 4, Rep. 4 32b-33c; Q. 57, A. 4, Ans. 38a-39a; A. 5, Ans. and Rep. 3 39a-40a; Q. 58, A. 3, Rep. 2 43b-44a; A. 4, Ans. and Rep. 1 44a-d; A. 5 44d-45c; Q. 65, A. 1, Ans. and Rep. 3-4 70b-72a; A. 2, Ans. and Rep. 3 72a-d; A. 3, Ans. and Rep. 1 72d-73d; Q. 90, A. 2, Rep. 3 206b-207a; Q. 91, A. 3, Ans. 209d-210c; Part II-II, Q. 26, A. 1, Ans. and Rep. 1 510c-511a; Q. 27, A. 6, Ans. 524c-525c; Q. 181, A. 2 617d-618c
23 Hobbes: Leviathan, Part I, 76c-d; Part IV, 272c
30 Bacon: The Advancement of Learning, 69d-70a
31 Spinoza: Ethics, Part I, Appendix 369b-372d; Part IV, Pref. 422b,d-424a; Def. 7 424b
33 Pascal: Pensées, 98 190b / On the Geometrical Demonstration, 440b
35 Locke: An Essay Concerning Human Understanding, Bk. II, Ch. XXI, Sect. 52-53 191d-192b; Sect. 62 194c-d
42 Kant: Critique of Pure Reason, 234c-240b esp 235a-b, 236d-237a, 238c-239a / Fundamental Principles of the Metaphysic of Morals, 253d-254d; 256a-b; 257c-d; 260a-c; 266a-267d; 271d-279d esp 274d-275b; 282b-283d; 286c-287d / Critique of Practical Reason, 318c-321b esp 320c-321b; 327d-329a; 338c-355d / Preface to the Metaphysical Elements of Ethics, 367c / Critique of Judgement, 477b-c; 478a-479d; 584d-587a; 588b [fn 2]; 591b-592a; 594b-595c
43 Mill: Utilitarianism, 445a-447b; 456a-457b; 461c-464d; 475b,d [fn 1]
51 Tolstoy: War and Peace, Bk. XII, 586d-587a
53 James: The Principles of Psychology, 796a-b

4b. The natural moral law and the categorical imperative

12 Marcus Aurelius: Meditations, Bk. III, Sect. 11 262a-b; Bk. IV, Sect. 4 264a; Bk. VII, Sect. 55 283b-c
19 Aquinas: Summa Theologica, Part I, Q. 79, A. 12 425c-426b
20 Aquinas: Summa Theologica, Part I-II, Q. 91, A. 2 208d-209d; A. 3, Ans. 209d-210c; Q. 94 220d-226b; Q. 95, A. 2 227c-228c; A. 4 229b-230c
23 Hobbes: Leviathan, Part I, 86b-87a; 91a; 95c-96b; Part II, 134c; Part III, 165a; Conclusion, 282a; 283c
30 Bacon: The Advancement of Learning, 96a-c
38 Rousseau: A Discourse on… Inequality, 330d-331b; 343d-345c
42 Kant: Critique of Pure Reason, 190c-d; 235a-b / Fundamental Principles of the Metaphysic of Morals, 253d-254d; 260a-261d; 265c-266d; 268c-270c esp 269c; 273d-287d esp 277d-279d, 282a-287b / Critique of Practical Reason, 297a-314d esp 307d-314d; 321b-329a esp 327a-329a / Preface to the Metaphysical Elements of Ethics, 373d / Introduction to the Metaphysic of Morals, 386b-387a,c; 388b-c; 390b,d-391c; 392b-393a / The Science of Right, 400b,d-402a; 416b-417b / Critique of Judgement, 571c-572a; 594b-595c; 604d-606d esp 605d-606b [fn 2], 606a-d
43 Mill: Utilitarianism, 445d-446d; 458b-459c; 464d-465b; 469d-470b
46 Hegel: The Philosophy of Right, Intro., Par. 29 19a-b; Part II, Par. 135 47b-d; Additions, 84 129b; 86 129c
49 Darwin: The Descent of Man, 304a

5. The skeptical denial of first principles or axioms: the denial that any propositions elicit the universal assent of mankind

7 Plato: Euthydemus, 72d-73a / Theaetetus, 532b-c
8 Aristotle: Posterior Analytics, Bk. I, Ch. 3 [72b5-18] 99b / Metaphysics, Bk. IV, Ch. 5-6 528c-531c; Bk. X, Ch. 1 [1053a31-b3] 580a; Ch. 6 [1057a7-11] 584b; Bk. XI, Ch. 6 [1062b12-1063a14] 590d-592a
12 Lucretius: On the Nature of Things, Bk. IV [469-477] 50b
12 Epictetus: Discourses, Bk. II, Ch. 20, 164c
18 Augustine: The City of God, Bk. XIX, Ch. 18 523a-b
25 Montaigne: Essays, 259d-261a; 271b-272d; 281a-284c
30 Bacon: The Advancement of Learning, 57d-58b
35 Berkeley: The Principles of Human Knowledge, Intro., Sect. 1-3 405a-c
35 Hume: An Enquiry Concerning Human Understanding, Sect. IV, Div. 26 460b-c; Sect. XII 503c-509d
42 Kant: Critique of Pure Reason, 224a-227a / Critique of Practical Reason, 294c-295d

CROSS-REFERENCES

For: Another discussion of principle in relation to element and cause, see ELEMENT 2.

For: The consideration of the laws of identity and contradiction as both logical and metaphysical principles, see LOGIC 1a; METAPHYSICS 3c; OPPOSITION 2a; TRUTH 3c; and for the treatment of contraries as principles, see CHANGE 2b; DIALECTIC 3d; OPPOSITION 2b, 3a.

For: Discussions bearing on sensations, ideas, and definitions as principles of knowledge, see DEFINITION 1c, 5; IDEA 1c, 2f; KNOWLEDGE 3; MEMORY AND IMAGINATION 1a; SENSE 5a.

For: The analysis of evident or self-evident truths, or of immediate as opposed to demonstrated propositions, see JUDGMENT 8a; KNOWLEDGE 6c(2); SENSE 4b; TRUTH 3b(3); and for the distinction between analytic and synthetic judgments a priori, and between constitutive and regulative principles, see IDEA 1d; JUDGMENT 8b-8d.

For: The conception of axiomatic knowledge as a natural habit of the mind and as one of the intellectual virtues, see HABIT 5c; VIRTUE AND VICE 2a(2).

For: The dependence of demonstration on axioms or self-evident truths, see INFINITY 2c; REASONING 5b(1); TRUTH 3c; and for the nature of reductio ad absurdum arguments in defense of axioms, see REASONING 4d.

For: Induction as the source of axioms, see INDUCTION 3.

For: Other discussions of the distinction between axioms and postulates, hypotheses, or assumptions, and for the bearing of this distinction on the difference between knowledge and opinion, or science and dialectic, see DIALECTIC 2a(2), 4; HYPOTHESIS 3-4; KNOWLEDGE 4b; MATHEMATICS 3a; OPINION 2c; TRUTH 4c; WILL 3b(1).

For: The principles of the several theoretic sciences, see ASTRONOMY 2b; DEFINITION 6a; LOGIC 1d; MATHEMATICS 3a; MECHANICS 2b; METAPHYSICS 2b, 3c; PHILOSOPHY 3b; PHYSICS 1b, 2a; TRUTH 4c.

For: The consideration of ends as principles in the practical order or in moral and political science, see GOOD AND EVIL 5c; GOVERNMENT 1c; HAPPINESS 3; MIND 9a; NECESSITY AND CONTINGENCY 5a(2); ONE AND MANY 5b; RELATION 5a(2); TRUTH 2c; and for other discussions of the natural moral law or the categorical imperative as the first principle of the practical reason, see DUTY 5; LAW 4b-4c; MIND 9a; NECESSITY AND CONTINGENCY 5a(2); PRUDENCE 2c, 3a; WILL 8d.

For: Other statements of the skepticism which results from denying first principles or axioms, see OPINION 3c; TRUTH 7a.

ADDITIONAL READINGS

Listed below are works not included in Great Books of the Western World, but relevant to the idea and topics with which this chapter deals. These works are divided into two groups:

I. Works by authors represented in this collection. II. Works by authors not represented in this collection.

For the date, place, and other facts concerning the publication of the works cited, consult the Bibliography of Additional Readings which follows the last chapter of The Great Ideas.

I.

Augustine. Answer to Skeptics
Aquinas. Super Boethium de Hebdomadibus
Descartes. The Principles of Philosophy, Pref.
Hegel. Science of Logic, Vol. I, Bk. II, Sect. I, Ch. 2
J. S. Mill. A System of Logic, Bk. II, Ch. 6

II.

Sextus Empiricus. Outlines of Pyrrhonism
Duns Scotus. Tractatus de Primo Principio (A Tract Concerning the First Principle)
Bruno. De la causa, principio, e uno
Suárez. Disputationes Metaphysicae, XII (1), XXI (2)
Arnauld. Logic or the Art of Thinking, Ch. 6-7
Leibniz. Discourse on Metaphysics, XXVI
———. New Essays Concerning Human Understanding, Bk. IV, Ch. 7-8
———. Monadology, Par. 31-37
T. Reid. Essays on the Intellectual Powers of Man, I, Ch. 2; VI, Ch. 4-7
Schopenhauer. On the Fourfold Root of the Principle of Sufficient Reason
W. Hamilton. Lectures on Metaphysics and Logic, Vol. II (5-6)
Whewell. The Philosophy of the Inductive Sciences, Vol. I, Bk. I, Ch. 4, 6
———. On the Philosophy of Discovery, Ch. 28
Helmholtz. Popular Lectures on Scientific Subjects, I
J. H. Newman. An Essay in Aid of a Grammar of Assent, Ch. 4
Lotze. Logic, Bk. III, Ch. 5
Bradley. The Principles of Logic, Bk. I, Ch. 5
Bosanquet. Logic, Vol. II, Ch. 7
E. Hartmann. Kategorienlehre
W. E. Johnson. Logic, Part II, Ch. 14
Rueff. From the Physical to the Social Sciences
Santayana. The Realm of Truth, Ch. 1
Dewey. Logic, the Theory of Inquiry, Ch. 17
B. Russell. The Problems of Philosophy, Ch. 7-8, 11
———. Human Knowledge, Its Scope and Limits, Part VI

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