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individuals are worthy of systematic consideration. Science has only to deal with those truths which relate (or may relate) to minds in general, and are formulated from comparisons of the experiences of a plurality of beings.

§ 3. Principles are either Empirical or Scientific. Empirical principles are Empirical laws (Chap. LIV.). They form a large portion of the generalisations which are made the ordinary bases for opinion and for action. They are not cognised as connected with other and higher principles in causation, nor are they yet resolved (though supposed to be resolvable) into higher uniformities. They express some knowledge but not reliable knowledge, except within very circumscribed limits. On the other hand, scientific principles express complete, ascertained, and defined uniformities of nature, whose truth, connections and extent are proved according to those methods which form complete arguments. Both the highest inductive generalisations and derivative laws are equally scientific principles.

§ 4. Principles may be regarded further as Theoretical or Practical. Theoretical principles are those which form the standards of science, practical those which lie at the foundations of the arts. In other language, theoretical principles are the principles of the theoretical sciences; practical principles are the principles of the practical sciences.

§ 5. There remains the most important classification of principles of all, namely, that according to their relative universality. According to this method of dividing, principles are (1) Principia Postulanda (Axiomata Abstracta, Postulates); (II) Principia Majora or Generaliora (Axiomata Generalissima, Higher Generalisations, More General Principles); (III) Principia Media (Axiomata Media, Middle Principles); (IV) Principia Minora (Axiomata Minora et Infima, Particular Principles). This classification is based upon that of Bacon,' and its import will receive illustration in the succeeding sections. It may be remarked here, however, that principles of any of the classes just enumerated may be theoretical or practical, and those of all except the first may be either empirical or scientific. Postulates are scientific, not empirical principles.

Etenim axiomata infima non multum ab experientia nuda discrepant. Suprema vero illa et generalissima (quæ habentur) notionalia sunt et abstracta et nil habent solidi. At media sunt axiomata illa vera et solida et viva, in quibus humanæ res et fortunæ sitæ sunt, et supra hæc quoque tandem ipsa illa generalissima: talia scilicet quæ non abstracta sint sed per hæc media vere limitantur.-Nov. Organum, Lib. I. Aph. CIV.

PRINCIPIA POSTULANDA.

§ 6. Under the term Postulates are embraced those truths which are ultimate, universal and necessary. They are ultimate in that they cannot be reduced to other truths or deduced from them; their universality is made manifest in the fact that, so far as is known, all men receive them; their necessity appears in the fact that no man is able to conceive them as otherwise than true without contradicting himself. These tests are the criteria of the postulates.

§ 7. A truth is a true proposition; a proposition is the expression of a judgment; and a judgment is a cognition of agreement or disagreement between two notions. All notions involve. judgments and all judgments notions. In a sense, therefore, it may be said that postulates are founded upon primitive or ultimate notions. It is more correct to say that those things which are the postulanda of our knowledge may be expressed as notions by a single term or name, or may be expressed as postulates by predications. Neither can logically be said to be more ultimate than the other.

The following are some examples of postulates:-Magnitudes that coincide are equal. The whole is greater than its part. Doubles of equals or of the same are equal. Two straight lines cannot enclose a space. Things equal to the same thing are equal. Whatever is, is. I exist. The same thing cannot be A and non-A. Every effect has a cause. Every event is uniformly preceded by some other event. Force persists. The Ego is different from the non-Ego. Every attribute has a substance. Every phenomenon has its noumenon. The expression of postulates may be indefinitely varied. The above makes no claim to being a complete or a scientific mutually exclusive enumeration: but what are given are intended merely as illustrations. The list includes some of the most important and some of the most familiar postulates.

§ 8. Postulates are not intuitive, but are inferential. They are generalisations from experience. The individual cases from which they are generalised have relations which were intuitively apprehended, but the judgments which are expressed by the postulates are the accumulated results of many experiences, both of the individual and of the race. Neither are the postulates necessarily self-evident, in the simple sense of the word. Sometimes

they are so and sometimes they are not; their self-evidence depends on the degree of familiarity we have with the notions which are compared and with their association. That The whole is greater than a part may fairly be called self-evident; that Force persists, or that Every effect has a cause, may not be self-evident. If, however, by self-evident is meant incapable of logical contradiction, all these truths are self-evident. When once the meaning of these terms is understood, they cannot be denied without selfcontradiction.

PRINCIPIA MAJORA.

§ 9. The remaining classes of principles are distinguishable solely by their relative generality and particularity. The divisions are entirely relative and their boundaries not fixed, but liable to change and changing at all times. A principle which one would put in one class another would put in a lower or higher one perhaps, and what in one view or with regard to one science would be a more general principle, would be for a higher science a more particular principle. Nevertheless we can roughly define the four classes we have named, not claiming infallibility in assigning places to the various principles cited, nor asserting that the lists may not require emendation and correction. As knowledge increases and grows more definite, the relative generality of many principles will be altered.

§ 10. Among the principles not to be ranked as postulated truths, as not ultimate though universal and necessary, are the propositions of geometry, depending directly upon ultimate postulated truths and deducible from them. So, also, any directly deduced truths from the postulates should be ranked in this class-not, however, mere repetitions of the postulates in other words. The propositions of arithmetic and of algebra should find their place here rather than among postulates, excepting a few of the most fundamental, perhaps, as 1= 1, 1+1=2, 2−1=1,1×1=1, etc. So far as the latter are universal formulas and ultimate truths they may be placed among the postulates. Deduced formulas, however, in general should fall into a lower rank.

§ 11. We may also enumerate here the three laws of motion, the law of universal gravitation, the more general expressions of the laws of the nature of light and heat, the law of the atomic constitution of matter, the law of chemical combination, generalised statements of what life is, of mind, the concomitance of mind and

body, ground principles of the sciences of character, sociology, politics and practical sciences, which rest upon fundamental and ultimate axioms.

PRINCIPIA MEDIA.

§ 12. These principles constitute the great mass of what may be denominated working principles-the more familiar generalisations, sufficiently high to furnish proximate explanations of phenomena, but not going back far enough to weary and confuse the mind. First should be mentioned deductions from the class next above; then the immense number of propositions of physics, which create points of departure for practice, as the laws of the composition and resolution of motions and forces, of areas, of the mechanic powers of pneumatics, acoustics, electricity and optics, of crystallisation, of heat and light, of chemical elements and substances, various derivative laws of biology, laws of the classifactory sciences, of ethics, ethology, politics, &c. This division will embrace the most of the empirical laws of nature and the intermediate derivative laws. It includes by far the greatest proportion of the laws of nature. The character of these principles is sufficiently marked by the illustrations given; they are attained both inductively and deductively. Their importance for practical purposes is superior to that of any other class of principles.

PRINCIPIA MINORA.

§ 13. These principles, in the words of Bacon, non multum ab experientia nuda discrepant. Yet there are statements of general facts, above an individual or single observation, and yet not sufficiently general to occupy the rank of mediate principles of a science, which require to be placed in a class superior to nuda experientia and inferior to the other. Deductions from mediate principles occur here, and the lowest generalisations of which any science takes cognisance. Expressions of the distinctive characteristics of species and varieties in the classificatory sciences may be instanced; so also expression of the minor characteristics of the chemical elements.

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CHAPTER LVI.

SYSTEMS.

§ 1. THE last distinctive product of Cognition to which reference will here be made is the System. A system is an organised body of knowledge including notions and judgments, single terms and propositions, definitions and divisions, arguments and principles. Systems, in other words, are the larger aggregates of cognitions, inclusive of many or all of the minor aggregations indicated by the names just given. It is somewhat difficult to fix the constitutive boundaries of these products. The term system may be applied to a narrower or wider range of beings or events, and may be founded on generalisations which are narrower and wider, or on inductions which are more or less profound. They may include a single kingdom of organic or inorganic existences, or may embrace all material things. They may define and arrange these according to the more obvious properties and laws which are open to common observation, or may employ those properties which appear to hasty observation to be very remote, and which are reached only by the most sagacious conjectures and the most skilful experiments. They may include the domain of spirit only, or extend to the kingdoms of both matter and spirit, and arrange the two domains by the properties and laws which can be established as common to the two.'1

§ 2. A line of classification of systems may be followed which is very similar to that adopted in treating of principles. To begin with, systems may be either Empirical or Scientific. The former are the loose, unregulated, unverified, popular associations of knowledge, which have little regard to the principles of scientific classification, and which are adopted to suit temporary convenience or to harmonise with prejudices which have already taken possession of the mind. In them empirical laws, incomplete arguments, doubtful or false judgments, accidental definitions and artificial divisions make up the total. Scientific systems are sciences, and a classification of scientific systems is a classification of the sciences. It is needless to say that it is only with scientific arrangements that science has to do. In so far as there is any co-ordination of

Porter, Human Intellect, Part III. Chap. IV.

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