Ideas on the Philosophy of the History of Mankind by Johann Gottfried Herder. Quern te Deus esse iussit et humana qua parte locatus es in re disce. Part One. 318 pp. Quarto. Hartknoch: Riga and Leipzig. 1784.

In this work, our ingenious and eloquent author displays those distinctive qualities of mind for which he has already gained recognition. For this reason, the work is perhaps as little subject to ordinary standards of judgement as are some of the other products of his pen. It is as if his genius did not simply bring together ideas from the broad sphere of the arts and sciences in order to supplement them with other ideas which might be communicated to others, but as if he adapted them, by a certain law of assimilation (to borrow his own expression) and in a way peculiar to himself, to his own specific mode of thinking. They thus become markedly different from those by which other minds are furthered and sustained (p.292), and are accordingly less capable of being communicated to others. Consequently, what he understands by the philosophy of the history of mankind may well be something quite different from what is usually understood by that term. His approach does not entail, for example, a logical precision in the definition of concepts or careful distinctions and consistency in the use of principles, but rather a cursory and comprehensive vision and a ready facility for discovering analogies, together with a bold imagination in putting these analogies to use. This is combined with an aptitude for arousing sympathy for his subject—which is always kept at an obscure distance—by means of feelings and sentiments; and these in turn, as the product of weighty thoughts or as highly significant pointers, lead us to expect more of them than cool assessment would ever be likely to discover. Nevertheless, since freedom of thought (which is present here in ample measure), as exercised by a fertile mind, always affords food for thought, we shall attempt as far as possible to extract the most important and characteristic of the author's ideas and to present them in his own words, adding in conclusion a few remarks concerning the whole.

This work begins with a preface and a general introduction. Its main body falls into two parts—The Metaphysical Elements of the Theory of Right and The Metaphysical Elements of the Theory of Virtue. The extracts included in the present edition are taken only from The Metaphysical Elements of the Theory of Right. They include the most important paragraphs from the introduction to this part of the work, and its second main section, which deals with The Theory of Public Right. In order to place the relevant passages in their proper context, I have provided a brief summary of the other sections preceding The Theory of Public Right.

In the preface to The Metaphysics of Morals, Kant points out that a complete metaphysics of right is impossible because completeness in an account of empirical matters is impossible. He refers only to The Metaphysical Elements of the Theory of Right because the second part, The Metaphysical Elements of the Theory of Virtue, was published at a later date. Kant also states that, in his treatise, he has put into the body of the text those arguments relating to the system of right which were arrived at by a priori reasoning and has relegated those relating to specific empirical cases to the notes. Kant then defends the apparent obscurity of his style by saying that it is impossible to aim at popularity in a work involving a system of criticism of the faculty of reason.

In his general introduction to the Metaphysics of Morals, Kant discusses the fundamental terms and presuppositions of this work, pointing out that science can make progress without explicit reference to a priori laws, but that the case of morality is different. Moral laws are laws only in so far as they have an a priori basis and are necessary. He explains why he distinguishes between legal and moral laws: the former admit of no incentive except that of duty, the latter do not.

A full account of this introduction would be too long to justify inclusion here. Kant proceeds to provide definitions for many of the terms which he uses, thus supplying a brief account of the principles underlying his moral philosophy (cf. my introduction pp. 17-21 for a brief discussion of his moral philosophy).

THE AIM OVER the next two chapters is to construct a solution of Einstein's equations with sources that will provide a model for the large scale features of the universe. First, we must find a reasonable form for the metric and energy-moment urn tensor consistent with the observed symmetries of the universe. Then we shall be led to specific cosmological models by the imposition of the Einstein equations.

We are thinking of the average features of the universe on the scale of tens of millions of light years and we may regard the basic building blocks as clusters of galaxies. The first observational fact about the universe that we must use is that the observed distribution of the clusters of galaxies is isotropic to a high degree. If we assume that our position is in no particular way privileged, we must assume the universe is isotropic about every point, which leads to an assumption of homogeneity.

We must distinguish a preferred class of observers, namely those that actually see the universe as isotropic. Thus our cosmological model admits a preferred time-like vector field ua , tangent to the world lines of the preferred or ‘fundamental’ observers.

WE PROCEED to solve the geodesic equations in the Schwarzschild solution and use the solution to describe the classical tests of general relativity. These are the precession of the perihelion of planetary orbits and the bending of light by the sun, effects that arise from the small differences between orbits in Newtonian gravitation and orbits, i.e. geodesies, in general relativity.

Whatever conception of the freedom of the will one may form in terms of metaphysics, the will's manifestations in the world of phenomena, i.e. human actions, are determined in accordance with natural laws, as is every other natural event. History is concerned with giving an account of these phenomena, no matter how deeply concealed their causes may be, and it allows us to hope that, if it examines the free exercise of the human will on a large scale, it will be able to discover a regular progression among freely willed actions. In the same way, we may hope that what strikes us in the actions of individuals as confused and fortuitous may be recognised, in the history of the entire species, as a steadily advancing but slow development of man's original capacities. Thus marriages, births, and deaths do not seem to be subject to any rule by which their numbers could be calculated in advance, since the free human will has such a great influence upon them; and yet the annual statistics for them in large countries prove that they are just as subject to constant natural laws as are the changes in the weather, which in themselves are so inconsistent that their individual occurrence cannot be determined in advance, but which nevertheless do not fail as a whole to sustain the growth of plants, the flow of rivers, and other natural functions in a uniform and uninterrupted course. Individual men and even entire nations little imagine that, while they are pursuing their own ends, each in his own way and often in opposition to others, they are unwittingly guided in their advance along a course intended by nature. They are unconsciously promoting an end which, even if they knew what it was, would scarcely arouse their interest.

Since men neither pursue their aims purely by instinct, as the animals do, nor act in accordance with any integral, prearranged plan like rational cosmopolitans, it would appear that no law-governed history of mankind is possible (as it would be, for example, with bees or beavers). We can scarcely help feeling a certain distaste on observing their activities as enacted in the great world-drama, for we find that, despite the apparent wisdom of individual actions here and there, everything as a whole is made up of folly and childish vanity, and often of childish malice and destructiveness.

Immanuel Kant was born on 22 April 1724 in Königsberg (now Kaliningrad) in East Prussia which, except for occasional journeys into the immediate vicinity, he hardly ever left during the whole of his long life of almost eighty years. Königsberg in the eighteenth century was a lively city which, owing to its flourishing trade, was by no means isolated from the world at large. Kant, who was anything but a recluse, enjoyed social life and intelligent conversation. He was friendly with many Königsberg merchants, among whom there were also Englishmen, two of whom, Green and Motherby, were particularly close friends. Although he was meticulous and regular in his habits, punctual to a fault, he was also a man of urbanity and wit.

Kant's parents were not rich. His father was a harness-maker who lived in Königsberg. His family was steeped in Pietism, the Protestant religious movement which stressed emotional religiosity and the development of the inner life. The pietistic atmosphere of his parents’ household was a formative influence in his childhood, and he was particularly impressed by his mother's simple piety. After the early death of his parents (his mother died in 1738, his father in 1746), Kant's relations with his family were not very close.

Kant's outstanding intellectual gifts were recognised at school. It was made possible for him to enter the University of Königsberg, where he was a brilliant student. In 1755 he was granted the right to lecture as Magister legem or Privatdozenty i.e. as an unsalaried lecturer who depended on his lecture fees for his income. Since his lectures were popular and since he gave a large number of them—twenty a week at least—he was able to eke out a meagre living. He lectured on many subjects—logic, metaphysics, ethics, theory of law, geography, anthropology etc. He began to make his name as a scholar and scientist by his writings. In his General History of Nature and Theory of the Heavens (1755), he Put forward a highly original account of the origin of the universe similar to the one later elaborated by the French scientist Laplace.

Cartesian tensors: an invitation to indices

LOCAL DIFFERENTIAL GEOMETRY consists in the first instance of an amplification and refinement of tensorial methods. In particular, the use of an index notation is the key to a great conceptual and geometrical simplification. We begin therefore with a transcription of elementary vector algebra in three dimensions. The ideas will be familiar but the notation new. It will be seen how the index notation gives one insight into the character of relations that otherwise might seem obscure, and at the same time provides a powerful computational tool.

The standard Cartesian coordinates of 3-dimensional space with respect to a fixed origin will be denoted xi (i = 1,2,3) and we shall write A = Ai to indicate that the components of a vector A with respect to this coordinate system are Ai . The magnitude of A is given by A · A = AiAi . Here we use the Einstein summation convention, whereby in a given term of an expression if an index appears twice an automatic summation is performed: no index may appear more than twice in a given term, and any ‘free’ (i.e. non-repeated) index is understood to run over the whole range.

Enlightenment is man's emergence from his self-incurred immaturity. Immaturity is the inability to use one's own understanding without the guidance of another. This immaturity is self-incurred if its cause is not lack of understanding, but lack of resolution and courage to use it without the guidance of another. The motto of enlightenment is therefore : Sapere aude! Have courage to use your own understanding!

Laziness and cowardice are the reasons why such a large proportion of men, even when nature has long emancipated them from alien guidance (naturaliter maiorennes, nevertheless gladly remain immature for life. For the same reasons, it is all too easy for others to set themselves up as their guardians. It is so convenient to be immature! If I have a book to have understanding in place of me, a spiritual adviser to have a conscience for me, a doctor to judge my diet for me, and so on, I need not make any efforts at all. I need not think, so long as I can pay ; others will soon enough take the tiresome job over for me. The guardians who have kindly taken upon themselves the work of supervision will soon see to it that by far the largest part of mankind (including the entire fair sex) should consider the step forward to maturity not only as difficult but also as highly dangerous. Having first infatuated their domesticated animals, and carefully prevented the docile creatures from daring to take a single step without the leading-strings to which they are tied, they next show them the danger which threatens them if they try to walk unaided. Now this danger is not in fact so very great, for they would certainly learn to walk eventually after a few falls. But an example of this kind is intimidating, and usually frightens them off from further attempts.

Thus it is difficult for each separate individual to work his way out of the immaturity which has become almost second nature to him. He has even grown fond of it and is really incapable for the time being of using his own understanding, because he was never allowed to make the attempt.