Space, time, and gravitation

GENERAL RELATIVITY is Einstein's theory of gravitation. It is not only a theory of gravity: it is a theory of the structure of space and time, and hence a theory of the dynamics of the universe in its entirety. The theory is a vast edifice of pure geometry, indisputably elegant, and of great mathematical interest.

When general relativity emerged in its definitive form in November 1915, and became more widely known the following year with the publication of Einstein's famous exposé Die Grundlage der allgemeinen Relativitätstheorie in Annalen der Physik, the notions it propounded constituted a unique, revolutionary contribution to the progress of science. The story of its rapid, dramatic confirmation by the bending-of-light measurements associated with the eclipse of 1919 is thrilling part of the scientific history. The theory was quickly accepted as physically correct—but at the same time acquired a reputation for formidable mathematical complexity. So much so that it is said that when an American newspaper reporter asked Sir Arthur Eddington (the celebrated astronomer who had led the successful solar eclipse expedition) whether it was true that only three people in the world really understood general relativity, Eddington swiftly replied, “Ah, yes—but who's the third?”

The Cambridge University Press and the editors of the new series of Cambridge Texts in the History of Political Thought have kindly invited me to produce a second edition of Kant's Political Writings, of which the first edition first appeared in an earlier series almost twenty years ago. They also agreed that the volume might be enlarged by three additional texts. To decide on the most suitable texts presented me with anything but an easy choice. The three suitable pieces chosen, the reviews of Herder's Ideas on the Philosophy of the History of Mankind, Conjectures on the Beginning of Human History and What Is Orientation in Thinking?, are not ‘political’ writings in the narrow sense of the word. They do, however, supply a context for the strictly political writings published in the first edition; for all of them illustrate Kant's critical approach to reasoning and his attitude to the public use of reason without which political justice could not, in his view, be achieved. What Is Orientation in Thinking? does so particularly clearly. It also introduces the reader to the moral basis of Kant's politics, while the other two texts illustrate Kant's conception of history, another pillar of his political thought. I greatly regret that there was no space to include the other pieces relating to politics mentioned in the preface to the first edition. Perhaps one day the constraints on space will be less pressing and all writings by Kant which refer to politics, including the whole of the Theory of Right, can be printed in a later edition.

In order to keep down printing costs and make the volume affordable by students the text of the first edition could not be substantially altered. For this reason, it has unfortunately not been possible to revise and enlarge my introduction itself. I have, however, been able to add a postscript in which I take up issues raised during the discussion of Kant's political thought over the past two decades. I have also provided a more extensive bibliography and a new index.

My thanks are due to Barry Nisbet for translating the additional texts and for giving me invaluable help by commenting on and checking my manuscript.

Kant's essay was occasioned by a dispute between Moses Mendelssohn (1729-86), a Jewish philosopher of Berlin with whom Kant corresponded and whom he esteemed greatly, and Friedrich Heinrich Jacobi (1743-1819), a writer and friend of Goethe's who had attacked Mendelssohn's interpretation of Spinoza. It was a bitter dispute because Jacobi had, in Mendelssohn's view, maligned the reputation of their late common friend, the writer and dramatist Gotthold Ephraim Lessing (1729—81) when he claimed that Lessing had been a follower of Spinoza and hence a pantheist who did not believe in a personal God. Mendelssohn rebutted this charge and maintained that Jacobi had misunderstood Lessing. Their argument is of historical interest only.

Kant's essay, however, provides an introduction to his critical philosophy and shows how his discussion of the theoretical use of reason, as argued in detail in the Critique of Pure Reason and in the Prolegomena to Any Future Metaphysics That Can Claim the Status of a Science ﹛Prolegomena zu einer jeden künftigen Metaphysik die als Wissenschaft wird auftreten können) (1783), necessarily leads on to the practical use of reason as defined in his writings on ethics (for instance, in the Critique of Practical Reason (1788) and the Groundwork of the Metaphysics of Morals (Grundlegung zur Metaphysik der Sitten) (1785)), which in turn provide the foundation of his political writing. Kant did not openly attack either of the two writings in question, but thought it necessary to defend his late friend Mendelssohn while at the same time pointing out some shortcomings in Mendelssohn's argument (Mendelssohn had put forward proofs for the existence of God which Kant held to be illegitimate). He proceeds to show that the belief in reason is a ‘signpost or compass'1 which enables us to orientate our thinking. The use of reason is necessary in order to limit our enquiries to what can, in principle, be discovered and to prevent us from seeking to discover what is beyond the boundaries of knowledge. But the right use of reason also makes it possible for us to act morally. We have to avoid falling victim to zealotry or superstition—that would even be politically dangerous, for it would sooner or later lead to political repression by the authorities who would not be willing to tolerate the spreading of foolish and subversive opinions.

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.