Preface

These prolegomena are not for the use of apprentices, but of future teachers, and indeed are not to help them to organize the presentation of an already existing science, but to discover this science itself for the first time.

There are scholars for whom the history of philosophy (ancient as well as modern) is itself their philosophy; the present prolegomena have not been written for them. They must wait until those who endeavor to draw from the wellsprings of reason itself have finished their business, and then it will be their turn to bring news of these events to the world. Otherwise, in their opinion nothing can be said that has not already been said before; and in fact this opinion can stand for all time as an infallible prediction, for since the human understanding has wandered over countless subjects in various ways through many centuries, it can hardly fail that for anything new something old should be found that has some similarity with it.

My intention is to convince all of those who find it worth while to occupy themselves with metaphysics that it is unavoidably necessary to suspend their work for the present, to consider all that has happened until now as if it had not happened, and before all else to pose the question: “whether such a thing as metaphysics is even possible at all.”

The translation has been made using the original edition of the Prolegomena zu einer jeden künftigen Metaphysik die als Wissenschaft wird auftreten können (Riga, Hartknoch, 1783; reprint, Erlangen, Harald Fischer Verlag, 1988), and Karl Vorländer's edition, as revised (Hamburg, Felix Meiner Verlag, 1976); on occasion, Benno Erdmann's edition in Ak, vol. 4, has been consulted. As is customary, the page numbers of Ak are shown in the margins of the present translation. Vorländer's edition, completed after Ak, collects significant textual variants from many previous editions; both editions contain much useful information on texts and printings. Vorländer's edition incorporates a major reorganization of the Preamble and first General Question in accordance with Hans Vaihinger's “galley switching” thesis. Vaihinger convincingly argued, on internal textual grounds and by comparison with corresponding sections of the “B” edition of the Critique, that a galley of 100 lines was transposed during the printing of the Preamble. The emended text is not without minor problems (for the correction of which a paragraph break has been added), but it is much improved over editions that do not accept the reorganization.

The present translation varies slightly from my contribution to the Cambridge Edition, in Theoretical Philosophy After 1781. That publication contains more extensive critical apparatus than would be useful here, where the original German is given only occasionally, to permit a general understanding of Kant's terminology.

Preface to the Second Edition

Whether or not the cultivation of those cognitions that belong to the occupation of reason treads the sure path of a science can be assessed quickly from the results. If, after repeated preparations and provisions, this cultivation gets bogged down as soon as it reaches the goal, or if it must often backtrack and take another path to arrive at this goal; or equally, if it is not possible to unite the various collaborators on the manner in which their common aim should be pursued: then one can always be convinced that such a pursuit has not yet (by far) taken the sure path of science, but is merely groping about; and the discovery of this path, if possible, is already a service to reason, even if much should have to be abandoned as futile that was contained in the goal as previously accepted (without reflection).

That logic has tread this sure path from the most ancient times up to now can be seen from the fact that since Aristotle it has not had to take a single step backward, if the removal of a few superfluous subtleties or the clearer determination of what is presented are not to be reckoned as improvements, which anyway pertain more to the elegance than to the surety of the science.

The Göttingen Review

Critique of Pure Reason, by Immanuel Kant

1781. 856 p. Octavo

This work–which always exercises the understanding of its reader if not always instructing it, often strains the attention to exhaustion, occasionally comes to its aid with fortunate images or rewards it with unexpected, generally useful conclusions – is a system of higher, or, as the author calls it, transcendental idealism; an idealism that comprehends spirit and matter in the same way, transforms the world and our self into representations, and has all objects being generated from appearances, in that the understanding connects them into one experiential series and reason necessarily though vainly seeks to extend and unite them into one whole and complete world system. The author's system rests on approximately the following main principles. All our cognitions arise from certain modifications of our self that we call sensations. What they exist in, whence they are aroused, that is at bottom completely unknown to us. If there might be an actual thing in which the representations inhere, or actual things independent of us that produce them, we do not know even the lowliest predicate from the one or the other. All the same, we postulate objects; we speak of our self, we speak of bodies as real things, we believe we are acquainted with both, we make judgments about them. The cause of this is nothing other than the fact that the various appearances have something in common with one another.

It was characteristic of the great modern philosophers to attempt, each in his own way, to rebuild philosophy from the ground up. Kant embraced this goal more fully than any other classical modern philosopher. And his work did in fact change philosophy permanently, though not always as he intended. He wanted to show that philosophers and natural scientists were not able, and would never be able, to give final answers to questions about the nature of the physical world and of the human mind or soul, and about the existence and attributes of a supreme being. While he did not accomplish precisely that, his work changed philosophy's conception of what can be known, and how it can be known. Kant also wanted to set forth new and permanent doctrines in metaphysics and morals. Though his exact teachings have not gained general acceptance, they continue to inspire new positions in philosophical discussion today.

Kant stands at the center of modern philosophy. His criticism of previous work in metaphysics and the theory of knowledge, propounded in the Critique of Pure Reason and summarized in the Prolegomena, provided a comprehensive response to early modern philosophy and a starting point for subsequent work. He rejected previous philosophical explanations of philosophical cognition itself. His primary target was the rationalist use of reason or “pure intellect” – advanced by Descartes and Leibniz – as a basis for making claims about God and the essences of mind and matter.

INTRODUCTION

The subject of CMOS RF integrated circuit design resides at the convergence of two very different engineering traditions. The design of microwave circuits and systems has its origins in an era where devices and interconnect were usually too large to allow a lumped description. Furthermore, the lack of suitably detailed models and compatible computational tools forced engineers to treat systems as two-port “black boxes” with frequency-domain graphical methods. The IC design community, on the other hand, has relied on the development of detailed device models for use with simulation tools that allow both frequency- and time-domain analysis. As a consequence, engineers who work with traditional RF design techniques and those schooled in conventional IC design often find it difficult to converse. Clearly, a synthesis of these two traditions is required.

Analog IC designers accustomed to working with lower-frequency circuits tend to have, at best, only a passing familiarity with two staples of traditional RF design: Smith charts and S-parameters (“scattering” parameters). Although Smith charts today are less relevant as a computational aid than they once were, RF instrumentation continues to present data in Smith-chart form. Furthermore, these data are often S-parameter characterizations of two-ports, so it is important, even in the “modern” era, to know something about Smith charts and S-parameters. This chapter thus provides a brief derivation of the Smith chart, along with an explanation of why S-parameters won out over other parameter sets (e.g., impedance or admittance) to describe microwave two-ports.

INTRODUCTION

Phase-locked loops (PLLs) have become ubiquitous in modern communications systems because of their remarkable versatility. As one important example, a PLL may be used to generate an output signal whose frequency is a programmable, rational multiple of a fixed input frequency. The output of such frequency synthesizers may be used as the local oscillator signal in superheterodyne transceivers. Phase-locked loops may also be used to perform frequency modulation and demodulation, as well as to regenerate the carrier from an input signal in which the carrier has been suppressed. Their versatility extends to purely digital systems as well, where PLLs are indispensable in skew compensation, clock recovery, and the generation of clock signals.

To understand in detail how PLLs may perform such a vast array of functions, we will need to develop linearized models of these feedback systems. But first, of course, we begin with a little history to put this subject in its proper context.

A SHORT HISTORY OF PLLS

The earliest description of what is now known as a PLL was provided by H. de Bellescize in 1932. This early work offered an alternative architecture for receiving and demodulating AM signals, using the degenerate case of a superheterodyne receiver in which the intermediate frequency is zero. With this choice, there is no image to reject, and all processing downstream of the frequency conversion takes place in the audio range.