Incompleteness Read online

  Post-1918 Vienna provided a grand tier seat from which to view the rapid disintegration of anachronisms. The Hapsburg Empire, that elaborate variation on the themes of status quo and patriarchy, had imploded with the close of the Great War. Eleven different nationalities—Germans, Ruthenes, Italians, Slovaks, Rumanians, Czechs, Poles, Magyars, Slovenes, Croats, Transylvanians, Saxons, and Serbs—were joined in the ungainly empire; the resultant realm lacked, rather significantly, an accepted name. Its last leader was the long-reigning Franz Joseph, Emperor of Austria since 1848 and King of Hungary since 1867. And the capital city of the nameless realm was Vienna. Though a unifying consciousness eluded the multifarious nationalities of the empire, the “City of Dreams,” as Vienna was almost too aptly dubbed, was in fact able to achieve something like that supranational cosmopolitan consciousness entailed by the myth of empire.

  Vienna, at its height, had been an imperial capital that had ruled over some 50 million subjects. Now it was the capital of a small and ruined Alpine republic of a little over 6 million citizens, almost all German. (Many of the Czechs who had been living in the city left, which somewhat eased the housing shortage.) But if Vienna was vastly diminished in political terms, its importance as an intellectual capital of the world was unparalleled. The very sense of a spiritual and cultural collapse (whose imminence had been evident to the Viennese thinkers even while the Hapsburg dynasty tottered on) intensified the felt need for the search for new foundations. The collective consciousness of the city’s most conscious citizens was suffused with a sort of nervous intensity, the rash of ideas erupting like the symptomatology of diseased genius.

  So we find in Vienna not only the birthplace of Zionism in the figure of Theodore Herzl but also of the most extreme manifestation of those ideas that had provoked Zionism as a response, Nazism. It provided the breeding ground for Freud’s theory of the unconscious, repression, hysteria, and neurosis; it was where Klimt and Schiele and Kokoschka painted the lushly sensual canvasses of the Secession.4 Arnold Schönberg and Alban Berg brought forth atonal music and Adolph Loos designed a new sort of architecture, where form would be strictly determined by function, the excessive ornamentation and über-stuffed rooms of the Hapsburg bourgeoisie equated with moral rot.

  An influential voice (an acerbic one), sounding throughout Vienna’s overlapping cultural circles, belonged to the journalist Karl Kraus, the tireless editor (and primarily the sole writer) of the satirical journal Die Fackel, or The Torch. Kraus used his journal to clobber every variety of Viennese hypocrisy, whether practiced by the old guard or the avant-garde. (He was, for example, harshly critical of Freud.) Kraus focused much of his fierce crusading attention on language, blasting the deceit that lies curled up in the banalities of respectable forms of speech, the hollowness and insincere sentimentality in works of literature and the empty phrases of journalists. “Speaking and thinking are one,” he declared in his book Die Sprache (Language): The road not only to better theories but to a better society is paved with linguistic precision. Kraus himself was a consummate stylist, skewering his targets in elegant epigrams: “The psychoanalyst picks our dreams as if they were our pockets.” “The secret of the demagogue is to appear as dumb as his audience so that these people can believe themselves as smart as he is.” “The esthete stands in the same relation to beauty as the pornographer to love, and the politician stands to life.”

  Kraus’s attention to language as the single most important topic in his critique of thought will strike contemporary students of philosophy as so familiar as to seem a truism. Though Kraus was not himself a philosopher, he had a decided impact on Viennese philosophers, and thus on philosophers throughout the world. Ludwig Wittgenstein, in particular, was a regular reader of Die Fackel.

  Kraus’s view that intellectual shoddiness is not only an offence against truth but also against morality had great cogency among his Viennese contemporaries. A sense of moral urgency underlay their discussion of intellectual and artistic questions, and the exhortatory tone of the Hebrew prophets of old, calling the tribe to repentance, often broke through into discussions of the most dryly abstract sorts of subjects, for example, the conditions for the meaningfulness of propositions. Discredited ideas, solecisms, half-truths, and elaborately phrased nonpropositions carry the fatal taint of moral failure; there is a moral imperative to break with the past and think clearly.

  The densely swirling culture of Viennese ideas was very much on public display, conducting itself across the round little tables of the city’s many cafés. (This, by the way, had something to do with the bleak housing situation in Vienna. The ill-heated and generally inadequate domiciles inclined the Viennese to spend their hours elsewhere.) The literati and other artists favored such places as the Café Museum, the Herrenhof, or the Café Central, where Peter Altenberg, for example, answered so gratifyingly to the popular image of “the poet” in his brightly colored shirt, his wide-striped pants, and his pince-nez dangling poetically from a black ribbon. At another table, Alban Berg and other composers might be found discussing the exhaustion of tonality; or Adolph Loos, discussing the outrages of traditional architecture; or the novelist Franz Werfel, who wrote of the café’s “shadowy realm” in his novel Barbara or Piety. Another writer, Alfred Polgar, propounded a “Theory of Café Central,” explaining that the establishment was a veritable Weltanschauung, “a world-view, but one whose essence it was to avoid viewing the world.” Its habitués were “for the most part people whose misanthropy was only equaled by their longing for their fellow man, who want to be alone but need company for that.”

  As for the mathematicians like Gödel, there was the Akazienhof, only a three-minute walk from the university, as well as other places—the Arkadencafé, the Reichsrat, the Schattentor, the white marble tabletops providing a scribbling surface for equations. Not only location, but also the category of people the place attracted and their respective status, as well as the selection of periodicals and newspapers that were offered, influenced where a particular group would gather.

  In addition to café society, the intellectual life of Vienna was also organized into various Kreise, or circles, more or less formal discussion groups that met on a weekly basis, centered around the leading intellectuals of the city. Many of these circles overlapped. Some were connected with the university, others not. A large number were devoted to discussions of socialism (one, surrounding Max Adler, was Kant-focused), and others were oriented around the various factions within the psychoanalytic movement. A large number of the circles were meant for the discussion of philosophy, not only of Kant, but of such figures as Kierkegaard and Leo Tolstoy, who enjoyed an enormous influence at the time. The philosopher Heinrich Gomperz, in whose class Gödel had become convinced of Platonism, had a discussion group centered on the history of philosophy. The intellectual geometry of Vienna was densely inscribed with circles.

  The Vienna Circle

  By far the most prominent of these circles was the one that revolved around the philosopher Moritz Schlick, first dubbed, accordingly, the Schlick Kreis, though it came eventually to be known, as an acknowledgment of its preeminence, as the Der Wiener-Kreis, the legendary Vienna Circle. It was from this group of thinkers that the influential movement known as “logical positivism” largely disseminated. The reforming edicts of the group reshaped attitudes of scientists, social scientists, psychologists, and humanists, causing them to reformulate the questions of their respective fields; the effects are still with us.

  Attendance at the meetings of the Vienna Circle was by invitation only. The philosopher Karl Popper, who went on to eminence and was even then an up-and-coming intellectual force, waited with impatience and in vain for an invitation to join the most important Kreis in town.

  Kurt Gödel was invited to join while still an undergraduate and was a regular attendant at the weekly sessions between the years 1926 and 1928. Interestingly, 1928 is the year when he turned to mathematical logic, which would of course yield him his famous proof
. No wonder he no longer had the time or the inclination for the weekly sessions.

  His association with the logical positivists has led to the misconception that he himself was a positivist and that his incompleteness theorems are a consequence of positivist principles. Gödel’s incompleteness theorems are still often tallied among positivism’s greatest success stories: the revolutionary result of applying its principles to mathematics. So, for example, in the recent Wittgenstein’s Poker, authors David Edmonds and John Eidinow write:

  The Circle’s voice can still be heard in a number of philosophical eponyms. In 1931 Gödel published his theorem that scuppered all attempts to construct a logical foundation for mathematics. He showed that a formal arithmetical system could not be demonstrated to be consistent from within itself. His fifteen-page article proved that some mathematics could not be proved—that, whatever axioms were accepted in mathematics, there would always be some truths that could not be validated.

  Here Gödel’s two theorems are more or less correctly stated, though they are merged into one “theorem.” But that the Circle’s voice can be heard within Gödel’s theorems could not be further from the truth. The voice that Gödel heard within his theorems was that of Platonism. Any metaphysical position, let alone Platonism, is downright anathema to a logical positivist.

  Gödel had become a Platonist in 1925, a year before joining the discussion group. Their anti-metaphysical orientation had no influence on him, and, for their part, they never seemed to suspect—not for a long time at least—that he was not one of them. He apparently gave them little indication. It was not then, and never would be, in his nature to argue face-to-face with those with whom he disagreed. His distaste for engaging in conflict was so extreme as to qualify as an eccentricity, though hardly among his most pronounced. He refused to oppose another person’s viewpoint unless he had absolute certainty on his side, unless, that is, he had a proof. All his life, he wanted to have his mathematical proofs do all his speaking for him. (Perhaps it is no accident that this man, whose extreme reticence cloaked intense convictions, should have produced the most prolix mathematical results in the history of mathematics.) He was dismayed when others did not catch all that he was trying to say in them. He was dismayed until the end of his life that people still considered his views consistent with those of the Vienna Circle.5

  What were the views of the Vienna Circle? Logical positivism was first and foremost a movement that spoke in the name of the precision and progress associated with the sciences. It sought to appropriate the methodology that had served the sciences so well, to distill the essence of this methodology not only to cleanse science itself of its more mystically vague and metaphysical tendencies—no characterization carried more positivist opprobrium than “metaphysical”—but also similarly to cleanse all intellectual areas. It was a program for intellectual hygiene.

  In the Viennese spirit of the time, this group of thinkers from various fields—mathematics, philosophy, the physical and social sciences—were intent on giving the decaying remains of old ideas as hasty a burial as decency required and on resurrecting in their stead a system whose wholesome soundness would derive from the empirical sciences. Logical positivism disseminated out far beyond the little bare room where the group would meet and deeply penetrated the philosophical orientation of philosophers, scientists, and social scientists, many of whom were not even aware that they had a philosophical orientation. But the preferred absence of a specifically philosophical orientation was one of the major points emphasized by the logical positivists. It was a philosophical orientation meant to abolish all philosophical orientations, which might strike the reader as paradoxical.

  Logical positivism is sometimes referred to as “logical empiricism” or “radical empiricism.” Traditional empiricism, exemplified by the views of the Scottish philosopher David Hume (1711–1776), had sought to delineate the limits of knowledge. There were, on the one hand, the sort of questions that could be answered through a priori reasoning; these, according to Hume, had no ontological import. They were merely conceptual truths that do not tell us anything about the way the world really is; they merely reflect abstract relationships between concepts. Hume called them “relations of ideas.” So the truth that bachelors are unmarried is analogous to the truth that ghosts are the disembodied spirits of the dead and to the truth that fat-free ice cream has no fat. Each is true regardless of whether its subject—bachelors or ghosts or fat-free ice cream—actually exists. On the other hand, there are propositions that reach out beyond the merely conceptual and purport to describe the nature of the world, to say what things exist and what are the properties of, and relations between, things: According to traditional empiricism, any propositions that bear on the nature of the world—Hume called them “matters of fact and existence”—can only be shown to be true or false through the use of empirical means. Some evidence or other is of the essence. The faculty of a priori reason can tell us how our concepts are related to one another, but it cannot tell us what the world beyond our concepts is like. For that sort of knowledge we require some sort of experiential contact with the world.

  To use a favorite example, consider the question of the existence of God, defined as a transcendent Being who stands outside space and time, severely limiting the possibilities for experiential contact. (At the least, such experiences would have to occur in time.) Many traditional empiricists had declared the existence of such a trans-empirical God inviolably unknowable, since the cognitive means at our disposal are in principle inadequate for answering the question one way or the other. So remote a God—beyond our experience—may exist, but we’ll never know. (Bertrand Russell, when asked what he would say were he to find himself before the pearly gates face-to-face with the Almighty, quipped that his response would be, “Oh Lord, why did you not provide more evidence?”)

  The logical positivists turned the empiricist theory of knowledge into a theory of meaning. According to the latter, the empirical means that would be relevant to discovering whether a particular proposition is true also provide the very meaning of the proposition. The positivist theory of meaning is therefore often called “the verificationist criterion for meaningfulness,” and it legislates that the borders of empricial knowability map the borders of meaningfulness. If one cannot, in principle, imagine any possible set of experiences that would count as corroboration for the proposition, then what one has is the mere semblance of a proposition, hollowed out of meaning, what the positivists dubbed a “pseudo-proposition.”

  By declaring the limits of knowability one and the same with the limits of meaningfulness, the positivists took the problematic aspect of such questions as the existence of God (or of moral values or of abstract entities) up a notch, so that now the unanswerability of certain questions no longer takes the measure of our cognitive inadequacies, but rather signals that the questions ought never have been posed at all. Unknowability is regarded as a sign that a mistake in the use of language has been made. If God (or moral values or universals or numbers) is so defined that no empirical data could possibly be relevant to the question of his (or their) existence, then that question is exposed as ipso facto meaningless: nothing could count as a genuine answer to it. The putative answers—yes, God exists! or no, He does not! are both propositional poseurs. Anything that can legitimately be said can be said clearly, the conditions for its meaningfulness one and the same with the conditions for its verifiability (which is not to say that all meaningful propositions are true, of course, but rather that there would be some set of experiences—not forthcoming if the proposition is false—that would establish that the proposition is true). Precision (provided by the verificationist criterion of meaning) becomes the positivist analogue to prayer.

  The positivist transformation of the empiricist theory of knowledge into a theory of meaning meant that the single damning word “meaningless” was to be pronounced over the remains of much that had formerly passed for knowledge. Here was the single word w
ith which to accomplish a program of cognitive hygiene such as the world had never seen. The Vienna Circle, which lasted from 1924 to 1930, ending with the tragic murder of Moritz Schlick by a psychotic former student,6 had an effect that rippled out from Vienna and is still actively circulating today, quite often in the introductory “philosophical” chapters of textbooks in science or social science. (The presence in these chapters of such phrases as “a meaningless question because empirically unanswerable” is a dead giveaway. In psychology, for example, the behaviorist school that held dominance for many decades of the twentieth century often asserted that all psychological terms that could not be reduced to the observables of stimulus and response were meaningless.)

  Dramatis Personae of the Vienna Circle

  Moritz Schlick, if not the most dynamic and innovative of the thinkers of the Circle, was a man whose positivist sincerity and organizational abilities seem to have been instrumental to its success. As philosopher Rudolf Carnap said, “The pleasant atmosphere at the meetings of the Circle was due above all to Schlick’s personality, his inexhaustible friendliness, tolerance and modesty.” Having trained as a physicist in Germany under the great Max Planck, he had come to Vienna in 1922 to take up the prestigious chair in the Philosophy of the Inductive Sciences at the university, the very chair that had been held both by Ernst Mach and by the towering physicist, Ludwig Boltzmann (for whom Mach’s rejection of the molecular hypothesis had constituted both a professional and personal tragedy7).