A. W. Carus

Carnap, completeness, and categoricity:The gabelbarkeitssatz OF 1928

In 1929 Carnap gave a paper in Prague on “Investigations in General Axiomatics”; a briefsummary was published soon after. Its subject lookssomething like early model theory, and the mainresult, called the Gabelbarkeitssatz, appears toclaim that a consistent set of axioms is complete justif it is categorical. This of course casts doubt onthe entire project. Though there is no furthermention of this theorem in Carnaps publishedwritings, his Nachlass includes a largetypescript on the subject, Investigations inGeneral Axiomatics. We examine this work here,showing that it provides important insights intoCarnaps development during this critical period, thetransition from Aufbau to Syntax,especially regarding the nature and motivation ofCarnaps logicism. Moreover, we show how theAxiomatics influenced Carnaps student Gödel inreaching the fundamental logical results that soonafterwards undermined Carnaps project.

Institutions and Economic Growth in Historical Perspective

This chapter surveys the historical evidence on the role of institutions in economic growth and points out weaknesses in a number of stylized facts widely accepted in the growth literature. It shows that private-order institutions have not historically substituted for public-order ones in enabling markets to function; that parliaments representing wealth holders have not invariably been favorable for growth; and that the Glorious Revolution of 1688 in England did not mark the sudden emergence of either secure property rights or economic growth. Economic history has been used to support both the centrality and the irrelevance of secure property rights to growth, but the reason for this is conceptual vagueness. Secure property rights require much more careful analysis, distinguishing between rights of ownership, use, and transfer, and between generalized and particularized variants. Similar careful analysis would, we argue, clarify the growth effects of other institutions, including contract-enforcement mechanisms, guilds, communities, serfdom, and the family. Greater precision concerning institutional effects on growth can be achieved by developing sharper criteria of application for conventional institutional labels, endowing institutions with a scale of intensity or degree, and recognizing that the effects of each institution depend on its relationship with other components of the wider institutional system.

Carnap’s intellectual development

ORIGINS The young Carnap is not easy to classify. He was neither really a scientist nor a proper philosopher. Among scientists he felt temperamentally at home, but he regretted the slovenliness of the enterprise. The officers at headquarters, he thought, needed to bring some order to operations on the front. Unfortunately these “officers” – the neo-Kantian philosophers whose lectures he attended in Jena and Freiburg before the First World War – seemed too unsure of the terrain to guide the scientific sappers in their spadework of intellectual trench warfare. But Carnap did not reject the neo-Kantian tradition he grew up in. He assimilated a good deal of it. The impulse for the revival of Kant in mid-nineteenth-century Germany had originally come from the natural sciences rather than philosophy, particularly from the great physicist and physiologist Hermann von Helmholtz. He and the philosophers who followed his lead had wanted to complete the job of eliminating metaphysics that Kant, in their view, had left unfinished. Helmholtz’s physiology of perception, they thought, could render the transcendental aesthetic metaphysically harmless. Though they held that the subjective feelings of spatiality and temporality are built into our perceptual system, just as Kant had argued, this did not mean that the geometry governing the perceived world was put there by human perception. We have no idea, Helmholtz said, whether physical space is Euclidean or non-Euclidean; this is an empirical question like any other, to be settled by going out and looking. So much, Helmholtz had thought, for Kant’s best example of supposedly synthetic a priori knowledge.

From Wittgenstein's prison to the boundless ocean : Carnap's dream of logical syntax

The Logical Syntax is a revolutionary book. How did the author of the Aufbau, whose viewpoint is so very different, come to write such a book? It was a drama in two acts, comprising not one but two major breakthroughs within less than two years. The first of these, in January 1931, was the one Carnap describes vividly in his autobiography: After thinking about these problems for several years, the whole theory of language structure and its possible applications in philosophy came to me like a vision during a sleepless night in January 1931, when I was ill. On the following day, still in bed with a fever, I wrote down my ideas on forty-four pages under the title ‘Attempt at a Metalogic’. These shorthand notes were the first version of my book Logical Syntax of Language.(Carnap 1963a, p. 53)

Carnap, Syntax, and Truth

Tarski’s definition of truth had a major impact on analytic philosophy. It unquestionably had a major impact on Carnap. It helped motivate his shift, in the mid-1930’s, from pure syntax to the incorporation of semantics (and then pragmatics) into his overall view of scientific language. But it is sometimes said (e.g. by Coffa1) that this change of Carnap’s, from pure syntax to a broader view including semantics, involved the abandonment of a coherence theory of truth, and the acceptance of a correspondence theory. Along with this comes the accusation — levelled, for instance, by Russell2 — that the supposed coherence theory of the syntax phase led Carnap to give up an empiricist criterion of meaning.

The Philosopher without Qualities

The revival of interest in Carnap’s philosophy over the past two decades has shed much light on particular aspects of his intellectual development and its context. We now have a better appreciation of the background and motivation of the Aufbau. 1 The radical nature of the Syntax program has fmally, more than half a century after its first publication, begun to be acknowledged.2 And the later Carnap has also been re-assessed; the previously widespread impression that Quine was “right” and Carnap “wrong” in the analytic-synthetic debate has yielded to a more balanced view3, and the broad outlines of Camap’s late philosophy have begun to emerge.4

Engineers and Drifters: The Ideal of Explication and Its Critics

On the surface, Carnap’s writings give the appearance of enormous heterogeneity, and are often read through the distorting lens of a popular mythology about the Vienna Circle and logical positivism. In my book (Carus 2007a) I tried, following the hints given by certain students of the late Carnap such as Richard Jeffrey and Howard Stein, to set the myths aside and find a thread of coherence. I told a story that made the ideal of explication — a species of Enlightenment engineering ideal1 — central, and the specific language projects more peripheral.

Carnap and Phenomenology: What Happened in 1924?

In late 1924, Carnap radically changed the Aufbau framework. Up to then, the logical construction of “realities” or “secondary worlds” by quasi-analysis had proceeded on the basis of a fixed, phenomenologically articulated “primary world.” This distinction disappears in 1924, and logical construction is now applied directly to the basis itself, following the published book’s Russellian motto, “Wherever possible, logical constructions are to be substituted for inferred entities.” This paper first reviews the available documentary evidence for this radical change, but finds only hints, which are then placed in the larger context of Carnap’s development during this period.

History and the Future of Logical Empiricism

When Kuhn published his Structure of Scientific Revolutions in 1962, he and many of his readers thought that introducing a historical dimension into the study of scientific theories and their languages was a decisive break with logical empiricism. But it has now been shown that Carnap himself — the editor of the series in which Kuhn’s book was published — welcomed it unreservedly, and that he had good reason to.1 Kuhn’s position, it is now widely agreed, was to some degree compatible with Carnap’s later view, which had developed considerably since the Vienna Circle doctrines of the 1920s.2 But why, then, have history and philosophy of science since Kuhn largely rejected logical empiricism? Evidently, Kuhn added more than just a historical dimension; his conception of knowledge was also quite different from Carnap’s (Section 1 below). Could Carnap have accommodated a historical dimension that fit better? This chapter argues that Carnap’s framework (Section 2) allows a role for the history of science that is distinct from ‘history proper,’ or history as it is ordinarily conceived by historians (Sections 3 and 4). Moreover, history of science in just this Carnapian spirit began to appear soon after Kuhn’s first writings (Section 5). And although it attracted less attention than Kuhn at the time, it has grown into a flourishing alternative tradition, which, I conclude (Section 6), deserves more attention, as it can interact fruitfully with the post-Kuhnian mainstream to open new perspectives for a historically-informed logical empiricism.