¹ It is instructive to compare Carnap, Reichenbach, and Schlick in this regard. Reichenbach appears to have had a much better understanding of logic than did Schlick, and he does attempt to formulate his views and arguments with “logical precision”. Nevertheless, Reichenbach does not really put modern logic to work in his philosophizing; even more so than Schlick, his primary technical orientation is towards physics. Only Carnap is able to grapple technically and philosophically with both modern logic and modern physics, and this is undoubtedly a central reason for his preeminence.

² The neo-Kantian and neo-idealist influence on the early positivists has been widely neglected—again, largely because of positivism's own anti-Kantian rhetoric. To get an initial appreciation of this influence, one has only to list some of the authors referred to by the two great works of the period: Schlick's General Theory of Knowledge and Carnap's Aufbau (1928). Names such as Cassirer, Driesch, B. Erdman, Külpe, Natorp, Schuppe, Vaihinger, and Wundt predominate. (As Alberto Coffa has emphasized to me, Schlick's own initiation into neo-Kantianism probably came from Helmholtz via Planck, who was the adviser of Schlick's Ph.D. dissertation.)

³ I do not want to mislead the reader by calling General Theory of Knowledge the “background” to Schlick's work on relativity. After all, the former was published in 1918, while the two major works on relativity appeared in 1915 and 1917 respectively. Nevertheless, General Theory of Knowledge reads like a pre-relativistic piece of philosophy. It is striking that there are very few explicit references to Einstein, and, in addition, it seems quite clear that the paradigm of a physical theory is late nineteenth-century Maxwellian electrodynamics. Warren Goldfarb has suggested to me that Schlick had indeed incorporated relativity into his philosophy in General Theory of Knowledge, but he kept its influence veiled in order to “soften up” and avoid shocking his philosophical audience. I confess that this suggestion seems implausible to me in view of the militant anti-Machian stance of Schlick's book; I think it is more likely that he had simply done most of the thinking and writing for the book before he grappled philosophically with Einstein's new theories. But these are matters for further scholarship to decide.

⁴ I do not want to mislead the reader by calling Schlick a “neo-Kantian”. Schlick always rejected the synthetic a priori and Kant's theory of space and time. Yet Schlick's theory of judgment and cognition was Kantian (and anti-empiricist) in its “holism” and “formalism”. Schlick's view results from accepting a Kantian (or neo-Kantian) conception of judgment and cognition while rejecting Kant's doctrine of pure intuition.

⁵ As such, the view of General Theory of Knowledge has close affinities with Russell's Analysis of Matter (1927), which also rejects phenomenalism in favor of “structural correspondence”. One can get a partial sense of Schlick's view of this period from vol. 1, pp. 201–205.

⁶ Although Schlick, for one, is far from clear about this, these nineteenth century foundational developments require, for the first time, complicated patterns of polyadic reasoning (as is evident in the Cauchy-Bolzano-Weierstrass treatment of continuity, convergence, etc. and, especially, in Weierstrass’ distinction between pointwise and uniform properties). It is no accident that Frege's work follows closely on the heels of that of Weierstrass. For Kant, on the other hand, logic is essentially monadic or syllogistic: Kantian “concepts” are monadic concepts.

⁷ It is now more-or-less generally known that this positivistic interpretation of general relativity is completely untenable. General covariance implies neither a generalized relativity of motion nor a “conventionalist” conception of physical space (or space-time) as “metrically amorphous”. As a matter of fact, any spacetime—including the space-times of Newtonian physics and special relativity—can be given a generally covariant description. What distinguishes general relativity is the use of a non-flat (non-Euclidean) spacetime of variable, mass-energy dependent curvature. General relativistic space-time has a perfectly determinate and objective (although variable) metrical structure, and absolute acceleration and rotation have much the same status as they do in special relativity: Machian relativity is not realized. Furthermore, these (essentially mathematical) facts were established in Schlick's own time via the work of Kretschmann (1917) and Weyl (1918). (The final clarification was provided by Cartan's great papers of 1923–24, which showed, in particular, how Newtonian gravitation theory also makes use of a non-flat space-time structure). Yet the philosophical pressures leading towards a “conventionalist” misunderstanding of general relativity were quite irresistable (even to Einstein himself), and the notion of covariance is remarkably subtle and elusive. As a result, verificationist misinterpretations of general relativity have persisted almost to the present day.

⁸ It appears that Schlick's work on relativity was instrumental in “converting” the other early positivists to strict empiricism. Thus, Reichenbach's early work, The Theory of Relativity and A Priori Knowledge (1920), takes an explicitly anti-empiricist and neo-Kantian line. In marked contast to the well-known views of The Philosophy of Space and Time (1928), he argues that, although the choices of coordinate system and rest system are indeed arbitrary or conventional, the choice of a metric is not. Accordingly, he rejects Poincaré's “conventionalism” (see the first footnote to Reichenbach's book). Schlick criticizes Reichenbach in the above-mentioned article on Cassirer (vol. 1, p. 333), and by 1922 Reichenbach has capitulated: “conventionalism” is correct and Poincaré is vindicated (see Reichenbach, Selected Writings, 1909–1953, ed. by M. Reichenbach and R. S. Cohen, vol. 2, pp. 34–35, 38–39, 44). Similarly, although it would certainly be incorrect to describe Carnap's position in Der Raum (Kantstudien, Band 56, 1922) as empiricist (his central conclusion is also neo-Kantian: n-dimensional topology is an a priori condition of the possibility of experience), he does present a very clear and rigorous defense of “conventionalism” with respect to metrical structure that is directly inspired by Schlick's account of the significance of general covariance in Space and Time in Contemporary Physics (see Der Raum, p. 83).

⁹ Such a conception of pure geometry would make no sense at all to Kant, for whom even geometrical reasoning requires the a priori manifolds supplied by pure intuition. Geometrical thinking is necessarily spatial in the intuitive sense, and “uninterpreted geometry“ is a contradiction in terms.

¹⁰ Similar views are very much in evidence throughout the period. I have in mind especially C. I. Lewis’ Mind and the World Order (1929) and Russell's Introduction to Mathematical Philosophy (1919) and Analysis of Matter. Carnap's Aufbau presents the logically most sophisticated version. (For Russell and Carnap see W. Demopoulos and M. Friedman, “The Concept of Structure in Russell's Analysis of Matter“, forthcoming in Minnesota Studies in the Philosophy of Science.)

¹¹ Again, such a view only begins to make clear sense in the context of modern polyadic logic. Monadic concepts correspond to unstructured sets whose only formal property is their cardinality. Polyadic concepts, on the other hand, can have infinitely many distinct formal properties: transitivity, reflexivity, connectedness, n-dimensionality, and so on. In Russell's terminology from Introduction to Mathematical Philosophy and The Analysis of Matter, only polyadic concepts have “relation-numbers”. See also Carnap's Aufbau, §§ 11–16.

¹² This is precisely the path taken by the “logical idealism” of Cassirer and the Marburg school. Cassirer is perfectly happy to throw away the autonomous role played by Kant's pure intuition, and equally happy to dethrone mathematical physics from its position of preeminence. All coherent “symbolic forms”—mathematics, physics, art, religion, myth, etc.—are equally respectable and, in particular, have their own characteristic standards of “objectivity”. We can no longer equate the objective with the results of natural science. See, e.g., Einstein's Theory of Relativity (1921).

¹³ Schlick is again ill-served by his poor understanding of the logicist tradition, especially as represented by Wittgenstein's Tractatus. From such a logicist point of view the problem cannot even be set up. For, to formulate Schlick's problem we must take a metalinguistic stance towards the language of physics and regard the primitive terms of that language as uninterpreted schematic letters. But neither of these steps makes sense on a strict logicist conception. First, there is no distinction between object language and metalanguage. There is only one language: the single linguistic framework in which all our concepts and judgments are ultimately related. Second, there are no uninterpreted schematic letters. All symbols are either variables or constants (primitive or defined), and there is no room for a choice of interpretation. The interpretation of variables, for example, is fixed once and for all by their logical forms: first-level variables range over all individuals, second-level variables range over all functions of individuals, and so on. Similarly, there is no problem of distinguishing natural science (synthetic propositions) from pure mathematics (analytic propositions). On a logicist conception, pure mathematics is part of the logical framework of language itself, and so cannot possibly be confused with non-logical propositions. Empirical science is just the totality of non-logical (non-tautologous) truths. (Of course this conception of empirical science has nothing in particular to do with “experience” in the traditional sense, nor does it supply any kind of justification for mathematical physics as it now is or may become. Wittgenstein, for one, is quite sanguine about this: see Tractatus 6.363–6.372). Hence, if Schlick had really understood the Tractatus, he would never have become so hopelessly entangled with the form/content distinction. Nevertheless, we are fortunate that Schlick did misunderstand Wittgenstein, for our conception of logic is in many ways closer to Schlick's “Hilbertian” conception than to the logicist tradition (hence our contemporary problems about “inscrutability of reference” and “ontological relativity”). It would be wrong, however, to simply equate our conception of logic with Schlick's “Hilbertian” view. For our conception is the result of an evolution within the logicist tradition that took its present form only in the synthesis wrought by Gödel in 1930. See the excellent account in W. D. Goldfarb, “Logic in the Twenties”, Journal of Symbolic Logic 44 (1979): pp. 351–368. I am also indebted to Thomas Ricketts for very helpful conversations about these matters.