Abstract
In recent years, attention for the work of Rudolf Carnap has shifted from polemical discussion to placing Carnap in his intellectual context. Thus, the central question is no longer whether Carnap contributes to solving our current problems, but whether he solved the problems of his day and age. This contextualist approach has resulted in a deeper and more refined understanding of, in particular, Carnap’s early works and has focused on Der logische Aufbau der Welt.
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Notes
E.g., Goodman’s and Quine’s well-known worry about the “at”-relation employed in §§126127.
Rudolf Camap, Der logische Aufbau der Welt. Berlin: Weltkreis-Verlag 1928, §16; the notion of “structure” is introduced in §12. As has been pointed out by Friedman and others, Camap’s goal in the Aufbau is to show that at least one constitution system is possible. This means, among other things, that Carnap is concerned with showing that there is at least one way of casting all of science in a purely structural form.
Camap, Aufbau,00A712.
Camap, Aufbau, 00A7 00A7153–155.
Michael Friedman, “Camap’s Aufbau reconsidered”, in: Noûs 21, 1987, p.533; Alan Richardson, Carnap’s Construction of the World. Cambridge: Cambridge University Press 1998, p. 194.
My presentation in this section owes a lot to the following papers: Thomas Ryckman, “Conditio Sine Qua Non? Zuordnung in the Early Epistemologies of Cassirer and Schlick”, in: Synthese 88, 1991, pp.57–95, and Don Howard, “Relativity, Eindeutigkeit,and Monomorphism: Rudolf Carnap and the Development of the Categoricity Concept in Formal Semantics”, in:Ronald N. Giere/Alan W. Richardson (eds.), Origins of Logical Empiricism. Minneapolis: University of Minnesota Press 1996, pp.115–164. These papers elucidate the concepts of “co-ordination” and “univocalness”, respectively.
Göran Sundholm suggested to me that “correlation” may be a better translation of Zuordnung. Although `correlation“ is used in Blumberg’s translation of Schlick’s Allgemeine Erkenntnislehre, I will stick with the more usual `co-ordination” here.
Compare “The connection between members [of a series] is in any case created by means of some general law of co-ordination…”,(Emst Cassirer, Substanzbegrii f and Funktionsbegrff Berlin: Bruno Cassirer 1910, p.21) with “The manifold of sensations is co-ordinated with the manifold of real objects in such a way that every connection that can be established in one totality indicates a connection in the other.” (ibid.,pp.404–5) Since the connections co-ordinated in this way are referred to as `co-ordinations“ themselves, the ambiguity is clear.
The elements, which we first obtained from intuition, have to be analysed ever more thoroughly, they must be resolved ever more completely in purely conceptual definitions in order to become truly objects of mathematical consideration. Thus intuition, wherever we appeal to it, does not constitute the proper ground of truth of theorems. It is rather like an ultimate unresolved remainder, which awaits further division and operation by thought; it is the goal that points the way for our purely logical formation of concepts.“ (Ernst Cassirer, ”Kant and die moderne Mathematik“, in: Kantstudien 17, 1907, pp.29–30). All translations from German texts in this paper are my own, unless a translation is mentioned in the reference.
That Schlick is aware of the problem of univocalness is clear from: “(…) the individual entity is to be designated uniquely with the help only of the most general names (…)” (Moritz Schlick, General Theory of Knowledge. transl. by A.E. Blumberg, Wien: Springer Verlag, 1974, p.14.)
Schlick, op.cit.,p.32.
The co-ordinating of two objects with one another, the relating of one to the other, is in fact a fundamental act of consciousness, not reducible to anything else. It is a simple ultimate that can only be stated, a limit and a basis, which every epistemologist must ultimately press toward.“ (Schlick, op.cit.,p.383) Schlick is quite outspoken on the elimination of pure intuition: ”(…) we have looked in vain for a pure intuition that might serve as the basis for empirical intuition by supplying it with its form and lawfulness.“ (ibid.,p.358)
These terms are listed in the references of: Rudolf Carnap, Der Raum. Ein Beitrag zur Wissenschaftslehre. Kantstudien Erganzungsheft Nr.56, ( Berlin: Reuther and Reichard, 1922 ), p. 85.
Carnap, Der Raum,p.61.
Carnap, Der Raum,p.23.
Rudolf Carnap, “Über die Aufgabe der Physik”, in: Kantstudien 28, 1923, pp.90–107; Rudolf Carnap, “Dreidimensionalität des Raumes und Kausalität”, in: Annalen der Philosophie und philosophischen Kritik,4, 1924, pp.105–130; Rudolf Carnap, “Über die Abhängigkeit der Eigenschaften des Raumes von denen der Zeit”, in: Kantstudien 30, 1925, pp.331–345; Rudolf Carnap, “Eigentliche und uneigentliche Begriffe”, in: Symposion I, 1927, pp.355–374.
physics expresses itself neutrally by means of a purely formal relation of co-ordination“ (”Über die Aufgabe“, loc.cit.,p. 100); ”The relation between this kind of experience of the second stage and that of the first stage is produced by co-ordination“ (”Dreidimensionalitat“, loc. cit.,p.107)
In fact, Carnap shows that the principle of simplicity can be applied in one of two forms (“Über die Aufgabe”, loc.cit.,pp.103–105)
Ibid.,p.106.
Ibid,p.107.
Compare Schlick’s statement of formalism: “None of the concepts that occur in the theory designate anything real; rather they designate one another in such a fashion that the meaning of a concept consists in a particular constellation of a number of the remaining concepts.” (Schlick, op.cit.,p.37)
The main argument is reconstructed, in slightly different terms than mine, in Howard, loc.cit.,pp.156–160; and Richardson, op.cit.,pp.43–47. Richardson focuses on the contrast with Schlick’s formalism, but he puts little emphasis on the problem of univocalness as the driving force behind Camap’s discontent with it.
Carnap, Aufbau, §136.
Carnap, Aufbau, § 179.
This optimism is expressed elegantly in the well-known railway metaphor of Camap, Aufbau,§ 14: if the structure of the relation of “railway-connectedness” does not suffice to individuate cities, we can first use relations of connectedness by other means of transportation, then “historical” relations, and finally “all concepts from factual disciplines (Realwissenschaften)”. Surprisingly, Carnap resolves the remaining lack of univocalness by stipulating that the difference between cities is a merely subjective one. In my opinion, this might show that Carnap has written this part of the Aufbau while still under the influence of Schlick’s formalism. In §153, apparently written at a later time, Carnap again discusses univocalness in the context of implicit definition, but he claims that a lack of univocalness is highly improbable, not that it would be merely subjective.
Carnap, Aufbau,§95.
Cf. Jean van Heijenoort, “Logic as Calculus and Logic as Language”, in: Synthese 17, 1967, pp.324–330 for a discussion of universalism in the work of Frege and the Principia Mathematica.
Carnap, Aufbau, §154.
Logic (including mathematics) consists only of conventional stipulations about the use of signs and of tautologies based on these stipulations.“ (§107); ”Logic does not have a domain of its own at all, but it contains those statements that hold (as tautologies) for all objects of any arbitrary domain.“ (§154)
Bertrand Russell, Introduction to Mathematical Philosophy, London: Allen and Unwin, 1919, p. 169.
Russell, op.cit.,pp.203–205. For Camap, there is well-known autobiographical evidence to support his incomplete apprehension of the Tractatus cf. the passage from the Archives cited by Jodle Proust, “Formal Logic as Transcendental in Camap and Wittgenstein”, in: Noils 21, 1987, p.502.
I would like to thank Michael Friedman, Jaakko Hintikka, David Hyder, Herman Philipse, and Göran Sundholm for their comments on earlier drafts of this paper and the version read during the HOPOS 2000 conference in Vienna. Any mistakes remaining are, of course, purely my own.
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Houkes, W. (2002). Carnap on Logic and Experience. In: Heidelberger, M., Stadler, F. (eds) History of Philosophy of Science. Vienna Circle Institute Yearbook [2001], vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1785-4_22
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