Abstract
One way of explaining Rudolf Carnap’s mature philosophical view is by drawing an analogy between his technical projects—like his work on inductive logic—with a certain kind of conceptual engineering. After all, there are many mathematical similarities between Carnap’s work in inductive logic and a number of results from contemporary confirmation theory, statistics and mathematical probability theory. However, in stressing these similarities, the conceptual dependence of Carnap’s inductive logic on his work on semantics is downplayed. Yet it is precisely the conceptual resources made available to Carnap from his work on semantics which allows him to understand his work on inductive logic as a kind of conceptual engineering project. The aim of this paper is to elucidate this engineering analogy in light of Carnap’s mature views through the lens of both inductive logic and semantics.
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- 1.
I would like to thank Alan Richardson, S. Andrew Inkpen, Taylor Davis and Stefan Lukits for their comments and suggestions on earlier drafts of this paper.
- 2.
The claim is not, however, that a theory of semantics is required to make this distinction as Carnap draws a similar distinction between mathematical and empirical geometry (e.g. in Carnap 1939).
- 3.
Here \(\mathfrak{L}\) is simply a first-order language with N many named constants representing the balls in the urn and T many basic monadic, “color,” properties. Early on, Carnap assumed these properties, expressed as Q-properties, were independent. However, following the work of John G. Kemeny, this earlier assumption was soon relaxed with the technical devices of meaning postulates and families of properties (see Carnap 1971).
- 4.
For example, Reichenbach’s straight rule (which is just the relative frequency \(s_{t}/S\)) is given by Eq. 1 when λ = 0; but note that \(\mathfrak{c}_{0}\) is not regular.
- 5.
Later Carnap instead uses models and sigma algebras, see Carnap (1971, §§1, 3).
- 6.
- 7.
Kuipers (1978) recognizes Carnap’s project as a philosophical project of concept formation.
- 8.
Using the semantic concept of a constituent, Hintikka extends the λ-system to two parameters so as to assign non-zero confirmation values to universal generalizations. For details, see Niiniluoto 2011 and the references therein.
- 9.
Importantly, Carnap’s views on pragmatics, semantics and syntax precede Carnap’s introduction of the explication nomenclature in 1945.
- 10.
Carnap is explicit in 1962 that his aim is neither to provide confirmations for entire scientific theories nor to automate scientific inference, e.g. see his discussion (motivated by results from Alan Turing) of “the impossibility of an automatic inductive procedure” (192 ff.).
- 11.
Thanks to an anonymous referee for prompting me to clarify this paragraph.
- 12.
Richardson (2013), for example, has suggested that Carnap’s treatment of logical languages as instruments was influenced by his earlier interests in metrology. Carus (2007), on the other hand, offers a more systematic, but controversial, account of Carnap as conceptual engineer. A more extensive discussion of the engineering analogy—including how to understand engineering itself—can be found in French (2015).
- 13.
Technicalities aside, the main idea is that each state description \(\mathbf{k}\) has a certain degree of order, which Carnap understands as an explication of the regularity of the actual world. Letting r 1, …, r T be the actual relative frequencies of the T many monadic properties in \(\mathbf{k}\), Carnap explicates the degree of order of \(\mathbf{k}\) as the squared sum of the r i ’s, ∑ r i 2. The value \(\hat{\lambda }\) is optimal for \(\mathbf{k}\) when \(\hat{\lambda }= (1 -\sum r_{i}^{2})/(\sum r_{i}^{2} - 1/T)\). Moreover, \(\mathbf{k}\) is “non-extreme” in the sense above means that \(\sum r_{i}^{2}\not =1\); also, note that \(\hat{\theta }\) is equal to one of the r i ’s (see §24). Carnap had plans to published more on this concept but did not; although see the manuscripts regarding this concept and the related abstract concept of entropy, RC 086-07-01 and RC 080-15-01, at the Rudolf Carnap archives at the Archives of Scientific Philosophy (ASP) at the University of Pittsburgh.
- 14.
Although Carnap does have written correspondence with statisticians like L. J. Savage, de Finetti, Jerzy Neyman and Harold Jeffreys, besides Savage pointing out to Carnap in 1952 that λ cannot vary with sample size (ASP RC 084-52-25), there seems to have been little interest among statisticians in Carnap’s λ-system (but see Good 1965). In this sense, Carnap’s intervention in the problem of estimation is a failure of sorts.
- 15.
A much less condensed discussion of the ideas in this paragraph can be found in French (2015). In future work I plan to extend this view of Carnap as conceptual engineer to various other ares of contemporary philosophy of science, for example, with various notions of “progress” in empirical concept formation (e.g. see Kuipers 2007); with other kinds of engineering relevant for philosophy, viz. in terms of Herbert Simon’s notions of “bounded rationality” and “satsificing” (e.g. see Wimsatt 2007); or finally with how social scientists, especially economists, use and employ mathematical models (e.g. see Morgan 2012).
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French, C.F. (2015). Rudolf Carnap: Philosophy of Science as Engineering Explications. In: Mäki, U., Votsis, I., Ruphy, S., Schurz, G. (eds) Recent Developments in the Philosophy of Science: EPSA13 Helsinki. European Studies in Philosophy of Science, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-23015-3_22
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