The image of Carnapian Wissenschaftslogik adumbrated in the last section may not be similar to the image of logical empiricism many analytical philosophers are familiar with. In “Two Dogmas of Empiricism” and his other writings, for example, Quine suggests that Carnap’s use of symbolic logic to investigate the foundations of science in the Aufbau should be understood as a continuation of British epistemology as Carnap, purportedly, tries to make good on Russell’s attempt to use symbolic logic to rationally reconstruct the empirical world from sense data alone.
31
Famously, of course, Quine argues that Carnap’s foundational epistemology fails in one of two ways. We have already encountered the first way, that Carnap cannot adequately characterize analyticity in terms of L-truth. The second failure is that Carnap provides us with no reason to think that complicated, theoretical concepts, e.g, concepts from relativistic space-time theory, can be univocally logically reconstructed on the basis of observational concepts alone. In either case, Carnap, according to Quine, is engaged in an untenable foundationalist project. As an alternative, Quine suggests that we instead adopt a non-foundational and holistic approach to the foundations of science, an approach which does not countenance a clear separation between artificial and natural languages but instead draws on the conceptual resources from empirical psychology to inform our epistemological projects.
Another worry about Carnap’s logic of science is that it is, quite literally, on the wrong side of history. In his 1962 The Structure of Scientific Theories (SSR), Thomas S. Kuhn had a permanent influence on the way historians and philosophers study science and its history. Rather than adopting a view about the history of science which tracks the logical structure of scientific theories as they progressively get closer to the truth, Kuhn investigates the material history of how scientists are trained to do science using a specific set of assumptions, scientific concepts and techniques, or a “paradigm”, and finds that, at least for cases of scientific revolutions, scientific communities do not smoothly transition from older to newer paradigms. The central insight is that there is no straightforward way to isolate a single notion of progress defined over changes in scientific theories within scientific communities. For post-Kuhnian philosophers of science, Carnap’s logic of science is seen as embracing exactly that ahistorical and logical revisionist conception of scientific theories which Kuhn’s SSR rejects in favor of a philosophy of science which is invariably intertwined with the history of science.
Fortunately, pioneered by scholars like Alberto Coffa, Michael Friedman, Warren Goldfarb and Thomas Ricketts, there now exists a quite extensive Carnap reappraisal literature which attempts to explain Carnap’s own philosophical views in his own terms rather through the historical narratives bolstered by Quine or Kuhn. Much of this literature has focused, in partic- ular, on Carnap’s philosophy of mathematics, including not only Carnap’s influences like Frege, Russell and David Hilbert, but also his later work on metalogic and his principle of logical
tolerance.32 In contrast to Quine’s version of events, we now have much textual and histori-
cal evidence that Carnap, in his Aufbau, was not concerned with the foundationalist problem of alleviating Cartesian doubts but rather with the problem discussed by nineteenth century German-speaking Marburg neo-Kantian epistemologists: this is the problem of showing how scientific knowledge, through the activity of rational reconstruction, is objective, viz. as in- tersubjectively communicable (see Richardson, 1998). Also, rather than Carnap and Quine being indefinitely at loggerheads, we find that not only do they both reject “intuition” or “com- mon sense” as an independent source of knowledge (see Creath, 1991) but that their separate approaches to the philosophy of science are nearly identical aside from a few methodological differences (see Stein, 1992). When it comes to the philosophical differences between Carnap and Kuhn, not only do we find that Carnap was sympathetic to a manuscript of Kuhn’s SSR (see Reisch, 1991), there are plenty of similarities between Kuhn’s talk of revolutionary/normal science in terms of “paradigm shifts” and Carnap’s own talk of making the practical decision to adopt a linguistic framework (see Earman, 1993; Friedman, 2001; Irzik and Grünberg, 1995). Finally, from a historical perspective, the supposed grip the logical empiricists had on North American philosophy around 1950 doesn’t quite fit the facts: although it is true that logical em- piricism has left a lingering imprint on contemporary philosophy of science, logical empiricism, as a philosophical movement, was far from the dominant movement in post-World War Two North American philosophy (see Creath, 1995; Reisch, 2005; Richardson, 1997a; 2002; 2007).33
Consequently the Carnap reappraisal literature provides us with a subtle and complex ac- count of not only Carnap’s Wissenschaftslogik but of logical empiricism in general. At the end of the previous section, for example, we found that in LSL Carnap does, loosely speaking, embrace some sort of holism for scientific concepts while simultaneously rejecting any foundationalist reading of his logic of science. And it is not as if Carnap leaves no room for sociological and historical investigations about the nature of science provided, of course, that we recognize that such investigations belong to the methodology or pragmatics of science and not the logic of sci-
32
See, for example, Awodey and Carus (2007); Carus (2007); Coffa (1991); Creath (1992; 1996; 2003); Friedman (1999; 2001); Friedman and Creath (2007); Frost-Arnold (2013); Giere and Richardson (1996); Goldfarb and Ricketts (1992); Hardcastle and Richardson (2003); Reck (2013); Richardson (1994; 1996; 1997b; 2004); Ricketts (1994; 1996; 2003); Uebel (2007); Uebel and Richardson (2007); Wagner (2009; 2012).
33
For more of the sociological and larger historical perspective of the Vienna circle, see Cartwright et al. (1996); Stadler (2001); Uebel (2007; 2012b).
ence – in later chapters, we will even see that the history of probability theory and statistics does in fact inform Carnap’s work on inductive logic. Nevertheless, despite these interpretive efforts to clarify Carnap’s mature philosophical project, we may still have lingering doubts about the adequacy of turning to logical machinery, like logical syntax, in order to answer philosophical questions. These worries are to be taken seriously. Far too often in contemporary philosophical discourse genuine philosophical questions are seemingly hijacked by irrelevant technical details and problems.
For example, in a paper originally intended for, but never published in, Carnap’s Schilpp volume, Kurt Gödel attempts to isolate a tension between Carnap’s attitude of logical tolerance and the application of logical systems to the empirical sciences.34 In what follows I outline
Gödel’s argument as found in Goldfarb (1996) and Ricketts (1994). First, Gödel notes that, for Carnap, it seems that the logical relations or rules which fix the consequence relations of a language should satisfy the following constraint: that they don’t determine the truth or falsity of empirical propositions. For to do so would mean that those relations or rules improperly classify such propositions as “analytic.” Gödel calls those logical relations or rules which satisfy the above constraint “admissible.” However, if our logical rules really are admissible, by Gödel’s second incompleteness theorem, a stronger metalanguage is needed to show that our logical language is consistent.35 However, now it seems like all the important philosophical work has
been relocated from the object language to the metalanguage. Carnap cannot now suggest that the decisions to adopt the rules of formation and transformation for the language are purely practical as such decisions must now be informed by whether or not those rules are admissible. But now Carnap’s appeal to logical syntax does little to ameliorate Gödel’s concern about whether the rules of transformation are admissible – isn’t this problem now best left to a logical analysis in the metalanguage, especially natural languages like English?
As Ricketts (1994) points out, Gödel seems to presuppose that while the truth of analytic sentences is determined by the logical rules of the language, the truth of empirical sentences is determined, in some sense, by the world. In other words, “Gödel’s definition of admissibility,” says Ricketts, “employs a language-transcendent notion of empirical fact or empirical truth”
34
See Gödel (1953); Goldfarb (1995). 35
(180). Yet according to Ricketts, “Carnap, in adopting the principle of tolerance, rejects any such language-transcendent notions” (1994, 180). This is indicative of the philosophically radical nature of Carnap’s views on the foundations of logic and mathematics and the application of logic and mathematics to the foundations of science. Given an attitude of logical tolerance, we are free to investigate (and here I adopt a spatial metaphor) a space of alternative logical forms or rules without presupposing that there are any antecedently given, well-defined, notions of “fact”, “verifiable” or “confirmable” according to which a logical relation or rule could be evaluated as admissible.
Of course, as Ricketts clarifies, Carnap can appeal to the standards and methodology of science in order to articulate what Gödel may have in mind by “admissibility”. But Carnap does not take such standards for granted; instead, Carnap understands his commitment to empiricism in a way similar to his commitment to tolerance. Neither is an assertion; rather, both are proposals. Thus Carnap’s commitment to empiricism is to be understood as the adoption of a particular attitude; namely, that our current scientific language provides us with the standards of rational inquiry and empirical significance. In adopting a principle of empiricism, Carnap can appeal to empirical standards of our current scientific theories in order to better inform our practical choices about which logical system will be satisfactory. Consequently, Carnap can only understand Gödel’s concerns about whether our logical system is admissible after one has made the practical decision to embrace an empiricist attitude or stance – otherwise Carnap can at best only make informal sense of Gödel’s attempt to characterize a notion of admissibility, or some other notion of “adequacy,” relative to the empirical world.
Whatever we may think of Gödel’s argument and Ricketts’s rendition of how Carnap could possibly respond to it, we now have a better sense of what is so revolutionary about Carnap’s mature philosophical views. In contradistinction to philosophical methods, like conceptual anal- ysis, which purportedly allow philosophers to “discover” the meaning of concepts or to obtain access to some realm of propositional facts in light of our intuition or a priori reason, Carnap’s mature views emphasize the conventional, volitional and constructivist activities involved in investigating the foundations of science. Rather than answer philosophical questions about the nature of logic and mathematics by arguing that it is the case that X, Carnap, quite character- istically, instead constructs a language which contains the syntactical and semantical resources
to express a question like X – but he never claims that his own logical reconstruction of X is logically, empirically or conceptually identical to X. But what is particularly philosophical about that?36 In a sense, the rest of the dissertation draws on the history of philosophy of science to
try and provide some explanation using my own account of conceptual engineering (from chapter 3) as an interpretive framework for explaining the philosophical upshot of Carnap’s work on a pure inductive logic and his various attempts to explain how that inductive logic can be applied to the empirical sciences, especially the foundations of statistics and decision theory (see my chapters 4 and 5).
For the moment I want to discuss Carnap’s own attempt to explain his mature views when, in 1945, he adopts the vocabulary of explications instead of Wissenschaftslogik.37 The method of
explication, according to Carnap, concerns the “replacement of a pre-scientific, inexact concept (which I call “explicandum”) by an exact concept (“explicatum”), which frequently belongs to the scientific language” (1963b, 933). More specifically, the method of explication is, for Carnap, a theory of scientific concept formation based on the historical observation that scientific concepts, after being initially introduced informally, later come to be replaced with more exact qualitative, comparative or quantitative concepts.38 The basic idea is that we first focus on an explicandum
in natural language, call it C, the usage of which we agree is vague or inexact and then study the ways in which C is inexact or vague by trying to clarify how it is used in ordinary speech. In which contexts is the term used? In those contexts, if we all agree that it is being used correctly, why is it useful? When is it being misused? This is the clarification step in an explication. After this step is finished, we next adopt some logical system, call it L, which already has well-defined syntactic and semantical rules. We then define, in L, one or more semantical concepts, call them ‘C’ and ‘C†’, which are each possible explicata. Lastly, we can then give an interpretation for ‘C’ and ‘C†’ in L and then investigate the mathematical properties of these new concepts;
36
As Peter Strawson puts the point in Carnap’s Schilpp volume: “For however much or little the constructionist technique is the right means of getting an idea into shape for use in the formal or empirical sciences, it seems prima facie evident that to offer formal explanations of key terms of scientific theories to one who seeks philosophical illumination of essential concepts of non-scientific discourse, is to do something utterly irrelevant – is a sheer misunderstanding, like offering a text-book on physiology to someone who says (with a sigh) that he wished he understood the workings of the human heart” (1963, 504-5).
37
Carnap first introduces this method in Carnap (1945b): it is not a coincidence that this paper is also one of his first published papers on the nature of probability and induction.
38
In general, Carnap talks about this method in the following places (this list is not exhaustive): §§1-6 and chapter IV of Carnap (1962b), Carnap’s replies to Peter Strawson in Schilpp (1963) and Carnap (1956).
if we find these interpretations satisfactory, we can then apply the language L, which now includes the concepts ‘C’ and ‘C†’, to some domain of objects. Thus we can then study how each applied explicatum measures up, so to speak, to our expectations regarding the usefulness and exactness of C in particular contexts. Carnap’s talk of explication is none other than the process of locating an adequate application of a pure logic.
It is crucial to keep in mind, however, that what I call the measure of the “success” for any process of explicating an explicandum with a particular explicatum is, for Carnap, not an all-or- nothing affair but is rather a matter of weighing the differing degrees to which the explicatum satisfies a number of practical requirements; namely, the requirements of (i) similarity to the explicandum, (ii) exactness, (iii) fruitfulness and (iv) simplicity (The Logical Foundations of Probability; hereafter LFP, 7). According to Carnap, the reason why the explicatum should be exact is so that it can be introduced “into a well-connected system of scientific concepts” and a concept is as fruitful insofar as it can be used to formulate “universal statements,” like empirical laws or logical theorems (LFP 7). Of all the requirements, simplicity is the least important. Lastly, for Carnap there is no limitation on how many explicata we can design and construct – this is a consequence, it seems, of his attitude of logical tolerance.
We will return to the details of Carnap’s method of explication in chapter 4. Before we move on, however, it is important to note that the explicit use of a logical system is not always necessary for the provision of an adequate explicatum. As Carnap clarifies his views in response to criticism from Strawson’s contribution to Carnap’s Schilpp volume, Carnap says that he “[sees] no sharp boundary line but a continuous transition” between “everyday concepts and scientific concepts” (1963b, 934). In contrast to Carnap’s method of rational reconstruction in the Aufbau, explications for concepts are not limited to artificial languages but can be carried out in natural language too. But that doesn’t mean that artificial languages, like symbolic logic, have no use. “A natural language,” Carnap explains,39
is like a crude, primitive pocketknife, very useful for a hundred different purposes. But for specific purposes, special tools are more efficient, e.g., chisels, cutting-machines, and finally the microtome. If we find the pocketknife is too crude for a given purpose and creates defective products, we shall try to discover the cause of the failure, and then either use the knife more skillfully, or replace it for this special purpose by a more suitable tool, or
39
Strawson uses the tool metaphor himself to describe the difference between two philosophical methods, Carnap’s method of rational reconstruction and naturalism (here: ordinary language philosophy) (1963, 503).
even invent a new one. The naturalist’s thesis is like saying that by using a special tool we evade the problem of the correct use of the cruder tool. But would anyone criticize the bacteriologist for using a microtome, and assert that he is evading the problem of correctly using a pocketknife? (Carnap, 1963b, 938–9)
The working analogy Carnap employs in this passage explores how using logic to study the foun- dations of science is similar to using a tool or instrument to accomplish some task. In the next section, after discussing how Carnap himself uses this analogy, I discuss a number of philosophers who adopt this engineering analogy to help illuminate Carnap’s mature philosophical views.