The basics

Throughout his career, Carnap developed a number of constructed formal systems, as early as in Der logische Aufbau der Welt (1928) and Logische Syntax der Sprache (1934). Indeed, the notion of a constructed language is perhaps the main theme running through all of Carnap’s large oeuvre. In his later writings, in particular in Meaning and Necessity (1947) and Logical Foundations of Probability (1950), the key methodological concept became that of explication,Footnote 8 which is not exclusively tied to constructed languages and formalization,Footnote 9 but often does take the form of applications of artificially constructed languages. Explication is a process whereby a vague, informal concept, either from everyday life or from more regimented contexts such as scientific contexts (but in earlier stages of development), is given a more exact, often formalized formulation.Footnote 10 As such, the approach is a successor of some related earlier methodologies used by Frege, Russell, and others (Beaney 2013). Here is one of Carnap’s earlier formulations of the idea of explication, from Meaning and Necessity:

The task of making more exact a vague or not quite exact concept used in everyday life or in an earlier stage of scientific or logical development, or rather of replacing it by a newly constructed, more exact concept, belongs among the most important tasks of logical analysis and logical construction. We call this the task of explicating, or of giving an explication for, the earlier concept; this earlier concept, or sometimes the term used for it, is called the explicandum; and the new concept, or its term, is called an explicatum of the old one. (Carnap 1947, pp. 7–8)

The most worked-out exposition of the concept of explication is to be found in Chapter 1 of Logical Foundations of Probability. It is there that Carnap offers the now famous Fish-Piscis example to illustrate the general idea:

When we compare the explicandum Fish with the explicatum Piscis, we see that they do not even approximately coincide […]. What was [the zoologists’] motive for […] artificially constructing the new concept Piscis far remote from any concept in the prescientific language? The reason was that [they] realized the fact that the concept Piscis promised to be much more fruitful than any concept more similar to Fish. A scientific concept is the more fruitful the more it can be brought into connection with other concepts on the basis of observed facts; in other words, the more it can be used for the formulation of laws. (Carnap 1950, p. 6).

It is thus the fruitfulness of the concept Piscis that motivates the adoption of Piscis in certain contexts where Fish had so far been used, in particular scientific contexts. But fruitfulness is not all that it takes for an explication to be successful (though it is arguably the main criterion, as will be argued below). Carnap in fact presents four main criteria of adequacy for an explication:

A concept must fulfill the following requirements in order to be an adequate explicatum […]: (1) similarity to the explicandum; (2) exactness; (3) fruitfulness; (4) simplicity. (Carnap 1950, p. 5)

Indeed, while there is considerable room for maneuver when engaging in explication (a theme related to Carnap’s famous principle of tolerance: “In logic, there are no morals”), this does not mean that ‘anything goes’. There are standards that an explication must satisfy to be deemed adequate, and some explications will be more successful than others (though it is possible that one fares better on one criterion while a different one fares better on another, for one and the same explicandum). Let us briefly look into three of the requirements, which on the list above are presented in a somewhat unsystematic order. (I leave simplicity aside, as it does not have much to add to the present discussion).

(1) Similarity is a rather weak criterion for Carnap; as we saw with the Fish-Piscis example, the two concepts “do not even approximately coincide”. However, to ensure that an explicatum is an explicatum for a given explicandum, some degree of similarity must be in place; otherwise, the two concepts might end up being about completely different things. (This then leaves room for the ‘change of topic’ objection, more on which below.) Carnap resorts to the notion of use in order to ground the relation of similarity:

The explicatum is to be similar to the explicandum in such a way that in most cases in which the explicandum has so far been used, the explicatum can be used; however, close similarity is not required, and considerable differences are permitted. (Carnap 1950, p. 7)

In the case of Fish-Piscis, the idea is that zoologists would henceforth use Piscis in most of the situations where they would have used Fish prior to the introduction of the concept Piscis.

(2) Exactness might prima facie appear to be the main requirement for a successful explanation; indeed, Carnap says that the explicatum being more exact than the explicandum is essential for an explication.Footnote 11 Critics of Carnapian explication (e.g. Strawson—see Sect. 3.2 below) often object to what they perceive as an excessive preoccupation with criteria and methods imported from the exact sciences that are (arguably) out of place in philosophical contexts—in other words, they object to the perceived scientism of the general approach espoused by Carnap and other members of the Vienna Circle.

The scientism charge has been amply discussed in recent reappraisals of the Vienna Circle movement, and has been shown to be at the very least questionable (Wartofsky 1982; Uebel 2004; Romizi 2012). Importantly, within the specific interpretation of Enlightenment ideals by some members of the Vienna Circle, in particular Neurath and Carnap (Carus 2008) (more on which shortly), formalism and mathematization were in fact viewed as means for intellectual emancipation, “an instrument against obscurantism” (Wartofsky 1982, p. 89). Setting aside the criticism of Enlightenment ideals that have been put forward by a wide range of authors (with varying degrees of success), what matters for us here is the idea that, for Carnap, exactness is not an end an sich; it is an instrument, a means to an end, or to a variety of specific ends as the case may be. This brings us directly to the third, arguably most important requirement for a Carnapian explication: it must be fruitful.

(3) Fruitfulness is the crucial requirement for a successful explication (as argued in Carus 2008; Dutilh Novaes and Reck 2017), and yet Carnap says surprisingly little on what he means by fruitfulness. Here is one of his few relevant remarks:

The explicatum is to be a fruitful concept […] useful for the formulation of many universal statements (empirical laws in the case of a nonlogical concept, logical theorems in the case of a logical concept). (Carnap 1950, p. 7)

The idea of an explicatum leading to many universal statements may be understood in terms of predictive power and testability: if it allows for the formulation of universal statements, then it will generate predictions that can be tested. In the case of non-empirical theories, allowing for the derivation of many theorems might amount to the general idea of the fruitfulness of concepts and definitions [as discussed by Frege (Tappenden 1995)]. Moreover, as suggested in the passage quoted above on the Fish-Piscis example, an explicatum’s fruitfulness is related to its ability to connect with other concepts on the basis of observed facts.Footnote 12

However, an account of the fruitfulness of an explicatum solely in terms of its capacity to generate universal statements and predictions, and to be connected to other observed facts, remains somewhat meager. Interpreters of Carnap have taken upon themselves to flesh out what fruitfulness might mean beyond Carnap’s own inchoate remarks. Carus (2008) developed a resolutely pragmatic interpretation of fruitfulness; elsewhere (Dutilh Novaes and Reck 2017) I have offered an account of fruitfulness in terms of the cognitive boost afforded by explication and formalization. In the next section, I further argue that fruitfulness may also be understood in political terms, i.e. in terms of promoting much-needed social reform and liberation from obscurantism (thus agreeing with the main lines of Carus’ interpretation).

Fruifulness and political engagement

In Carnap’s own writings, little textual evidence can be found to ground a fully-fledged political articulation of the fruitfulness criterion for explication specifically. Formulations of more explicit political commitments, and in particular of the idea that philosophy was of critical relevance to the project of socio-historical changes towards socialism, are mainly to be found in Carnap’s earlier writings, as one of the members of the ‘Left Vienna Circle’ (Uebel 2004).Footnote 13 The concept of explication, in turn, was to be fully articulated only in his later writings. But granting at least some degree of methodological continuity between Carnap’s earlier work and his later work (given the centrality of formal systems and constructed languages throughout his career), as well as continuity in his political commitments,Footnote 14 a case can be made for the relevance of these political commitments also with respect to his later work, and explication in particular.

For Carnap, explication embodies the value of intellectual liberation from the shackles of paralyzing traditions. A passage by one of his students, Richard Jeffrey, illustrates this connection particularly well:

Philosophically, Carnap was a social democrat; his ideals were those of the enlightenment. His persistent, central idea was: “It’s high time we took charge of our own mental lives”—time to engineer our own conceptual scheme (language, theories) as best we can to serve our own purposes; time to take it back from tradition, time to dismiss Descartes’s God as a distracting myth, time to accept the fact that there’s nobody out there but us, to choose our purposes and concepts to serve those purposes, if indeed we are to choose those things and not simply suffer them. […] For Carnap, deliberate choice of the syntax and semantics of our language was more than a possibility—it was a duty we owe ourselves as a corollary of freedom. (Jeffrey 1992, p. 28)Footnote 15

In other words, explication exemplifies the ideal of epistemic autonomy, most famously captured by Kant’s Enlightenment motto: ‘Sapere Aude!’Footnote 16

The general political background for Carnap’s thought has been amply documented and discussed by a number of authors (Carus 2008; Romizi 2012; Uebel 2004), so we need not rehearse the details here. So far however, while setting up the stage, these brief considerations remain much too general to ground an interpretation specifically of Carnap’s criterion of fruitfulness as related to political engagement. Fortunately, there is at least one fairly clear connection between his brief remarks on fruitfulness mentioned above and political ideals, through the concept of prediction. Recall that he emphasized the role of explication as leading to the formulation of universal statements, which in turn allow for testable predictions to be made regarding the relevant subject matter. One might think that prediction thus understood is not a particularly politicized concept; the idea of predictions which can be tested and thus can refute or corroborate theories is a core component of classical conceptions of science. But predictions also allow for interventions to be brought about, thus bringing us closer to political ideals of social reform. The political dimension of predictions is well described in the following passage by Wartofsky, commenting on Neurath:

Further, one of the hallmarks of the scientific conception of the world, and certainly central to Neurath’s view, was the importance of prediction in the sciences. The social value of prediction was seen by Neurath as a means of applying rational controls over hypothetical plans of action—whether in research in the sciences, involving the use of experiment, or in social planning (or in Neurath’s own term, “social engineering”). (Wartofsky 1982, p. 89)

(Wartofsky then goes on to comment on how this project of ‘social engineering’ came to be seen as inherently authoritarian and oppressive by critics such as the Frankfurt School philosophers.) Given that on these points Carnap and Neurath were very much in agreement, it is not too much of a stretch to connect the idea of the fruitfulness of an explication as generating universal statements to the social value of prediction within projects of social engineering.Footnote 17

At this point, it might seem that a fruitful explication may well have the potential to serve the purposes of social engineering, but that this potential is rarely or perhaps never truly realized. To alleviate this worry, I now discuss a concrete example of an explication of a socially relevant concept, which leads to precise predictions and thus can serve as an instrument for social intervention and social reform: the explication of the concept of intersectionality offered in Bright et al. (2016).

Bright et al. indeed explicitly present their analysis as an instance of explication. The explicandum, in this case, is the concept of intersectionality, which is a theoretical concept but might be said to be “in an earlier stage of scientific or logical development” (a phrase from the passage from Meaning and Necessity quoted above). It was introduced in the 1990s by legal scholar K. Crenshaw to capture the idea that different dimensions of oppression, targeting different disadvantaged groups, may interact (intersect) in non-trivial ways. For example, the challenges encountered by black women in the United States are different from the challenges encountered by either black men or white women, because gender and race intersect in ways that give rise to different kinds of challenges. But while intersectionality thus described is a powerful and useful concept, it has also been the target of fierce criticism, in particular with respect to its ability to generate predictions about the phenomena in question. (As described by Bright et al., some proponents in fact reject the idea that the concept of intersectionality should lead to testable predictions at all.)

Bright et al. thus give the concept of intersectionality a causal interpretation in terms of the formalism of graphical causal modeling, which in the last decades has become an influential approach in a number of areas (Spirtes et al. 1993; Pearl 2000). As seen in Fig. 1 (taken from Bright et al. 2016, p. 67), directed acyclic graphs (DAGs) allow for the representation of causal relations between different phenomena. In this graph, Parental Income and Education are represented both as direct causes of Wealth, and additionally, Parental Income is an indirect cause of Wealth via its influence on Education. In turn, Education is independent of Gender given Race and Parental Income (no arrow between these two nods), which roughly means that, in the contexts that the graph represents/describes, boys and girls have the same access to education holding these two parameters fixed (say, within the same family).Footnote 18 But Gender does affect Wealth, as typically men are wealthier than women even holding the other parameters fixed.

Fig. 1 Directed acyclic graph (DAG) Full size image

Equipped with this formalized causal account of intersectionality, researchers are better prepared to understand the underlying causal relations between different aspects of the phenomena in question (i.e. being a member of different social groups and being thereby privileged or disadvantaged in certain respects), make relevant predictions, and potentially formulate interventions that may address the social inequalities in question. In Fig. 1, for example, the fact that Education is independent of Gender given Race and Parental Income suggests that the kind of intervention needed to bridge the pay gap between men and women that is still observed even in so-called modern, industrialized societies is not that of investing in early education for girls. Instead, the phenomenon seems to be caused by factors within the dynamics of the labor market itself and the distribution of domestic labor at home. These observations indicate the kind of intervention needed to address this inequality, such as: policies for gender pay equity in the workspace; policies to increase male involvement in childrearing, such as paternal leave.Footnote 19

And thus, the explication of intersectionality in terms of graphical causal modeling by Bright et al. is an excellent example of the potential for social and political relevance of the explication methodology, and indeed an illustration of the links between predictions and potential for social engineering. In effect, this explication scores high on the fruitfulness criterion as described by Carnap because it leads to a number of general statements which can then both serve to test the empirical adequacy of the framework, and to guide targeted social interventions at a later stage.Footnote 20 While this is but one example of how Carnapian explication, including its focus on formalization, can be enlisted for politically and socially relevant projects, there is no reason to think that this should be an isolated case. Concrete uses of explication for such projects may still be somewhat rare, but this simply means that there is much potential for future work to be done in this direction.Footnote 21