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Explication as a Method of Conceptual Re-engineering

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Taking Carnap’s classic exposition as a starting point, this paper develops a pragmatic account of the method of explication, defends it against a range of challenges and proposes a detailed recipe for the practice of explicating. It is then argued that confusions are involved in characterizing explications as definitions, and in advocating precising definitions as an alternative to explications. Explication is better characterized as conceptual re-engineering for theoretical purposes, in contrast to conceptual re-engineering for other purposes and improving exactness for purely practical reasons. Finally, three limitations which call for further development of the method of explication are discussed.

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  1. Many other uses of “explication” can be found in the literature. In the tradition of Kant, for example, explication is frequently understood as a less ambitious alternative to a proper definition. I will not discuss such uses here. See Beaney (2004) for a historical study of Carnap’s notion of explication in relation to Frege’s, Kant’s and Husserl’s.

  2. It might be argued that these examples should be interpreted as instances of some other method such as conceptual analysis or definition. In Sect. 4, I will discuss some arguments which tell against interpreting them as definitions, but defending the view that they are best interpreted as explications would require case studies, which cannot be undertaken here.

  3. Developments less directly relevant to the project of this paper include Martin’s (1973) proposal to extend the method from concepts to theories, and Justus and Shepherd’s methodological work (Justus 2012; Shepherd and Justus 2015), which focuses on combining explication with experimental philosophy, and on the potential uses of these methods.

  4. Other relevant passages in LFP are referenced in what follows. The remarks on explication which can be found in Carnap’s other writings of the 1940s and 50s (esp. 1945; 1947; 1953; 1956; Creath 1990) are in line with the account in LFP. “Explication” first appears in Carnap (1945: 513); earlier, Carnap used other terms such as “systematization” (in a letter to Neurath, 29.1.1943; see Hegselmann 1985: 283); see also footnote 47.

  5. RSE was written in the mid fifties and completed by October 1958 (Creath 1990: 449).

  6. Italics signal that “fish” does not refer to the animals labelled by the word “fish” but to the concept of being a fish.

  7. Carnap alludes to this in when he points out that philosophers often neglect the clarification of explicanda such as causality, life, mind and justice (LFP 4).

  8. That this is Carnap’s view is confirmed by his emphasis that “the explicandum cannot be given in exact terms” (LFP 4) and that “Naturally, such an elucidation [of the explicandum] can be rendered only in terms that are themselves not yet exact.” (1990: 430; with reference to LFP §2). I pick up on this point in Sect. 5.3.

  9. To simplify, I limit the discussion to explications of concepts that involve n-ary predicates. I leave open how the method can be extended to other categories of expressions [Carnap (1956: 8) mentions, e.g. the definite descriptor the; cf. Siegwart 1997a: 27].

  10. Maher (2010) argues this point against Quine (1960) and Hanna (1968).

  11. Maher (2010: 17) comments: “to talk of a term ‘as used in’ a particular way is just a misleading way of talking about a concept”. As an argument against Carnap’s position in LFP, this misses the point since there Carnap holds that concepts are abstract entities, not terms used in a certain way. The latter, however, reflects Carnap’s use of “concept” in some earlier writings (e.g. Carnap 1966: 3–4).

  12. Siegwart notes that his interpretation targets LFP but not RSE.

  13. This is not to say that there is a tacit distinction between two languages. I will not discuss criteria of identity for languages here, but simply assume that in general the target system of concepts can, but need not belong to the same language as the explicandum.

  14. See Justus (2012) for a more extensive discussion.

  15. See, e.g., Singh (2010: 82).

  16. Carnap (LFP 7) reports that Menger endorses such a criterion of similarity for definitions. It is clear from the context, that Carnap does not approve of Menger’s criterion but rather of the fact that Menger states an explicit criterion (contra Hanna 1968: 33).

    Hanna’s criterion is proposed as an alternative, not as an interpretation of Carnap. Bizarrely, Hanna’s official definition (1968: 37–38) does not require that everything clearly (not) in the explicandum’s extension is (not) in the extension of the explicatum because he allows for the explicandum and the explicatum to have different domains linked by an “effective mapping” (which need not be 1–1). Hence explicandum and explicatum may even have disjoint extensions.

  17. Hanna (1968: 41) concludes that Carnap’s position in LFP is inconsistent. I suggest a more charitable reading which resolves the tensions in line with Carnap’s explanations in RSE (which Hanna does not mention).

  18. Another argument is due to Goodman, who was the first to note explicitly that similarity does not require overlapping extensions (Goodman 1977: 5–7). Carnap accepts this diagnosis in RSE (945) and acknowledges that in some situations similarity may be captured, as Goodman suggests, by a certain kind of isomorphism, which admits that explicandum and explicatum may have disjoint extensions. However, Carnap’s acceptance of Goodman’s isomorphism does not withstand closer analysis because Goodman’s proposal cannot be interpreted as a similarity condition fitting into Carnap’s method of explication. Goodman’s criterion is not meant to be applied to individual concepts but to entire systems of concepts (Goodman 1963: 556; Goodman 1977: 16).

  19. Carnap emphasizes this point: “The new definitions should be superior to the old in clarity and exactness, and, above all, should fit into a systematic structure of concepts.” (2003: v; italics GB). His account of Frege’s explication of the number two points in the same direction. Frege’s achievement was not so much reducing the vagueness of two, but giving a definition in logical terms (RSE 935; cf. LFP 17).

  20. This includes that the logical form of the explicatum needs to be determined (cf. Hempel 1952: 12–14).

  21. For theories of inconsistent concepts, see Eklund (2014).

  22. The distinction between consistency and exactness in the context of explications (though not the terminology) is due to Hanna (1968).

  23. Contra LFP 5, this leaves open the possibility that the explicandum is not vague at all.

  24. Carus (2007a: 265–267) argues for a profound difference between Quine’s and Carnap’s account of explication. However, he “takes a broader view of explication than is usual in the literature” (2007a: 21n23) and uses “explication” to refer to the philosophical programme of Carnap after the introduction of the principle of tolerance. From this perspective, he argues for example that explication is an “external matter” for Carnap, whereas Quine restricts it to internal questions and uses it as a tool for his eliminativist ontological programme. Other writers argue that the similarity between Carnap’s and Quine’s explanations of the method of explication is misleading since the two in fact put the method to different uses. Gustafsson (2014), e.g. argues that Quine’s explications aim at eliminating ontological commitments, whereas Carnap’s aim at incorporating a concept into a formal framework. However, these points do not directly bear on the approach of this paper, which takes a narrower perspective and discusses explication as a method of conceptual re-engineering available to different philosophical programmes. That Carnap and Quine had similar views on the workings of method of explication is compatible with their making different use of it.

  25. Somewhat surprisingly, the literature shows little awareness of the tensions within LFP and between LFP and RSE (exceptions include Hanna 1968; Justus 2012; Siegwart 1997b; Sjögren 2011). It is, for example, hardly ever mentioned that requiring explications to reduce vagueness or to use a formal target language is incompatible with the example of fish and piscis.

  26. The recipe also incorporates ideas from Greimann (2007) and Siegwart (1997a). For a simplified version see Brun and Hirsch Hadorn (2014).

  27. In its most general form, a similarity condition is a statement involving the explicatum that we expect to have a certain truth value. Contra Siegwart (1997a: 32), similarity conditions need not be statements which are framed in terms of the target system and use the explicatum; they can also be metalanguage statements which mention the explicatum (e.g. stating that the explicatum should be an n-place predicate).

  28. The explicatum need not have the same logical form as the explicandum. It may have more argument places if, for example, a comparative concept is explicated by a quantitative one. However, I cannot think of good reasons for introducing an explicatum with less argument places than the explicandum.

  29. Contra Reck (2012: 103), this makes room for conclusive counterexamples. In the example given below: any explication of hardness which deems diamonds to be soft has failed.

  30. Applying this recipe to a specific problem of explication is a creative task, but it can be facilitated by various practical strategies. The most important is to learn from previous or rival attempts at explicating the same or related explicanda. Studying the history of explications may reveal, for example, important ambiguities in the explicandum-term, merits or demerits of different ways of introducing an explicatum, or that certain conditions of adequacy may not be satisfiable (see Carnap 1945: 516–521; Carus 2007a: 270; Hahn 2013: ch. 2.3.2–7; Siegwart 1997a: 33–34).

  31. See Schumann (2008: 20).

  32. Technically, the range of meaningful application (here: minerals) can be captured in two ways. Either the explicatum is introduced by a conditional definition limited to that range (e.g. If x and y are minerals, then: x is harder than y iff …). Or it is introduced by a non-conditional definition with a definiens which includes a condition ensuring that predicating the explicandum is trivially false for all objects outside the range of meaningful application (e.g. x is harder than y iff x and y are minerals and …).

  33. Even Carnap (1945: 513) spoke of “redefining an old [concept]” in his first explicit explanation of explication.

  34. I leave aside here the explicandum-term and the expression connecting definiendum and definiens (e.g. “=df”, or “is defined as”) as additional parts of explications and definitions.

  35. The following arguments are independent of whether a stronger form of equivalence is required for true reportive definitions.

  36. A note on terminology: my use of “stipulative” neither implies that a new term is introduced nor that the definition is not aimed at capturing an established use of the definiendum-term. Definitions with the former property I call “inventive”, those with the second “purely stipulative”.

  37. See The Oxford English Dictionary. 2nd ed. 1986. Oxford: Oxford University Press, entry “vegan”.

  38. Hilbert (1894/1895).

  39. The expression “precising definition” is especially popular in textbooks (e.g. Sinnott-Armstrong and Fogelin 2010; Pfister 2013) and goes back at least to Copi 1953. Sometimes “precisifying definitions” is used (e.g. Sorensen 1991). In the terminology of this paper, ‘precising’ and ‘precisifying’ definitions improve exactness, not precision; hence the scare-quotes.

    This paragraph describes views I have regularly been confronted with in discussions. In print, it is hard to find them defended explicitly, probably just because advocates of ‘precising’ definitions virtually never discuss Carnapian explication. In any case, the following analysis is relevant to all who advocate ‘precising’ definitions or commit themselves to such an idea in their methodological remarks.

  40. This is roughly the kind of explication Hanna (1968) focused on.

  41. The term “re-engineering” is chosen in analogy to “reconstruction” in order to underline that there are two dimensions of adequacy, similarity to an existing concept and usefulness of the new concept. Speaking of “re-engineering” is not meant to suggest that the original concept is already the product of some previous conceptual engineering. The literature usually follows Carnap, who speaks of “engineering” (e.g. 1956: 43; “re-engineering” can be found in Carus (1999); see Eklund (2015) for other uses of “conceptual engineering”). Carnap’s idea of philosophy as a form of engineering has recently been widely discussed, esp. in Carus (2007a) and Richardson (2013).

  42. Conceptual re-engineering with socially relevant goals plays also a key role in Carus’s (2007a) defence of the ideal of explication as a tool of enlightenment.

  43. Actually Hanna’s way of dealing with the distinction between two systems of concepts leads him into serious problems; see footnote 16.

  44. An extension of the method of explication to theories was suggested by Martin (1973), who understands explication exclusively as a matter of vagueness reduction. As far as I know, his idea has not been pursued further.

  45. Hempel (2000) provides a clear account of this shift from individual concepts to theories both from a historical and systematic perspective. See also the references given in Sect. 2.3.

  46. As he occasionally explicitly underlines (e.g. LFP 173; 1953: 190).

  47. In the foreword to the second edition of The Logical Structure of the World (Carnap 2003: v), Carnap declares “explication” to be a more recent replacement for “rational reconstruction” (rationale Nachkonstruktion), although the latter was in fact explained with respect to theories not individual concepts in (2003: § 100). Hempel (2000: 206; see also 1952: 11) reports that the logical empiricists used “explication”, “logical analysis” and “rational reconstruction” in the same sense.

    Carus (2007a) has recently argued for a deep-running distinction between explication and rational reconstruction, while underlining that both proceed by “piecemeal” replacement of concepts (e.g. 2007a: 15–16, 20, 278). The contrast Carus draws primarily relates to the development of Carnap’s overall philosophical programme. In his interpretation, rational reconstruction rests on the “hope that there could be a single, permanent logical framework for the whole of knowledge” (2007a: 20). Explication, on the other hand, rests on the principle of tolerance and a new position on internal and external questions, which admits of introducing alternative explicata and choosing between them on practical grounds (2007a: 263–265).

  48. An example can be found in Bar-Hillel and Carnap (1953: 150), where it is argued that we need two explicata for amount of information since no explicatum will meet the following two conditions: “the content of a conjunction should be equal to the sum of the contents of its components if and only if these components […] have no factual consequences in common” and “the content of the conjunction of two basic statements, say ‘P1a1’ and ‘~ P2a3’ [where P1 and P2 are different primitive predicates] should be equal to the sum of the contents of these statements since they are independent, and this not only in the weak deductive sense of this term, but even in the much stronger sense of initial irrelevance [i.e. inductive independence].”.

  49. Carus emphasizes that Carnap’s philosophical outlook recognizes “the dialectical relation between [ordinary language and constructed systems]” (2007a: xi; see also 2007b: 41–42). However, he also acknowledges that Carnap gives no explicit account of this dialectics (2007a: 19). His interpretation of Carnap’s programme is therefore compatible with the diagnosis I give with respect to Carnap’s explicit methodology.


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A first draft of this paper was written while I was a visiting scholar at Harvard University sponsored by the Swiss National Science Foundation Grant IZK0Z1-125823. For helpful discussions and critical comments, I would like to thank audiences in Zurich, Frankfurt am Main and Karlsruhe, and in particular Christoph Baumberger, Claus Beisbart, Gregor Betz, Catherine Elgin, Jonas Pfister, Geo Siegwart and Inga Vermeulen. Thanks also to two anonymous referees of this journal.

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Brun, G. Explication as a Method of Conceptual Re-engineering. Erkenn 81, 1211–1241 (2016).

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