Abstract
The method of explication has been somewhat of a hot topic in the last 10 years. Despite the multifaceted research that has been directed at the issue, one may perceive a lack of step-by-step procedural or structural accounts of explication. This paper aims at providing a structural account of the method of explication in continuation of the works of Geo Siegwart. It is enhanced with a detailed terminology for the assessment and comparison of explications. The aim is to provide means to talk about explications including their criticisms and their interrelations. There is hope that this treatment will be able to serve as a foundation to a step-by-step guide to be established for explicators. At least it should help to frame and mediate explicative disputes. In closing the enterprise will be considered an explication of ‘explication’, though consecutive explications improving on this one are undoubtedly conceivable.
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Notes
Carnap (1950, ch. I). Note especially the technical remarks on pages 7 and 8, but also his talk about terms on page 3. At any rate, one should take care not to interpret Carnap’s use of the expression ‘concept’ in any of the current thick senses. (1950) is not Carnap’s first investigation into the method of explication: (1945) is an earlier one.
Siegwart’s work seems to have fallen into oblivion with respect to current methodological and metaphilosophical debates. The earlier Hanna (1968) has suffered a similar fate. It seems, only Greimann (2007) and Brun (2016) refer to Siegwart. Quite remote from metaphilosophical debates Glatzer (2012), Hahn (2013), Paasch (2016), and Cordes (2016) employ Carnapian explication in its Siegwartian implementation.
Greimann (2007) and Hanna (1968) have been mentioned already. Justus (2012), Schupbach (2015), and Shepherd and Justus (2015) make some contributions from exental philosophy. Interestingly, Justus (2012, p. 162) observes a related methodological deficit in contemporary (meta)philosophy as I do: “Rather than become a staple of philosophical methodology, explication has been challenged on several grounds.” However, with respect to the works referred to at the end of the preceding note, the first part of the quote appears debatable. As to the current discourse on explication, however, even such dedicated volumes like Wagner (2012) do not boast any systematic descriptions of the full procedure of explication, though it sheds light on many historical issues and includes several comparative investigations into aspects of methodology. To give one (maybe representative) example from this book: Carus’s essay (2012) presents an intuitively interesting distinction between local and global explication; but he describes neither in sufficient detail for the reader to get some clear directions as to how to perform a local or global explication or even what components must be stated when presenting any such explication. It would be desirable to have Carus’ local and global explication defined in an explicit fashion comparable to, for example, Definitions Definitions 17, 18, 20 or 21 below.
In connection with explication Quine (1960, §§53–55) prefers to talk about expressions, too. That there may be a more or less vague concept behind the explicandum (or the explicatum) is not contested here. Theories about the explicandum concept and the explicatum concept can be built upon the explication theory that is developed here and that deals with explicandum and explicatum as expressions. It would be more difficult the other way around if we agree that concepts are abstractions from expressions between which some kind of semantic or syntactic equivalence relation holds.
Some authors prefer the term ‘explicans’ instead of ‘explicatum’ (e. g. Reichenbach (1951, p. 49); an anonymous reviewer drew my attention to this article). I stick with ‘explicatum’ for two reasons: First, the thing doing the explication (literally, the explicans) is not the expression but that what will be called ‘explicative introduction’ below. Second, ‘explicatum’ is the technical term employed in most of the literature.
Usually, if the explicandum language is formal in some sense already, so will be the explicatum language.
These specific requirements are to be distinguished from the generic requirements proposed by Carnap (similarity, exactness, fruitfulness, simplicity), though in some cases the specific requirements may be seen as appropriations of the generic requirements to the explicative scenario at hand. Toward the end of the current section the exclusion of Carnap’s requirements will be briefly motivated.
Siegwart (1997a, §17) lists the same six constituents of an explication (“Explikationsfaktoren”).
Additional constituents could be incorporated (cf. Sect. 5). For now the six constituents named shall suffice. That is, they will at least suffice to make a point about what a structural account of explication could look like.
In accord with the decision not to dive too deep into the syntactic structure of the expressions of the object languages, I will not distinguish between closed and open formulas here. In a more detailed analysis one should be more precise.
If such a language with an empty consequence relation is employed as explicatum language and not only as explicandum language, it will be impossible to prove the success of an explication (cf. Definition Definition 10).
The conception of a language supposed here can be modified to accomodate more complex consequence conceptions. For example, as one reviewer suggests, Bayesian settings may require a consequence relation that admits of strengths.
Siegwart’s rather material definition of an ((in)adequate) explication (1997b, p. 262, 01-02) is not equivalent. Most notably, Siegwart demands the fifth constituent (the criteria of adequacy) to represent distinguished use patterns (“ausgezeichente Verwendungsmöglichkeiten repräsentieren”). In addition, the sixth constituent is just a formula here while, in fact, the explicative introduction may as well assume the form of, say, a metalanguage rule. This is possible in Siegwart’s definition. (For further discussion see Sect. 5!) Despite the differences, I take Definition Definition 3 and the following definitions to keep in the spirit of Siegwart’s theory of explication.
If one reads Definition Definition 3 as (part of) an explication of ‘explication’ (cf. Sect. 5), one may object with Carnap (1950, p. 479): “The result that a proposed explicatum is found too narrow constitutes a much less serious objection than the result that it is too wide.” But the truth of this comparative statement largely depends on what the explicator aims for.
This refers to Carnap’s language I with its successor function ‘nf’. The two definitions D1 and D7-1, here conjoined by conjunction, are the following: ‘nf\((x)=x'\)’ and ‘\(1=0'\)’, respectively (Carnap 1934, pp. 15, 51, 52).
An anonymous reviewer confronted me with such a scenario.
The definitions in (Siegwart 1997b, p. 262) are different in two respects from the ones given here. (i) His definitions are conditional definitions. (ii) He defines by identity and not by biconditional. Each of the two techniques on its own allows him to avoid providing a substitute referent like the empty set. The latter option just moves the reference problem elsewhere. That is why it is avoided here. In addition, conditional definitions are avoided here in order to guarantee eliminability, which Siegwart sacrifices. The resulting disjunctive form of each definiens given here is not seen as overly displeasing and the second disjunct can be ignored for most purposes.
Note that these definitions are not circular. At any stage this is obvious from just one look at the preceding postulates and definitions. It is true that even before Definition Definition 3 reference was made to the six constituents. But it was made only in the motivating prose, not in the postulates or in Definition Definition 3. In fact, one reason for choosing a formal presentation for the theory of explication lies in the ease of monitoring and preventing such semantic troubles as circularity. (There is occasion for this remark: A commentator on an early version of this paper saw some “weird circularity” in these structural definitions.)
To elaborate further: The explicandum of anything that is not an explication is the empty set and it is identical with its explicatum and even with its explicandum language and so on. The underlying mistake here is to speak about the explicandum (explicatum, ...) of a non-explication at all. One reviewer drew my attention to the fact that some find this way of talking problematic. I agree, but this way of talking is not avoided by a conditional definition—conditional definitions just move the matter to the realm of the undecidable. In order to prevent talk about the explicandum of a non-explication, one would have to resort to syntactical exclusion. But this kind of intervention seems disproportionate.
Again, this definition excludes Carnap’s requirements. This will be motivated toward the end of this section.
D7-B in (Carnap 1942, pp. 27–28) is an explicit example for a criterion of adequacy of a truth predicate (in a book that is not explicitly concerned with explication methodology).
By ‘rule of introduction’ I mean the same as by ‘rule of inference’ except what is being licensed is an act of definition or of setting an axiom. Here is one example rule of introduction: If \(\phi \) is a closed formula consistent with any axioms and definitions already set, then one may set \(\phi \) as an axiom. For a full treatment see Reinmuth (2013).
An anonymous reviewer drew my attention to Theorem Theorem 16 and requested the inclusion of more theorems like, for example, Theorem Theorem 11.
In instances of explication the Carnapian requirements are sometimes refined into more specific criteria that would fit well into what is here called the criteria of explicative adequacy (Pinder 2016, Sect. 4.2). This happens particularly often with the requirement of similarity. Here Siegwart (1997b, pp. 270–272) sees a transformation of Carnap’s similarity requirement via Quine into what is now known as the criteria of explicative adequacy.
Additional distinctions of success in explications are given in (Cordes 2016, p. 38).
Cf. Siegwart (1997a, §17): “Binnenexplikation” and “Brückenexplikation”.
The reader may consider it an exercise to formulate a similar paragraph for another picturebook explication, for example for Carnap’s fish/piscis explication.
A paper providing further methodological references is in preparation.
In the proposed conception the introduction of the explicatum cannot be facilitated by the setting of rules for inferring or for constating formulas—at least if the explicatum language does not include its own metalanguage. In this respect the account differs from Siegwart’s.
Creath (2012, p. 162) describes the related but distinct method of logical analysis in these words.
See (1997b, pp. 263–264). Some adjustments to the current framework are made. Definitions Definitions 27 and 30 are entirely new.
Instead of ‘introductory’ some may prefer ‘semantical’ for the fourth kind of explication alternative. This would recognize the explicative introduction as a semantical entity or as related to semantics. But it may also be perceived as inscribing specific meaning-theoretic views into the terminology. I would like to avoid this for now. With regard to lexical explication alternatives theorists may further want to distinguish between whether two explicata differ in their grammatical category or in the arity or in another respect. See (Siegwart 1997b, p. 263).
The CEA for the first explication could be {‘for any person p it should hold that when asked for their gender in most cases p names g(p)’} and for the second {‘the range of values of g is male and female’}. (There may be explications that satisfy both criteria, coincidentally or on purpose.)
Justus (2012, p. 168) draws attention to the fact that lexical explication alternatives are sometimes advisable even if the explicandum is not ambiguous in the explicandum language.
Defining ‘is a definitional explication alternative’ (without ‘just’) would be more adequately achieved by accepting any pair of introductory explication alternatives which are both definitional explications.
Here, in distinction to Siegwart (1997b, p. 264), the binary consonance relation is reflexive for definitional explications.
For an explicative study of ‘pseudo-sentence’ and similar terms see (Cordes 2016).
The title of this section has been used before: (Hanna 1968), (Wilson 2012, p. 205). Greimann’s employment of this construction (2007, Sect. 2) is problematic: According to his own characterization of ‘explication’ he does not provide an explication of ‘explication’. Kitcher (2012, p. 202) applies this term to Carnap’s exposition.
To be sure, staying within the boundaries of CPE still allows us to transition from a less exact part of CPE to “a more exact part of it” (Carnap 1963, p. 935).
This does not mean that each such investigation is problematic. This is most decidedly not so. Carnap’s criteria can be discussed without setting up a whole theory of explication. But one has to accept, that this way a particular systematic shortcoming in the overall explication debate will always remain.
One may compare this enhanced approach to the crutch employed earlier in this section in the identification of the explicative introduction as a conjunction of multiple definitions.
Greimann (2007, p. 266) misleadingly talks about explications without explicata.
This is true at least if the pre-explicative use refers to single authors writing on explication. Presumably the cumulative pre-explicative talk about explication by all authors writing on that topic is much more diverse than the expressions defined here. Glatzer (2012) is an example for disambiguation by means of explication.
This goes for some other desiderata, too. One reviewer drew my attention to the Carnapian desideratum of fruitfulness, specifically.
One example: In (Reinmuth and Cordes 2017, Sects. 4–5) a formal language is introduced which includes ‘Therefore’ as an illocutionary operator. Its application to a formula does not yield a formula. So criteria of adequacy limited to object language formulas will not involve ‘Therefore’. Still, this expression may be seen as an explicatum. Suitable explicanda are any natural language terms expressing acts of inference. Cf. (Hinst 1982; Siegwart 2007a).
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Acknowledgements
For very valuable comments I would like to thank all the participants of the advanced seminar on Theoretical Philosophy at the University of Greifswald and several anonymous reviewers. This considerably improved the text.
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Cordes, M. The constituents of an explication. Synthese 197, 983–1010 (2020). https://doi.org/10.1007/s11229-017-1615-5
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DOI: https://doi.org/10.1007/s11229-017-1615-5