Abstract
According to a seminal paper by Barsalou (Frames, fields, and contrasts, 1992), frames are attribute-value-matrices for representing exemplars or concepts. Frames have been used as a tool for reconstructing scientific concepts as well as conceptual change within scientific revolutions (Andersen and Nersessian, in Philos Sci 67:224–241, 2000; Chen and Barker, in Philos Sci 67:208–223, 2000; Chen, in Philos Sci 70:962–974, 2003; Barker et al., in Thomas Kuhn, 2003; Andersen et al., in The cognitive structure of scientific revolutions, 2006; Votsis and Schurz, in Stud Hist Philos Sci 43:105–114, 2012, in Concept types and frames. Application in language, cognition, and science, 2014). In the frame-based representations of scientific concepts developed so far the semantic content of concepts is (partially) determined by a set of attribute-specific values. This way of representing semantic content works best for prototype concepts and defined concepts of a conceptual taxonomy satisfying the no-overlap principle. In addition to the semantic content of prototype concepts and defined concepts, frames can also contain empirical knowledge that is represented as constraints between the values of the frame. Beside prototype concepts and defined concepts, theoretical concepts that are multiply operationalized play an important role in science. However, so far no frame-based representation of theoretical concepts has been proposed. In this paper, it will be shown that theoretical concepts can be represented by frames and that frame-based representations of prototype concepts and defined concepts have another structure than frame-based representations of theoretical concepts. In order to explicate this difference, we will develop a frame-based method for representing all three kinds of concepts by means of mathematical graph-theory. One important consequence will be that the constraints of a frame representing a theoretical concept are entailed by the structure of the frame, as opposed to a frame representing defined or prototype concepts.
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Notes
Beside the representation of prototype concepts, frames are often used to represent family resemblance concepts in order to reconstruct incommensurability and conceptual change in scientific revolutions (cf. Andersen et al. 1996, 2006; Chen et al. 1998). For the sake of brevity, we do not discuss the similarities and differences between prototype and family resemblance concepts and confine to the former.
The prototypicality i.n.s. of a property corresponds to the notion of cue validity of Rosch et al. (1976, p. 384).
Note that we presuppose a narrow view of definitions as conjunctions of properties. More complicated versions of definitions—for example, a disjunction of properties—will not be discussed in this article.
In the following, we will always refer to standard English and standard Spanish. However, some of the examples that are unacceptable in standard English might be acceptable in some idiolects.
The symbol “*” designates the unacceptability of the clause that follows the symbol.
Since the publication of Chomsky and Lasnik (1977), constructions of this kind have usually been referred to as that-t filter violations. However, in this paper we use the original notion of Perlmutter (1971) that, in accordance with Gilligan (1987, p. 105), is assumed to address the same grammatical phenomena.
Perlmutter (1971) is considered to be the first analysis that correlates the three grammatical phenomena SSE, NTS and NNTS and explains the typological differences with a single principle. Although Perlmutter (1971) did not call the explaining principle a parameter, in the generative literature he is considered to be one of the initiators of parameter research, especially of the research on the pro-drop parameter, since “the data Perlmutter noted is the first cross-linguistic generalization, i.e., parameter, in generative grammar. For better or worse, it has served as the basis for all subsequent work on Pro-drop phenomena” (Gilligan 1987, p. 76).
For the following definitions, we refer to Hartsfield and Ringel (1990, Ch.1, Ch. 6.2 and Ch. 7.3).
The notion of specialization originates in structuralism (also called non-statement view of theories), according to Sneed (1971), Stegmüller (1976, 1979), and Balzer et al. (1987) (for a short introduction see Moulines 2002; Andreas and Zenker 2014; Kornmesser 2008, 2014). The non-statement view of theories follows Suppes’ (1957) method of axiomatizing a theory by the definition of a set-theoretic predicate that contains the concepts and laws of the theory. A structure that satisfies the conditions of the predicate axiomatizing the theory is called a model of the theory. Hence, according to the non-statement view of theories, a theory T is represented extensionally as a set of models. A specialization \(\hbox {T}^{\prime }\) of a theory T is a strengthening of the logical content of T by adding further special laws to T (Balzer and Sneed 1977, pp. 201–202; Balzer et al. 1987, pp. 168–171). Therefore, the set of models satisfying \(\hbox {T}^{\prime }\) is a subset of the set of models satisfying T. Thus, the main idea of our notion of specialization remains the same as in structuralism, but is translated to a frame-based representation: The content of the operationalized concept is strengthened by adding further operationalizing conditions. Thus, the number of contraints entailed by the multiple operationalization increases (see below), and, from an extensional point of view, the number of entities in the extension of the operationalized concept decreases.
Safir (1985) uses the terms NOM-drop Parameter and Free Inversion Parameter to designate the two parameters.
Even every single axiom entails empirical content, since SSE, NTS, and NNTS are reconstructed as permanent dispositions. Hence, we get from one of the axioms, say Ax-1, the following empirical content: \(\forall \hbox {x}_1 ,\hbox {x}_2 ,\hbox {y}\left( {\hbox {L}\left( \hbox {y} \right) \wedge \hbox {NTS}\left( {\hbox {x}_1 ,\hbox {y}} \right) \wedge \hbox {NTS}\left( {\hbox {x}_2 ,\hbox {y}} \right) \rightarrow \left( {\hbox {G}\left( {\hbox {x}_1 ,\hbox {y}} \right) \leftrightarrow \hbox {G}\left( {\hbox {x}_2 ,\hbox {y}} \right) } \right) } \right) \).
Beside the similarities to the linguistic representation of theories, we think that there are interesting parallels to the non-statement view of theories (see footnote 10). Elaborating on the relations between frame-based representations of theories and the more common methods of representing theories linguistically as sets of statements (Carnap) or as sets of models (Sneed, Stegmüller) is of great interest for the comparison of different methods of theory-representation as, for example, it is done by Zenker (2014) and Zenker and Gärdenfors (2014), who compare the representation of conceptual change in empirical science by frames, conceptual spaces, and sets of models.
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Acknowledgments
For valuable comments I am indebted to Michael Schippers, Mark Siebel, and two anonymous referees.
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Kornmesser, S. A frame-based approach for theoretical concepts. Synthese 193, 145–166 (2016). https://doi.org/10.1007/s11229-015-0750-0
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DOI: https://doi.org/10.1007/s11229-015-0750-0