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Linguistic Untranslatability vs. Conceptual Nesting of Frames of Reference

Linguistic Untranslatability vs. Conceptual Nesting of Frames of Reference Giovanni Bennardo (bennardo@niu.edu) Department of Anthropology and Cognitive Studies Initiative, Northern Illinois University DeKalb, IL 60115 USA content that instantiate these ‘abstract’ relationships. 1 A computational approach to cognition can be proposed by accepting compositionality without embracing a Fregean (logico-positivist) point of view and by turning to the domain of mathematics (e.g., algebra and geometry). In mathematics the primitives of a system are a set of axioms. These axioms generate indefinitely many theorems and each theorem can establish a foundation for yet another theorem. Furthermore, theorems may share parts with other theorems in a redundant manner. The set of relational properties of any cognitive system could be, then, nothing but a theorem derived from a set/s of other theorems. Such a system is compositional by definition. The linguistic analyses in Lehman & Bennardo (2003) yielded the following set of spatial concepts. 2 State : Object; Place Or Locus; Neighborhood: Vicinity, Contact, Interiority; Motion : Time; Direction; Path: Beginning*, Body*, End, (Direction)*; Verticality : Angle: Unit, Quantity (+ or -); Horizontality : Visibility, Left or Right; Center ; Part . (*conceptual content of Vector) Some concepts are not primitives, but rely on other concepts of the same group to function as their axioms. This is the minimal set of axioms that is necessary to account for the theorems (e.g. prepositions, directionals, spatial nouns) that make up the representations of spatial relationships in the languages analyzed. The concept of Object is used with the meaning of any entity existing in a possible world, either concrete or abstract, e.g. table, idea. The place of an Object is the actual amount of Space that it occupies. In other words, a Place is the set of all points within the boundary of an Object (including the boundary points). The Locus of an Object in projective geometry is defined as the collapse of a Place onto any of its interior points. Then, a Locus is a neighborhood of possible projection points, the lower limit being one point. Thus, while a Place is defined by the size, shape, and specific geometry of the Object, a Locus is not and can be arbitrarily reduced to a point. The concept of Neighborhood includes the concept of Vicinity (more than zero distance) between two Objects, the concept of Contact (zero distance) between them and the concept of Interiority, or, one Object in the interior of another. The Neighborhood's border is pragmatically determined. These concepts make up the concept of State. The concept of Motion is an ordered sequence (consequently, with a Direction) of Places (of an Object) Abstract This work focuses on the concept of frame of reference. Levinson (2003) suggested that spatial information encoded in one frame of reference cannot be translated into another one. While this is partially true in language, I argue for a nesting relationship between frames of reference at the conceptual level. A set of spatial concepts suggested by Lehman & Bennardo (2003) informs this investigation. In closing a new typology of frames of reference is proposed. Introduction The concept of frame of reference (FOR) is widely used in the literature about the mental and linguistic representations of spatial relationships. After a review of the terminologies used in different disciplines such as philosophy, linguistics, psycholinguistics, developmental and behavioral psychology, brain sciences, and vision theory Levinson (2003) proposed a definition of the concept and a typology of frames of reference. A FOR is defined as a system of three coordinated axes that create a 3-dimensional space within which spatial relationships are established cognitively and expressed linguistically. Levinson’s typology of FOR includes three systems labeled relative, intrinsic, and absolute. When a FOR is realized linguistically, the information coded in one FOR (e.g., ‘the ball is behind me’) is not translatable into another (e.g., ‘the ball is south of me’). While I agree with most of the discussion presented by Levinson, I find problematic the untranslatability issue. I suggest that untranslatability only holds between linguistically instantiated FORs, while at the conceptual level they are nested into each other. This investigation uses a set of spatial concepts found in Lehman & Bennardo (2003). This conceptual apparatus is the result of analyses conducted on English spatial prepositions, and languages like Burmese, Thai, Italian, and Tongan (Polynesian). After sketching the apparatus, the three FORs are analyzed ending with a suggestion about their conceptual contents and a new typology. The conceptual apparatus A computational approach to the general architecture of cognition was adopted to arrive at the set of spatial concepts suggested by Lehman & Bennardo (2003). Within this approach, cognition is conceived as computational (cf. Ballim & Wilks, 1992), thus generatively ‘abstract’. Only the characteristics of the computational, or, relational spaces that make up what we call ‘cognition’ are reiterated in each cognitive module and not the specific characteristics of the substantive 1 Hirschfeld & Gelman (1994) draw a similar distinction between ‘module’ and ‘domain.’ 2 From now on a concept is indicated by initial capital letter.