In a journal article on conceptual change, Carey (2004) proposed that we develop a concept of numbers by a process she refers to as “bootstrapping”. This process was similar to Deacon’s (1997) framework for how we develop an understanding of symbolic representation. Carey described how we develop an understanding of systems of relationships within two sets of objects, one being number words (“one”, “two”, “three”, etc.) and the other being quantities (e.g., 1, 2, 3, etc.), then later develop a system of mappings between the two systems which establishes the basis for conceptual understanding. In Deacon’s description, the process of developing a one-to-one mapping between a referring object (e.g., the word “one”) and the object of reference (e.g., the quantity of 1) represented a third kind of system, distinct from the systems of relationships and the system os mappings between systems.
Both researchers suggested that conceptual or symbolic meaning was derived from the mapping of a system of relationships among words to a system of relationships among referents. Number words (“one”, “two”, “three”…), without an underlying understanding of what those words mean, are just sounds we perceive. At this stage, learning the words and even their ordered relationships is a kind of memorization / behaviorism (Deacon, 1997). We eventually develop connections between our perceptions of quantities and their corresponding number words, identifying the perception of the word “one” with the perception of one thing, the perception of the word “two” with the perception of two things, and so on. However, this too is initially a kind of learning as memorization / behaviorism. Assuming that we inherently develop a system of relationships among all perceptions, it is still necessary to either have (Carey, 2004) or develop (Deacon, 1997) a distinct system of relationships among words before both systems and the connections between them can be fully integrated for conceptual or symbolic understanding.
Yet it is important to note that this integration goes beyond what is usually meant by “mapping”. It is necessary to make the distinction between perceiving a relationship connecting a word and a quantity, and perceiving the word as the quantity / the quantity as the word. According to Deacon’s original definitions, the representations transform from a relationship of indexical reference to a relationship of iconic reference. That is, at a certain level, we no longer differentiate between the representation of the word and the representation of the quantity. It is this step that allows us to further integrate two levels of information — the sense of the word and the sense of the quantity, as well as the relationships of the word to other words and the relationships of the quantity to other quantities — into a singular concept / symbolic representation.
What Carey refers to as conceptual understanding and Deacon refers to as symbolic reference are developed through this process of integrating two systems of perceptual and associative relationships. The primary distinction between their descriptions is a question of sequencing. This, however, can be explained by the different contexts they were studying. Carey was focused on number concepts as a specific instance of learning symbolic references underlying language, while Deacon was focus on the initial comprehension of symbolic reference. Nonetheless, both inform an understanding of a concept/symbol as the emergent effect of integrating the perception of a reference, the perception of its referent, and the associations of both.
Bootstrapping capitalizes on our ability to learn sets of symbols and the relations among them directly, independently of any meaning assigned to them in terms of antecedently interpreted mental representations. These external symbols then serve as placeholders, to be filled in with richer and richer meanings. The processes that fill the placeholders create mappings between previously separate systems of representation, drawing on the human capacity for analogical reasoning and inductive inference. The power of the resulting system of concepts derives from the combination and integration of previously distinct representational systems.
Bootstrapping and the Origin of Concepts | Susan Carey
First, a collection of different indices are individually learned [mappings between words and objects]. Second, systematic relationships between index tokens are recognized and learned as additional indices [mappings among words]. Third, a shift in mnemonic strategy to rely on relationships between [words] to pick out objects indirectly via relationships between objects [mappings among objects].
The Symbolic Species: The Coevolution of Language and the Brain | Terrence Deacon