Cognitive Grounding

The Gärdenfors model of cognition

I will make use of a model of our cognitive system proposed by Gärdenfors (2000). This model is structured in three levels – the symbolic, conceptual and connectionist ones – and provides a gradual transition from the outward interactions with the world towards the neuronal network in the brain.

Gärdenfors’s knowledge interest is to model representations of the cognitive system for explanatory and constructive purposes such as developing artificial neuron networks. According to him, there are two dominating approaches for modeling the cognitive system: the symbolic and the associative ones. A particular type of association is connectionism, where the information carrying elements are modeled on the neural network in the brain.

This has resulted in two branches of research concentrating on either the symbolic or the connectionist approach. In the symbolic approach, the brain is regarded as a Turing machine that manipulates symbols according to certain rules. The connectionist approach models the brain as a system of connected neurons that respond to stimuli of various kinds. These two approaches should be seen as complementary rather than separate, since the symbolical representation presumes the connectionist one in the sense that the nervous system is a prerequisite for symbol formation.

However, Gärdenfors claims that important aspects of the cognitive system such as conceptacquisition, i.e., how concepts are learnt and internalized, cannot be adequately captured by either one of these approaches. It is also unclear how to model the transition between the connectionist and the symbolical levels since the representations used are very dissimilar. The step from neuron models to symbols becomes too wide. To this end, Gärdenfors proposes a third, intermediate level: the conceptual one. Thus, Gärdenfors winds up with three levels (see Figure 1): the symbolical, conceptual and connectionist ones.

Figure 1.

The model of cognition suggested by Gärdenfors

Gärdenfors proposes that the structure of the conceptual level is geometrical; hence the subtitle of the book: “The geometry of thought”. Human beings have a cognitive capacity for generating ordering relations of stimuli based on what Gärdenfors calls quality dimensions (ibid, p. 6). Examples of such quality dimensions are temperature, weight and spatial dimensions like height, width and depth. Some quality dimensions are culturally dependent, e.g. time which may be conceived as linear or circular (ibid, p. 28).

The quality dimensions can be associated with geometrical, topological or ordering structures (time being one of them), and they provide the basis for building what Gärdenfors calls conceptual spaces. The cognitive elements on the conceptual level are concepts that are spatially related to each other (ibid, p. 5). Due to the structure of quality dimensions is it possible to talk about distances along these dimensions. Such distances in the conceptual space are closely related to similarity judgments,

The conceptual level provides an appropriate mechanism for grounding the symbolic level, which would otherwise have to be grounded directly in the connectionist level. A major point in Gärdenfors’s contribution is that such a direct grounding cannot be convincingly argued for:

The many dimensions of neural network converge into regular structures on the conceptual level through a reduction of neural dimensions to quality dimensions (ibid, p. 240). Thus, the conceptual level is a basis for the uppermost, symbolic one.

The conceptual structure makes it possible to inquiry into the nature of meaning. According to Gärdenfors, social meanings emerge from the heads of individuals:

Clearly, this position differs from the one taken in this book, where activity is regarded as the genesis of all cognitive effects. Gärdenfors’s position runs into problems regarding semiosis (the formation of signs) and the question of how the mental entities came into the head to begin with. Another problem is the social nature of meaning: how is communal meaning among individuals possible? Gärdenfors realizes this difficulty:

The way Gärdenfors tackles this problem is to start from the observation that any association between a thing and a concept must take place in the brain. There is nothing in the external world that can hold this association. Therefore, in a communicative situation where a speaker and hearer are communicating about things, their cognitive systems must be aligned to some degree. This imposes certain constraints on individual cognitive representations; constraints that are, according to Gärdenfors, related to the “linguistic power structure”:

One assumption put forward by Gärdenfors is that the situation will drive the representations towards the most economical way of achieving a reasonable communal meaning. Social interactions will result in a set of “communicable references”, which are located in the brains of both speaker and hearer as cognitive structures. This stance leads to a chicken-and-egg problem: are cognitive structures prerequisites for, or emergent results of successful communication? The answer given by Gärdenfors is “both”:

This position is in essence not far from the praxis perspective, although ontologically and epistemologically different. On the other hand, the praxis perspective is quite compatible with the position that meanings are elements of the cognitive system of humans.