1. The Paradigm of Cognitive Sciene
In the article on “Cognitive Science” in the online “Stanford Encyclopedia of Philosophy” (http://plato.stanford.edu/archives/fall2012/entries/cognitive-science/) the basic idea of the research paradigm of Cognitive Science is described as follows (Section 3):
The central hypothesis of cognitive science is that thinking can best be understood in terms of representational structures in the mind and computational procedures that operate on those structures. While there is much disagreement about the nature of the representations and computations that constitute thinking, the central hypothesis is general enough to encompass the current range of thinking in cognitive science, including connectionist theories which model thinking using artificial neural networks.
Most work in cognitive science assumes that the mind has mental representations analogous to computer data structures, and computational procedures similar to computational algorithms. Cognitive theorists have proposed that the mind contains such mental representations as logical propositions, rules, concepts, images, and analogies, and that it uses mental procedures such as deduction, search, matching, rotating, and retrieval.
So let’s assume we can describe the human mind in this way and explore some consequences.
2. Formal Descriptions in Cognitive Science
A theory of cognitive processes that models them in terms of representational structures thought of as some kind of data structure and computational procedures thought of as some kind of algorithm can be viewed as a formal theory or as an algorithm that describes the cognitive processes.
If the content of the representations is taken into account, the procedures and representations together may also be viewed as a formal theory about the world since it describes knowledge about the world and can be used to derive expectations or predictions about the world. However, as a theory of the world, it must necessarily be incomplete. The knowledge represented in the data structures may be partially incorrect and will contain gaps since there are always facts in the world that we do not yet know about.
So at any time, there is only a limited amount of circumstances in the world that is covered by our knowledge. We can think of this as those aspects of the world that we expect or those that we are able to predict.
3. New Information and Extensions of Theories
Now consider that a new piece of information enters the cognitive system that is not part of this set of expected facts, e.g. you see or hear something unexpected, something new and surprising. So if we think of the procedures and representations of the mind as a formal theory, this new piece of information cannot be derived from that theory (that it cannot be derived is why we call it “new”). Using some of our mental procedures, we would apply some of the knowledge contained in our “knowledge base” of representational structures to examine the properties of the new information, and then store the new information and what we have found out about it in the knowledge base. The knowledge base is thereby extended.
Since the new piece of information is not derivable from the old knowledge base, the extended knowledge base together with the procedures forms a new formal theory that is not equal to the old one and cannot be reduced to it or be derived from it. A larger set of expectations can be derived in this new theory, a larger set of circumstances in the world is covered by it.
In an information processing system, the processing of a piece of information can be influenced by another piece of information. In programming languages, for example, there is typically an “IF…THEN…ELSE” construct by which the processing of some information can be made dependent on a condition about some (possibly different) information. So if the formal theory describing the mind can be extended by new information, the processing of further information can be influenced by this new piece of information. Thus, the processing of further information is described by an extended theory that is not the same as the original theory. We can say: the system is reprogrammed by the new information.
4. A Dynamic View of Cognition
The classical view of cognitive science would be that the system is divided into a fixed core of procedures and a knowledge base in which some knowledge is stored by means of some representations. The representational language in which the bits of knowledge are encoded is fixed as well.
But if the processing of information can be influenced by information in the knowledge base, you can think of this as a modification of the procedures. Therefore, new procedures might arise in the system.
If new procedures can arise in the system then new representational structures or “languages” can arise as well. The way the procedures are using the information in the representational structures determines the syntax and semantics of those representational structures. If procedures can change, the representational structures they operate on may change as well. There would be no fixed knowledge representation language by which knowledge or thoughts are represented. Instead, such a “language” could be extended by new constucts.
Let us assume we had a formal theory of the mind that we think to be general. Then we could again add new information to it that is not derivable within it and thus arrive at a new theory. The mind extended by the new information would be capable of performing cognitive processes not describable in terms of the original theory since these processes could depend on the newly added information. So the hypothesis that the original theory is general could not be kept up. So in this dynamic view of cognition, the mind is a “creative system” in the sense the term is used on this blog: an information processing system that can develop out of the scope of any formal theory about it. Every such theory is incomplete.
The result of this line of thought is that there is no fixed structure of cognition. To sum it up: new information that enters the mind from the outside can modify the way the mind is working. And since this new information is not derivable from previously known information, there is no single formal theory that would cover all possible cognitive processes.
(The picture, showing a PET scan of a human brain, is from http://commons.wikimedia.org/wiki/File:PET-image.jpg.)
 The notions of “formal theories” and of “algorithms” as used here can be viewed as equivalent.