Veikko R. Rantala

One way to obtain a comprehensive semantics for various systems of modal logic is to use a general notion of non-normal world. In the present article, a general notion of modal system is considered together with a semantic framework provided by such a general notion of non-normal world. Methodologically, the main purpose of this paper is to provide a logical framework for the study of various modalities, notably prepositional attitudes. Some specific systems are studied together with semantics using non-normal worlds of different kinds.

Two different but closely related issues in current cognitive science will be considered in this essay. One is the controversial and extensively discussed question of how connectionist and symbolic representations of knowledge are related to each other. The other concerns the notion of connectionist learning and its relevance for the understanding of the distinction between propositional and nonpropositional knowledge. More specifically, I shall give an overview of a result in Rantala and Vadén (1994) establishing a limiting case correspondence between symbolic and connectionist representations and, on the other hand, study the problem, preliminarily investigated in Rantala (1998), of how propositional knowledge may arise from nonpropositional knowledge. I shall also try to point out that on some more or less plausible assumptions, often made by cognitive scientists, these results may have some significance when we try to comprehend the nature of human knowledge representation. Some of these assumptions are rather hypothethical and debatable for the time being and they will become justified in the future only if there will be more progress in the empirical and theoretical research on the brain and on artificial networks. The assumptions concern, besides some questions of the behavior of neural networks, such things as the relevance of pattern recognition for modelling human cognition, in particular, knowledge acquisition, and the relation between emergence and reduction.

The principal aim of this essay is to discuss some logical features of the so-called Classical model of cognitive architecture as it is advocated by J. Fodor and Z. Pylyshyn in their much discussed article 'Connectionism and Cognitive Architecture: A Critical Analysis'. It is pointed out that their structural assumptions have consequences of a logical kind which call into question the view that the Classical architecture (in their sense) can be employed to model human cognition. It seems that the consequences have escaped Fodor and Pylyshyn's notice, or else they have failed to appreciate them, since some of their claims evidently conflict with them. It is also investigated whether the human mind can be characterized as being logical in some weaker sense of logic. Furthermore, it is argued that J. H. Fetzer's view that it is a semiotic system is more realistic than the Classical model, but the distinction he suggests between human cognition and other kinds may be problematic

It used to be a common view in the philosophy of science as well as among the scientists themselves that scientic change has been and will be continuos. Even in the most radical changes of theories the growth of knowledge was claimed to be cumulative. Thus, for instance, physicists may say that in radical, revolutionary changes of theories there obtains, however, some kind of correspondence between the old and new theories; the old theory can be regarded at least as a limiting case of the new one. Thus, for instance, classical particle mechanics is a limiting case of both relativistic particle mechanics and quantum mechanics. Some philosophers, as, e.g., Stegmuller [17], go even further when they claim that there always obtains a reductive correlation in scientic change. The old theory can be reduced to the new one in some specic, or perhaps only intuitive, sense of reduction. However, in the light of what physicists say about correspondence and logicians about reduction, it seems obvious that correspondence should be distinguished from reduction and that one may claim the existence of the former relation, rather than the latter, in the scientic changes. We are not ready to say here what a correspondence relation would exactly consist of, but we will discuss what we think ought to be at least required in comparison with reduction and the related notion of interpre- tation. A detailed case study seems to sustain our views correspondence.