Jaakko Hintikka and Ilpo Halonen Quantum Logic as a Logic of Identification

The tremendous richness of Pat Suppes' work has duly been noted and praised in many of the papers in this collection. Yet it seems to us that the multiplicity of his interests and approaches has not been done full justice. We will try to fill one omission in this paper. It has been noted that one of the characteristics of Pat's work is the use of probabilistic concepts rather than old-fashioned logic. This observation is of course correct, but it should not lead us to forget that Pat has also evinced a great deal of interest in more purely logical methods, both those offered by ordinary logic and those provided by set theory. He has written excellent expositions of both, books that are still unique in their usefulness for applications to the philosophy of science. Moreover, earlier Pat showed a keen interest in one particular application of classical logic concepts to the foundations of scientific theories, viz. the application of the concepts of definition and definability to scientific theories. This paper is written in the spirit of this facet of Pat's work. We will try to show that there are ways of developing further the applicability of logical concepts to the philosophy of science so as to enable us to approach from a new angle a problem which Pat has been keenly interested in, viz. in the problem of quantum logic and perhaps more generally in the conceptual foundations of quantum theory. Pat has discussed this problem area from the vantage point of probabilistic concepts. The fact that we are not in this paper using probabilistic concepts is not due to any animus against them. We are merely trying to see how far another approach which Pat has also used can be employed in the interesting field of quantum theory. Quantum logic is usually studied von oben her. That is to say, quantum theory is viewed in all its conceptual richness and, starting