Semantical Structures for Indeterministic Theories

Dissertation, University of Illinois at Chicago (1984)

John F. Halpin
Oakland University
In chapter 1, I begin the task of giving a semantical theory which is appropriate for the general indeterministic context and which can profitably be applied to the special context of quantum mechanics. I treat the notion of indeterminism, and discuss tree structures. In the second chapter, I consider several theories of tense meant for the indeterministic context. All presuppose tree structures. I defend one of these as the best rendering of simple English future tense. ;In the third chapter, I begin discussing counterfactual conditionals. It is the burden of this chapter to show that one well known analysis of counterfactuals, Stalnaker's theory, is not appropriate for the context of quantum mechanics. I show that his analysis leads all too easily to a contradiction of experimental evidence. Stalnaker's analysis--like many theories of counterfactuals--is based on the relation of comparative similarity between worlds. Recently this basis has been questioned. In chapter 4, I step back a bit from the project of analyzing counterfactuals and consider the foundations for any such analysis. I first argue that the similarity approach is still a promising one. But I go on to argue that a similarity approach requires a non-ordinary notion of 'similarity'. So 'similarity' is in need of explication. This, I argue, is something that should be done on a piecemeal basis. ;In the fifth chapter, I attempt to unify the results of earlier chapters by relating them to the quantum mechanical context. I begin by defending an analysis of counterfactuals which is given in terms of similarity between worlds. I try to show that this theory is a natural one for the quantum mechanical context. And I discuss how, for purposes of the analysis of counterfactuals, 'similarity' is to be understood in the quantum mechanical context. Also, I consider the logical form of quantum mechanical attribution of probability. These attributions, I argue, involve counterfactuals and tense in interesting ways. Utilizing the results of chapters 1 and 2, I argue for a somewhat novel rendering of these quantum mechanical attributions
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