Krzysztof Wójtowicz

Some remarks on Hartry Field's notion of “logical consistency”

In this article the notion of “logical consistency” in the sense introduced by Field in [Field 1991] is discussed. Field argues, that it is possible to introduce the notion of “logical consistency” as a primitive metalogical notion, which is independent from model-theoretical and proof-theoretical notions. In this article I want to indicate some difficulties of this standpoint, and to identify some hidden presuppositions. I also would like to show, that introducing this concept (at least in the form considered by Field) does not really support Field’s argumentation against realism. I confine myself to the analysis of Field’s standpoint, and will not discuss the more general issue, whether it is possible to treat the notion of “logical consequence” as a primitive notion.

Theory of quantum computation and philosophy of mathematics. Part I

The aim of this paper is to present some basic notions of the theory of quantum computing and to compare them with the basic notions of the classical theory of computation. I am convinced, that the results of quantum computation theory (QCT) are not only interesting in themselves, but also should be taken into account in discussions concerning the nature of mathematical knowledge. The philosophical discussion will however be postponed to another paper. QCT seems not to be well-known among philosophers (at least not to the degree it deserves), so the aim of this paper is to provide the necessary technical preliminaries presented in a way accessible to the general philosophical audience.