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Teoria wielości rzeczywistości Leona Chwistka. Rys krytyczny

100%

Bożek H.

ARGUMENT: Biannual Philosophical Journal

2014

tom 4

nr 2

405-424

The purpose of this paper is to offer a logico‑philosophical critical overview of the theory of multiple realities (TWR). The paper is divided into three sections. In the first section I present a brief history of the development of some ideas, which combined together form the conceptual framework of the theory in question, whose main thesis is that there is more than one reality. In the second part I present (and try to address) some interpretations of TWR, which can be described as: ontological; epistemological; esthetical; logical ad mixed interpretations. When doing so, a special emphasis is laid on the presentation of an explication of TWR based on theory of models, an explication authored by Teresa Kostyrko. This explication rests on a conditional recognition of the particular ‘realities’ of Chwistek’s theory as proper models (i.e. those, which fulfill the condition of the identity of meaning of theory’s fundamental notions) of the theories of reality, with the provision that such models are indeed constructible. In the last section of my paper I propose a preliminary appraisal of the TWR as well as a way to reengineer this theory in order to avoid some of its difficulties. By appealing to Kostyrko’s idea on one hand and the spirit Quinean ontological relativism on the other, I wish to argue as follows: (1) ‘reality’ is the name of the set comprising all meanings of the term ‘reality’; (2) under particular conditions these meanings can be arranged in a theory, which posseses a proper model (scientific discourse, some forms of the common talk); (3) model proper designate by definition classes of objects, which we regard as existent on the grounds of a given theory. The above set of theses forms the core of a concept, which I propose to call the ‘manifold reality’ in order to differentiate it from TWR, the development of which theory it is, as well as its modification towards a new kind of ontology.

Analiza krytyczna podstaw teorii wielości rzeczywistości Leona Chwistka

84%

Bednarz G.

Estetyka i Krytyka

2017

nr 1(44)

25-38

The aim of the article is to present a few criticisms of the foundations of Leon Chwistek’s philosophy. Completeness postulate, imposed on all correct philosophical systems by Chwistek, and which is supposed to be in conflict with conventionalism, is criticised. Correctness of some Chwistek’s axioms is called into question. Axioms for six intermediate realities are given. I argue in favour of model theory interpretation of manifold reality.

J-energy preserving well-posed linear systems

67%

Staffans O. J.

2001

tom Vol. 11, no 6

1361-1378

The following is a short survey of the notion of a well-posed linear system. We start by describing the most basic concepts, proceed to discuss dissipative and conservative systems, and finally introduce J-energy-preserving systems, i.e., systems that preserve energy with respect to some generalized inner products (possibly semi-definite or indefinite) in the input, state and output spaces. The class of well-posed linear systems contains most linear time-independent distributed parameter systems: internal or boundary control of PDE's, integral equations, delay equations, etc. These systems have existed in an implicit form in the mathematics literature for a long time, and they are closely connected to the scattering theory by Lax and Phillips and to the model theory by Sz.-Nagy and Foias. The theory has been developed independently by many different schools, and it is only recently that these different approaches have begun to converge. One of the most interesting objects of the present study is the Riccati equation theory for this class of infinite-dimensional systems (H2- and Hinfty-theories).

J-energy preserving well-posed linear systems

67%

Staffans O. J.

International Journal of Applied Mathematics and Computer Science

2001

tom 11

nr 6

1361-1378

The following is a short survey of the notion of a well-posed linear system. We start by describing the most basic concepts, proceed to discuss dissipative and conservative systems, and finally introduce J-energy-preserving systems, i.e., systems that preserve energy with respect to some generalized inner products (possibly semi-definite or indefinite) in the input, state and output spaces. The class of well-posed linear systems contains most linear time-independent distributed parameter systems: internal or boundary control of PDE’s, integral equations, delay equations, etc. These systems have existed in an implicit form in the mathematics literature for a long time, and they are closely connected to the scattering theory by Lax and Phillips and to the model theory by Sz.-Nagy and Foiaş. The theory has been developed independently by many different schools, and it is only recently that these different approaches have begun to converge. One of the most interesting objects of the present study is the Riccati equation theory for this class of infinite-dimensional systems (H^2 - and H^∞ -theories).