On comparison of theories by their contents
type: Item
instance of: scholarly article
title: On comparison of theories by their contents
zbMATH Open document ID: 0714.03006
DOI: 10.1007/BF00370211
author: Jan Woleński
published in: Studia Logica
publication date: 1989-01-01T00:00:00Z
review text: The author considers the claim that Popper's definition of verisimilitude has paradoxical consequences in the case of false theories. According to Popper, a reasonable definition of verisimilitude of empirical theories, regarded as deductive systems, should satisfy a condition (P) that compares the truth and falsity contents of theories: A theory \(T_ 2\) is closer to truth than a theory \(T_ 1\) iff either a) the truth content of \(T_ 1\) is a proper subset of the truth content of \(T_ 2\) and the falsity content of \(T_ 2\) is equal to or a subset of the falsity content of \(T_ 1\); or b) the truth content of \(T_ 1\) is equal to or a subset of the truth content of \(T_ 2\) and the falsity content of \(T_ 2\) is a proper subset of the falisity content of \(T_ 1\). In \textit{Objective Knowledge}, Popper proposes a definition of the content of a theory T as the union of the truth and falsity contents of T, and defines the truth content of T as all the true consequences of the axiomatic base A of T, and the falsity content of T as all the false consequences of A. Miller and Tichy have proved that this definition does not satisfy the adequacy condition (P). The author suggests that the problems indicated by them are caused by the application of the consequence relation (Cn) to false sentences, and he proposes that Cn should be applied to true sentences only and the dual consequence operation dCn to false ones. On this basis he proposes an alternative definition of the content of theories. He shows that this definition avoids the paradoxes of Miller and Tichy, and brings some other arguments in favour of it. He concludes by observing that the applications of metalogic to the analysis of theories have hitherto been dominated by the concept of assertion and the consequence relation Cn, although the concept of rejection and related consequence operations also seem indispensable in such analyses.
reviewed by: I.Gullvåg
Mathematics Subject Classification ID: 03A05
zbMATH DE Number: 4174883
zbMATH Keywords: philosophy of science
zbMATH Keywords: verisimilitude
zbMATH Keywords: false theories
zbMATH Keywords: Popper
zbMATH Keywords: empirical theories
zbMATH Keywords: adequacy condition
zbMATH Keywords: dual consequence operation
zbMATH Keywords: content of theories
MaRDI profile type: Publication
cites work: POPPER'S QUALITATIVE THEORY OF VERISIMILITUDE
cites work: ON THE COMPARISON OF FALSE THEORIES BY THEIR BASES
cites work: Theory of rejected propositions. I
cites work: Q4063408
cites work: ON POPPER'S DEFINITIONS OF VERISIMILITUDE1
cites work: Verisimilitude revisited
full work available at URL: https://doi.org/10.1007/bf00370211
OpenAlex ID: W2031462950
description: scientific article; zbMATH DE number 4174883