Miller, David (2018) Independence (probabilistic) and independence (logical). In: Popper and the Philosophy of Mathematics, Klagenfurt, Austria, 05-07 Apr 2018. Published in: Proceedings of the Karl Popper and the Philosophy of Mathematics Conference pp. 36-40.

Preview	PDF WRAP-Independence-probabilistic-and-independence-logical-Lecture-Miller-2018.pdf - Other - Requires a PDF viewer. Download (788Kb) | Preview
Preview	PDF WRAP-Independence-probabilistic-and-independence-logical-Slides-Miller-2018.pdf - Presentation - Requires a PDF viewer. Download (237Kb) | Preview

Request Changes to record.

Abstract

This paper is concerned with the problem of defining the relation of probabilistic independence in a way that reveals how, if at all, it is a generalization of one of the various relations of logical independence that are familiar to logicians. It is well known that in this regard not all is well within the classical theory of probability, in which probability is intrinsically a singulary function, or within the modern variant of that theory that was given currency in the axiom system of Kolmogorov (1933). More incisiveness might have been hoped for in those subtler axiomatizations in which a relative (binary) probability function is adopted as primitive, especially the axiomatic theory analysed in appendix *iv, and presented systematically in appendix *v, of The Logic of Scientific Discovery (Popper 1959). But it turns out that the classical definition is even less satisfactory here than it is in its classical setting. Near the end of his life Popper became aware that something was amiss, and in the final appendix to the 10th edition of Logik der Forschung (Popper 1994) he proposed an alternative definition of probabilistic independence. This appendix, on which Dorn (2002), §2.4, reports, has, predictably enough, been neglected, anyway in English-language publications (by me as much as by anyone). A recent paper (Fitelson & Hájek 2017) devoted to the same topic does not notice it. It is the primary purpose of the present paper to show to what extent Popper's definition is an advance on the definitions commended by Fitelson & Hájek. But I shall also address once more the question of what logical significance the relation of probabilistic independence en joys, and shall broach the idea that there is a genuinely attractive alternative.

Item Type:	Conference Item (Lecture)
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Social Sciences > Philosophy
Library of Congress Subject Headings (LCSH):	Probabilities, Logic, Symbolic and mathematical, Mathematics -- Philosophy
Journal or Publication Title:	Proceedings of the Karl Popper and the Philosophy of Mathematics Conference
Publisher:	Universität Klagenfurt
Official Date:	2018
Dates:	Date Event 2018 Published
Page Range:	pp. 36-40
Status:	Not Peer Reviewed
Publication Status:	Published
Reuse Statement (publisher, data, author rights):	This paper belongs to the author. Please note that unpublished papers are subject to correction, revision, and modernization, without explicit notice. No version, current or obsolete, of any of these papers and lectures should be cited in print without the author's written permission.
Access rights to Published version:	Restricted or Subscription Access
Copyright Holders:	D. W. Miller
Conference Paper Type:	Lecture
Title of Event:	Popper and the Philosophy of Mathematics
Type of Event:	Conference
Location of Event:	Klagenfurt, Austria
Date(s) of Event:	05-07 Apr 2018
Related URLs:	Organisation Other Other

Request changes or add full text files to a record

Repository staff actions (login required)

View Item

Downloads