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Philosophical Studies

, Volume 176, Issue 2, pp 437–471 | Cite as

Studies in the logic of K-onfirmation

  • Clayton PetersonEmail author
Article

Abstract

This research article revisits Hempel’s logic of confirmation in light of recent developments in categorical proof theory. While Hempel advocated several logical conditions in favor of a purely syntactical definition of a general non-quantitative concept of confirmation, we show how these criteria can be associated to specific logical properties of monoidal modal deductive systems. In addition, we show that many problems in confirmation logic, such as the tacked disjunction, the problem of weakening with background knowledge and the problem of irrelevant conjunction, are also associated with specific logical properties and, incidentally, with some of Hempel’s logical conditions of adequacy. We discuss the raven paradox together with further objections against Hempel’s approach, showing how our analysis enables a clear understanding of the relationships between Hempel’s conditions, the problems in confirmation logic, and the properties of deductive systems.

Keywords

Confirmation Modal logic Monoidal logic Tacked disjunction Monotonicity Irrelevant conjunction Raven paradox 

Notes

Acknowledgements

I am indebted to the comments and suggestions made by anonymous reviewers on previous drafts of this paper. I am also grateful to Stephan Hartmann as well as to the people of the Munich Center for Mathematical Philosophy, where I had the chance to work on that project. This work was financially supported by the Social Sciences and Humanities Research Council of Canada.

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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Munich Center for Mathematical PhilosophyLudwig-Maximilians-Universität MünchenMunichGermany

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