Studies in the logic of K-onfirmation
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.
KeywordsConfirmation Modal logic Monoidal logic Tacked disjunction Monotonicity Irrelevant conjunction Raven paradox
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.
- Crupi, V. (2015). Confirmation. In E. N. Zalta (Ed.), The Stanford encyclopedia of philosophy. Palo Alto: Stanford University.Google Scholar
- Fitelson, B., & Hawthorne, J. (2010). How Bayesian confirmation theory handles the paradox of the ravens. In E. Eells, J. H. Fetzer (Eds.), The place of probability in science: In honor of Ellery Eells (1953–2006) (pp. 247–275). Springer: Dordrecht.Google Scholar
- Goodman, N. (1983). Facts, fiction and forecast (4th ed.). Cambridge: Harvard University Press.Google Scholar
- Maher, P. (2004). Probability captures the logic of scientific confirmation. In C. Hitchcock (Ed.), Contemporary Debates in Philosophy of Science (pp. 69–93). Blackwell Publishing Ltd.Google Scholar
- Maher, P. (2005). Confirmation theory. In D. M. Borchert (Ed.), Encyclopedia of philosophy (2nd ed.). Basingstoke: Macmillan.Google Scholar
- Peterson, C. (2014a). Analyse de la structure logique des inférences légales et modélisation du discours juridique. Ph.D. thesis, Université de Montréal.Google Scholar
- Peterson, C. (2014c). Monoidal logics: How to avoid paradoxes. In A. Lieto, D. P. Radicioni, M. Cruciani (Eds.), Proceedings of the international workshop on artificial intelligence and cognition (AIC 2014) (Vol. 1315, pp. 122–133). CEUR Workshop Proceedings.Google Scholar
- Peterson, C., & Kulicki, P. (2016). Conditional normative reasoning with substructural logics: New paradoxes and De Morgan’s dualities. In O. Roy, A. Tamminga, & M. Willer (Eds.), Deontic logic and normative systems (pp. 220–236). London: College Publications.Google Scholar
- Schurz, G. (1991). Relevant deduction: From solving paradoxes towards a general theory. Erkenntnis, 35(1–3), 391–437.Google Scholar
- Sprenger, J. (2009). Hempel and the paradoxes of confirmation. In D. M. Gabbay, S. Hartmann, & J. Woods (Eds.), Handbook of the history of logic (Vol. 10, pp. 235–263). Amsterdam: Elsevier.Google Scholar
- Swinburne, R. G. (1971). The paradoxes of confirmation: A survey. American Philosophical Quarterly, 8(4), 318–330.Google Scholar
- Sylvan, R. & Nola, R. (1991). Confirmation without paradoxes. In G. Schurz & G. J. W. Dorn (Eds.), Advances in scientific philosophy: Essays in honour of Paul Weingartner on the occasion of the 60th anniversary of his birthday, Pozniań studies in the philosophy of the sciences and the humanities (Vol. 24, pp. 5–44). Amsterdam: Rodopi.Google Scholar