This paper offers a probabilistic treatment of the conditions for argument cogency as endorsed in informal logic: acceptability, relevance, and sufficiency (RSA). Treating a natural language argument as a reason-claim-complex, our analysis identifies content features of defeasible argument on which the RSA conditions depend, namely: (1) change in the commitment to the reason, (2) the reason’s sensitivity and selectivity to the claim, (3) one’s prior commitment to the claim, and (4) the contextually determined thresholds of acceptability for reasons and for claims. Results contrast with, and may indeed serve to correct, the informal understanding and applications of the RSA criteria concerning their conceptual (in)dependence, their function as update-thresholds, and their status as obligatory rather than permissive norms, but also show how these formal and informal normative approachs can in fact align.
KeywordsAcceptability Argument appraisal Bayes theorem Informal logic Jeffrey conditionalization Relevance Sufficiency
We consider this joint work; our names are listed in alphabetical order. For comments that helped improve an earlier version of this paper, we thank Mike Oaksford as well as an anonymous reviewer (the latter particularly on the issue briefly discussed in Sect. 4.4, footnote 24). A version of this paper was presented at the workshop on Argument Strength hosted by the Research Group for Non-monotonic Logics and Formal Argumentation at the Institute of Philosophy II, Ruhr-University Bochum, Germany, 30 November–2 December, 2016. We thank that audience for their comments and discussion. Frank Zenker acknowledges a European Union Marie Sklodowska Curie COFUND fellowship (1225/02/03) as well as funding from the Volkswagen Foundation (90 531) and the Ragnar Söderberg Foundation.
- Bayes, T. (1763/1958). An essay towards solving a problem in the doctrine of chances. Philosophical Transactions of the Royal Society of London, 53, 370–418. Reprinted in Biometrika, 45, 296–315.Google Scholar
- Blair, J. A. (2011). Informal logic and its early historical development. Studies in Logic, 4, 1–16.Google Scholar
- Blair, J. A. (2012). Relevance, acceptability and sufficiency today. In C. Tindale (Ed.), Groundwork in the theory of argumentation (pp. 87–100). Dordrecht: Springer.Google Scholar
- Bradley, S. (2015). Imprecise probabilities. In E. N. Zalta et al. (Eds.), Stanford encyclopedia of philosophy, 2015 edition. Stanford, CA: Center for Study of Language and Information. http://plato.stanford.edu/archives/sum2015/entries/imprecise-probabilities/
- Cohen, J. L. (1989). An introduction to the philosophy of induction and probability. Oxford: Oxford UP.Google Scholar
- Carnap, R. (1962). The logical foundations of probability (2nd ed.). Chicago: University of Chicago Press.Google Scholar
- Corner, A., Hahn, U., & Oaksford, M. (2006). The slippery slope argument: Probability, utility and category reappraisal. In R. Sun (Ed.), Proceedings of the 28th annual meeting of the cognitive science society (pp. 1145–1150). Mahwah, NJ: Erlbaum.Google Scholar
- Cox, R. T. (1961). The algebra of probable inference. Baltimore, MD: Johns Hopkins UP.Google Scholar
- Fitelson, B. (2001). Studies in Bayesian confirmation theory. Dissertation, University of Wisconsin at Madison. http://fitelson.org/thesis.pdf.
- Govier, T. (2010). A practical study of argument (7th ed.). Belmont, CA: Wadsworth, Cengage Learning.Google Scholar
- Hahn, U., Oaksford, M., & Bayindir, H. (2005). How convinced should we be by negative evidence? In B. Bara, L. Barsalou, & M. Bucciarelli (Eds.), Proceedings of the 27th annual conference of the cognitive science society (pp. 887–892). Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
- Hahn, U., Oaksford, M., & Corner, A. (2005). Circular arguments, begging the question and the formalization of argument strength. In A. Russell, T. Honkela, K. Lagus, & M. Pöllä (Eds.), Proceedings of AMKLC’05, International symposium on adaptive models of knowledge, language and cognition (pp. 34–40). Espoo: Helsinki University of Technology.Google Scholar
- Hajek, A. (2008). Dutch book arguments. In P. Anand, P. Pattanaik, & C. Puppe (Eds.), The Oxford handbook of rational and social choice (pp. 173–195). Oxford, UK: Oxford University Press.Google Scholar
- Hamblin, C. (1970). Fallacies. London: Methuen.Google Scholar
- Harris, A. J. L., Hahn, U., Madsen, J. K., & Hsu, A. (2015). The appeal to expert opinion: Quantitative support for a Bayesian network approach. Cognitive Science. doi: 10.1111/cogs.12276.
- Hertwig, R., Ortmann, A., & Gigerenzer, G. (1997). Deductive competence: A desert devoid of content and context. Current Psychology of Cognition, 16, 102–107.Google Scholar
- Howson, C., & Urbach, P. (2006). Scientific reasoning: The Bayesian approach (3rd ed.). La Salle, IL: Open Court.Google Scholar
- Jeffrey, R. (1983). The logic of decision (2nd ed.). Chicago: University of Chicago Press.Google Scholar
- Johnson, R. (2000). Manifest rationality: A pragmatic theory of argument. Mahwah, NJ: Lawrence Earbaum.Google Scholar
- Johnson, R. (2011). Informal logic and deductivism. Studies in Logic, 4, 17–37.Google Scholar
- Johnson, R., & Blair, J. A. (2002). Informal logic and the reconfiguration of logic. In D. Gabbay, R. Johnson, H. Ohlbach, & J. Woods (Eds.), Handbook of the logic of argument and inference: Turn towards the practical (pp. 340–396). Amsterdam: Elsevier.Google Scholar
- Johnson, R., & Blair, J. A. (2006). Logical self defense (3rd ed.). New York: International Debate Education Association (First edition 1977, Toronto: McGraw-Hill Ryerson).Google Scholar
- Joyce, J. (2009). Bayes’ theorem. In E. N. Zalta et al. (Eds.), Stanford encyclopedia of philosophy, 2009 edition (pp. 1–47). Stanford, CA: Center for Study of Language and Information. http://plato.stanford.edu/archives/spr2009/entries/bayes-theorem/
- Kolmogorov, A. N. (1933). Grundbegriffe der Wahrscheinlichkeitrechnung, Ergebnisse Der Mathematik. Berlin: Springer (translated as: (1950). Foundations of Probability. New York: Chelsea Publishing Company).Google Scholar
- Ramsey, F. (1926/1931). Truth and probability. In R. Braithwaite (Ed.), The foundations of mathematics and other essays (pp. 156–198). London: Routledge & Kegan Paul.Google Scholar
- Strevens, M. (2012). Notes on Bayesian confirmation theory. http://www.strevens.org/bct/
- Talbot, W. (2011). Bayesian epistemology. In E. N. Zalta et al. (Eds.), Stanford encyclopedia of philosophy, 2011 edition (pp. 1–34). Stanford, CA: Center for Study of Language and Information. http://plato.stanford.edu/archives/sum2011/entries/epistemology-bayesian/
- Woods, J., & Walton, D. (2007). Fallacies: Selected papers 1972–1982. London: College Publications.Google Scholar
- Zenker, F. (2016). The polysemy of ‘fallacy’—or ‘bias’, for that matter. In: Bondy, P., and Benaquista, L. (eds). Argumentation, objectivity and bias (Proceedings of the 11th conference of the ontario society for the study of argumentation, 18–21 May, 2016) (pp. 1–14). Windsor, ON: OSSA. http://scholar.uwindsor.ca/ossaarchive/OSSA11/