Abstract
Everyday life reasoning and argumentation is defeasible and uncertain. I present a probability logic framework to rationally reconstruct everyday life reasoning and argumentation. Coherence in the sense of de Finetti is used as the basic rationality norm. I discuss two basic classes of approaches to construct measures of argument strength. The first class imposes a probabilistic relation between the premises and the conclusion. The second class imposes a deductive relation. I argue for the second class, as the first class is problematic if the arguments involve conditionals. I present a measure of argument strength that allows for dealing explicitly with uncertain conditionals in the premise set.
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- 1.
Note that the propositional-logically atomic formulae B and F in argument \( {\mathcal{A}_1} \) can be represented in predicate logic by bird(Tweety) and can_fly(Tweety), respectively. Moreover, F may be represented even more fine-grained in modal logical terms by ◊F, where “◊” denotes a possibility operator. However, for the sake of sketching a theory of argument strength, it is sufficient to formalize atomic propositions by propositional variables.
- 2.
I argued elsewhere (Pfeifer 2008) that violation of coherence is a necessary condition for an argument to be fallacious.
- 3.
Since the conditional event is nonpropositional, it cannot be combined by classical logical conjunction. Conditional events can be combined by so-called quasi-conjunctions (Adams 1975, p. 46f). As Adams notes, however, quasi-conjunctions lack some important logical features of conjunctions.
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Acknowledgments
This work is financially supported by the Alexander von Humboldt Foundation, the German Research Foundation project PF 740/2-1 “Rational reasoning with conditionals and probabilities. Logical foundations and empirical evaluation” (Project leader: Niki Pfeifer; Project within the DFG Priority Program SPP 1516 “New Frameworks of Rationality”) and the Austrian Science Fund project P20209 “Mental probability logic” (Project leader: Niki Pfeifer).
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Pfeifer, N. (2013). On Argument Strength. In: Zenker, F. (eds) Bayesian Argumentation. Synthese Library, vol 362. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5357-0_10
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