Frege: A fusion of horizontals

In Die Grundgesetze der Arithmetik (I, §48), Frege introduces his rule of the fusion of horizontals, according to which if an occurrence of the horizontal stroke is followed by another occurrence of the same stroke, either in isolation or “contained” in a propositional connective, the two occurrences can be fused with each other. However, the role of this rule, and of the horizontal sign more generally, is controversial; Michael Dummett notoriously claimed, for instance, that the horizontal is “wholly superfluous” in Frege’s logical system. In this paper, we challenge Dummett’s view by providing a comprehensive analysis of the significance of the horizontal stroke. After some preliminary remarks, we argue that even if Frege’s connectives in some sense “contain” the horizontal, yet they are total functions. Then, we take up the question of the sense expressed by the horizontal, and we claim that, unlike other sentential operators, the horizontal is not sense-compositional. Finally, we consider the semantic and pragmatic aspects of Frege’s horizontal in connection to his judgment stroke and the double judgment stroke. Contra Dummett, we argue that the horizontal is a special and indispensable element of Frege’s logic

Philosophical aspects of probabilistic seismic hazard analysis (PSHA): a critical review

AbstractThe goal of this paper is to review and critically discuss the philosophical aspects of probabilistic seismic hazard analysis (PSHA). Given that estimates of seismic hazard are typically riddled with uncertainty, different epistemic values (related to the pursuit of scientific knowledge) compete in the selection of seismic hazard models, in a context influenced by non-epistemic values (related to practical goals and aims) as well. We first distinguish between the different types of uncertainty in PSHA. We claim that epistemic and non-epistemic considerations are closely related in the selection of the appropriate estimate of seismic hazard by the experts. Finally, we argue that the division of scientific responsibility among the experts can lead to responsibility gaps. This raises a problem for the ownership of the results (“no one’s model” problem) similar to the “problem of many hands” in the ethics of technology. We conclude with a plea for a close collaboration between philosophy and engineering.</jats:p