Postdoc in Formalism, Formalization, Intuition and Understanding in Mathematics - Archives Poincaré (Nancy) and IHPST Paris are advertising for a 20-month postdoc fellowship.
2 hours ago
Formal languages, deductive systems, and model-theoretic semantics are mathematical objects and, as such, the logician is interested in their mathematical properties and relations. Soundness, completeness, and most of the other results reported below [in that SEP entry] are typical examples. Philosophically, logic is the study of correct reasoning. Reasoning is an epistemic, mental activity. This raises questions concerning the philosophical relevance of the mathematical aspects of logic. How do deducibility and validity, as properties of formal languages--sets of strings on a fixed alphabet--relate to correct reasoning? What do the mathematical results reported below [in that SEP entry] have to do with the original philosophical issue?Shapiro goes on to list some possibilities; e.g. perhaps "the components of a logic provide the underlying deep structure of correct reasoning."