Logical rules, principles of reasoning and Russell's paradox
Francesco Orilia · U-PAD Unimc - Open Digital Publications (University of Macerata) · 2003
The logical rules (e.g., modus ponens, universal quantifier elimination or lambda-conversion) allow us to construct a deduction, whereas the principles of reasoning guide us in the goal-driven effort to rationally obtain new beliefs (propositions) from given ones by means of deductions (cf. G. Harman, Change in View - Principles of Reasoning, MIT Press, Cambridge, 1986). Which ones are the "correct" logical rules and what kind of language reflects the structure of propositions and beliefs? Prima facie, the language has a type-free grammar and the rules involve both classical logic and lambda-conversion. However, "logical paradoxes" such as the Liar, Russell's and Curry's seem to beset this assumption. I thus propose that the set of logical rules making up our standard logical competence is in fact inconsistent and investigate what the principles of reasoning and belief revision must be like for us to cope with this. This paper is published in a volume edited b T. Childers and O. Majer.