Traditional Logic,Modern Logic and Natural Language

In a recent paper Johan van Benthem reviews earlier work done by himself and colleagues on ‘natural logic’. His paper makes a number of challenging comments on the relationships between traditional logic, modern logic and natural logic. I respond to his challenge, by drawing what I think are the most significant lines dividing traditional logic from modern. The leading difference is in the way logic is expected to be used for checking arguments. For traditionals the checking is local, i.e. separately for each inference step. Between inference steps, several kinds of paraphrasing are allowed. Today we formalise globally: we choose a symbolisation that works for the entire argument, and thus we eliminate intuitive steps and changes of viewpoint during the argument. Frege and Peano recast the logical rules so as to make this possible. I comment also on the traditional assumption that logical processing takes place at the top syntactic level, and I question Johan’s view that natural logic is ‘natural’.     

Dialogue protocols for formal fallacies: A reply to Kacprzak and Yaskorska

This note comments on the paper ‘Dialogue protocols for formal fallacies’ by Kacprzak and Yaskorska (this issue). Points discussed include the use of the notions of ‘claiming’, ‘conceding’ and ‘commitment’, and the role of Lorenzen dialogues as a device for checking whether a proposition is a tautology.