One True Logic

The idea that only one logic is correct, so that every argument is either valid or invalid by a single standard, has strong pull. It fits how people reason in daily life and how mathematicians, scientists and lawyers work, since each of them assumes there are definite facts about whether an argument holds. That view still faces two hurdles. The first is pluralism, the position that several logics can each be correct. The second is working out which version of the single-logic view is the right one.

Owen Griffiths's book is the first monograph to set out a version of this single-logic position explicitly and to defend it against pluralism. It opens with a critical survey of the debate between the single-logic and many-logic camps and takes the single-logic side. To meet the second hurdle, it defends one specific form of the view, grounded in a very infinitary logic.

Along the way, the work advances several new positions and draws together scattered threads from the philosophical and logical literature. It extends the Tarski-Sher account of what makes a logic logical, offers a fresh justification for that extension, gives a new argument that infinitary logic counts as logical, and responds to recent arguments for pluralism.