The Limits of Logic

Logical validity is relative to logical systems. Some arguments are logically valid in one logic but logically invalid in another logic. There are various logical systems, each of which has been developed based on some notion of what logic is or should be. Whether an argument is logically valid or not depends on one’s notion of logic. The main purpose of my dissertation is to establish a new notion of logic and propose a new characterization of logical validity. The new notion, which I call the minimal notion, is that logical validity is the validity grounded in a special kind of formal law. Using such special formal laws, I identify the logical systems that validate all and only arguments whose validity can be justified from the minimalist's point of view.