logic and possible worlds

13/11/23

Logic focuses on abstract content rather than the structure of the real world, allowing logicians to disengage from worldly matters. Historically, twentieth-century logicians were primarily engaged in establishing consistent foundations for mathematics, which, in many cases, is their most significant interaction with real-world concepts. My own immersion into the 'real world' primarily began with the writing of 'Logic in the Wild' and my collaboration with Tim Dare, teaching a course on Logical and Critical Thinking to a diverse international group of students.

My re-engagement with the real world involved understanding feminist critiques of critical thinking. These critiques emphasize the presence and experiences of people in the world, highlighting how rigid, mathematical approaches to thinking can be oppressive in situations that don't warrant such strict methodologies.

In philosophy, metaphysics deals directly with worldly concepts. It differs from physics, which seeks to uncover and understand the physical laws governing our world, enabling prediction and control. Metaphysics, however, asks broader questions: What are the potential states of the world? Are certain features of the world necessary? For instance, physical laws operate under specific conditions, but they could potentially be different. How might physics look in a world where, say, gravity is stronger or the speed of light varies (can it?)?

These inquiries lead to reflections on the nature of mathematics. Are mathematical laws inherently necessary, or could they be different? What about the existence of necessary entities, like God, does it exist by necessity? Such questions guide logicians to explore the concept of possible worlds. Unlike scientists, who focus on making predictions about our world, logicians adopt a broader perspective, contemplating all the ways the world could potentially be. The primary criterion for considering a world in this context is consistency. Thus, logicians explore a multitude (infinitely many!) of possible worlds, accepting any that are internally consistent. This exploration of possible worlds represents the closest that logicians typically come to engaging with the concept of 'the world'.