Welcome to my blog!
Every morning, I begin with a cup of coffee and 15 minutes of free thinking. I write down everything that comes to mind, from new ideas to thoughts that emerged overnight. This is where I develop and refine my new research. You'll find some repetition and ideas still in progress. Some might seem unusual or unclear at first, but that's part of the journey! I'm excited to share how my ideas form and evolve.
logic and possible worlds
In this blog post, I explore how my journey as a logician, initially focused on abstract content, evolved to embrace real-world interactions, from teaching diverse students to considering feminist critiques and the nature of metaphysics and mathematics.
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'.
Logic and the world
Does logic care about the world?
Logic remains indifferent to the world's specifics. Professional logicians often describe logic as absolute and universal, signifying its principles apply regardless of content or context. In my book, "Logic in the Wild," I characterise logic as the guardian of coherence, focusing on the structure of beliefs (or theories, etc.), rather than their subject matter. It's crucial to distinguish logic from truth: logic is not equipped to discern whether the world harbours giant flying pigs or exists as a computer simulation. By this, I don't imply logic is irrelevant to reality, but rather that it's not a tool for determining factual truths about the world.
Some logicians and mathematicians subscribe to the notion that logic, perhaps akin to mathematics or in its exploration of mathematical concepts, belongs to a Platonic realm. This realm, a domain of ideas or abstract entities like numbers, is considered as tangible as the physical world. If logic were to hold any knowledge about reality, it would pertain to this Platonic realm. This view was espoused by eminent 20th-century logician Kurt Gödel and has influenced thinkers like Roger Penrose, who posits that humans, unlike computers, have direct access to this Platonic part of the world. However, even if we accept that logic (and humans) may interact with a Platonic realm of ideas, logic still remains detached from our physical world.
Interestingly, logic's engagement with the world didn't begin by limiting itself to observable truths. Logicians expanded their purview to include the study of worlds through analyses of possibility and necessity. This aligns with the pursuit of universal truths, but in this context, the universality pertains to necessity. Questions like, "Is it necessary that two plus two equals four?" or "Is it necessary that all humans mortal?" and "Is the existence of giant flying pigs possible?" mark a shift in logic's focus from pure mathematics to an exploration of metaphysical possibilities.
Examining the ways populism exploits incoherence and bad logic to make truth irrelevant, and the dangers this poses to political discourse.