Logic and 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.