Incommensurability - Philosophical Concept | Alexandria
Incommensurability: A term suggesting a profound divergence, a chasm between seemingly related things that resists all attempts at direct comparison or reduction to a common scale, hinting at a deeper, almost forbidden knowledge. Think of it as a mathematical riddle with philosophical undertones, a concept that has haunted thinkers for millennia.
The earliest seeds of the idea can be traced back to the very cradle of mathematics and philosophy in ancient Greece, around the 5th century BCE. The discovery that the side and diagonal of a square are incommensurable – that their ratio cannot be expressed as a simple fraction – is traditionally attributed to the Pythagoreans. Legend has it that Hippasus, a member of their brotherhood, was drowned at sea for revealing this unsettling truth, a potent symbol of the era's fervent belief in the perfection and rationality of the universe. This revelation challenged the bedrock of Pythagorean philosophy, which held that all things could be understood through whole numbers and their ratios. This early encounter highlights the anxiety triggered when mathematical concepts lead to conclusions that challenge human intuition.
Over time, the concept has transcended pure mathematics to find resonance in diverse fields, from the philosophy of science to comparative literature. Thomas Kuhn's influential work on scientific revolutions in the 20th century introduced the concept of incommensurability to the world of science. Kuhn argued that different scientific paradigms are so fundamentally different in their assumptions, methods, and conceptual frameworks that they cannot be directly compared or evaluated against a common standard, which stirred significant debate and reshaped the understanding of scientific progress. Outside the scientific community, language translation studies have tackled the notion that certain concepts within a culture are so uniquely embedded that they resist direct equivalents in other languages, thereby posing limits to understanding and meaning.
Today, incommensurability continues to challenge our desire for neat, universally comparable frameworks. The idea forces us to confront the limitations of human understanding, acknowledge the existence of irreducible difference, and reconsider the assumption that everything can be neatly categorized and evaluated on a single scale. Is true understanding ever fully possible when dealing with fundamentally different perspectives or systems? Perhaps acknowledging incommensurability is the first step towards a more nuanced and tolerant engagement with the world around us.