Commensurability - Philosophical Concept | Alexandria
Commensurability, at its heart, is the tantalizing idea that seemingly disparate entities can be measured against a common standard, revealing their underlying equivalence. It hints at a unified scale where everything, from geometric lengths to abstract values, finds its place. But is this harmonious vision truly attainable, or are we chasing a mirage of our own making?
The concept of commensurability stretches back to ancient Greece, inextricably linked with the Pythagorean brotherhood of the 6th century BCE. Initially, it represented a core tenet of their worldview: that all things could be expressed as ratios of whole numbers. The discovery of incommensurable magnitudes, such as the side and diagonal of a square (resulting in the irrational number √2), sent shockwaves through their belief system. This revelation, often attributed to Hippasus of Metapontum, was so unsettling that legend has it he was drowned at sea for revealing the secret. Iconically, Pythagoras grappled with the numerical harmony of the universe.
Over centuries, the interpretation of commensurability has evolved, extending beyond mathematics into moral philosophy, social theory, and even ethics in AI. Thinkers have grappled with the thought experiment of whether fundamentally different values, such as justice and mercy, or efficiency and social well-being, can be meaningfully compared and traded off. This leads to the "problem of commensurability." Can the subjective experience of happiness, a core tenet of utilitarianism, be quantified and aligned with other outcomes? The question reverberates from everyday moral dilemmas to complex policy decisions. Arguments for sustainability and the limits to growth depend on commensurating different forms of capital--natural, social, and economic.
The legacy of commensurability remains a potent force, fueling both the quest for universal understanding and the recognition of inherent limits. In an age dominated by data-driven decision-making and complex algorithms, the allure of finding a common metric for everything is stronger than ever. Yet, the specter of the diagonal of the square reminds us that some truths may lie beyond easy quantification, challenging us to consider the qualitative aspects of existence and the importance of values that defy simple commensuration in any ethics game or morality game. As we increasingly rely on AI to guide our choices, are we in danger of overvaluing what can be measured at the expense of what truly matters?