Elimination - Philosophical Concept | Alexandria
Elimination, a pivotal operation cutting across mathematics, logic, and philosophy, represents the systematic removal of elements, possibilities, or realities to refine understanding, solve problems, or arrive at a desired outcome; yet is it truly as simple as removing the extraneous?
The concept of elimination threads its way through the history of thought, appearing implicitly in early forms of argumentation and explicitly in the formalization of logic. Aristotle's development of the syllogism, particularly the reductio ad absurdum, shows an early understanding of elimination, dating back to approximately 350 BCE, wherein a proposition is validated through demonstrating the absurdity of its negation. Later, in the writings of logicians like Peter Abelard in the 12th century, clearer methods of exclusion can be seen as they refined arguments. The great icons of reason, masters of rhetoric and argumentation, have wielded the principal of elimination, that of reduction, to refine and hone their arguments, like a metal worker at the forge burns away the impurities in the smelting of the steel.
As mathematics and logic became more formalized, elimination gained a firm foothold in techniques such as Gaussian elimination in linear algebra and truth table reduction in Boolean algebra. Its cultural impact stretches into the realm of cognitive science, demonstrated in the Wason selection task, an experiment revealing the common difficulty people face in applying deductive reasoning to eliminate possibilities. Meanwhile, in philosophy, elimination appears implicitly in thought experiments and moral dilemmas, forcing us to choose between alternatives, thus scrutinizing our moral principles. Consider the enduring "trolley problem" and its array of permutations that serve as tools for exploring ethical frameworks like utilitarianism and deontology; these scenarios hinge on an individual’s response to various forms of elimination, be it lives, duties, or consequences. Is there ever a truly acceptable form of elimination, or is it always a compromise?
The legacy of elimination persists in modern algorithms, artificial intelligence, and decision-making processes. From the "Monty Hall" problem to the optimization algorithms of machine learning, the systematic removal of undesirable data points guides us toward desired outcomes. Even philosophical arguments, such as refuting specific free will tenets through hard determinism, implicitly utilize principles of elimination. Elimination, in essence, remains a foundational tool in our quest to understand the world, constantly prompting us to re-evaluate our assumptions and refine our understanding of what is real, possible, and ethical. The question now turns to its limitations: Can we ever truly eliminate all possibilities, and what responsibility do we bear for what is left behind?