The Meaning Of Words
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The word analysis derives from the ancient Greek term analusis. The prefix ana means up, and lusis means loosing, release or separation, so that analusis means loosening up or dissolution. The term was readily extended to the solving or dissolving of a problem, and it was in this sense that it was employed in ancient Greek geometry and philosophy. The method of analysis that was developed in ancient Greek geometry had an influence on both Plato and Aristotle. Also important, however, was the influence of Socratess concern with definition, in which the roots of modern conceptual analysis can be found. What we have in ancient Greek thought, then, is a complex web of methodologies, of which the most important are Socratic definition, which Plato elaborated into his method of division, his related method of hypothesis, which drew on geometrical analysis, and the method(s) that Aristotle developed in his Analytics. Far from a consensus having established itself over the last two millennia, the relationships between these methodologies are the subject of increasing debate today. At the heart of all of them too lie the philosophical problems raised by Menos paradox, which anticipates what we now know as the paradox of analysis, and Platos attempt to solve it through the theory of recollection, which has spawned a vast literature on its own.
Analysis was first used in a methodological sense in ancient Greek geometry, and the model that Euclidean geometry provided has been an inspiration ever since. Although Euclids Elements dates from around 300 BC, and hence after both Plato and Aristotle, it is clear that it draws on the work of many previous geometers, most notably, Theaetetus and Eudoxus, who worked closely with Plato and Aristotle. Plato is even credited by Diogenes Laertius (LEP, I,