Objects and Identity

Identity has for long been an important concept in philosophy and logic. Plato in his Sophist puts same among those fonns which "e;run through"e; all others. The scholastics inherited the idea (and the tenninology), classifying same as one of the "e;transcendentals"e;, i.e. as running through all the categories. The work of Locke and l.eibniz made the concept a problematic one. But it is rather recently, i.e. since the importance of Frege has been generally recognized, that there has been a keen interest in the notion, fonnulated by him, of a criterion of identity. This, at first sight harmless as well as useful, has proved to be like a charge of dynamite. The seed had indeed been sown long ago, by Euclid. In Book V of his Elements he first gives a useless defmition of a ratio: "e;A ratio is a sort of relation between two magnitudes in respect of muchness"e;. But then, in definition 5 he answers, not the question "e;What is a ratio?"e; but rather ''What is it for magnitudes to be in the same ratio?"e; and this is the definition that does the work.