  The modern understanding of intensional issues and problems begins with a fundamental paper of Gottlob Frege, (Frege 1892). This paper opens with a recital of the difficulties posed by the notion of equality. In his earlier work, Frege notes, he had taken equality to relate names, or signs, of objects, and not objects themselves. For otherwise, if \(a\) and \(b\) designate the same object, there would be no cognitive difference between \(a = a\) and \(a = b\), yet the first is analytic while the second generally is not. Thus, he once supposed, equality relates signs that designate the same thing. But, he now realizes, this cannot be quite correct either. The use of signs is entirely arbitrary, anything can be a sign for anything, so in considering \(a = b\) we would also need to take into account the mode of presentation of the two signs—what it is that associates them with the things they designate. Following this line of thought, equality becomes a relation between signs, relative to their modes of presentation. Of course the notion of a mode of presentation is somewhat obscure, and Frege quickly shifts attention elsewhere.