From the standpoint of logic, similarity is a relation. As such, it is expected to have some regular logical properties, as relations normally do. However, as Quine (1969, 114-138) pointed out, this is not the case, since any standard logical property assigned to the relation of similarity can be challenged. For instance, is similarity symmetrical? In other words, if A is similar to (or resembles) B, does it follow that B is similar to A? The answer is sometimes positive, but sometimes, perhaps more frequently, negative. Although infrequent, one can further inquire whether similarity is transitive: Does ‘A is similar to B and B is similar to C’ imply that ‘A is similar to C’? Can we assign reflexivity to similarity? What does it mean to say that A is similar to itself, or that A resembles itself? (except in figurative uses, of course) Other difficulties, such as those having to do with quantification, were raised by Goodman in his well-known “Seven Strictures on Similarity” (1972, 437-447). Along with other questions, Goodman asked whether a
twin is more similar to his twin brother than to his own photograph. Aside from determining how to answer this question advantageously, there is the more general issue of whether any known method of measuring similarities exists. Any object or event can be similar to any other object or event concerning some of its attributes, out of the infinite number of possible attributes, as long as there is no criterion for choosing what constitutes a relevant attribute. Thus, it seems crucial to establish such a criterion. Here, however, we are caught in a dilemma: either everything is similar to everything else, or else a relevance criterion should select for salience and order relevant aspects and properties. These and other arduous questions about similarity led Goodman several decades ago to abandon all hope of finding any theoretical explication for the relation of similarity.