In this paper I shall bring together some philosophical and logical ideas about randomness many of which have been said before in scattered places. For less philosophical aspects see, for example [27].When philosophers define terms, they try to go beyond the dictionary, but the dictionary is a good place to start and one dictionary definition of ‘random’ is ‘having no pattern or regularity’. This definition could be analyzed in various contexts but, at least for the time being, I shall restrict (...) my attention to sequences of letters or digits, generically called ‘digits’. These digits are supposed to belong to a generalized alphabet; perhaps a new word should be used, such as ‘alphagam’, but I shall use the word ‘alphabet’ in the generalized sense so as to avoid a neologism. For simplicity I shall assume that the alphabet is finite and consists of thetdigits 0, 1, 2,…,t— 1. (shrink)