  Peirce praised O. H. Mitchell as being his very best student in logic. Mitchell was trained as a mathematician even befoe coming to Johns Hopkins, and he was especially noted by all those who knew him as being extraordinarily meticulous and attentive to detail. He was so attentive to exactitude that he was even noted for slowness and ponderousness in speech. But what was there in Mitchell’s 1883 paper that stimulated Peirce’s high praise? It seems to be closely connected, perhaps identical, with what Peirce praises Mitchell for accomplishing in Peirce’s entry in Baldwin’s Dictionary of Philosophy and Psychology, particularly in his article there for the word “dimension.” In the article Peirce credits Mitchell with having introduced “the concept of a multidimensional logical universe” into exact logic, and Peirce claims that it is one of the “fecund contributions” that Mitchell made to exact logic. There seem to be two components to the idea of a multidimensional logical universe. The first one is simply the idea of multiple quantification in connection with polyadic predicates, so that (in modern terminology) we can have propositions with quantifiers occurring within the scope of other quantifiers. That Mitchell employs a formalism suggestive of this idea is undeniable, but whether he successfully distinguishes (for all x)(there exists a y) from (there exists a y)(for all x) is very much less than obvious. Moreover, that Mitchell was the very first logician to have conceived of multiple quantification and polyadic predicates seems a bit dubious, especially since by 1870 Peirce himself was already making use of notions for which multiple quantification and polyadic predicates are involved. The second component of the idea of a multidimensional logical universe is (again, using modern terminology) the idea that the universe of discourse relevant to one variable might not be the same as the universe of discourse relevant to another variable. Moreover, since the universe of discourse relevant to one variable might be all the times there are, all the places there are, all possible situations, or even all possible worlds, it is not difficult (though it is perhaps a bit far-fetched) to connect Mitchell’s idea of a multidimensional logical universe to the idea of tense logic or even modal logic. Whether a careful study of Mitchell’s logical contribution really supports such a reading of Mitchell’s contributions to logic is not as yet clearly determined.