 As the systematicity debate has evolved, attention has been focused on defining the benchmarks that would answer Fodor and Pylyshyn’s challenge. Hadley (1994a, 1994b) distinguishes three brands of systematicity. Connectionists have clearly demonstrated the weakest of these by showing that neural nets can learn to correctly recognize novel sequences of words (e.g., “Mary loves John”) that were not in the training set. However, Hadley claims that a convincing rebuttal must demonstrate strong systematicity, or better, strong semantical systematicity. Strong systematicity would require (at least) that “Mary loves John” be recognized even if “Mary” never appears in the subject position in any sentence in the training set. Strong semantical systematicity would require as well that the net show abilities at correct semantical processing of the novel sentences rather than merely distinguishing grammatical from ungrammatical forms. Niklasson and van Gelder (1994) have claimed success at strong systematicity, though Hadley complains that this is at best a borderline case. Hadley and Hayward (1997) tackle strong semantical systematicity, but by Hadley’s own admission it is not clear that they have avoided the use of a classical architecture. Boden and Niklasson (2000) claim to have constructed a model that meets at least the spirit of strong semantical systematicity, but Hadley (2004) argues that even strong systematicity has not been demonstrated there. Whether one takes a positive or a negative view of these attempts, it is safe to say that no one has met the challenge of providing a neural net capable of learning complex semantical processing that generalizes to a full range of truly novel inputs.