 The arguments from productivity and systematicity differ in what they aim to prove. First, the argument from systematicity proves something weaker than (any version of) compositionality. If we run the argument for the pair of sentences ‘The dog is asleep’ and ‘The cat is awake’ we can conclude that the meanings of ‘the dog’, ‘the cat’, ‘is asleep’ and ‘is awake’ plus predication determine the meaning of ‘The dog is awake’. It does not follow that the meanings of ‘the dog’ and ‘is awake’ plus predication do that. Second, if this problem can be fixed somehow, the argument from systematicity proves not only global, but local compositionality: it tells us that the meanings of immediate constituents and immediate structure fix the meanings of complex expressions. Finally, if successful, the argument from systematicity proves not only a version of the compositionality principle, but also reverse compositionality. We are invited to conclude that the meaning of an arbitrary complex expression determines its immediate structure and the meanings of its immediate constituents; cf.  section 1.6.4, Fodor &amp; Lepore 2001: 59; Pagin 2003: 292.