Faced with the convolutions of this model, it is perhaps not surprising that Bloomfield’s successors concluded that it contained “contradictions” (Harris 1942:169) or “didn’t make sense” (Hockett 1968:20), and proceeded to develop those aspects that seemed most transparent. Consequently, as Matthews (1993) observes, the issues addressed by Bloomfield’s followers are not intrinsic to the model itself but appear to rest on their reinterpretations of Bloomfield’s position. The central assumption introduced by the Post-Bloomfieldians was the idea that units at one level of analysis were directly composed of units at the next lower level of analysis, so that morphemes were composed of phonemes, complex forms composed of morphemes, etc. The source of this assumption is set out explicitly in Hockett (1961):
The simplest and earliest assumption about the relation between morphemes and phonemes was that a morpheme is composed of phonemes: the morpheme cat is composed of the phonemes /к/, /к/, and /t/ in that arrangement. This put phonemes and morphemes in line with words, phrases, and sentences, since it was also assumed that a word consists of one or more morphemes (in a specified arrangement), a phrase of one or more words, and so on.
This assumption is either explicit, or implicit but very close to the surface, in much of the early Prague discussion and in Bloomfield’s postulates [Bloomfield (1926)]. In the latter, for example, morphemes are defined first (§9), and phonemes later (§15, §16). The wording of the two sections last cited, together with §18, clearly implies that morphemes are composed of phonemes. While Bloomfield does not say quite this, he does say, in the commentary on Assumption 6 (§18), that ‘The morphemes of a language can thus be analyzed into a small number of meaningless phonemes.’ (Hockett 1961:29)
As Hockett acknowledges, Bloomfield does not directly assert that morphemes are composed of phonemes; this claim is merely an inference that Hockett and his contemporaries drew from Bloomfield’s sometimes opaque discussions of morphology. Bloomfield characteristically spoke of larger units being “described by” smaller parts, as in the claim that “[a]ny utterance can be fully described in terms of lexical and grammatical forms” (Bloomfield 1933:167). Description in this sense involves, as noted above, a general process of classification. The shift to a more decompositional part-whole perspective is clear in Hockett’s discussion of Bloomfield’s postulates and in his restatement of ‘full description’ as a general principle of total accountability:
Every morph, and every bit of phonemic material, must be determined by (i.e. predictable from) the morphemes and the tagmemes (if any) of which the utterance is composed. (Hockett 1947:235)
This shift was the decisive step in the development of what Hockett (1954) termed the ‘item and arrangement’ (IA) model. Reinterpreting Bloomfield’s model in terms of relations between utterances and the items out of which they were “composed” achieved the same formal clarity that could be obtained by simplifying Bloomfieldian constituency analysis to phrase structure analysis:
The origin of phrase structure grammar was, in short, Bloomfieldian constituency analysis, and the origin of that, in turn, was what remained of Bloomfield’s model when, first, grammatical arrangement is reduced to selection and order and, secondly, all reference to meaning is taken out. (Matthews 1993:148)
-  Pike (1943:65) similarly remarks that “part of the difficulty of Bloomfield’s material for thebeginning student was the lack of clarity in his statements of the relationship between taxemes andtagmemes, and the actual operation with these principles”.