 Iamblichus’ interpretation characteristically included a definition of the “target” (skopos) of Aristotle’s treatise, which Iamblichus regarded as focusing on signifying expressions insofar as they signify things via concepts (see Hoffmann 1987). This view was not new and Simplicius traces it back to the previous tradition starting from the early Peripatetic commentators (Simplicius, In Categorias, 13.15–18). Iamblichus, however, added two distinctive features. First, he gave a more systematic account of the target of Aristotle’s treatise (for example, Porphyry too claimed that Aristotle’s Categories focus on simple signifying expressions insofar as they signify things, but to the best of our knowledge he did not refer to concepts). In addition to this, Iamblichus’ discussion of semantics incorporated a Neoplatonist account of language and signification grounded in Neoplatonic metaphysics and psychology (Simplicius, In Categorias, 12.16–13.12: see Griffin 2012). Iamblichus referred to analogy (analogia) as a resource that explains how Aristotle’s account of categories can be applied to intelligible beings too. For example, Simplicius reports that according to Iamblichus the property of being receptive of contraries while being one and the same in number (see Arist., Cat., 5, 4a10–11) applies to all levels of substance (both sensible and intelligible) via analogy (kata analogian, Simpl., In Categorias, 116.25–26 [DL-1972: Fr. 33]): in intelligible substance contraries belong to substance simultaneously whereas in sensible substance they exist successively. Accordingly, different levels of being reveal corresponding structures (where lower degrees in the hierarchy entail increasing multiplicity and dispersion). This metaphysical framework accounts for Iamblichus’ views about genera and predication. Iamblichus is critical of the previous Peripatetic tradition: he criticizes Alexander of Aphrodisias for mistakenly regarding corporeal and incorporeal beings as species ranked under the same genus (that of substance, ousia) (Simplicius, In Categorias, 83.20–23 [DL-1972: Fr. 24]). Iamblichus’ point is that the Peripatetic reading of the Categories does not account for the hierarchical structure of reality. On Iamblichus’ view, full weight should instead be given to the hierarchical notion of the genus as a unity of derivation from a principle (actually the genus is both the principle itself and the hierarchy of items depending on it). This structure does not entail that levels ranked in the same genus share any common item. Rather, different and hierarchically ordered levels are connected via analogy, so that lower items mirror higher ones while not sharing any common item with them. Analogy, then, allows Iamblichus to combine two complementary aspects of his metaphysics: on the one hand the vertical hierarchy that separates different levels of beings, on the other hand the continuity that connects these different levels together within a unified whole. Iamblichus’ approach emerges in his account of essential or synonymous predication (the predication of items within the same category). Porphyry argued that in this kind of predication subject and predicate denote two different items, the akatakakton (uncoordinated or unallocated) and the katatetagmenon (coordinated or allocated) (Simplicius, In Categorias, 53.6–9; 79.24–30). The meaning of these expressions is debated. The “allocated genus” is to be identified with the in re universal shared by particulars; the unallocated may be either the separated and Platonic ante rem universal or the abstracted and post rem universal concept. Whatever we make of Porphyry’s view, Iamblichus started from Porphyry’s exegesis and gave a different slant to it (see Chiaradonna 2007). In doing so Iamblichus suggested that Aristotle’s essential predication is a way of expressing the participation of corporeal beings in their transcendent genera (Simplicius, In Categorias, 53.9–18 [DL-1972: Fr. 16]). More precisely, “Socrates is man” would be a way of expressing the fact that the corporeal Socrates participates in the transcendent Form of Man. Separate genera provide the basis for essential predication, though they are not properly predicated in themselves (what is predicated is rather the participated item). Interestingly, Iamblichus refers to the technical notion of ptōsis (“case”), which is associated with Aristotle’s account of paronymy in the Categories: a ptōsis is an inflected form of a term (such as “grammatical” or “courageous”) which is paronymous with the noun form and  derives from it (“grammatical” and  “courageous” are both adjectival forms which derive from “grammar” and “courage” respectively). So Iamblichus held that in the predicative statement “Socrates is man”, “man” improperly occurs in the predication instead of its ptōsis: Iamblichus is probably referring here to an adjectival construction like “human”. Such a paronymous form would correctly refer to the participation of Socrates in his transcendent Form. Simplicius informs us too that Iamblichus focused on Aristotle’s account of motion and activity: Plotinus had criticized Aristotle for not regarding motion as a single category and had argued that motion in sensible beings is a form of complete activity (Simplicius, In Categorias, 303.35–306.12 [DL-1972: Fr. 86]). Iamblichus rejects Plotinus’ account and aims to integrate Aristotle’s account of sensible motion as “incomplete actuality” into a Platonist philosophical framework (see Taormina 1999: chap. III).