 The ultimate building-blocks of definitions (directly) and of syllogisms (indirectly) are intelligible notions (maʿānin maʿqūla). Logic deals with a special kind of intelligible notions, which in the Ilāhiyyāt are characterized as second-order intelligible notions (maʿqulāt ṯāniya) (Ilāhiyyāt I.2, 10–11). Assuming that first-order notions are things like “human”, “rational”, “whiteness”, or “stone”, second-order (or more generally, higher-order) notions are either genuinely distinct concepts such as “subject”, “predicate”, “genus”, “proposition”, and “syllogism” or, on a weaker reading, ways to ascribe second-order properties (such as being a universal or being a genus and so on) to first-order notions. Logic investigates the salient properties that hold of second-order notions, such as the properties of being a genus, the characteristics of propositions and their terms, the types of predication (essential and accidental), the truth-conditions of propositions, the conditions under which arguments are valid and those under which arguments that seem to be valid are not. On the identification of secondary intelligibles and the subject matter of logic, see (Street 2013) and (Sabra 1980).