 According to his first theory, (elaborated in the first decade of the 14th century), these so-called ‘real’ propositions do not properly exist in the extramental world, although they do exist in our minds as objects of acts of intellection or judgment. Burley clearly states that whereas mental propositions exist in our minds as subjects of inherence (habent esse subiectivum in intellectu), real propositions exist in our minds as intentional objects (habent esse obiectivum in intellectu solum) (QP, q. 3, pp. 248–49; CP, p. 61; see also QPo, q. 2, p. 63). Real propositions are complex entities formed by the things to which their subjects and predicates refer, together with an identity relation (if the proposition is affirmative) or a non-identity relation (if the proposition is negative). The things signified exist in the extramental world, but the identity relation is produced by our minds and exists only in them. This identity relation is a sort of intellectual composition by which we understand that the thing (res) signified by the subject term and the thing signified by the predicate term of a proposition belong to the same substance(s) (QP, q. 3, p. 250). On the other hand, it is correct to call the significatum of a sentence a ‘real proposition’, since the fact that two or more things share the same substance does not depend on our minds (CP, pp. 61–62). As the subject of a standard philosophical sentence must be the name of a substance and the predicate a general expression signifying a substantial common nature or an aggregate of substance and accidental form, it is clear that the identity relation can hold only between the things which the subject and predicate of a true affirmative proposition stand for in personal supposition, i.e., between the particular substances named by the subject and predicate expressions of the proposition. In a standard proposition, the significata of a subject and predicate are diverse, but what they stand for has to be the same if the proposition is true. Since the things a term stands for are not established a priori but dependent on propositional context, the analysis of the structure of a proposition in terms of the identity relation requires a correspondence theory of truth. In his middle commentary on the De Interpretatione (pp. 59–60), Burley speaks openly of truth in terms of the “adequation” or congruity between thought and reality (adaequatio intellectus ad rem—see also EPh., prol., fol. 66ra). Every being (ens) is true (verum) in itself, insofar as its structure and inner organization are plainly revealed to the mind. This structural truth (veritas rei) corresponds to a mental truth (veritas in intellectu) (CP, p. 60): when our minds successfully reproduce the internal structure of what is signified by a simple expression or when they grasp the lack of any relationship between the significata of two simple expressions, a diminished being (ens diminutum), which has our mind as its subject of inherence, is generated by the mind. This diminished being is the veritas in intellectu, which corresponds to the veritas rei. If our attempt fails, falsity (falsitas) is generated instead (CP, p. 61).