Leibniz considers every elementary sentence (i.e. a sentence that cannot be analysed into further sentences) as having the general form: 'subject + copula + predicate'. As for the copula, Leibniz thinks that it expresses a relation of inherence or containment that may be read in two different ways. Given, for example, the sentence 'Every man is mortal', the copula says that: 1) Every individual falling under the concept of man, belongs to the collection (aggregate, set, or class) of the individuals falling under the concept being mortal ('extensional' point of view); 2) The concept associated with the word 'man' has amongst its component parts the concept associated with the word 'animal' ('intensional' point of view). Leibniz firmly claims that, of the two points of view, that according to the extension and that according to the intension, he prefers the second, thus aiming to construct a logical calculus of 'pure concepts', in which logical consistency is the sole criterion for admissibility. In his logical essays, Leibniz employs the relation of containment, which subsists between concepts (or aggregates corresponding to concepts) and the operation of juxtaposition between letters denoting concepts (or aggregates). The relation of containment is reflexive, transitive and anti-symmetric, thus inducing a semi-order on the set of concepts (aggregates), whereas the operation of juxtaposition is commutative, idempotent and associative. From the extensional point of view, Leibniz gives rise to a logical calculus equivalent to a semi-lattice with meet and negation. Therefore, he disposes of all ingredients to form a Boolean algebra. Unfortunately, however, he never edited his logical essays, which still remained unpublished until the beginning of the 20th century.
