  According to Leśniewski’s dissertation and first paper, all positive existential propositions are analytic. This sounds absurd, but Leśniewski has reasons. Like Mill, he distinguishes between a term’s denotation, which is the object or objects it stands for, and its connotation, which is the property or properties it ascribes to something. A proposition is defined to be analytic if it is (1) in positive subject–predicate form, and (2) contains no predicates connoting properties not connoted by the subject. A proposition is synthetic if it is (1) positive and (2) contains some predicate connoting a property not connoted by the subject. Contrary to Mill, who said that ‘being’ connotes the property of existing, Leśniewski thinks the predicate ‘exist’ does not connote any properties. A fortiori, ‘exist’ used as a predicate connotes no property not contained in the subject. Negative existential propositions, which have the form ‘\(X\) is/are non-existing’ are synthetic, except for such whose subject connotes non-existence, e.g. ‘A square circle does not exist’ does not, so it is synthetic, but ‘All non-existing objects are non-existing’ is analytic. All negative existential propositions are contradictory, because every subject connotes something of the form ‘being which possesses properties \(A, B, C, D\), etc.’ Analytic negative existentials have contradictory subjects. So instead of saying ‘\(X\) exists’ we should, to express the proposition we want to be synthetic and contingent, rather say ‘Some being is the object \(X\)’.