Résumé
Aristotle considered particular quantified sentences in his study of syllogisms and in his famous square of opposition. Clearly logical formulas in Aristotle work were not formulae of mathematical logic, but were sentences of natural language. Nowadays the formulas are written in predicate logic as defined by Frege, but, as we shall recall, it is not clear if they are faithful representations of the natural language sentences. Indeed, the usual modeling of quantifiers suffers from some inadequacies. This is the reason why Hilbert’s epsilon and tau quantifiers (that go beyond usual quantifiers) have been used to model natural language quantifiers. Here we interpret Aristotle quantified sentences as formula of Hilbert’s epsilon and tau calculus, who yield to two potential squares of opposition, one of them being actually a square of opposition, i.e. satisfying the relations of contrary, contradictory, subalternation.