Summary and Conclusion

Abstract

The following problem was investigated: what is, in traditional philosophy, the logic of the articles, in particular of the definite article? Points of departure for this investigation were the following four data:

• (1) Definite articles (in Latin the zero article and in English often the indefinite article) are used with remarkable frequency in traditional philosophical literature and used in such a way that, from the point of view of modern logic, the logical form of the sentences in which these articles occur, cannot in most cases be recognized.

• (2) In E.W. Beth’s study Über Lockes ‘Allgemeines Dreieck’ it is argued that the following traditional problem has only recently been solved. What is the logic of proofs of theorems with general validity, particularly of theorems in geometry? The solution we are referring to here is one that is quite clearly independent of the traditional restriction of the problem to the objects of geometry.

• (3) The dialogical formulation of the modern logic (or logics) of syncategoremata as described by P. Lorenzen.

• (4) In 1955 a new study in traditional logic was published: Logik, ihr System und ihr Verhältnis zur Logistik by B. Baron von Freytag-Löringhoff. In this work the dialogical point of view is altogether absent. The use of definite articles in this Logik is not in accordance with the modern uses of these articles and it is not explained by von Freytag either.