Ernst Mally’s Gegenstandstheoretische Grundlagen der Logik und Logistik (1912) proposes that the abstract object “the circle” does not satisfy the properties of circles, but instead “determines” the class of circles. In this he anticipates the notion of “encoding” that Edward Zalta proposes for his theory of Abstract Objects. It is argued that Mally did anticipate the notion of “encoding”, but sees it as a way of taking the concept as the subject of a proposition, rather than as a primitive notion (...) in the theory of a new ontological category of abstract objects, as Zalta does. (shrink)

In 1910, Jan Łukasiewicz published a groundbreaking book, On the Principle of Contradiction in Aristotle. The book contained a critique of the traditional attitude to the Principle of Non-Contradiction, and a reevaluation of its significance in the light of contemporary developments in logic. In the first half of the book, Łukasiewicz produced an analysis of Aristotle’s defence of the Principle in the Metaphysics, showing its deep inadequacy. In the second half of the book, Łukasiewicz, in his own terms, considers the (...) pros and cons of the principle. The present paper provides an analysis and commentary on the second half of the book. Łukasiewicz is seen to be badly torn. Though he eventually endorses the principle, he does so, not in virtue of the evidence he considers, but in despite of it. In particular, he considers arguments against the Principle, drawn from Hegel, Meinong, and the paradoxes of self-reference, but rejects them for what appear to be patently inadequate reasons. (shrink)

The brief article of 1910 which is translated here is, as the prefatory note explains, significant for understanding both the way in which ?ukasiewicz came to many-valued logic and the influences under which he stood at the time.