Lukaseiwicz's introduction to symbolic logic: What was he doing?

David Sweeney

With Holger Heine I am writing a short commentary on Holger's translation of Lukaseiwicz's  'The Principle of Contradiction and Symbolic Logic' which is an introduction to symbolic logic. This appeared as Appendix I of Lukaseiwicz's 'The Principle of Contradiction in Aristotle' of 1910. The introduction was for a time the main introductory work on symbolic logic in the Polish language. With Holger I am working on placing the Introduction historically and working out precisely what Lukaseiwicz is doing in this interesting and early introduction to symbolic logic.

I am particularly interested in working out what presciently is being formalised by Lukaseiwicz. For although it looks in many ways almost the same as so many introductions to formal logic it has its distinct differences. For instance the symbol 'a' represents not 'a is true' but rather 'X contains a'. We are also interested in working out what king of implication is being used.

I will present what we have worked out so far and hope for an interesting discussion and suggestions about what we may have missed.