Meaningfulness and Structure

Abstract

During a visit to Poland in the summer of 1929, I learned about the parenthesis-free notation that Łukasiewicz had just devised for logic — a simple but fascinating idea. Today this symbolism is widely known and its variations are even utilized in mass-produced calculators; but at that time, probably no other Western mathematician was acquainted with it. So upon my return to Vienna, I spoke about it before my Mathematics Colloquium as well as in the Circle. The latter, I felt, should be informed of Łukasiewicz’ idea since in the Tractatus Wittgenstein had emphasized how significant was “the apparently unimportant fact that the logical pseudo-relations such as ∨ and ⊃ (for or and implies) require parentheses — in contrast to the real relations.” Łukasiewicz’ notation demonstrated that the alleged requirement did not exist.