 Łukasiewicz came across propositional logic, which he originally followed Whitehead and Russell in calling ‘theory of deduction’, in their work and also in that of Frege. In 1921 Łukasiewicz published a ground-clearing article, “Two-Valued Logic”, in which he brought together results in the algebra of logic governing the two truth-values true and false, which, like Frege, Łukasiewicz construed as what sentences or propositions denoted, but for which, unlike Frege, he introduced constant propositional symbols ‘1’ and ‘0’. He intended it as the first part of a monograph on three-valued logic, which however was never completed, probably because Łukasiewicz became dissatisfied with the rather hybrid approach which was already being outdated by his rapid development. The article is notable for several innovations. Using a symbolism derived from those of Couturat and Peirce, it introduces the idea of axiomatic rejection alongside that of axiomatic assertion, which latter was of course familiar from Frege, Whitehead and Russell. The constants ‘0’ and ‘1’ also occur in asserted and rejected formulas, in effect setting up an object-language version of truth-tables. To show this we use Łukasiewicz’s later parenthesis-free notation (see the supplementary document  (Łukasiewicz’s Parenthesis-Free or Polish Notation)  and his symbols ‘\(\vdash\)’ for assertion and ‘\(\dashv\)’ for rejection, to be read respectively as “I assert” and “I reject”. The first principles of logic are simply \({\vdash}1\) and \({\dashv}0\) but to indicate the tabulation for implication the following principles must be adhered to: \({\vdash}C00, {\vdash}C01, {\dashv}C10, {\vdash}C11\). When Łukasiewicz employed propositional variables, he quantified them in the manner of Peirce, using ‘\(\Pi\)’ for the universal and ‘\(\Sigma\)’ for the particular quantifier.