  To modern students of logic accustomed to streamlined methods of working with propositional logic, Leśniewski’s Protothetic, especially in its “official” versions, must appear very cumbersome and difficult to understand and work with. In part this is a question of the age of the systems and Leśniewski’s aversion to semantics (see above). However, Leśniewski did not always present his work so fiercely. For purposes of everyday derivation he employed what can only be described as a system of natural deduction, making assumptions, following their consequences, collecting them and inferring conditionals and biconditionals, in the manner to which all students of logic have since become accustomed. Astonishingly, neither he nor any of his students thought fit to codify these practices into a system of rules. This was done instead at Łukasiewicz’s suggestion by Stanisław Jaśkowski. The discovery of natural deduction is generally attributed to others, but there is a chance that Leśniewski used it, in a recognizably modern form, earlier than others. That he did not codify it probably resulted from his viewing it as a pedagogical device and a way of sketching out how a “proper” (i.e. axiomatic) proof was to go. Another way to take some of the forbidding appearance out of Protothetic is to look for more readily comprehensible axioms. The following two-axiom set based on implication as the primitive (an alternative Leśniewski also looked at) is rather straightforward; the result was again obtained by Tarski: