1. In the bibliography of Łukasiewicz' works contained in vol. V ofStudia Logica, this article bears the number 2. In order to inform the reader about a discussed or quoted paper given in the bibliography the respective number will be given in brackets.
2. Under the titleDie logischen Grundlagen der Wahrscheinlichkeitsrechnung (34).
3. A note on this theorem is contained in the summary of the lectureO wartościach logicznych (On logical values) [24].
4. The paperWahrscheinlichkeitslehre was published in 1935.
5. More details about the notion of logical implication are given by Łukasiewicz in his paperO pojęciu wielkości [39] (On the notion of magnitude). In order to assert that a certain „determinate” sentence is logically implied by other sentences these sentences should — according to Łukasiewicz — be changed into „indeterminate” sentences, hence variables should be put in the place of determinate terms. Łukasiewicz does not explain which are the terms to be replaced. The implication of determinate sentences is thus reduced to the implication of indeterminate sentences. On the other hand, the indeterminate sentenceZ is” a consequence of the indeterminate sentencesP, R, S, ... in other words, it follows from these sentences if there exist no such values of the variables contained in the sentencesP, R, S, ..., Z, which would statisfy the sentencesP, R, S, ... but not satisfy the sentenceZ”. The similarity of this definition to the definition of logical implication as given byA. Tarsk in 1936 is distinct.