The theory of rejected propositions. II

This paper is a continuation of Part I under the same title. Its Chapter III contains results given in the following publications: U. Wybraniec-Skardowska, Teoria zdań odrzuconych (Theory of Rejected Sentences), (doctoral dissertation under the supervision of Jerzy Słupecki, published as a monograph), Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Studia i Monografie, Nr 22 (1969), 5-131. G. Bryll, Związki logiczne pomiędzy zdaniami nauk empirycznych (Logical relations between sentences of empirical sciences). Zeszyty Naukowe Wyższej Szkoły Pedagogicznej w Opolu, Studia i Monografie, Nr 22 (1969), 155-216. This chapter contains an attempt to formalize some questions of methodology of empirical sciences. The theory T is enriched here not only by new definitions but also by a new primitive term and new axioms. The most important notion defined in this chapter is the set IndX of all inductive conclusions obtained on the basis of sentences of the set X. The function CnI defined by the equality: CnI X = X u IndX, satisfies the axioms of the general theory of deductive systems. The set CnI X can be understood as a system of empirical sciences in a narrower sense. This paper is a development of the considerations of G. Bryll, included in the above-listed article by this author.