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This is a trivial consequence of 2. For we can replace ‘ i- A’ by ‘ A R l ’ , where 1 is a new atom. 43. For a study of such transformations in connection with propositional algebra see [LLA] Chapter 11. 44. The term ‘proposition’ is allowable here since we have not used it in another sense. That would agree with [IFIJ,where it is proposed to use it henceforth for a categorv of obs. However, the term ‘formula’ is more usual. 45. If there are several Fategories of obs in 6, there will be corresponding categories of basic obs in 6’.

Unary) and = (binary). Examples of incompletely formalized formal systems would be : (1) a system whose morphology divides the obs into several “types”, (2) a system with a rule of substitution, as this rule has to specify a peculiar class of obs upon which the substitution may be performed. 53 It is plausible that any formal system can be reduced to a completely formalized one by introducing additional primitive ideas, so that the morphological and auxiliary notions can be expressed in the A-language (their rules being transferred to the theoretical part of the primitive frame).

1) Axioms. (2) Deductive rules. This formulation removes some of the vagueness which remains inherent in the definition of 3 B, since morphology is formalized as well as theory. I t might be taken as the basic conception; the notion of incompletely formal system is a concession to practical needs. 52 is completely formalized, as its morphology consists The system 52. Cf. LLLAj p. 24, [OFP] p. 36 f. , ’(unary) and = (binary). Examples of incompletely formalized formal systems would be : (1) a system whose morphology divides the obs into several “types”, (2) a system with a rule of substitution, as this rule has to specify a peculiar class of obs upon which the substitution may be performed.