Abstract
Part I of this paper presented an axiomatized theory of general syntax, defined the usual notions of general syntax, and proved some typical theorems of general syntax. We claimed that this system is strong enough to precisely state the formative and deductive rules of formal languages. In Part II we support this claim by formulating, in a very precise way, the rule of procedure of Leśniewski’s Protothetic. Section 1 is an informal introduction to Protothetic and its rule of procedure. Our metalogical system is extended there to a theory MP which is concerned explicitly with the syntax of Protothetic. This section is intended to motivate the Terminological Explanations of Section 2 which culminate in the statement of the rule of Protothetic. In Section 3 we sketch a proof that our formulation of the rule is equivalent to that given by Leśniewski (1929). This proof shows that our system is strong enough to conduct certain metalogical investigations.
Bibliographical Note. This paper originally appeared in the Notre Dame Journal of Formal LogicXIV (1973), pp. 1–52, by permission of the Notre Dame Journal of Formal Logic.
Part I of this paper appeared in the Notre Dame Journal of Formal Logic XIII (1972), pp. 1–33. The author would like to thank Professor Bolesław Sobociński for considerable advice.
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References
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Rickey, V.F. (1998). Axiomatic Inscriptional Syntax Part II: The Syntax of Protothetic. In: Srzednicki, J.T.J., Stachniak, Z. (eds) Leśniewski’s Systems Protothetic. Nijhoff International Philosophy Series, vol 54. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5736-0_7
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