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Leśniewski on metalogic and definitions. (English) Zbl 1398.03032

Summary: Leśniewski’s metalogic is often considered to be difficult to understand because it differs greatly from its standard formulation. In this paper, I try to explain the reasons of these idiosyncrasies. I claim that they have mainly two sources. First of all there is Leśniewski’s conviction that a formal system should be conceived as a set of concrete marks that can always physically and syntactically be expanded by the addition of new theses. Secondly, there is Leśniewski’s conviction that definitions should neither be formulas belonging to the metalanguage, nor deduction rules, but formulas belonging to the object-language and expressed with the help of the biconditional functor. The realisation of the first point is linked to the second one in so far as the metalinguistic rule for the writing out of definitions has to be formulated in a way that makes it possible to build the formal system in agreement with Leśniewski’s conception. While explaining these points, I give an overview of the main peculiarities of Leśniewski’s metalogic.

MSC:

03A05 Philosophical and critical aspects of logic and foundations
03-03 History of mathematical logic and foundations
01A60 History of mathematics in the 20th century
03B05 Classical propositional logic
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