ISSN:
1572-8730
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Philosophy
Notes:
Abstract The most difficult problem that Leśniewski came across in constructing his system of the foundations of mathematics was the problem of ‘defining definitions’, as he used to put it. He solved it to his satisfaction only when he had completed the formalization of his protothetic and ontology. By formalization of a deductive system one ought to understand in this context the statement, as precise and unambiguous as possible, of the conditions an expression has to satisfy if it is added to the system as a new thesis. Now, some protothetical theses, and some ontological ones, included in the respective systems, happen to be definitions. In the present essay I employ Leśniewski's method of terminological explanations for the purpose of formalizing Łukasiewicz's system of implicational calculus of propositions, which system, without having recourse to quantification, I first extended some time ago into a functionally complete system. This I achieved by allowing for a rule of ‘implicational definitions’, which enabled me to define any propositionforming functor for any finite number of propositional arguments.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00370202
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