The notion of problem, intuitionism and partiality

Pavel Materna

doi:10.12775/LLP.2008.016

Authors

Pavel Materna Academy of Sciences of Czech Republic, Prague

DOI:

https://doi.org/10.12775/LLP.2008.016

Keywords

abstract procedures, constructions, effective procedures, concepts, partiality

Abstract

Problems are defined as abstract procedures. An explication of procedures as used in Transparent Intensional Logic (TIL) and called constructions is presented and the subclass of constructions called concepts is defined. Concepts as closed constructions modulo α- and η-conversion can be associated with meaningful expressions of a natural or professional language in harmony with Church’s conception. Thus every meaningful expression expresses a concept. Since every problem can be unambiguously determined by a concept we can state that every problem is a concept and every concept can be viewed as a problem.Kolmogorov’s idea of a connection between problems and Heyting’s calculus is examined and the non-classical features of the latter are shown to be compatible with realistic logic using partial functions.

Author Biography

Pavel Materna, Academy of Sciences of Czech Republic, Prague

Institute of Philosophy

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