[FOM] Nature of semantics of formal lenguages
barov at mccme.ru
Sat Apr 8 13:08:52 EDT 2006
I whish to ask peoples on FOM to explain their understanding of nature of
semantics (of formal languages). I know possibly three positions
i) Platonist view asserting existence of third world (in Poppers
terminology) of pure mathematical abstractions, e.g. universe of sets or
category of all categories. Internal logic of this world is logic of
being and so is classical. Semantics appears as absolute denotation.
ii) Constructive view asserting mental nature of mathematical objects
existing as constructions. Logic of this world is logic of knowledge base
and so is logic of realisability or (super) intuitionistic, and varies on
subject of reasoning. Denotation of names run trough mental construction
in second world.
iii) Formalist view postulate what semantics is translation form one
language to another
there second one has more simple and primitive structure like set
theoretic semantics. Truth of sentences here is only correspondence to
some selected element in some algebra.
First two cases accept nonformal objects which can or can't be fully
described. Third is
dont run out of formal languages and accept only syntactical models.
I will be glad to hear abut your view on this subject.
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