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Seppo Heikkilä [3]S. Heikkilä [3]
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Seppo Heikkilä
University of Oulu
  1. What Mathematical Theories of Truth Should Be Like (and Can Be).Seppo Heikkilä - manuscript
    Hannes Leitgeb formulated eight norms for theories of truth in his paper [5]: `What Theories of Truth Should be Like (but Cannot be)'. We shall present in this paper a theory of truth for suitably constructed languages which contain the first-order language of set theory, and prove that it satisfies all those norms.
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  2.  40
    Theories of Truth for Countable Languages Which Conform to Classical Logic.Seppo Heikkilä - forthcoming - Nonlinear Studies.
    Every countable language which conforms to classical logic is shown to have an extension which has a consistent definitional theory of truth. That extension has a consistent semantical theory of truth, if every sentence of the object language is valuated by its meaning either as true or as false. These theories contain both a truth predicate and a non-truth predicate. Theories are equivalent when sentences of the object lqanguage are valuated by their meanings.
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  3.  73
    A Mathematically Derived Definitional/Semantical Theory of Truth.Seppo Heikkilä - 2018 - Nonlinear Studies 25 (1):173-189.
    Ordinary and transfinite recursion and induction and ZF set theory are used to construct from a fully interpreted object language and from an extra formula a new language. It is fully interpreted under a suitably defined interpretation. This interpretation is equivalent to the interpretation by meanings of sentences if the object language is so interpreted. The added formula provides a truth predicate for the constructed language. The so obtained theory of truth satisfies the norms presented in Hannes Leitgeb's paper 'What (...)
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  4. A Mathematical Theory of Truth and an Application to the Regress Problem.S. Heikkilä - forthcoming - Nonlinear Studies 22 (2).
    In this paper a class of languages which are formal enough for mathematical reasoning is introduced. Its languages are called mathematically agreeable. Languages containing a given MA language L, and being sublanguages of L augmented by a monadic predicate, are constructed. A mathematical theory of truth (shortly MTT) is formulated for some of those languages. MTT makes them fully interpreted MA languages which posses their own truth predicates. MTT is shown to conform well with the eight norms formulated for theories (...)
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  5. On a Theory of Truth and on the Regress Problem.S. Heikkilä - manuscript
    A theory of truth is introduced for a first--order language L of set theory. Fully interpreted metalanguages which contain their truth predicates are constructed for L. The presented theory is free from infinite regress, whence it provides a proper framework to study the regress problem. Only ZF set theory, concepts definable in L and classical two-valued logic are used.
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  6.  78
    A Theory of Truth for a Class of Mathematical Languages and an Application.S. Heikkilä - manuscript
    In this paprer a class of so called mathematically acceptable (shortly MA) languages is introduced First-order formal languages containing natural numbers and numerals belong to that class. MA languages which are contained in a given fully interpreted MA language augmented by a monadic predicate are constructed. A mathematical theory of truth (shortly MTT) is formulated for some of these languages. MTT makes them fully interpreted MA languages which posses their own truth predicates, yielding consequences to philosophy of mathematics. MTT is (...)
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