A note on typed truth and consistency assertions

TY - JOUR

T1 - A note on typed truth and consistency assertions

AU - Nicolai, Carlo

PY - 2016/2

Y1 - 2016/2

N2 - In the paper we investigate typed (mainly compositional) axiomatizations of the truth predicate in which the axioms of truth come with a built-in, minimal and self-sufficient machinery to talk about syntactic aspects of an arbitrary base theory. Expanding previous works of the author and building on recent works of Albert Visser and Richard Heck, we give a precise characterization of these systems by investigating the strict relationships occurring between them, arithmetized model constructions in weak arithmetical systems and suitable set existence axioms. The framework considered will give rise to some methodological remarks on the construction of truth theories and provide us with a privileged point of view to analyze the notion of truth arising from compositional principles in a typed setting.

AB - In the paper we investigate typed (mainly compositional) axiomatizations of the truth predicate in which the axioms of truth come with a built-in, minimal and self-sufficient machinery to talk about syntactic aspects of an arbitrary base theory. Expanding previous works of the author and building on recent works of Albert Visser and Richard Heck, we give a precise characterization of these systems by investigating the strict relationships occurring between them, arithmetized model constructions in weak arithmetical systems and suitable set existence axioms. The framework considered will give rise to some methodological remarks on the construction of truth theories and provide us with a privileged point of view to analyze the notion of truth arising from compositional principles in a typed setting.

U2 - 10.1007/s10992-015-9366-6

DO - 10.1007/s10992-015-9366-6

M3 - Article

SN - 0022-3611

VL - 45

SP - 89

EP - 119

JO - JOURNAL OF PHILOSOPHICAL LOGIC

JF - JOURNAL OF PHILOSOPHICAL LOGIC

IS - 1

ER -