Related papers: A mathematically derived definitional/semantical t…
Hannes Leitgeb formulated eight norms for theories of truth in his paper: `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…
In this paper a class of languages which are formal enough for mathematical reasoning is introduced. First-order formal languages containing natural numbers and numerals belong to that class. Its languages are called mathematically…
Every countable language which conforms to classical logic is shown to have an extension which conforms to classical logic, and has a definitional theory of truth. That extension has a semantical theory of truth, if every sentence of the…
We study the structure of the partial order induced by the definability relation on definitions of truth for the language of arithmetic. Formally, a definition of truth is any sentence $\alpha$ which extends a weak arithmetical theory…
Using techniques developed in the revision theory of truth, I build a model for the set theory NF (New Foundations) developed by Quine in ZF, therefore proving its consistency relative to ZF. The model is essentially a term model; the sets…
We consider the foundational relation between arithmetic and set theory. Our goal is to criticize the construction of standard arithmetic models as providing grounds for arithmetic truth (even in a relative sense). Our method is to…
Justification theory is a unifying framework for semantics of non-monotonic logics. It is built on the notion of a justification, which intuitively is a graph that explains the truth value of certain facts in a structure. Knowledge…
Knowing the truth is rarely enough -- we also seek out reasons why the fact is true. While much is known about how we explain contingent truths, we understand less about how we explain facts, such as those in mathematics, that are true as a…
Our approach is basically a coherence approach, but we avoid the well-known pitfalls of coherence theories of truth. Consistency is replaced by reliability, which expresses support and attack, and, in principle, every theory (or agent,…
I outline a new theory of truth that resolves the classical and constructive versions of the liar paradox. The theory features a provably consistent axiomatization of a global self-applicative truth predicate. Truth is defined using…
On the basis of elementary thinking about language functioning, a solution of truth paradoxes is given and a corresponding semantics of a truth predicate is founded. It is shown that it is precisely the two-valued description of the maximal…
This paper aims to provide an analysis of what it means when we say that a pair of theories, very generously construed, are equivalent in the sense that they are interdefinable. With regard to theories articulated in first order logic, we…
Axiomatic set theory is almost universally accepted as the basic theory which provides the foundations of mathematics, and in which the whole of present day mathematics can be developed. As such, it is the most natural framework for…
This project contains two chapters. Chapter 2 has two sections. First, we define the well-formed formulas of the Language of Sentential Logic using Construction Sequences. Second, we prove the Truth Assignments using the Language of…
We begin with a context more general than set theory. The basic ingredients are essentially the object and functor primitives of category theory, and the logic is weak, requiring neither the Law of Excluded Middle nor quantification. Inside…
We investigate abstract model theoretic properties which holds for models in which a truth or satisfaction predicate for a sublanguage of the signature is definable. We analyse in which cases those properties in fact ensure the definability…
This work uses mostly model-theoretic methods to establish new proof-theoretic theorems about several axiomatic theories of truth over KP (Kripke-Platek set theory) and stronger theories, especially ZF (Zermelo-Fraenkel set theory).
This is the first paper in a series in which we lay down the foundations of the theory of interpretations. We systematically study different types of interpretations and their properties. Some of these interpretations are known, while…
Underlying the theory of inferences, a primary task of logic is language analysis. Such a task can be understood as depending on a general theory of representation, taking as a starting point the idea that some entities (`` representations…
Currently it is widely accepted that the language of science is mathematics. This book explores an alternative idea where the future of science is based on the language of algorithms and programs. How such a language can actually be…