Related papers: Truth and the liar paradox
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…
The concept of informal mathematical proof considered in intuitionism is apparently vulnerable to a version of the liar paradox. However, a careful reevaluation of this concept reveals a subtle error whose correction blocks the…
We propose a constructive interpretation of truth which resolves the standard semantic paradoxes.
Tarski's undefinability theorem states that a formal system based on conventional predicate logic (PL) cannot talk about its own truth predicate. PL is, however, not the only formal language imaginable. In this paper, it will be shown that…
The fact that the famous Godel incompleteness theorem and the archetype of all logical paradoxes, that of the Liar, are related closely is, of course, not only well known, but is a part of the common knowledge of logician community.…
Inspired by the early Wittgenstein's concept of nonsense (meaning that which lies beyond the limits of language), we investigate two different types of nonsense: formal nonsense and pragmatic nonsense. The simpler notion of formal nonsense…
The aim of this text is to present, in a technically accessible way, Tarski's definition of truth, the indefinability theorem, and to discuss two aspects of Tarski's work on truth, namely, whether or not the definition captures the notion…
The theory of institutions is framed as an indexed/fibered duality, where the indexed aspect specifies the fibered aspect. Tarski represented truth in terms of a satisfaction relation. The theory of institutions encodes satisfaction as its…
In this paper we concentrate on the nature of the liar paradox as a cognitive entity; a consistently testable configuration of properties. We elaborate further on a quantum mechanical model [Aerts, Broekaert, Smets 1999] that has been…
A true lie is a lie that becomes true when announced. In a logic of announcements, where the announcing agent is not modelled, a true lie is a formula (that is false and) that becomes true when announced. We investigate true lies and other…
Notions of unknown truths and unknowable truths are important in formal epistemology, which are related to each other in e.g. Fitch's paradox of knowability. Although there have been some logical research on the notion of unknown truths and…
Iterated reflection principles have been employed extensively to unfold epistemic commitments that are incurred by accepting a mathematical theory. Recently this has been applied to theories of truth. The idea is to start with a collection…
The classical logical antinomy known as Richard-Berry paradox is combined with plausible assumptions about the size i.e. the descriptional complexity of Turing machines formalizing certain sentences, to show that formalization of language…
This article informally presents a solution to the paradoxes of truth and shows how the solution solves classical paradoxes (such as the original Liar) as well as the paradoxes that were invented as counterarguments for various proposed…
In this article we propose an approach that models the truth behavior of cognitive entities (i.e. sets of connected propositions) by taking into account in a very explicit way the possible influence of the cognitive person (the one that…
Logical bilateralism challenges traditional concepts of logic by treating assertion and denial as independent yet opposed acts. While initially devised to justify classical logic, its constructive variants show that both acts admit…
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 presents a formal theory which describes propositional binary logic as a semantically closed formal language, and allows for syntactically and semantically well-formed formulae, formal proofs (demonstrability in Hilbertian…
Defining various dishonest notions in a formal way is a key step to enable intelligent agents to act in untrustworthy environments. This review evaluates the literature for this topic by looking at formal definitions based on modal logic as…
The paper defends the thesis that analysis of truth problem in the context of interpretations of quantum logic allows to reveal the prospect of elicitation of specifics of the relations between quantum mechanics and quantum logic in a…